Talk:Logic/Archive 2

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Logic, a branch of philosophy?

map of sciencs

logic is before math and phylosephy(meta-physics) is after math and next to physics.Saeed.Veradi (talk) 11:43, 13 February 2009 (UTC)

Logic and philosophy

I think some changes should be made to the way logic is defined in the leading section of the entry. There is disagreement as to the relationship with logic and philosophy and mathematics. In the opening section is says that logic is a part of mathematics, whereas people like Gottlob Frege believe math is a branch of logic. What do you guys think? JEN9841 (talk) 17:55, 10 May 2009 (UTC)

Can of worms... Obviously math is a branch of logic because all math is, is correct reasoning about mathematical truths, whereas logic is about reasoning in general. We also know that math is subordinate to logic because all mathematics can be expressed in terms of logic. Furthermore for all the brilliant analysis, equations, clarifications, representations, etcetera that mathematicians engage in, it will still always be true that the analysis, the equations, the clarifications, the representations and etcetera are EITHER T OR THEY ARE F, period. In effect the immediate supervisor of every mathematician, is always a logician. Pontiff Greg Bard (talk) 18:12, 10 May 2009 (UTC)
I disagree with all of the conclusions. Logic has been part of a philosophy in the European tradition, but it broke its moorings about 75 years ago, and Indian logic was more closely related to linguistics than philosophy. Suffuciently polished mathematical demonstrations are expressible in first-order logic, based on axiomatised mathematical theories, but it remains the case that (i) we have no logical basis for supposing those theories to be consistent, only mathematical ones, and (ii) the mathematical intuition behind those formalisable demonstrations cannot, as far as we know, be captured formally. Each of mathematical, philosophy, and logic have large overlaps with each other; none is a branch of another. — Charles Stewart (talk) 08:02, 11 May 2009 (UTC)
So can we come to some consensus about what to do with this line "Logic is a branch of philosophy, a part of the classical trivium, as well as a branch of mathematics."? JEN9841 (talk) 05:11, 13 May 2009 (UTC)
How about "Logic in classical times was a branch of philosophy and part of the trivium; today it has rich overlaps with many disciplines, such as mathematics, linguistics, and computer science"? — Charles Stewart (talk) 08:00, 14 May 2009 (UTC)
I wouldn't approve of anything that implies that logic isn't a branch of philosophy at all. Logic certainly is a branch of philosophy, more so than mathematics, even today. Surely the moorings of some topics have "broken," however other topics have not. The primary change that is needed in the lead paragraph is emphasizing that logic is about reason. That fact has been de-emphasized to an afterthought. However, reasoning is actually the fundamental, primary concept of all logic. I think some formulation of the neo-logicist view of logic belongs in it pretty early as well, juxtaposed with the anti-logicist view. I think this would be quite informative, and a good basis for the evolution of the article. Pontiff Greg Bard (talk) 16:17, 14 May 2009 (UTC)

I like this as a stab at changing the leading section:

Logic is the study of the principles of valid demonstration and inferenceEmpty citation (help) . Logic is a branch of philosophy and was part of the classical trivium. Its relationship with mathematics is disputed; logicists hold that mathematics can be reduced to logic, while others disagree. JEN9841 (talk) 21:54, 14 May 2009 (UTC)
That's wonderful as far as I'm concerned. More emphasis than I would hope, but it's probably more than will be allowed due to the pragmatic reality of wikipedia. Also, I think that the whole "study of the principles ... inference" doesn't really capture the "first sentence" essence of logic. I think
Logic is the art and science of reasoning.
should be the first sentence, followed by the rest. Unfortunately, it will probably be too controversial for the wikipedia regulars in logic to call it an art, even though that is really the basis of the disagreement between math and philosophy over logic.
I can agree to disagree with Charles Stewart's view (the dude knows his stuff). My original statement was more of a strong ideological view intended to elicit the inevitable response from the mathematical logicians. They have the strong view against logicism, and I think neologicism has responded to their objections sufficiently. Some account of these prevailing views may belong in the lead section, but perhaps not the very first paragraph. However, I feel pretty strongly that "reason" or "reasoning" belongs in the very first sentence.
BTW, my response to Charles' response is that the objections he raises consist only in semantics; i.e. what is called math and what is called philosophy really has no bearing on any argument about the principles behind the concepts. Be well, Charles, I am sorry I still haven't responded to your last note to me. I do always think quite a bit about what I'm going to write back to you. I haven't forgotten, believe it or not! Pontiff Greg Bard (talk) 00:12, 15 May 2009 (UTC)

Logicism doesn't belong in the lede: today it is an extremely marginal position; as a movement in the philosophy of mathematics it is dead. My objection to saying that logic is a branch of philosophy is that it means that all parts of logic are parts of philosophy. There are an awful lot of logic papers out there written by people who have no interest in philosophy. I would guess that there are many more people working on logic, particularly in computer science, than there are people working in philosophy departments. If logic were a branch of philosophy, what would this say about philosophy? I agree that logic has a deep and intimate relationship to philosophy, but this is something else. I'm going to be away for about a week. — Charles Stewart (talk) 08:38, 15 May 2009 (UTC)

How about we start with a compromise. Logic's close relationship with math and computer science etc. needs to expressed while simultaneously not asserting something that is in dispute.
Logic is the art and science of reasoning which studies the principles of valid demonstration and inferenceEmpty citation (help) . Logic is a branch of philosophy and was part of the classical trivium. It has a long history which dates back to Aristotle and still remains vital to mathematics and computer science. The word derives from Greek λογική (logike), fem. of λογικός (logikos), "possessed of reason, intellectual, dialectical, argumentative", from λόγος logos, "word, thought, idea, argument, account, reason, or principle". JEN9841 (talk) 20:00, 15 May 2009 (UTC)
Or how about this:
Logic is the art and science of reasoning which studies the principles of valid demonstration and inferenceEmpty citation (help) . Logic is a branch of philosophy and was part of the classical trivium. As a formal discipline, logic dates back to Aristotle and remains integral to the fields of mathematics and computer science. The word derives from the Greek λογική (logike), fem. of λογικός (logikos), "possessed of reason, intellectual, dialectical, argumentative", and from λόγος logos, "word, thought, idea, argument, account, reason, or principle". JEN9841 (talk) 21:42, 15 May 2009 (UTC)
Or:
Logic is the art and science of reasoning which seeks to understand the principles of valid demonstration and inferenceEmpty citation (help) . Logic is a branch of philosophy and was part of the classical trivium. As a discipline, logic dates back to Aristotle and remains integral to fields such as mathematics, computer science, and linguistics. The word derives from the Greek λογική (logike), fem. of λογικός (logikos), "possessed of reason, intellectual, dialectical, argumentative", and from λόγος logos, "word, thought, idea, argument, account, reason, or principle". JEN9841 (talk) 00:05, 17 May 2009 (UTC)

Logic as an untestable hypothesis?

If I come up with a logical proof that says that logic works, I must preemptively assume that logic works in order to take my proof seriously. In other words, I have to assume that logic works in order to prove that logic works. This means that I have presupposed my conclusions, and so my logic becomes circular, and therefore does not prove anything at all (even if it is internally ‘true’). and… If I use logic to prove that logic does not work, then I will negate my proof as soon as I complete it, and so won’t actually have proven anything at all. SO Logic cannot be justified or discounted through logic. And it seems to me that any other justification for logic outside of logic would be by definition illogical.

Would anyone like to resolve this issue for me?--Heyitspeter 22:13, 27 December 2006 (UTC)

Here's what'll really twist your mind: you can't use logic to disprove logic either.
Computers work.
Computers are based on logic.
Therefore, logic works.
(This is a test through the physical/scientific. It makes the same assumptions, but at least it isn't all in the mind.)
Logic assumes the axioms (basic statements) that meaningful description is possible, and that meaningful descriptions interact consistently through logic. Without those axioms, there is no logic. See epistemology. --BlueNight 16:54, 3 January 2007 (UTC)
Have this discussion elsewhere, please. Wikipedia talk pages are not for having conversations about the subject of an article. Simões (talk/contribs) 19:33, 3 January 2007 (UTC)

I brought this up because I wondered if it should be included in the 'criticisms' section. I didn't mean to create a philosophical argument, just to see if anyone knew of a current debate on the subject that could be included. --Heyitspeter 22:44, 5 January 2007 (UTC)

I think this topic, which the the epitome of what is meant by sophmoric (that is, everybody discovers this in their sophmore year in college), belongs in philosophy if it belongs anywhere. It is, after all, not only logic that cannot be proved. Nothing can be proved absolutely, except, maybe, "I think therefore I am." or, as I like to phrase it, "The universal set is not the null set." You may be the only being that exists in the entire universe, and you may be totally mad. Rick Norwood 14:30, 6 January 2007 (UTC)


/archive-1 created

I copied the page up to Wikiproject? to the archive, then selectively extracted material that still seems relevant in sections Specialized logics to Wikiproject?. leaving later sections intact. The sections that have been copied to the archive I've noted with (archived); additionally sections that are incomplete I note with (../pruned). Deleted sections are deleted silently. I've gone to the efforts, because lots of this stuff is still relevant... ---- Charles Stewart 07:52, 10 Nov 2004 (UTC)z

Above already s=archived topics deleted. --- Charles Stewart 15:23, 27 May 2005 (UTC)

Big changes applied

Now applied the restructring I've been threatening... Two issues:

Aristotelian logic is sometimes referred to as formal logic because it specifically deals with forms of reasoning, but is not formal in the sense we use it here or as is common in current usage. It can be considered as a precursor to formal logic.

  • I've deleted this, because I think it is wrong: it is perfectly easy to see how syllogistic is formal, c.f. the work of John Corcoran expressing syllogistic in modern notation. Do any authorities seriously dispute the formal nature of syllogistic? I would be surprised. I've completely rewritten these paragraphs.

Mathematical logic refers to two distinct areas of research: The first, primarily of historical interest, is the use of formal logic to study mathematical reasoning

Not at all! The application of logic to the study of mathematics and mathematical proofs is still one of the main driving forces of mathemcatical logic. Just look at applied model theory, reverse mathematics, Borel spaces. I've completely rewritten this paragraph.

I obect! I wrote that sentence! By that I meant the following: once it became clear (in historical time possibly in the late 1920s but I'm guessing) that informal arguments in mathematics can be reduced to purely formal proofs, hardly anyone regarded purely formal proofs as useful (caveat of course: formal verification does stress formal proof and it is useful, I suppose for many critical applications, but it is highly debatable whether formal proof-checking is mathematics at all! Despite MIZAR and Isabelle, in the current state of the mathematical sciences it would be misleading, I think, to regard this area is of any interest outside of a relatively small group of specialists. This of course is a sociological fact more than anything else, but in fact the assertion in question is also sociological). Notice that I stated
use of formal logic to study mathematical reasoning
The area of research you describe in Borel spaces or model theory (which I think would include non-standard analysis) could be called formal logic only by a stretch, I think. In other words, though logic may occur in the subject of these investigations, logic is itself regarded as an object of study (e.g., somewhat fancifully, say one could regard formal structures as a kind of space on which a group acts such as a Tits building or some such thing -- and actually as you point out above somewhere domain theory is an area where the mathematization of formal systems becomes more visible ). CSTAR 02:55, 26 Aug 2004 (UTC)
I guess it's possible to argue that both what I changed this section from and what I changed it to are not NPOVs. I hope not, because I like what I wrote. OK, quibbles with what you wrote first: all the stuff about Borel sets, analytic sets, projective sets did change the systems that set theorists studied, since they gave rise to new large cardinal axioms via the work on descriptive set theory. By applied model theory, I mean the stuff that MacIntyre was doing -- applying model theoretic techniques to algebra to get new mathematical results algebraists think are valuable; it really couldn't be a clearer application of logic to mathematics; whilst in reverse mathematics, you need to really go back and think about how you prove things one is really recreating mathematics according to logically imposed constraints. With Macintyre's work, I think it couldn't be clearer that the objectives are mathematical ones (indeed, see [1] why this might not be logic anymore...), and withthe other two, while we may have foundational motivations for studying them, it should be clear that the objects of study themselves are mathematical. I think from this point of view, what I wrote is OK (do I need to say more so that this is clear?)
There is another issue you raise, namely that few logicians (the applied model theorists being exceptions) are genuinely close to mathematical practice. In fact I'm reading a nice book by David Corfield at the moment "Towards a Philosophy of Real Mathematics", and it is abundantly clear that he would agree with you. When a logician studies mathematics, he learns something, but not something that is of much use to the mathematician, and this is something that the pioneers of mathematical logic did not expect.
Resolution: maybe we need to divide up mathematical logic into more kinds of activity: both foundations of mathematics and applied logic would fall under the use of formal logic to study mathematical reasoning, and maybe we need to make clear that these are two different kinds of activity. ---- Charles Stewart 10:01, 26 Aug 2004 (UTC)

Do I have the right indentation here?... :)
Yes I generally I am very happy with what you wrote -- though I think the point I raise is more than a minor quibble. In applying logic (i.e. model theory) to mathematics in the way you mention is hardly different than noting that the transfer principle is useful in translating certain nonstandard statements to standard ones. I use this equivalence just because I am very familiar with non-standard analysis. Now where does logic begin or end in non-standard analysis? This is the perennial question, what are the limits of pure logic? I certainly don't know.
But my main point is that the study of logic and logical systems is more like the emprirical study of physics: There are these systems of inference, we propose models for them and study them using mathematics. I believe a very weak version of this in that I am not a Putnamist on this, i.e., I am not prepared to argue as does Putnam that logic is empirical. See Quantum logic.
BTW the logic page as it now stands is of very high quality.CSTAR 13:49, 26 Aug 2004 (UTC)

Comments welcome on all changes ---- Charles Stewart 00:36, 26 Aug 2004 (UTC)

I merged the "types of logic" and "motivations for logic" sections, because it was confusing to have types split between the two. The specific motivations are inherent to what type of logic being considered, though so I think they go well together this way. Perhaps a little general idea of motivation could be placed in the introductory secont above the TOC if you wish. [[User:Siroxo|—siroχo

siroχo]] 05:03, Aug 26, 2004 (UTC)

Hmmm. I separated them out because it was clear to me that they were different kinds of subsection: in particular, I don't think that, say, mathematical logic is a type of logic, but rather a set of interests and concerns that certain kinds of logician bring to whatever branch of logic they study. Philosophical logicians and mathematical logicians study one and the same first-order logic, and they study one and the same S4 modal logical system. Instead, they just ask different questions about them, and do different kinds of investigations into them. I agree, though, that "motivations for logic" was a clumsy section heading. Maybe "Types of logician" would be better...
On rereading what I wrote, the preamble to the types of logic section is not consistent with the contents, and so needs to be rewritten anyway.
And thanks for the cleanup work with the all the red I left on the pages, and sorry there was so much: I actually 'corrected' many of these links, but corrected them to new broken links. ---- Charles Stewart 06:32, 26 Aug 2004 (UTC)
You make a good point regarding "types" of logic and all. I changed the name to "paradigms of logic" in hopes that it would imply a more general idea that these were various ideas that different logicians followed. [[User:Siroxo|—siroχo

siroχo]] 07:48, Aug 26, 2004 (UTC)


Maybe the true definition of Logic should be Ex nihilo.

--8.7.69.29 (talk) 04:01, 29 April 2009 (UTC)

Preamble and terminology

Four main things bother me about the article as it now stands. Firstly is that there are subsections that are stub-like (eg. modal logic); second, I'm not at all happy with what I wrote in "Dialectical logic", either wrt. the name or the content, also to some extent there are issues outstanidng in mathematical logic raised by CSTAR; third, I think that while I agree with Siroxo's merge inot the one paradigms of logic, I think there are two different kinds of topic there, and I think that should be reflected in the article structure; fourth, I think the article should introduce some key terminology that can act as a baseline for other articles on logic; last, I think there are some POV issues with the preamble (ie. the part before the first section); to a lesser extent I have some issues with the text in . The last two points I think are most worthwhile to be tackled next.

My points:

  • I think the preamble should be shortened: I think articles are more navigable if the TOC appears quite early;
  • In the first paragraph appears: where "formal" means that the relations are independent of the assertions themselves -- I could quibble that the inference "A&B therefore A" most certainly does depend on there being an "&" in "A&B", but more seriously, I think this cannot be corrected in a NPOV manner: skeptics about the existence of logical form will not agree to these kinds of assertions about the independence of logical arguments. These sentences establish an important and fruitful view of logic, but it should as far as possible be moved to a subsection within "Scope of Logic";
  • Also It is thus seen that logic plays an important role in epistemology in that it provides a mechanism for extension of knowledge: true, but it doesn't go far enough -- logic is a controversial topic, and to decide on this or that shape for logic is to have decided on the outcome of both epistemological questions (what is a judgement? what is an inference?), philosophy of language (what is a proposition? how do propositions relate to assertoric utterances?), and metaphysics (what are individuals? what is truth?);
  • Next paragraph: logic provides prescriptions for reasoning, that is, how people—as well as other intelligent beings, machines, and systems—ought to reason -- This view is widely held but far from universal: the conjunction of the ideas that logic tells you when certain arguments are truth-preserving, and that one need not always be rational, I think is common enough.
  • and How people actually reason is usually studied in other fields, including cognitive psychology -- maybe so today, but it was not always so (rhetoric was part of logic according to the Stoics), and I think this way of putting things seems to prejudice against the many philosophers and didacticians who think this is wrong. Cf. term logic and Fred Sommers, I personally am for having jointly computational and psychological foundations for logic;
  • Next paragraph: including reasoning about probability and causality -- very controversial!
  • There are several pieces of terminology, and relationships between terms, that I think should be fixed in this article, so that the article can fulfil he standardising role I suggested above; these should be in Scope of logic:
    • Some possible definitions of logic, no need to be exhaustive...
    • Symbolic logic and its relationship to formal logic;
    • Inference: deductive and other forms;
    • Proposition, sentence, judgement;
    • Possibly a very brief outline of the main definitions in Tarski's theory of logical consequence is appropriate here, since it is so ubiquitous.

I have some ideas about how to apply the changes, but I think I will wait until I hear some reactions first ---- Charles Stewart 21:09, 31 Aug 2004 (UTC)


I follow philosopher Paul Grice, Benson Mates (Elementary Logic, Oxford, 1965) et alia in reserving the word "logic" to deductive reasoning only. Some alternative solutions are:

Formal Sciences,

which include Deductive, Inductive, Instrumental, Probabilistic, Mathematical Reasoning,Italic text with each having its own features specified. These are considered "Formal" because of their methodological applications, and thus should include Scientific Method and Philosophical MethodItalic text.

Under

Deductive Reasoning

Propositional Calculus, Predicate Calculus, Modal Calculus, Metalogic,Italic text and "Aristotlean Logic" Italic textas a historical precursor to Modern Formal Symbolic Logic, commonly known as Mathematical Logic, or simply

Formal Symbolic Logic.Italic text

It's how I've distinguished it to my freshmen students, and they get it. Dshsfca (talk) 21:45, 7 September 2008 (UTC)dshsfca

Revert of lexor's edits

The small change made the first sentence more awkward, there is no requirement to have the title as the first word. siroχo 03:28, Sep 6, 2004 (UTC)

Wikiversity course logic

User:Passw0rd added a wikiversity logic stub. I tend to think that this is not beneficial yo the page, since:

  1. The course (wikibooks:Wikiversity:Logic) is so raw, it contains less information and is less structured than this page;
  2. It isn't clear that a single logic course is appropriate: it may be appropriate to have several introductory courses, eg. Logic for critical reasoning, Logic for mathematicians, Logic for philosophers, etc. Hence linking to a particular book may be premature.

Hence, I am reverting this edit. ---- Charles Stewart 19:37, 22 Oct 2004 (UTC)

Hey, that was me. I've moved some of the logic stuff from the wikiversity philosophy dept to a chapter of wikibooks' 'intro to philosophy', which is a work in progress. I need some of you clever ppl to help me edit it. Anyway I don't really know what to put in a wikiversity page except 'read these texts, and talk to us' - wikipedia and wikibooks seem to be the place for most of the writing.--Publunch 18:20, 27 Oct 2004 (UTC)

I notice that the article says 'philosophers assume ... '. I've never known philosophers to willingly assume very much for very long. When they do assume things it is like mathematicians assuming x to show that x entails a contradiction.--Publunch 18:20, 27 Oct 2004 (UTC)

Mathematics

This section has been archived in Talk:Logic/Mathematics. Brianjd 07:04, 2004 Nov 16 (UTC)

Is logic empirical?

I've been meaning to provide comments on User:CSTAR's excellent content on the Is logic empirical? subsection. Just a note to say I've still not skimmed the articles I meant to, but I hope to this week. In the meantime some non-content comments:

  • I had a dialog with CSTAR in my talk page, User_talk:Chalst#Quantum_logic, which may be of interest to other editors here;
  • There's really too much content here for a side topic on the main logic page. I propose to put what CSTAR wrote on a new page, and put a short precis in its place on the Logic page. In addition, there's more to the question of the empiricalness of logic than quantum logic: CSTAR's material has the potential to grow quite a bit;
  • I won't pass the comments onto my chosen philosopher until the material has a bit more meat; no point underutilising this input.

It's probably better if I do the surgery than CSTAR: all the stuff about many eyes being better than two... ---- Charles Stewart 07:25, 10 Nov 2004 (UTC)


Vas-y CSTAR 17:57, 10 Nov 2004 (UTC)

Some initial comments: I've done a bit of reading, and I've applied the change above, also detailing another article by the same name:

  • An interesting fact: actually Quine was the first to suggest that the Birkhoff/Von Neumann logic suggested that logical principles could be revised in response to empirical observations;
  • Michael Dummett wrote a response to Putnam's article, also entitled Is logic empirical?, which makes a lot of nice points, and I have summarises it. Dummett ties in the question to the general issue of realism/anti-realism and the question of bivalence, making a lot of nice points on the way. Tis is good for this article, since the same questions arose wrt. intuitionism; actually this potential relationship was the first thing I thought of when CSTAR first asked for my comments.
  • The article I've created is a bit weak in the sections on both Quine and especially quantum logic: the latter really needs an explanation about what are tests in QM and why should we consider them to be propositions.

-- Charles Stewart 23:26, 13 Nov 2004 (UTC)


The quantum logic article tries to establish, in a passing sort of way, the case that "quantum questions" are a sort of atomic proposition. However, when I wrote it I wasn't very much concerned with the issue of its relation to epistemological problems and in particular, didn't address any of the issues (such as distributivity and so on) which are relevant to Dummett's article. I mainly wanted to have some reference for other articles on physics and measurement. So perhaps that should be a separate section in that article.

Also there is a distinction which physicists will not usually make between the logic and the semantics. However, getting into that (philosophically important) distinction may be a bit too much for an article written primarily for physicists.CSTAR 23:44, 13 Nov 2004 (UTC)

I agree that it is best to keep the Quantum logic article oriented the way it is now, but it might be nice to add a subsection Philosophy of quantum logic that might have the Is logic empirical? page as its main article. The section Quantum logic needs, as you observe, more flesh before it can stand as an introduction to Dummett's critique. ---- Charles Stewart 21:58, 16 Nov 2004 (UTC)

Alternative Logics

I just ran into this 2002 Kuro5hin article entitled Alternative Logic. It seems to have content that could be usefully added to this article ---- Charles Stewart 21:58, 16 Nov 2004 (UTC)

There's already a topic on Paraconsistent logics in WikiPedia. Shouldn't a link to it be inserted int the Logic article? --Hgfernan 08:54, 27 Apr 2005 (UTC)
Right. It would be a good topic under Controversies in logic, maybe following the subsection dealing with paradoxes of implication. --- Charles Stewart 09:15, 27 Apr 2005 (UTC)

I've created the section Is what we know consistent?, although I've ducked the question I raised... --- Charles Stewart 09:28, 27 Apr 2005 (UTC)

New external link

I looked at that new external link inserted by an anon user. The site seems extremely rudimentary and it may possibly be a veiled advertisment.CSTAR 01:05, 22 Nov 2004 (UTC)

The link leades to part of somebody's webpage/blog. Is this a legitimate use of an external link? No product appears to be sold here, but the link does appear to me to be unwarranted promotion of some kind. I will (soon) remove it, if nobody objects.CSTAR 14:49, 22 Nov 2004 (UTC)

I'd say that if we don't say anything about what sort of material one can expect to find by following external links, then anything logic related, no matter how lame, is in principle legitimate. Maybe starting a page "List of logic-related resources", and moving the link there, is best? ---- Charles Stewart 16:19, 22 Nov 2004 (UTC)

OK, let's leave the link in for now, but I do want to register my concern about this kind of link.CSTAR 17:35, 22 Nov 2004 (UTC)

Dialectical logic and Hegel

The current contents of this section are mostly not within the scope of this article (very few people think that Hegel's logic is actually about logic; in his Science of Logic he says logic must certainly be said to be the supernatural element which permeates every relationship of man to nature [2]...). I'm not sure what best to do with the text here, most of which is from a 7-week old edit by User:210.21.221.178 (text added). Does it have any value? Should it be merged with dialectic? My current inclination is to say that the term dialetical logic dos not mean what that text says it means and simply delete the text. --- Charles Stewart 16:02, 19 May 2005 (UTC)

My inclination would be to include a distillation of your remarks above into the article (as a sort of disclamer) and merge the rest of the text in that section into the article on dialectic or Hegel or something else, but in any case nothing about logic itself. I certainly never understood in what sense Hegel's logic is in any way logic. --CSTAR 16:12, 19 May 2005 (UTC)

Changed section title to Deduction and reasoning

Following the problems with the title Dialectical logic, I changed the title of this section to Deduction and reasoning, and made the main subsection article point to deductive reasoning. I toyed with logical argument as the link, since it is a much better article, but I think in the long run we need the broader context of reasoning. I deleted the following text:

These cautions aside, the notion of a dialectical logic at least reminds us of differing ways of critical thinking about real problems. For example, in daily life, people often seem to act "irrationally" and in defiance of their own interests when they do not feel sufficiently recognized. Their actions may be a perverse attempt to raise a conversational issue, suspect to the push-pull of dialectic, but perverse only when, unlike Hegel, one doesn't make individual and social will a prime mover.
Another important meaning of "dialectical logic" is found in Hegel, who described the logic of history as proceeding less in a syllogistic fashion than in the form of his "thesis", which produces the dialectical antithesis and, in most cases a synthesis or higher truth that combines (in a way practically opaque to formal logic) features of both.
Examples of this process are found most frequently in "unexpected" historical events such as the support by German socialist parties for Germany's entry in WWI and the rise of Islam or Christianity. When superficially described, such explanations seem often uniquely after the fact and contrived. In depth they can be far more useful in accounting for mass movements considered as made up, not of syllogistically predictable automata but of reasoning beings engaged in political and historical "conversations".
The most developed form of dialectical logic as found in Hegel appears in the Marxist tradition. Responsible members of this tradition (cf., for example, George Novack's Introduction to the Logic of Marxism) emphasize the ability of syllogistic and mathematical logic, on the one hand, and dialectic on the other, to coexist, where the former is useful in solving the problems of daily life and the latter is useful for understanding large events.
However, it seems impossible to treat dialectical logic as a field independent of its application for the very good reason that our way to do so would be to simplify dialectics...down to a micro level where syllogisms and formal logic applied; where a computer program (by definition having no truck with dialectic) could be written to predict the outcome. Like the related "transcendental deductions" in Kant, dialectical logic is all philosophical praxis and no independent theory. Hegel himself seems to have regarded any form of decontextualization of logic as forms of charlatanry (such as the Phrenology and Mesmerism of his day) which could be used to obtain any result desired.

...which I don't suppose anyone will shed any tears about, but maybe some of the text can be scavenged for articles such as dialectic. --- Charles Stewart 15:01, 27 May 2005 (UTC)

Ethnocentrism et al

Moved from above, where I missed it until just now:

3-25-2005 Edward G. Nilges spinoza1111@yahoo.com w
An excellent article in its way on Logic but as ethnocentric as the 1913 Encyclopedia Britannica, as if Mo Tzu or the Arabs had nothing special to contribute.
And, nothing at all on dialectical or Marxist logic.
I am not qualified at this time to contribute anything on non-Western logical traditions. I have been so bold, however, as to add the section on Hegel's "logic" and Marxist logic which derives from Hegel.
Please feel free to edit or to change. Note that even Copi mentions these forms of logic, albeit in a dismissive form, and I feel the general reader is ill-served by the latest news from computer science but nothing on what Hegel meant by the dialectic.
I have placed this discussion at the beginning of what seems to be the most appropriate location for it for visibility and to get feedback on my alteration.

I don't think the Arabic contribution is ignored, since the Arabs were the carriers of the Aristotelian and Platonist tradition to medieval Europe, but a more explicit mention would be in order. The text Edward G. Nilges wrote on dialectical logic is really not appropriate for the main logic article, but the existence of the Marxist & Hegelian contribution needs to be mentioned. I'll try to do both of these when I have a bit of time. As for Mo Tzu and other ethnic traditions: yes they deserve a place, but I don't know enough about them to write anything. Maybe User:Mel Etitis could say something? --- Charles Stewart 15:11, 27 May 2005 (UTC)

Just raising a quibble with myself: of course the Arabs were not the only source of Platonism in medieval Europe, since there was the indiginous neoplatonic tradition, but I understand that they were the source of real scholarship on Plato. --- Charles Stewart 15:17, 27 May 2005 (UTC)

New subsection

I've created a new subsection History of logic and made it the first topic in the topics section. I think this more or less deals with the ethnocentric part of EGN's complaint, and I don't think there is a real issue with not handling Hegelian "logic", although perhaps a subsection in controversies dealing with controversies as to what logic is about is worthwhile. --- Charles Stewart 19:56, 2 Jun 2005 (UTC)

Peer review

I think that this article is pretty much at Wikipedia:Featured article quality, and my plan is to submit it to peer review sometime next week. I'd be grateful for any comments on the current worthiness of the article as it now stands. --- Charles Stewart 20:22, 2 Jun 2005 (UTC)

Other than the statement that the article is very good, I have none. --CSTAR 13:49, 5 Jun 2005 (UTC)

Ah, but I have. I have two issues with the lead paragraphs: they are too long, and they assume that logic is the study of argument. I've shortened the lead paragraph, and created a new subsection of Scope of logic dealing with rival conceptions of logic. The following text gets deleted by my edit, which maybe CSTAR has issues with:

Arguments express inferences — the processes whereby new assertions are produced from already established ones. As such, of particular concern in logic is the structure of arguments — the formal relations between the newly produced assertions and the previously established ones, where "formal" means that the relations are independent of the assertions themselves. Just as important is the investigation of validity of inference, including various possible definitions of validity and practical conditions for its determination. It is thus seen that logic plays an important role in epistemology in that it provides a mechanism for extension of knowledge.

The lead paragraphs could still do with pruning, to fit the FA criteria (WP:FAC). --- Charles Stewart 16:43, 6 Jun 2005 (UTC)

Hmmm. Long paragraphs? Well I'm not suggesting paragraphs of Proustian proportions; even with a more modest gauge of length, the paragraph you deleted doesn't seem long. Is it wrong? And it seems deleting the paragraph really obliterates an important point of logic I think..namely the formal structure of an inference. Are you also suggesting that the claim that logic plays a role in epistemology is wrong or misleading? I'm really confused. What the hell is logic? --CSTAR 18:58, 6 Jun 2005 (UTC)
PS Hell added to make the argument more lively. It's hard to convey gestures.--CSTAR 19:09, 6 Jun 2005 (UTC)
Part of the argument for deletion was that the above is lengthy: it was a little over half the first paragraph. The larger part of the argument is that it becomes bit of a non-sequitur if we drop the "logic is the study of argument" claim. If you look at the new "Rival conceptions of logic" section: you will see that the new version of this article goes fence-sitting when the question "what the hell is logic?" is asked: not a bad thing, in my book, seeing as I didn't agree with the old definition. --- Charles Stewart 20:09, 6 Jun 2005 (UTC)
Postscript: I missed one of CSTAR's points, about the relation to epistemology: no, I don't think the claims are wrong, but I'm not sure where best to put them. --- Charles Stewart 20:23, 6 Jun 2005 (UTC)
The article does touch on many different points; having just read it again though, I don't think I retained much other than lots of names and that it is related to arguments in some way. Maybe I am thinking of logic too narrowly, although I don't think so. In particular, there are two areas in which I have thought carefully about the formal structure of inference: physics and economics. The article strives too strongly to be culturally neutral (which is certainly desirable) but in doing so I think it neglects the importance of attention to formal structure in areas of scientific research.--CSTAR 20:37, 6 Jun 2005 (UTC)
I hope that what you are saying is impatience speaking: I tried to minimise the impact of the de-ethnocentrisation on the readability of the article, and I think the impact is pretty small I could avoid talking about particular thinkers in the Rival conceptions section, though. The existence of some constitutive relationship between logic and argumentative is non-neutral: the logic is the study of states of affairs folk deny it: logic is about satisfaction relationships between language and the world, and does not depend upon any faculty of reason.
I think I can reinstate part of the deleted text in the Deductive and inductive reasoning section. --- Charles Stewart 21:05, 6 Jun 2005 (UTC)
logic is about satisfaction relationships between language and the world
Well I am glad this is out in the open; indeed I agree with it. However this position would be indefensible to many physicists who (contrary to belief) are instrumentalists rather than realists. That's one reason why I am so attached to the importance of formal relations between assertions in the definition of logic.--CSTAR 21:16, 6 Jun 2005 (UTC)
I don't agree with it (I think this view handles, among other things, counterfactuals badly), but the significance of the view means we can't make certain simplifying assumptions in the article about the relationship of logic to argument. (FYI my view is a mix of view I (logic is about arguments that have a valid form) and view II (the formality of argument comes from the structure of judgements); view III seems true (logic usually relates language to the world) because language is shaped by the use we make of it, but this connection is not necessary). I'm going home now: what you don't like of my edits, please change or at least complain about, but I still think we should be shortening the lead paragraphs still further. --- Charles Stewart 21:35, 6 Jun 2005 (UTC)


OK the article does do a good job of listing an array of subtopics to redirect the reader. I'll return to my specific objection later, although in some form it is addressed by text in the article.
The structure of the two sections immediately after the TOC is a bit odd. In particular, the section titles, Scope and Paradigms, what do these mean? Do the subsection headings express special topics corresponding to these headings? For instance is history of logic a paradigm in the same way predicate logic is?
As far as cutting down goes, how about deleting the 2nd and 4th paragraphs of the intro?
The remark about the relation between psychology and logic is important, but should go somewhere else in the article.
In fact, it would clarify matters if there were a section entitled Relation to other sciences. This would address my concern about the structure of argument and reasoning in the sciences. Though I believe in the importance of semantics to justify inference, this view is not universally accepted, I don't think. Our previous exchange seemed to be a bit garbled and this statement about semantics is what I meant by stating agreement with logic is about satisfaction relationships between language and the world--CSTAR 23:45, 6 Jun 2005 (UTC)
I'm happy with deleting paragraphs 2 & 4: and have applied the change. The "scope" section I thought was clear: it is meant to set the bounds in fuller detail what logic is about and introduce some key distinctions for the article. Maybe there is a better term. "Paradigms" is a bit vague: it was introduced by User:Siroxo to merge the two sections we had before, namely "Topics in logic" and "Motivations in logic", which wasn't a clean division. Here's some suggestions:
  • We rename the "Scope" section to "The Nature of Logic";
  • We rename the "Paradigms" section to "Topics in Logic";
  • The history subsection gets moved to the "Nature" section;
  • Discussion of reasoning and psychology can be reinstated in the "Nature" section

The two deleted paragraphs are:

As a byproduct, logic provides prescriptions for reasoning, that is, how people – as well as other intelligent beings, machines, and systems – ought to reason. Such prescriptions are not essential to logic, rather, they are an application. How people actually reason is usually studied in other fields, particularly psychology.
The ancient Greeks divided dialectic into logic and rhetoric. Rhetoric, concerned with persuasive arguments, would currently be seen as contrasted with logic, in some sense, as is dialectic in most of its acquired meanings.

That's a bit more work still to do before we get to peer review... --- Charles Stewart 19:24, 7 Jun 2005 (UTC)

Reworking the scope section

Re: Charles Stewart assertion The "scope" section I thought was clear: The first heading (Rival conceptions..., doesn't seem to parallel the following two (Inductive and deductive.., Formal and informal...).

I'm still not happy about how the article defines logic. With the exception of mathematics, it's not clear from this article where the limits of logic are in regard to other domains of knowledge.--CSTAR 15:29, 8 Jun 2005 (UTC)

I'm in complete agreement that the scope/nature section is the section most in need of work, but I'm wondering how much success we can hope to have placing clear limits on the scope of logic. It's no point of shame for us to be having difficulties in getting the basis of the article right: it's worth noting that the two major recent philosophy enclyclopedias (the Routledge and Stanford encyclopedias) both duck the problem of giving an encyclopediac overview of logic as a whole.
For the article to work at all, we do need some principled way of architecting the text. My personal favourite definition is Logic is the study of arguments correct in virtue of their form, but a blank assertion of this unfortunately falls is not neutral. I think we should base the article on some rival definitions instead, and observe that the foundational difficulties do not render the discipline incoherent.
I've made a beginning on rework the scope section in a mirror that we can treat in a more experimental manner, which is at Logic/alternate-start. I've done the changes indicated above, moved up the formal and informal logic section, which I think should be extended to cover the idea of form being constitutive of the subject, and its relationship to the topic-neutral nature of logic. --- Charles Stewart 17:21, 8 Jun 2005 (UTC)

paradox

I changed the red reference to paradoxes of implication to paradox of entailment. I don't think the paradox of enailment article exactly captures what is being references in the section, but I think it would be the appropriate place for such things to go. Either way, a slightly uninformative link is probably better than no link at all. Someone more versed in the subject than I should maybe work on paradox of entailment. -Kzollman 23:20, Jun 2, 2005 (UTC)

Distinction between arguments

The latest edit replacing "distinguish good from bad arguments" with "distinguishing between arguments" doesn't seem helpful.--CSTAR 00:48, 8 Jun 2005 (UTC)

Another idea

It would maybe be easier to get this article into a stable state simply by stating that the article is about logic understood to be in conformance with a given definition, and farm out rival conceptions of logic to another section. Might this work? --- Charles Stewart 20:45, 8 Jun 2005 (UTC)

This may be a possibility, although it does admittedly a problem for a source with pretensions of cultural neutrality. The article seems to have changed direction very recently and in my opinion has become too general and too ambitious. Unfortunately, I know nothing about the rival conceptions of logic, so I can't offer any useful insight here. I am completely out of my depth. --CSTAR 20:59, 8 Jun 2005 (UTC)
If the definition is one that spans several different cultures, as some possible definitions involving arguments would, then it doesn't result in an ethnocentric article. But I don't like this suggestion anyway: it is sure to create pointless duplication and I don't the simplification to be had is all that great. --- Charles Stewart 19:06, 10 Jun 2005 (UTC)




a "Silas" is somebody who attacks everything about a person EXCEPT the logic of that persons argument. —Preceding unsigned comment added by 88.108.165.206 (talk) 07:04, 18 November 2008 (UTC)

Restructuring & WikiProject for logic

I've done the reworing of the first section as I proposed. It's a pretty big change, but I think its a big improvement. Feedback eagerly sought.

While I'm on the topic, I raised the possibility of a WikiProject for logic on Wikipedia talk:WikiProject Mathematics. The text of that announcement follows:

Encouraged by User:Paul August on Talk:Aristotelian logic, I'm posting an invitation to comment on the idea for a WikiProject for Logic. I have a draft proposal at User:Chalst/WikiProject Logic proposal, and I am interested in:
  • Indications of interest
  • Criticisms of the what is on the page
Many thanks in advance for your comments.

--- Charles Stewart 06:49, 11 Jun 2005 (UTC)

Critique: One sentence at a time

(1) The crucial concept of form is central to discussions of the nature of logic, and it complicates matters that the term is commonly used in an ambiguous manner. We shall start by giving definitions that we shall adhere to in the rest of this article:


Form? Do you mean the form of argument? the term is used in ambiguous manner? The term in this case is logic?

Could this sentence be better written as:

(2) The concept of form of argument is central to discussions of the nature of logic, and it complicates matters that the term logic is commonly used in an ambiguous manner. We shall start by giving definitions that we shall adhere to in the rest of this article:

Or did I completely miss the point? --CSTAR 21:17, 11 Jun 2005 (UTC)

Next sentences

(3) Informal logic is the investigation of logical inference independent of any particular analysis of the structural regularities of the inference.

Is this really true? Informal logic pays to attention to form (although the form may not be specified by a set of formal rules) and in particular, analysis of fallacies does pay attention to their form. Also informal logic can be rigorous; most mathematics is informal and yet entirely rigorous.


(4) An inference possesses a purely formal structure if it can be expressed as a particular application of a wholly abstract rule, that is a rule that is not about any particular thing or property.

This deals with my previous concern, to some extent although abstract may not be the right word (I think it is more like formally specified structure, although this seems circular).

More later.--CSTAR 15:49, 12 Jun 2005 (UTC)

Reply

Note: I added numbers to your texts above.

  • (1,2): Ah, right, what I wrote in (1) was very unclear. I meant that the "formal" in formal logic is ambiguous. So (2) is saying something quite different to what I intended.
  • (3): This is a convention I am proposing for the article, and while it is along the lines of definitions I have seen used elsewhere, it is my original formulation. I'd say what is going on in informal analyses of fallacies fits my definition very nicely: one usually sees attempts to look at the fallacy from several different angles, rather than, as with formal logic, having a predetermined manner of analysing the argument that fixes a particular interpretation. I've no problem with informal rigour, actually the phrase deserves an article.
  • (4): Right. These definitions were hard work: they're probably not as accessible as they could be, but I guess it will be hard work again to improve on them.

Thanks for the close reading. I'll change (1) accordingly. --- Charles Stewart 15:54, 13 Jun 2005 (UTC)

Next sentences

While on the above analysis, formal logic is old, dating back more than two millenia, symbolic logic is comparatively new, and arises with the application of insights from mathematical abstraction to problems in logic. Certain conventions have become prevalent in the symbolic analysis of logic: the logic is captured by a formal systems, comprising a formal language expressing claims that may be demonstrated or refuted, which we call formula, and a set of rules of derivation (often called "rules of inference"), and sometimes a set of axioms.

Shouldn't formula should be formulae or forumlas? The other item in boldface I have a quibble with. Isn't formula something which is either true or false which is different from being demonstrable or refutable. Shouldn't expressing be consisting of a set of? Again these are quibbles; however, I am being deliberately argumentative.--CSTAR 17:14, 13 Jun 2005 (UTC)

On formula: yes it should be plural. On claims: the formal system can't establish the truth or falsity of the claim without a demonstration of soundness, which can't be established by purely symbolic means. On expressing: I wanted to keep the propositional claims separate from the symbolic formulae, but what I wrote is unclear. I'll fix the first and third points now, but I'll have to think a bit about the second to see what, if anything, needs fixing. --- Charles Stewart 13:48, 14 Jun 2005 (UTC)

Next sentences (cont'd)

The most essential property of a logical formal system is soundness, which is the property that under interpretation, all of the rules of derivation are valid inferences. The theorems of a sound formal system are then truths. Also of the essence is consistency, which states no theorem contradicts another.

Most essential sounds strange. Second boldface sentence: You mean I assume any theorem is a true statement. Could we use something else instead of of the essence.--CSTAR 17:57, 15 Jun 2005 (UTC)

The Opening Paragraph

The word "Logic" does not correctly come from "Logos". It comes from "Logikos". "Logikos" is derived from "Logos", "Logic" is not. Derivation is not transitive. I would change this myself, but I can't work out how to change the Greek letters (damn my eyes). There's more to change in this article, but I'm anally retentive about working methodically through articles. Pontifexmaximus 12:49, 26 Jun 2005 (UTC)

Where do you find this derivation? I seem to recall that User:Mel Etitis was the source of the current claimed derivation. --- Charles Stewart 16:43, 4 August 2005 (UTC)
Dictionaries are useful. Logic comes most directly from logikê tekhnê which was the phrase used by Aristotle (from memory). Logic does not come from logos, but logikê does derive from logos through logikos. Pontifexmaximus 15:25, 20 August 2005 (UTC)

Merge College logic

There probably isn't much of value over there, but you guys determine if there is anything of worth, and then make that a redirect here. KSchutte 23:09, 22 July 2005 (UTC)

I agree that they should both be merged. I honestly beleieve there isn't much worth ssaving in the college logic article and for the sake of quality should be merged into logic. StringDrawn 18:34, 23 July 2005 (UTC)

I agree with StringDrawn — College logic should just be made a redirect here. --Mel Etitis (Μελ Ετητης) 18:29, 31 July 2005 (UTC)
The college logic article, as it stands isn't really worth saving, but college logic is worth documenting in the wider context of the study of logic to improve reasoning skills, debating skills and/or to make one a better person: this is much of the pre-modern conception of logic. The current Deduction and reasoning section is the badly named home of this topic in the Logic article: I'd be grateful for better names for this: my best name so far is Logic and pedagogy. --- Charles Stewart 16:43, 4 August 2005 (UTC)
I agree that the College Logic article should probably be removed or merged. How about "Critical Reasoning " or "Informal Logic" for names of the corresponding section in this article?Wjwma 17:05, 4 August 2005 (UTC)
The logic courses at my college only deal with formal logic. There are separate courses about reasoning. The reasoning courses only mention formal logic briefly.

Capitalisation

Isn't formal Logic (what this article is about) usually written with a capital 'L', to distinguish it from 'everyday logic'? DirkvdM 07:30, 4 August 2005 (UTC)

I've never heard of this. If anyone follows it, it is not followed widely. --- Charles Stewart 16:43, 4 August 2005 (UTC)

The 'logic' of calling the USA America

An ongoing discussion (including many reverts) between me and Bkonrad needs resolving, so I thought I'd call in 'the expert' (a bit of flattery never hurt anyone :) ). My reasoning is that, formally speaking, calling the USA America is illogical because, for example, that would place South America outside America. See also the talk page on this (if you can stomach it...). Another issue was whether the naming is '(politically) correct', but that has now shifted to 'illogical'. Alas, that makes the discussion a bit long to follow. You might want to limit your readings to the later part, especially where a third person, Muke Tever, comes in. DirkvdM 12:50, 8 August 2005 (UTC)

Strictly speaking logic doesn't really bear on the issue of naming. I can call my computer "My Great Aunt Matilda". It might be confusing (e.g. "My Great Aunt Matilda crashed today.") but there is nothing illogical about it. One issue you may be grapling with is whether it makes sense to use a name intended to refer to a whole (America) in order to refer to one of its parts (in this case: The USA). In general this is not really problematic. We seem to do it all the time. For example we say things like "Eat your dinner." if a child has only their vegetables left on their plate. Or even better, picture your friend standing in the good ol' USA, saying "I am in America.". Is there anything really wrong with what he is saying? In such cases even though we don't explicitly state it, it is understood that we are not actually identifying the whole with the part. We don't really mean that the vegetables = the dinner or The USA = America. However, what your friend may be doing - which you may be finding objectionable - is identifying the whole with the part. That is, he is saying that America = USA. Though, I wouldn't say he is being illogical, there does seem to be some implicit political message being delivered in such an identification. This is possibly why the issue seems to be about political correctness in some way.Wjwma 05:42, 10 August 2005 (UTC)

The political correctness is another thing. That is a matter of opinion, so the edit saying it is "seen by some as politically incorrect" is just fine. But logic is not a matter of opinion, and that's what the quibble is about.

Your example is about two completely different sorts of things (like the word 'pole' can have various meanings). What about comparing her body parts? Let's say you call Matilda's upper arm ('the US') 'arm' ('America'). But a lower arm is part of an arm (a logic in language one can assume, I'd say, so in this sense 'South America' must be part of 'America'). 'Lower arm' ('South America') is then part of 'arm' ('America') (in the linguistic sense) even though it isn't (in the sense that 'arm' means 'upper arm' (the US)). So this whole naming system is not internally consistent. And therefore illogical. Consistency is a prerequisite for logic, right?

The solution of naming the continent 'America' 'the Americas' would be analogous to naming that arm 'the arms'. Which presents us with the problem that (assuming she has two arms), that term also gets two meanings. So, come to think of it, 'the America's' is also illogical. It just happens to be that there is no other 'America' to constitute another meaning of the plural 'the Americas'. DirkvdM 09:02, 10 August 2005 (UTC)

Dirk and Wjwma seem to be using different definitions of "logic." By "logic," do we mean "formal logic," or logic in the common-sense way? How can we clarify this issue? -Chira 01:09, 12 August 2005 (UTC)
Consistency in naming isn't part of logic. Whilst some countries may change their language use towards what they consider "sensible," this is a different field than that of logic... and in most situations (outside of a field's defined terminology) we are at the mercy of common usage. I suggest changing your argument to something such as "I find that using the terms 'USA' and 'America' interchangeably is ambiguous and not as useful as reserving the term 'America' to refer to the two continents." I suspect that saying that somebody should change their language use to something more logical is a tad pedagogical and may not be an effective strategy for reaching a mutual understanding. -Chira 01:49, 12 August 2005 (UTC)

You're now talking politics, which is fine, but there remains the question what is strictly logically correct. You say "Consistency in naming isn't part of logic", but surely logic requires consistency? The only linguistic assumption I make is that 'South America' should be part of 'America'. For the rest it's just a matter of applying the rules of logic. DirkvdM 09:59, 12 August 2005 (UTC)

Nay, not so much politics as the way that people use language. We should say that logic is not part of naming? And that it is usually only an academic exercise to tell people to change the way they use language? If you use the world 'logical' to describe naming practices, you're using a different meaning of 'logic' as it's used in this article.
As stated in the section on rival conceptions of logic, modern logic does not, however, cover good reasoning as a whole. That is the job of the theory of rationality. Whilst it may be common practice to use the word 'logic' to refer to good reasoning, or logical to describe sensible word choice, this is different from the field of logic. Also, "consistency" (of axioms and rules) is a local phenomenon in logic-- held across one issue of consideration-- and even at that, there are systems that allow you to transform both axioms and rules. You should be looking elsewhere than formal logic for support for your argument. Formal logic was designed for constructing conclusions rather than reinforcing them, anyway. -Chira 21:07, 12 August 2005 (UTC)

Legend of logic symbols

I'd like to see a prominent reference to symbols used in formal logic, it would be quite helpful to newcomers. -Chira 05:19, 12 August 2005 (UTC)

It would be useful to have such a guide, but i don't think this article is the place. The table of mathematical symbols, which covers several of the symbols used in mathematical logic, would make a useful starting point. --- Charles Stewart 19:36, 18 August 2005 (UTC)
Ah, this is very useful! Thank you for pointing it out. I've inserted a link to Table of logic symbols below the introduction in the main article. -Chira 15:53, 20 August 2005 (UTC)
Chira, your last edit had the effect of hiding this important link - so I reverted it, keeping it in the TOC. Banno 22:57, August 20, 2005 (UTC)
Oops, there was a flurry of confusing edits by various people... thanks for noticing and bringing it back. --Chira 00:02, 17 September 2005 (UTC)

This article sucks because it doesn't actually show the symbols used in logic. This article sucks. —Preceding unsigned comment added by 132.235.73.24 (talk) 19:52, 21 May 2008 (UTC)

Who is we?

"This conception can be criticised on the grounds that we do not regard the manipulation of just any formal system to be logic
 ;such an account omits an explanation of what it is about certain formal systems that makes them systems of logic."

Who is we? I removed the last sentence. Until you qualify the statement better I would consider it argumentum ad populum.

There is no argument being made here so I don't see how this can be a case of argument ad populum. The author is just reporting on the view and a possible objection to it. Still I'll remove the "we" if that helps.Wjwma 11:04, 22 August 2005 (UTC)

Logical consistency

Just a minor formalist nit-pick:

I wonder if there isn't a slightly better better wording for the recent statements of consistancy. The statement currently says: "A minimal condition which a sound system should satisfy is consistency, meaning that no theorem contradicts another.". Investigations into the differerent notions of "negation" when intuitionist logics were introduced led to investigations of logics with no negation operator (such as Hilbert's Positive Propositional Calculus that a number of intuitionist logics used as a base). As I understand the wording in the wikipedia article, no logic without negation could be other than consistant because you can't have a statement and its negation. But there are, in fact, appropriate notions of consistancy that are used for logics that don't have negation.

I believe that there should be an appropriate wording such that it gets the idea across to the novice, and still encompass th extended notion. I can't personally think of an appropriate wording, so I'll just drop the ideas here and maybe someone else has an appropriate wording. If not, the curent wording isn't actually bad.

Following one popular formal logic view, the real problem with systems that are not consistant is not the generation of a direct contradiction, it is that from such a contradiction one can generate any statement whatsoever (whether or not it is true, if you are interpreting the logic). A logic that can prove ANYTHING, instead of just True things, is "inconsistant" by this notion. (And it extends nicely to logics without negation, or that are themselves defining one notion of negation or another.)

Nahaj 02:24, 15 September 2005 (UTC)

I'd say the notion of contradiction is more fundamental than negation - I've contradicted myself if I claim that the sun is hot then later the sun is cold. The negation of a sentence can be seen as the weakest claim that contradicts it. But you are right, there are logics that do not even have that can still be inconsistent, the accepted meaning being that they prove anything. But that's no good, since there are logics in which inconsistencies don't produce explosion.
I'll think about this. It's noty good to get into all the technicalities here, but I'd like what we say to be true. --- Charles Stewart 23:51, 18 November 2005 (UTC)
There is a common factor at play with the usual concern with logics that they be consistent, and with logics that they don't prove enerything, which is that the point of logics is to help you distinguish between good and bad arguments, and logics that are defective in the above ways cannot do this, with a caveat that paraconsistent logics claim to be able to have a useful notion of argument even in the presence of inconsistency. I think this is the right way of putting things in the article, and I'll make the change shortly. --- Charles Stewart 20:25, 21 November 2005 (UTC)

Peer review

I cleaned up a couple of things (some of the definitions at the beginning and the Logic in computer science sections, mainly), and now I think it's in good shape for peer review. So take a look at Wikipedia:Peer review/Logic/archive1 --- Charles Stewart 23:45, 18 November 2005 (UTC)

Dean Buckner's proposal

Dean has proposed a new structure for the article that he argues is more principle and would make for a more substantial article than what we now have. The argument can be found at Wikipedia:Peer review/Logic/archive1 and the new text for the proposed change at User:Dbuckner/logic. I don't agree with everything in it, but it is a high quality proposal, Dean's criticisms of the current article are mostly sound, and I expect we will incorporate most of the new text Dean is proposing. Your comments of the new text are welcome. --- Charles Stewart 21:10, 8 December 2005 (UTC)

And please feel free to edit the draft. It was a hurried piece of work. In addition, I struggled with a concise definition of 'semantics'. Also, my knowledge of modern logic is not good. dean

Greek logic influenced by Islamic/Indian logic ?

This article implies that Greek logic was influenced by Islamic/Indian logic. On what basis? Just because some Ganeri (2001) published work in this regard? I think all references that imply Greek logic was influenced by Islam or India should be removed. These are not factual and distort the truth. Greek logic and thought was unique. It had no precedent or influence from any of the previous cultures. 158.35.225.229 15:57, 23 November 2005 (UTC)

  • The article claims no influence of either Islamic or Indian thought on Greek thought. The article asserts that the European's learnt most of what they knew of Greek logic through Islamic sources, an idea whose historical credentials are impeccable. I shall put sources for this reception in the article, however. (Ganeri 2001) is the source for the idea that George Boole and Augustus De Morgan were likely aware of Indian logic before some of their well known contributions to algebraic logic were made. The basis for this argument is that both were active members of the Royal Society, where Colebrooke presented his influential 1824 treatment of indian logic. That they were so aware does not show that this information at all impacted their work, but Ganeri argues plausibly that a familiarity with the contents of a tradition of logic very different from that derived from Aristotle would encourage willingness to break with tradition. I think this possibility is interesting and encyclopediac, and is worth including in the article provided (i) it isn't oversold and (ii) no contradictory information comes to light. --- Charles Stewart 20:44, 23 November 2005 (UTC)


And assuming this did have any influence on Boole and De Morgan, what influence did it have on later logicians via those two? I am looking through Venn's System of Logic which was easily the most influential work on logic in its day (and has an encyclopedic reference). I see nothing there of Indian logic. Dbuckner 20:37, 5 December 2005 (UTC)
"Ganeri argues plausibly that a familiarity with the contents of a tradition of logic very different from that derived from Aristotle would encourage willingness to break with tradition" - but Boole certainly did not break with tradition. He was simply trying to mechanise Aristotelian logic. The real decisive breakthroughs occured in the 1860's Dbuckner 20:40, 5 December 2005 (UTC)
I disagree with the assesment of Boole's work: if his aim was simply instrumental interpretation, why did he labour so hard with the peculiarities of his system (ie. all the stuff about uninterpretable terms)? Boole's system is distinguished by the algebraic identities, and I think that he stuck by them because he was trying to uncover a mathematical foundation underpinning both arithmetic and reason. And this is a big break with tradition. --- Charles Stewart 22:31, 7 December 2005 (UTC)
Postscript Ernst Schröder clearly thought Boole's work was revolutionary. --- Charles Stewart 15:31, 10 December 2005 (UTC)
If anyone would influence Greek thinking it would be someone more local. Given that the Greek script is phonecian, and that the only users of Semitic and pactitioners of oral deductive discussion in the area are Hebrews at the time of the evolution of known Greek theories, it would be logical to suggest that it is the influence from Israel that was dominant in the development. In fact the term for a practiotioner of logic, i.e. story teller, is logoi, and is a Hebrew expression lo goi, meaning 'not stranger' (suggesting that otherwise deductive thinking was considered foreign outside of Israel at the time?!)--Mrg3105 21:47, 26 December 2006 (UTC)

Logic Portal? Wikiproject?

Anybody else think logic needs a portal or a wikiproject or both? I'd like to see a huge amount of improvement on most of the articles on logical topics (nearly all of them lack the precision the topic deserves), and I think this might be helped if we had a unified place from which to start. I don't have the kind of time or energy required to start such a project, but I can certainly help contribute with design and editing. Let me know what you peeps think. KSchutte 22:12, 7 December 2005 (UTC)

I've had User:Chalst/WikiProject Logic proposal knocking about for some time, but never quite had the impetus to finalise it. The portal would probably be a good thing, but I don't have any sort of knack for graphic layout. --- Charles Stewart 22:34, 7 December 2005 (UTC)

FOL vs. second-order

An anonymous editor placed the following paragraph in the article:

Frege's original system of predicate logic was not first-, but second-order. Second-order logic is most prominently defended (against the criticism of Willard Van Orman Quine and others) by George Boolos and Stewart Shaprio.

There's interested ground here, but Frege's system of the Begriffschrift is not problematic in the way that the system the second-order logic article describes is. This needs fixing, no time now. --- Charles Stewart 21:43, 10 December 2005 (UTC)

Problems

Peeps, we really need to do some systematic review here. I've spent the morning fixing up the various conditionals pages, neglected for at least a year, and they could use a rough re-edit by someone else (especially counterfactual conditional, which I didn't spend much time on). Also, our articles on basic inference rules shouldn't have false claims and miswordings in them like Conditional proof, Destructive dilemma, and Hypothetical syllogism (and I'm sure many more) all do. I don't have a lot of spare time, so I can't be the only one trying to fix these things.

Sorry for the rant. I know you guys try. KSchutte 18:38, 19 December 2005 (UTC)

Natural deduction in propositional logic

There should be a section linking to, and briefly summarizing, natural deduction. I may add this, if anyone else agrees, but I am sure there are more qualified people to do it than me. --Kevin L. 03:31, 21 January 2006 (UTC) {{}}

Well how 'bout that..

a whole article dedicated to logic without a single example or piece of logic in it to give an idea of what the hck is being talked about.--Lacatosias 13:49, 3 February 2006 (UTC)

The currently-suspended work at User:Dbuckner/logic is going to result in big changes to this article, and contains several examples of formal inference. User talk:Dbuckner/logic is currenmtly the best place to talk about what should go in the revised article. --- Charles Stewart(talk) 17:29, 3 February 2006 (UTC)
Ok then. Thanks for the directions. I'll see if I can be of any help there.--Lacatosias 18:26, 3 February 2006 (UTC)

Logic as a science?

Maybe I'm just nitpicking, but I don't understand why the article repeatedly refers to logic as a science. Whether or not it's empirical is (apparently) controversial, it doesn't involve physical experimentation, and it's prescriptive- it seems more like a branch of epistemology than a science to me.

I dunno, it just seems to be either too controversial of an association to be made off-handedly, or there's some justification for it (e.g. it's a tradition) that could be made explicit in a subsection.

... forgot to add initially, I meant more justification than just what's in the "rival conceptions" section. It seems like only two conceptions call it a science, and I thought there might have been some unstated reason why all conceptions would agree to it being referred to as such, and that reason could be made explicit somewhere. Pamplmoose 18:38, 12 February 2006 (UTC)

Take a look at the very brief Formal science. --- Charles Stewart(talk) 19:11, 12 February 2006 (UTC)
  • JA: Long before the word "science" (Latin: scientia = knowledge) came to be restricted to its current connotations of empirical science, logic was classified as a "normative science", because it was intended to embody knowledge about norms, that is, statements about what we ought to do if we want to achieve certain ends, goals, or goods, in this case the good of logic being truth. Jon Awbrey 23:00, 12 February 2006 (UTC)
Whether or not it's empirical is (apparently) controversial, it doesn't involve physical experimentation, and it's prescriptive- it seems more like a branch of epistemology than a science to me.
This is also true of string theory but it is still considered a scientific theory.--Lacatosias 09:08, 23 February 2006 (UTC)
And that is why string theory is seen by some physicists as not being science either, or that is until we have the capabilities to test on of its predictions. Of course, thats a whole other conversation, more suited for the string theory talk page :) 130.179.39.66 18:11, 23 January 2007 (UTC)

String theory is, in principle, deniable by experiment. Logic is not, though it could be overthrown by an internal contradiction, such as the one Russell discovered in Frege. Rick Norwood 15:29, 23 February 2006 (UTC)

Please note the process of discovering internal contradictions derived is not unlike process a physicist would use.
  1. Tester creates or guesses a Hypothesis.
  2. Tester finds some method to test Hypothesis (call it Test) via reasoning about the system in question.
  3. Tester creates implication "if Test then Hypothesis", where Hypothesis may be a denial of a foundational theory or the affirmation of it. (In science, we note that we can never truly affirm a proposed foundational truth, only add evidence to the fact that it is indeed correct.
  4. Tester tests.
  5. If the Test is true, the tester has found something of significance, but he must judge whether the mechanism for performing the test was indeed sufficient, etc. If insufficient, back to step 1 (given time/resource/motivation), otherwise he makes note of the new discovery and hopefully tells others.
  6. if the Test is false, it doesn't mean there's another experiment that may better test the Hypothesis. The tester files away the results, perhaps taking some statistics to see how well the test was performed, etc. and goes back to step 1 if he has the resources/time/motivation.
This argument is incomplete... it ignores dual implications (p if and only if q) and more needs to be said about the tests in question. For example, we can physically test for the existence of something, we cannot test for something's non-existence without certain assumptions, whereas in mathematics, both non-existence and existence can both often be tested because we have a whole universe we can manipulate.
However, even mathematics is limited; "we" (humans) cannot test for the non existence of everything, such as proofs in certain logical systems. (See Gödel).
Aside:It is funny talking about anything's non-existence... it seems we're talking about a mapping an existing something to one of two values (True "it exists in some universe X", False "it does not exist in universe X, or its only exists in your and possibly our collective minds, etc"). Apparently, one needs to separate the concept of "it" from the actual entity which we've named "it", if it exists.
The only other difference I see is that with physics, the reasoning occurs in the mind but the experiment is generally carried out in the real world. The exception, of course, Thought Experiments. In math, it's all theoretically in the mind, excepting that we often make notes to ourselves in the real world portions and steps of proofs so that we don't have to keep track of it internally. And with today's use of computers to find high valued primes, etc, its increasingly becoming the case that proofs are performed in the real world as well.
One other thing to keep in mind, there's human logic, from which all kinds of illogical statements may follow and internal contradictions abound, and "Logic" the the wonderful metaphysical concept, which the entity of which I'm not sure even exists, or if it does, how to qualify it. With all our "logics" we can only use human logic to reason about them. I use experiments to test my human logic and my human conception of idealized logics all the time, and if you think about it, you'll probably conclude that so do most people. Root4(one) 15:21, 24 January 2007 (UTC)

The Law of noncontradiction

This law states that a substance can not be something and not that thing at the same time. Substance(A) can not be (B) and (-B) at the same time. This principle is important to understand if we are to have true thinking, comunicating and speaking. The hard thing about this law is that it can not be proven. In order to prove this law we must assume that the law is true. So in order for us to see that this law is true we must test it from that point of it not being true. Example: using the Modus Tollens form of reasoning; If a person has won the masters Golf Tournament, then he has played golf at Augusta National Golf Course. If it is false that he has never played at Augusta, then it is false that he has won a masters golf tournament. see if we deny the law of noncontrodiction it implies many false consequenses. (Nash 196) In order for anything to be true we must except the law of noncontrodiction, other wise this writing is meaningless. Please leave your thoughts about how to polish this. Dwalton512 (talk · contribs · logs)

The law of non-contradition cannot, and to my knoweldge has never been, proven. It is accepted ad a fundamntal self-evident axiom by Aristolte in the Logic. Howvere, modern dialetheists deny the law and argue that the consquences are not as dire as you suggest. Hegel and many other unorthodox logicians have also, historically, rejected non-contradiction. It must be either simply accepted or rejected and the sort of logics that follow will be dramatcially at variance between them. --Lacatosias 09:21, 23 February 2006 (UTC)

The writers above are using "logic" in two different senses. One sense is "reason" -- that's the sense Hegel used it. In that sense, the law of non-contradiction is just common sense. The other sense is mathematical logic -- in that sense, the law of non-contradiction (NOT NOT A IMPLIES A) is a consequence of the axioms. Rick Norwood 15:34, 23 February 2006 (UTC)

The dialetheists reject classical mathemetical logic, preferring instead forms of paraconsistent logics. Grahan Priest, and the like, are not talkign about rejecting a principle of "reason" but a fundemntal pricniple of logic, in the same way that intuitionaist reject the law of exluded middle and double negation. Quantum logic rjects the law of distributuon, etc.. Hegel aslo was rejecting the law of non-contradiction when he adopted the poistion that thesis + anthises (A and not A) = higher truth or some such wackiness. If he's talking about "reason", than it's even worse. He's rejecting what you just called "common sense". Iìve taken three semseters of formal logic. I know a little somthinf about. I'm far from an expert, but I'v never seen a proof of LNC from axioms. --Lacatosias 16:25, 23 February 2006 (UTC)

I recommend Hamilton's Logic for Mathematicians. Rick Norwood 16:50, 23 February 2006 (UTC)

The article on logic does seem too wrapped up in all of the theoretical controversies to be as useful as it could be. It would be helpful to at least summarize the basic laws of traditional syllogistic logic within the article somewhere. However, a discussion of how the law of noncontradiction cannot be proven but may be supported by a Modus tollens argument would probably need to go into the article on the Law of noncontradiction itself (where there seems to be no mention of this topic). --Jjhake 19:52, 25 February 2006 (UTC)

  • Do look at User:Dbuckner/logic. The writing of new content there has been in suspense for rather some time, but this is almost surely the direction this article will be taking. I don't think the current article is at all too technical, rather its problem is that it deals with many peripheral issues without having first properly tackled the core topics. --- Charles Stewart(talk) 20:03, 25 February 2006 (UTC)
    • I would concur with your basic diagnosis that "it deals with many peripheral issues without having first properly tackled the core topics." Dbuckner’s work looks very well organized and certainly has promise. Although there are many things that I like about the current article, it does need more focus at least initially. This is by no means an easy topic because it has such a broad reach, highly technical aspects, and popular appeal. My tendency would be to place a concise history of the subject even earlier in the article than it currently is.--Jjhake 20:27, 25 February 2006 (UTC)

How does this issue relate to the article? The article discusses this law, discusses alternatives to it, and does not take sides. Fundamental logical laws are not the kind of things that it is useful to justify by proofs: this is why in philosophy logic is so tied up with epistemology and metaphysics. Is there any suggestion here as to how the article can be improved? --- Charles Stewart(talk) 17:14, 23 February 2006 (UTC)


That (mis)spelling was annoying, so I went ahead and changed the past :) --CSTAR 18:23, 23 February 2006 (UTC).

Dialetheism is not a logic

The article makes numerous references to dialetheism as a "logic." Dialetheism is the philosophical view that some contradictions are true; it is not a logic, per se. (Graham Priest, for example, never uses the term dialetheism to refer to a logic or type of logic.) I tried to fix this before and it was reverted. How about changing "dialetheism" to "dialetheic logic" in the article? (Priest does use this term, occasionally, to refer to a type of logic, namely one whose semantics allows statements to be both true and false.) That would be far less objectionable. dbtfztalk 23:58, 4 March 2006 (UTC)

I say get rid of dialetheism entirely. Rick Norwood 00:20, 5 March 2006 (UTC)

This is an absolutely whopping error. Thanks for pointing this out. I sometimes scan through these articles too quickly to even spot such things.--Lacatosias 08:44, 5 March 2006 (UTC)

Jagged's dates

Please give a reference for the dates you have added to this article. The article on Indian logic gives different dates.

boundries of logic

hello, great page everyone. In epistemology class we have talked about potential boundries of logic, examples when logic stops working. zeno's paradox, Here is one hand. both examples of when great logic brings unintuitive, problematic results. think theres a spot for this epistemology theory on the page? Spencerk 04:39, 26 April 2006 (UTC)

At least as far as mathematicians are concerned, Xeno's paradoxes have been logically resolved. Xeno's mistake was to assume that an infinite series must have an infinite sum. We now know that, for example, 1/2 + 1/4 + 1/8 + 1/16 + ... sums to 1, even though it has an infinite numer of terms. Thus Achilles can win the race, because the infinite number of infinitessimal time intervals it takes him to cover the ground have a finite sum. Rick Norwood 13:01, 26 April 2006 (UTC)
  • well put rick norwood, i had heard it was resolved somehow, but always assumed it was way too confusing. thanksSpencerk 19:58, 26 April 2006 (UTC)

typo?

However the subject is grounded, the task of the logician is the same: to advance an account of valid and fallacious inference to allow one to distinguish good from bad arguments.

shouldn't that be 'non-fallacious'? and if so, isn't that, following on the heels of 'valid', redundant.

would:

However the subject is grounded, the task of the logician is the same: to advance an account of valid (i.e. non-fallacious) inference to allow one to distinguish good from bad arguments.

with 'fallacious' wikilinked to logical fallices be better? --DakAD 09:32, 16 May 2006 (UTC)


Speaking of formal logic, I'm pretty sure the conditional Rules: MP, MT, and Disjunctive Syllogism are the same-- meaning there's a more basic rule that governs them. Maybe I'm wrong 'though.

MP: premise P → Q premise P therefore Q = premise ¬P v Q premise ¬¬P therefore ? by Implication and Double Negation = premise (¬)¬¬P v Q premise(¬)¬P therefore (¬)Q by Disjunctive Syllogism which reads: premise P v Q premise ¬P therefore Q

Now here's MT: premise P → Q premise ¬Q therefore ¬P = premise ¬Q → ¬P premise ¬Q therefore ? by Transposition = premise ¬¬Q v ¬P premise ¬Q therefore ? by Implication = Path One: premise (¬)¬Q v ¬P premise (¬)Q therefore ? = premise (¬)Q → ¬P premise (¬)Q therefore (¬)¬P by MP.

or Path Two after Implication: premise Q v ¬P [by Double Negation of Q] premise ¬Q therefore ¬P by Disjunctive Syllogism

Need for Inline Citations

I added a {{unreferenced|article}} plate. This article has an utter lack of inline citations. I'll get on the task of tying statements to their sources, but any help would be appreciated. Simões (talk/contribs) 20:38, 8 October 2006 (UTC)

This article has ungone peer review and the header tag on this page has suggested items to be incorporated. You might check these suggestions to see if your tag is premature or needed. Amerindianarts 20:57, 8 October 2006 (UTC)
I checked the peer review page; it makes no mention of the article's lack of citations. Furthermore, Dbuckner's article proposal not only suffers from the same problem; it also seems to be an exercise in original research. If a signicant number of others think the tag is improper, feel free to revert, but I'm of the opinion that it is fitting for now. Simões (talk/contribs) 21:14, 8 October 2006 (UTC)
If there is no mention of the need for citation in the peer review, there should be. By all means, go for it. Amerindianarts 21:21, 8 October 2006 (UTC)
The article has many references at the end, so it is not unreferenced. It would be more helpful to the cause of getting inline citations if you pick the specific facts or sections where you would like to see inline citations, and tag them separately. There is no requirement that every fact have an inline cite, only that everything be verifiable. CMummert 12:14, 9 November 2006 (UTC)
Most of the sections in the article have information that we are to trust come from somewhere in one or more of the books listed in the references section. A list in Chicago style of random logic textbooks at the bottom of an article is not what I would call references. If I were to tag the article by section, a large majority of the sections would be so. I think it is appropriate to have the entire article tagged because of this and have therefore restored the {{unreferenced|article}} template. Simões (talk/contribs) 02:41, 10 November 2006 (UTC)
Tagging the article section by section would give other editors the ability to make incremental progress in satisying your request. If that is the majority of sections then so be it. Just putting the tag at the top of the article won't help anyone know which things need to be referenced, and so is unlikely to lead to any improvement in the article. Moreover, Template:Unreferenced suggests not using this tag if there is a references section. CMummert 02:48, 10 November 2006 (UTC)
Okay, I've done as you've suggested. That bullet point you mentioned doesn't say that, though. It tells us to not use the template if there is a combined external links/references section. That's an odd little piece of advice. I removed it. ;) Simões (talk/contribs) 03:30, 10 November 2006 (UTC)

Reductive Logic

I can see no section here (or anywhere alse in Wikipedia) regarding reductive logic. Before i attempt to source some reliable definitions and external references, is there any reason as to why it has not been included? Jarryd Moore 13:53, 2 November 2006 (UTC)

I think it's just because reductive logic is not as well-studied today as other non-classical logics. There appears to be no more than a single book, Reductive Logic and Proof-search, on the topic, and it came out in 2004. If you want to add a brief mention of it, go ahead. I wouldn't add its own subsection under topics, though, because the topics section is a broad categorization scheme, not an exhaustive list of every system of logic out there. Simões (talk/contribs) 18:19, 2 November 2006 (UTC)

First Sentence

The first sentence contains this bit: “and the practitioners such as Herodotus became a logios—a reciter of logoi or oral stories, eventually written in prose (but coming to mean thought or reason with revival of study of the Ancient Greek in Europe)” Not only does this belong in the “History of Philosophy” section, but it makes the first sentence unwieldy and grammatically incorrect. Since this is my first post on WikiPedia, I won’t change it, but will defer to the veterans.Pescofish 08:40, 31 December 2006 (UTC)

I strongly agree, and will make the necessary change myself if someone else does not. Rick Norwood 17:47, 1 January 2007 (UTC)

Compound proposition

"Compound proposition" redirects here, yet it isn't mentioned in the text. Fresheneesz 01:20, 14 January 2007 (UTC)

"and" and "or" statements are examples of compound propositions. Rick Norwood 13:36, 14 January 2007 (UTC)

From the Problem of multiple generality article

However, it is not possible to express this inference in the traditional system, because the manner we
should represent the first term in the classical subject-predicate form, ensures that the second term 
our predicate will be "X is feared by every mouse"

I realise this passage isn't from this article, but it is from a related one which gets rather less traffic. Anyone know what it's supposed to mean and how it would be better phrased? garik 11:42, 28 January 2007 (UTC)

I gave it a shot. The article still needs references. Rick Norwood 14:45, 28 January 2007 (UTC)

sources

surely the page on logic doesnt need sources, it should just be logical, as all things stm from that, it is its source 89.240.68.145 21:55, 11 February 2007 (UTC)

No, Wikipedia doesn't work that way. Applying your logic to the page is OR, you need to cite the logic of published, standard references. Rick Norwood 14:00, 12 February 2007 (UTC)
I wouldn't take him too seriously, Rick. To be fair, logic doesn't really work like that either. garik 15:49, 12 February 2007 (UTC)

Very poor article

Reading the above comments it is difficult to imagine that they can be talking about the same article. This article does not get an F in my book. Some reference to recent work in the foundations of logic would be relevant.

Just to clarify, the sub articles are in good shape, it seems to be mainly this overview article that needs help. It is fragmented and does not "flow."

Myscience (talk

Does Logic still exist?

I know this is a strange thing to ask, but in the past I have read a few books on philosophy and it's history, western philosophy I should say, and I remember reading that the term logic is actually mistaken and that true "logic" was a way of thinking that was debunked a long time ago. Does my memory fail me? I can't find the book I had that I'm sure said it, I believe the book was called "Basic Teachings of the Great Philosophers" that actually said it, but I could be mistaken about my source. Has anyone heard this before, or did my silly mind make this up? Jjmckool 00:29, 27 May 2007 (UTC)

They might have been referring to the displacement of Aristotelian logic by formal logic at the end of the nineteenth and beginning of the twentieth centuries. Grover cleveland 04:06, 27 May 2007 (UTC)

It is now generally agreed that "logic" is a worthless way of thinking, and blind belief in faith healing, flying saucers, dowsing, ghosts, and vampires is much more productive. Rick Norwood 19:01, 28 May 2007 (UTC)

Ha ha, thanks, I like that one. It's likely that it was the Aristotelian thing I was thinking about, and just confused something along the way. I just thought there was a different official word for it now, but it looks like my memory failed me there. Thanks. Oh, and logic can in fact be applied to all the goofy stuff Rick was talking about, it just isn't normally. For instance with faith healing, when it works, can sometimes be attributed to the "placebo effect." Not always, but sometimes. Thanks though. Jjmckool 19:15, 21 June 2007 (UTC)
Even supposing that success in faith healing is the result of the personal magical powers of the healer can be logically valid, although it obviously requires accepting certain lunatic premises. Belief in such supernatural things as Rick mentions isn't so much illogical (although it can be) as based on poor evidence. garik 13:26, 22 June 2007 (UTC)
It is now generally agreed that whatever is generally agreed is in fact false from which it follows, of course that, it isn't. Realizing this people generally act on the basis that Might is not just Right but also True, and if you do not agree I'll punch your head in. Therefore there is no dispute that cannot be settled with all speed by a swift blow from the bigger bloke to the back of the neck of the smaller. Right? --Philogo (talk) 22:17, 27 February 2008 (UTC)
Yeah, real logical inconsistencies are kind of hard to come by. But I've heard from quite a few philosophers who think that learning formal logic is basically a waste of time. It tends to not be very useful for constructing original arguments. It's usually pretty easy to reason logically as long as you think through what you're saying fairly carefully. So, the Russellian idea that philosophy should be a kind of formal analysis is out-dated in philosophy departments. It might be that you're remembering a reference to logical positivism (at the idea that philosophy is logical analysis) being outmoded.75.3.203.170 (talk) —Preceding comment was added at 07:17, 26 March 2008 (UTC)

I suspect that it is a lot easier to get published when you stop making sense. Rick Norwood (talk) 12:18, 26 March 2008 (UTC)

One shouldn't equate "logic" with "making sense". It can be perfect logic and yet not make much sense:
Socrates is a Martian
Martians are invisible
Therefore, Socrates is invisible
Conversely, many things that do make sense, such as scrubbing down before commencing surgery, are not logic. No interesting problem about reality can be solved by a purely logical argument.
Another question that can be asked is in what sense "traditional logic" (as a discipline) still exists, outside the field of mathematical logic. Anything new since Aristotle that hasn't been absorbed by mathematical logic?  --Lambiam 09:32, 27 March 2008 (UTC)

It is true that, today, mathematical logic has incorporated Aristotelian logic, and does it better, so I agree that the study of Aristotelian logic is only of historical interest. On the other hand, as Aristotle pointed out, "making sense" all boils down to logic. In your example, doctors strongly resisted washing their hands for many years after the germ theory of disease was propounded (it's only a theory). We accept it because of logic which, while seldom spelled out, goes something like this: more patients recover when doctors wash their hands. I want my patients to recover. Therefore, I should wash my hands, even though I am insulted by being told to do so. Without logic, all we have is disconnected thoughts. Most logic is taken care of by the unconscious mind, but I think the more we are aware of what our unconscious mind does, and how and why it does it, the better off we are. Rick Norwood (talk) 12:25, 27 March 2008 (UTC)

To suggest that something eg scrubbing" is either "logic" or "not logic" is to misunderstand logic. Logic is a subject concerned not with things but with assertions, and of assertions not whether they be true or false (let alone sensible) but whether they entail one another. Washing your hands before surgery is not Logic, but neither is it History, Music, Mathematics, Science or Politics. I grant that in Star Treck Mr Spock might condemn some action of Captain Kirk as "illogical" but that is just TV talk., like talking about a "scientific ingredient" or a "mathematical reason". —Preceding unsigned comment added by Philogo (talkcontribs) 12:56, April 1, 2008 (UTC)

Flawed logic.

I might suggest that a section be used to isolate flawed logic.

If justice can be used to do injustice. If health can be used to do unhealth. If equality can be used to do inequality, then logic can be used to do illogical things.

Case in point. (original research, you may find elsewhere)

Stop violence against women. "Since most violence is by men against women, then we must stop violence against women" and the assumption is that all violence is by men. (false jump of logic)

--Caesar J. B. Squitti : Son of Maryann Rosso and Arthur Natale Squitti 12:58, 15 June 2007 (UTC)

Flaws:

Here most becomes all. Also violence statistics, are manipulated to select the stats that match.

Example: In relationships,(half-truth, (ignoring society in general, another half-truth) most reported acts (a half-truth of violence, (ignoring all other forms of abuse, another half-truth), are by men against women. (generalized logic)

Here we are playing a statistical game, with a deceptive agenda, to paint one side black and the other side white.

--Caesar J. B. Squitti : Son of Maryann Rosso and Arthur Natale Squitti 17:27, 30 May 2007 (UTC)

Huh? Simões (talk/contribs) 03:49, 4 June 2007 (UTC)
This is one of the classic errors in logic. It is called false dichotomy. Rick Norwood 13:49, 15 June 2007 (UTC)

Hopefully the link will work..

--Caesar J. B. Squitti : Son of Maryann Rosso and Arthur Natale Squitti 14:07, 16 June 2007 (UTC)

Thanks seems we were able to create a bridge there...

--Caesar J. B. Squitti : Son of Maryann Rosso and Arthur Natale Squitti 14:15, 16 June 2007 (UTC)

Logic in ancient India and China

This article and the article History of logic make claims that are not supported by the sources. For example, we read "received sustained development originally only in three places: India in the 6th century BC, China in the 5th century BC, and Greece between the 4th century BC and the 1st century BC". Searching for evidence of this "sustained development" we find the "Chinese logician" Mozi. But very little by Mozi (or his school) survivies, and most of what does survive is about gods, ghosts, and anti-Confucian philosophy. The mathematical contributions of the Mozi school that have survived consist of a small handful of phrases such as "One and one cannot become two, since neither becomes two." I do not think these contributions can be considered as substantive as those of Aristotle. Comments? Rick Norwood 18:02, 1 August 2007 (UTC)

Question for Trovatore

I want to get this right, and my work in mathematical logic was back in the days when it was still called symbolic logic. At that time, it was an effort to capture the rules of language in symbols, for example, "not not A = A".

Would you say that this is still called "symbolic logic" and that "mathematical logic" is the larger field that is more loosely related (or maybe not at all related) to formal logic? I know we did not call what I was doing "formal logic", so your deletion has left it without a name. Rick Norwood 16:30, 2 August 2007 (UTC)

I suppose maybe I would still call that sort of thing "symbolic logic". The term "mathematical logic" has morphed into meaning "proof theory, model theory, recursion theory, set theory, and maybe a few other things that have a similar character". But surely the "not not A = A" stuff has all been cut and dried since the early part of the 20th century, except for variant weak logics (e.g. linear logic)? Could you enlighten me on just what there was left for you to do? --Trovatore 16:42, 2 August 2007 (UTC)

I could just say, "I'm older than you think," but a more honest answer would be questions involving, for example, languages in which the alphabet was infinite, and questions about examples of uncountable well-ordered sets. There were still a few open questions in the sixties. Rick Norwood 17:05, 2 August 2007 (UTC)

Oh, well that's "symbolic" in a sort of abstract sense, but at this point I'd say we're crossing over into set theory, given that the symbols aren't ones you can actually write down. Are we talking about stuff like the Barwise compactness theorem and Scott rank and so on? --Trovatore 17:14, 2 August 2007 (UTC)

Your examples sound like stuff that is after my time (after I moved over into knot theory). The big news in my day was Cohen's proof of the independence of the continuum hypothesis from ZF+choice. I once had a paper rejected because Godel had proved it first.

I notice that both of your examples are redlinks. If you write the articles, I'll read them. Rick Norwood 18:05, 2 August 2007 (UTC)

QUOTES

....... —Preceding unsigned comment added by 24.190.43.29 (talk) 21:44, 17 September 2007 (UTC)

++RULES OF INFERENCE==

Will the referee kindly link the rules of inference to this topic. I was dumbfounded that the constituent rules of inference, the CORE OF LOGIC, could not be followed in a Boolean tree, from this entry.

Also, is the PROBLEM OF INDUCTION raised anywhere? What about the Skeptic's "infinite regress" of deductive logic?

I'm not a logician, but it seems to me that LOGIC is the parent entry, split into DEDUCTIVE and INDUCTIVE (not "formal" and "informal") LOGIC then into subspecies.

The RULES OF INFERENCE precede classification the procedural: E.g., symbolic, syllogistic, mathematical, modern, instrumental, etc. Decision Theory is certainly an appropriate aspect that seems rather indifferent, here. But the rules of inference ARE logic.

Where's a discussion of the a priori versus a posteriori? What about the analytic synthetic? No links again.

For an entry on LOGIC, this one is highly illogical.

````dshsfca —Preceding unsigned comment added by Dshsfca (talkcontribs) 01:16, 21 December 2007 (UTC)

Abuse of logic

There needs to be an article which also explains how logic can be abused, or misused--mrg3105mrg3105 22:22, 17 January 2008 (UTC)

The article is titled fallacy. Rick Norwood (talk) 13:50, 18 January 2008 (UTC)


Can a new definition of Pure Logic be added here ?

Pure Logic defined by my person, is initially all the fields of rational/irrational thought analysis, and all the fields, and scopes known/unknown of logic/illogic, defined yet or not ! I do not have enough money as yet to publish these new writtings. Aiming to unite Science and Logic, without overpassing the Philosophy of Science, or philsophy in Science. (24.86.57.172 (talk) 07:29, 26 January 2008 (UTC)) (GeorgeFThomson (talk) 07:34, 26 January 2008 (UTC))

Wikipedia is an encyclopedia. It is not a place for publishing original thought. If you publish your ideas on "Pure Logic" elsewhere, and they are sufficiently notable that they are reported on independently in multiple reliable sources, then this can be given a place in Wikipedia – but by someone else than you, because you would have a conflict of interest.  --Lambiam 19:11, 26 January 2008 (UTC)

re Deductive argument follows the pattern of a general premise to a particular one, there is a very strong relationship between the premise and the conclusion of the argument.

i) P,Q therefore (P & Q) is a deductive argument,but P,Q is not a general premise and (P & Q) is not a particular one. Writer was thinking perhaps of All As are Bs, X is an A therefore X is a B? ii) Implicaton that argument can have but one premise (in sing. in quote) iii)The very strong relation is called enatilement, why not say so? Really this passage does not say very much and what is say is wrong, or so it seems to me --Philogo (talk) 21:57, 27 February 2008 (UTC)

The idea that all arguements are deductive goes back to Aristotle. Your example could be put in deductive form as follows:

Major premise: If P and Q are both true, then P & Q is true. Minor premise: P and Q are both true. Conclusion: Therefore, P & Q is true.

However, in modern mathematical logic, there is no requirement to put all arguements in the form of a sylogism -- there are several forms which are allowed. I agree that the sentence you quote should be rewritten. Rick Norwood (talk) 14:34, 28 February 2008 (UTC)

My first point was that it is just not true that Deductive argument follows the pattern of a general premise to a particular one" - some do and some do not as my example, and we should not in an encycopedia say of that which is not that it is. Would you care to edit or delete this passage?--Philogo (talk) 23:38, 28 February 2008 (UTC)
Rick Norwood just stated the rule of inference known as the "Conjunction": P, Q, Therefore P & Q. Just thought it worth noting.Prussian725 (talk) 17:44, 14 July 2008 (UTC)

Definition

Maybe I am a little off, but I have been studying logic for almost three years and it has always been my undetstanding that the base definition of "Logic" is "the science and art of reason". I did not see this in the opening section and was just wondering what everyone else's thoughts are.Prussian725 (talk) 17:40, 14 July 2008 (UTC)

The word "logic" can be used as a synonym for "reason" but these days I think that "reason" is used more broadly, "logic" more narrowly. Essentially, all logic can be reduced to deduction (though it often isn't, it can be in theory), while reason would include inductive reasoning as well. Rick Norwood (talk) 12:41, 15 July 2008 (UTC)
Good point. Thanks for the info!Prussian725 (talk) 20:52, 19 July 2008 (UTC)

This certainly is not true. Inductive logic exists and is used by science everyday. Charles Sanders Peirce is seen as one of its fathers. Do we need to add a section on this? Pjwerner (talk) 20:22, 24 October 2008 (UTC)

Meaning of what is, was or will be

I'd be happy to "learn basic of logic before reverting", but whether this is basic of logic or not, I just can't figure out the intended meaning of what is:

"Traditionally, logic is considered a branch of philosophy, a part of the classical trivium of grammar, logic, and rhetoric, meaning of what is, was or will be."

 --Lambiam 13:38, 22 August 2008 (UTC)

Nor I, so I have reverted to former content. If User:Francos22 or anybody else knows what was meant by that meaning of what is, was or will be." and can cite a source please say so here for further consideration.--Philogo 12:44, 26 August 2008 (UTC)

Link

Whats your opinion about Ch. Henke, The Mathematics of the Phaistos Disc, Forum Archaeologiae 48/IX/2008 (http://farch.net)?

--Kadmossios (talk) 15:15, 26 September 2008 (UTC) —Preceding unsigned comment added by Kadmossios (talkcontribs)

Why so few sources?

It is not a good reflection on Wikipedia that an article on such a vital subject as logic contains so few cited surces. Without references, the piece reads like a series of opinions, fables, myths, and dogmatic "take-this-as-gospel-because-an-anonymous-editor-said-so" half-truths. Surely those who make a study of logic in an academic setting and who care about this subject enough to ramble on and on about it should be able to somehow manage to supply the necessary inline citations to give this article some credibility! cat yronwode Catherineyronwode (talk) 08:18, 5 October 2008 (UTC)

Good point. Mathematicians assume that they speak with Authority, and we usually do know what we are talking about, at least when we confine ourselves to mathematics, but sources are available, and important. I'll try to add footnotes to both this article and Reason tomorrow. Personal PS: Hi! Rick Norwood (talk) 12:56, 5 October 2008 (UTC)
A feeling of certainty is not a reliable guide to truth; its just a little tingle after all - don't listen to the voices! See Truthiness--Philogo 12:53, 23 October 2008 (UTC)
Thanks for working to add citations. See also my comments to Andrew Lancaster on the Reason page. I do not mean to be a pest, but i do hope to see these foundational pages brought up to the same relatively simple level of verifiability that can be found, for instance, in the pages on the horse murders or White Rabbit Creamy Candy. :-) P. S. I just checked your user page and you are indeed the same Rick Norwood i know from Long Ago and Far Away! WOW! How fun to find you here! cat Catherineyronwode (talk) 19:20, 5 October 2008 (UTC)

I'm sorry to have been so long in finding time to address the problem of sources. Now I'm having trouble with the first request for references, which goes as follows: "However, except for the elementary part, the system of Principia is no longer much used, having been largely superseded by set theory.[citation needed]" Here is my problem. I look at the notation in Principia, and I look at the notation several major modern books on Logic, and I observe that the notations are very different. But I can't find anyone who says, "modern notation is different from Principia notation". As my old differential equations teacher used to say, "it's obvious". but that doesn't help me find a reference that says so. Any suggestions? Meanwhile, the more I read that sentence, the more I see it is badly written, and so at the very least I can rewrite it. Rick Norwood (talk) 19:41, 20 October 2008 (UTC)

The notations have changed continuously; its not a very interesting point to make about Principia. --Philogo 18:55, 21 October 2008 (UTC)

There have been some small continuous changes in the notation, but the notation in Principia is almost totally different from the notation used today, and the notation used today has been stable for at least the last forty years. Certainly, someone who, today, tries to read the principia is in for a shock. Rick Norwood (talk) 22:50, 21 October 2008 (UTC) The notation used by Frege was even more different and the notation has continued to change quite a bit. This is not at all intersting for the general reader and not very intersting for a Logician (unless perhaps a historian of Logic) aand really not a very intersting point to make about Principia and a point one could make about a whole heap of Logic books. Have a look eg at Strawson. If even compare the first and second version of Mendelson's text book. If you look at standards for notation in the Wiki Logic page you will see a variety of notations currently in use. Like a say only of esoteric interest. I'd dump the whole sentence--Philogo 12:18, 22 October 2008 (UTC)

I think the discussion is getting a little off track here. The challenged content was about the system of PM being mostly disused, not so much its notation. This is true, and everyone knows it, unless you take the point of view that the system of PM is really type theory in a bizarrely complicated disguise. (I am given to understand that this last is almost, but not quite, true.)
So it is useful, I think, to let people know that the system of PM is not a going concern, but the problem is to source it. Any ideas on that? --Trovatore (talk) 03:45, 23 October 2008 (UTC)
I do not think that the PM was a system to used as such: it was a book concerning the foundations of mathematics. It would be more interesting to set out what it was intended to acheivie and cricisms and shortcomings but this would duplicate the main aricle on PM. Saying that the notation has changed since then is not significant and not worth mentioning. I am minded to expunge it;any objections?--Philogo 12:26, 23 October 2008 (UTC) I have expunged the troublsome sentence and tidied up a little in the lede. This article is somewhat verbose and opiniated, with lots of padding. A bit like an undergrad essay I fear. Citations should be provided but waffle is waffle nonetheless even with a source.--Philogo 12:48, 23 October 2008 (UTC) PS If naybody is REALLY intersted in the PM notation read all about it here: http://plato.stanford.edu/entries/pm-notation/

I can live with Philogo's edit, but is it really true that nobody does work on foundations any more? Rick Norwood (talk) 22:34, 23 October 2008 (UTC)

No, that's certainly not true. I think what is true is that fewer people are foundationalist, but that's not the same as not working on foundations. --Trovatore (talk) 23:17, 23 October 2008 (UTC)

That being the case, do we really want this in the lede? "Godel raised serious problems with the foundationalist program and logic ceased to focus on foundational issues. The study of several resulting areas of mathematics came to be called mathematical logic.[citation needed]" I'm especially bothered by the suggestion that the use of the phrase "mathematical logic" either began or changed meaning with Godel. Rick Norwood (talk) 14:01, 24 October 2008 (UTC)

I would say no, we don't want that in its current form. (Certainly not with the misspelling of Gödel, </peeve>.) I do think that the phrase mathematical logic has changed meaning, though, in the sense that large parts of it, particularly set theory, are no longer seen as "logic" in the classical sense, but remain "mathematical logic". (And, for that matter, they're still "foundations" in a similar sense, even for anti-foundationalists.) --Trovatore (talk) 21:34, 24 October 2008 (UTC)
I think it is fair to say that Logic ceased to focus on foundationalist issues at that time and that it IS worth mentioning. If you think that is histrically inaccurate I can check it out. If anybody can say whther the adoption of the term "mathematical logic" over "symbolic logic" was more than just a new name for the same thing I would be interested to know the answer. My collection of books begins with those titled "symbolic logic" and mortphs into those "mathematical logic". Is it really more than an percievedly more attractive title (compare subects that added the word "science" to their title - mortuary SCIENCE, Sports SCIENCE, and more recently "INDUSTRY" as Banking INDUSTRY, Tourist INDUSTRY. Soon we will have Agricultural INDUSTRY and then the word will cease to have any real meaning at all, and no longer as opposed to COMMERCE and AGRICULTURE) --Philogo 22:51, 24 October 2008 (UTC)

focus moved from such issues

re I think it is fair to say that Logic ceased to focus on foundationalist issues. See e.g.

Nevertheless, the subsequent achievements of proof theory at the very least clarified consistency as it relates to theories of central concern to mathematicians. Hilbert's work had started logic on this course of clarification; the need to understand Gödel's work then led to the development of recursion theory and then mathematical logic as an autonomous discipline in the 1930s. The basis for later theoretical computer science, in Alonzo Church and Alan Turing also grew directly out of this 'debate'.

in David Hilbert--Philogo 23:01, 24 October 2008 (UTC) and

In 1931, Gödel published his famous incompleteness theorems in "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme" (called in English "On formally undecidable propositions of Principia Mathematica and related systems"). In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g. the Peano axioms or ZFC), that: If the system is consistent, it cannot be complete. (This is generally known as the incompleteness theorem.) The consistency of the axioms cannot be proved within the system.

These theorems ended a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's formalism, to find a set of axioms sufficient for all mathematics. The incompleteness theorems also imply that not all mathematical questions are computable.

[emphasis added] in Kurt Gödel--Philogo 23:09, 24 October 2008 (UTC)

Good quotes. Maybe you could do a slight rewrite to bring the article more in line with the quotes, to make it clearer that studies of foundations did not "cease" and that the phrase "mathematical logic" came to replace the earlier "symbolic logic".
Not VERY good quotes 'cos their quotes from elsewhere in WIki. Suggest division of labour: I can dig up some quotes from or about FREGE to show that his main motivation was foudationlist. Someone lese could do likewise to show liekwise for Rusell's PM. Then someone else can research Hibert and explain his "program" and someone else how Godel spoilt the fun (so to speak). Finally we should set out(a) what interst therir remains in fundamealist issues (b) what the main developments/interest in logic have been post Godel (not the how useful its turned out to be stuff about computers - that should come right at the end. This article I think should mention the "towering figures", provide a brief history, and summariese logic's key concerns, and povide links to the more specialist articles.

Really this stuff should be covered in History of Logic but the tiny paragraph headed "The advent of modern logic" ended, until quite rececently when I deleted it, with the delightful

Such work has added much to logical notation since Aristotle's time. However, outside of these notational changes little else has been developed in formal logic and it has become a rather neglected subject within academic philosophy

It's true: look at the history! It's like saying Descartes introtduced some new symbols, but apart from that not much has changed since Euclid. Good old Wiki! --Philogo 21:52, 28 October 2008 (UTC)

I am not at all clear of how the term mathematical logic" supplanted "symbolic logic": I suspect Russell started it when he declared somewhere that "Logic is Maths" (ironic somehow, since if PM were to have been successful it would show that, if anything, Maths is Logic. --Philogo 21:41, 28 October 2008 (UTC)

First, it's unclear to me what you mean by foundationalist issues. Foundations is an area of study; foundationalism is a philosophical position. You can work on foundations without being a foundationalist. Working set theorists have by and large moved away from foundationalism (often preferring something like coherentism or confirmational holism) but that doesn't mean they aren't doing foundations. Research into large cardinal axioms is clearly foundational in character, but probably would tend to be distasteful to foundationalists. --Trovatore (talk) 21:56, 28 October 2008 (UTC)
I recall we "inherited" the words "foundationlist issues" from a former editor, and maybe its not the best phrase. The article on Godel in quotation above uses the phrase "a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's formalism, to find a set of axioms sufficient for all mathematics". The article now says that (a) the focus was on such matters (and calls the matters "foundationlist issues") (b) post Godel the focus moved away from such matters. IF phraseology is not ideal please edit: be bold! Meanwhile other editors want material showing what interest continues in such matters. I have suggested a bit of a program to distribute workload --Philogo 22:27, 28 October 2008 (UTC)PS I have now substutured "such issues

" for "foundationalist issues" in this article and this talk paragraph, hoping to avoid comtrovery raised by "foundationalist issues"--Philogo 22:37, 28 October 2008 (UTC)

Say what? The change you made didn't remove the word foundationalist; it removed the word foundational. These are quite different, as I explained above. The reason I brought this up, in talking to you, is not specifically about the wording in the article, but to understand better what you're getting at, which frankly is not clear at all. --Trovatore (talk) 22:40, 28 October 2008 (UTC)
If you can improve the lede go right ahead!

Links or References that can be added to the Article

To the moderators: Can the topic on pure logic, be initially covered or made reference to, for historic reasons? And some links to a basis book ? As to any detail, it is my copyright, in the Book of Pure Logic (1). These are the links: [3] [4] William Thomson Archbp.,1819-1890 An outline of the necessary laws of thought: A treatise on pure and applied logic (GeorgeFThomson (talk) 00:45, 20 November 2008 (UTC))

History of logic

According to the article the history of logic stopped in the middle ages,--Philogo 12:49, 20 November 2008 (UTC) We have now reached the "later period of the Middle Ages"--Philogo 13:35, 10 December 2008 (UTC)


Math, Prime Numbers, Division, Muliplication - Lunar Calendar

File:Ishango bone.jpg
Ishango Bone, Calendar Sticks - Lunar Calendar

First Mathematical Logic Calendar Sticks - Lunar CalendarAlexander Marshack examined the Ishango bone microscopically, and concluded that it may represent a six-month lunar calendar.[1] Claudia Zaslavsky has suggested that this may indicate that the creator of the tool was a woman, tracking the lunar phase in relation to the menstrual cycle.[2][3]

The Lebombo bone dates from 35000 BC and consists of 29 distinct notches that were deliberately cut into a baboon's fibula. The Lebombo bone resembles the calendar sticks still used today by Bushmen in Namibia.

The Lebombo bone, a baboon fibula It was discovered within the Border Cave in the Lebombo Mountains of Swaziland.[4] 

http://en.wikipedia.org/wiki/Lebombo_bone


The Ishango bone is a bone tool, dated to the Upper Paleolithic era, about 18000 to 20000 BC. The central column begins with three notches, and then doubles to 6 notches. The process is repeated for the number 4, which doubles to 8 notches, and then reversed for the number 10, which is halved to 5 notches. These numbers then, may not be purely random and instead suggest some understanding of the principle of multiplication and division by two. The bone may therefore have been used as a counting tool for simple mathematical procedures.

Furthermore, the number of notches on either side of the central column may indicate more counting prowess. The numbers on both the left and right column are all odd numbers (9, 11, 13, 17, 19 and 21). The numbers in the left column are all of the prime numbers between 10 and 20 (which form a prime quadruplet), while those in the right column consist of 10 + 1, 10 − 1, 20 + 1 and 20 − 1. The numbers on each side column add up to 60, with the numbers in the central column adding up to 48. Both of these numbers are multiples of 12, again suggesting an understanding of multiplication and division.[8] http://en.wikipedia.org/wiki/Ishango_bone --Tales23 (talk) 15:24, 14 January 2009 (UTC)

The History and Begin of Logic

But when you see the history of logic section, it starts with "A", "not A", "A and not A", and "not A and not not A" so but now in 35000 they got this already 10 + 1, 10 − 1, 20 + 1 and 20 − 1, so in the respect of Mathematical Logic, and in particular the History, How did humans start to think logic - woman tracking menstrual cycles with lunar phases using a device the bone tools. This had a lot of logic applied! At least contributed here and therfor it has its place in History --Tales23 (talk) 08:01, 16 January 2009 (UTC)

This article is on the subject of logic. The material you add is not on the subject of logic. It may belong somewhere else, maybe in the article calendar, but it certainly does not belong here. Rick Norwood (talk) 19:41, 14 January 2009 (UTC)
Agree --Philogo 13:41, 15 January 2009 (UTC)
I also agree. dougweller (talk) 09:12, 16 January 2009 (UTC)
Tales23 put the off-topic material back again today so I have removed it again. Tales23 does not appear to understand that it is no the material itself that is the problem it is its lack of relevance to the subject of the article.

--Philogo 14:14, 16 January 2009 (UTC) Note on Tales23's talk page reads: "You need to change your behavior or you will be blocked permanently from Wikipedia." This is not the only aricle Tales23 has edited in an inappropriate way.--Philogo 14:33, 16 January 2009 (UTC)

On Tales23's talk page Tales23 appears to have come up with a fallacy of which I had not been previously aware. Tales23 says:

Philogo, please can you point out to me where it is off topic. Logic consist of mathematical logic. So the history of logic begun 35000 BC when woman invented the calendar, because they needed to keep track of menstrul cycles and birth control. Though this is logic

I beive this argument to be of the following form:

All As are Bs The first B was X Therefore the first A was X.

which at first glance seem reasonable, but to parody Lewis Carrol:

You might just as well say

All mad hatters are living organisms The first living organism lived in the primeval slime Therefore the first mad hatter lived in the primeval slime

Does this fallacy have a name and has anybody come across it before? --Philogo 01:23, 18 January 2009 (UTC) So you belive that it doesnt took any logic (mathematical exact and common basic logic thinking - along the line of connect the dots) to remember and follow and first off get aware of the moon phase and use this as a meassurement tool in coordination with a mathemetical system? Those bone tools contain prime numbers. The point is how human brains advanced (or not) and what forced it. See even when they invented the calendar today they still use this - as it is still the perfect solution. Anyway this is logic and belongs in the history of mathematical logic. But im tired of argueing and will not edit anymore any main page here. At least we got a debate! --Tales23 (talk) 01:31, 18 January 2009 (UTC)

You should not speculate on what other's beleive unless you are a mid-reader in which case you could make a fortune playing poker - I'll be your agent for 10%. You shold also clealy distinguish "arguing" and "asserting" usepecailly of the Logic talk page!- we are VERY hot and that point I can tell you. Your contribution to this article was not helpful because it was not relevant, as two other editors and I have been an some pains to point out, not because it was not true, although its veracity is not suppored by any citations. You may find a better place for the material. I do not believe that Logic is not your strong point nad perhaos not arheology and it is better to have at least an elementary knowledge of a subject before venturing making to make a contribution to an article in that subject. You are however to be congratulated on your apparently novel fallacy. If it is not mentioned in the fallacies article I will post it there, and if it has no name I'll suggest naming it after you, if I might be so bold. You may even become famous!--Philogo 02:20, 18 January 2009 (UTC)
That is not correct see above my contribution which are considered legit wiki pages. Also i still wait for an explanation as why this is not hystorical mathematical logic and you seem not to be able to make one. --Tales23 (talk) 09:35, 18 January 2009 (UTC)

More to the point

According to the article the history of logic stopped in the middle ages,--Philogo 12:49, 20 November 2008 (UTC) We have now reached the "later period of the Middle Ages"--Philogo 13:35, 10 December 2008 (UTC)--Philogo 14:06, 16 January 2009 (UTC)

I've moved us up at least to the start of the 20th Century. Rick Norwood (talk) 14:34, 17 January 2009 (UTC)
Well thanks for that but shouldn't Frege get just a teen-weeny mention? --Philogo 01:26, 18 January 2009 (UTC)

By all means. Go for it! Rick Norwood (talk) 14:03, 18 January 2009 (UTC)

After you!--Philogo (talk) 00:58, 14 February 2009 (UTC)


A curious logical universal expression

--Faustnh (talk) 15:40, 8 March 2009 (UTC)


( ScientificLaw1 AND ScientificLaw2 AND ScientificLaw3 )
--->
(
( ScientificLaw1 ---> ScientificLaw2 )
AND
( ScientificLaw2 ---> ScientificLaw3 )
AND
( ScientificLaw3 ---> ScientificLaw1 )
)


(Also shown at Paradoxes of material implication Talk page)


This is technically correct, but so is (A AND B) implies ("The moon is blue" implies B). By convention any implication with a true conclusion is considered true. The logical connective "implies" does not mean the same thing as the English language word "implies".Rick Norwood (talk) 13:39, 9 March 2009 (UTC)


--Faustnh (talk) 14:08, 9 March 2009 (UTC)

A MUCH MORE interesting re-versioning of the formula above:


( ScLaw1 AND ScLaw2 AND ( ScLaw1 --> ScLaw2 ) )
<--->
( ScLaw1 AND ScLaw2 AND ( ScLaw1 --> ScLaw2 ) AND ( ScLaw1 <-- ScLaw2 ) )



This discussion should not be happening both here and at Talk:Paradoxes of material implication. Please direct all comments to that talk page. — Charles Stewart (talk) 09:04, 10 March 2009 (UTC)


k no problem .--Faustnh (talk) 12:45, 10 March 2009 (UTC)


Disproving The Law of Non-Cotrodiction

I am not saying The Law of Non-Cotrodiction can completely be Disproven. Im saying that The Law of Non-Cotrodiction does not apply in most sercomstances. For instance.

Neutrality

A statement can not be true and false at the same time. But it can be neutral.

It is said.


All paths lead to God.

There is only one one true Path.


I say.


All raods lead to Rome. But a person can choose to walk in the other direction thereby creating a personal raod that does not lead to Rome.


This is were Neutrality begins and the The Law of Non-Cotrodiction fales.


I will now use a Biblical example of Neutrality.


There is a path between God and Satan. I can choose to go the true path and twords God or I can choose to go the false path twords Satan or I can stay in the midle. I can choose to go the neutral path. The path between God and Satan, between True and False is Neutral.


-The Big Switch, Nicholas Carr.

...and likewise all parts of the system must be considerd with refrence to all other parts, since, in one sense, all parts form one machine.

-Thomas Edison


All the parts. True and False. Form one machine.


Neutrality


--Gjeremy (talk) 07:06, 27 April 2009 (UTC)

The idea that logic ought to reject the law of non-contradiction is discussed in the subsection "Tolerating the impossible". — Charles Stewart (talk) 08:58, 27 April 2009 (UTC)


Do you think what I have said can be used to improve the article Logic?

--Gjeremy (talk) 17:00, 27 April 2009 (UTC)


The Law of Non-Cotrodiction: A statement can not be true and false at the same time.

Law of Controdiction: A statement can be true and false at the same time.


I right your wrong. No!!! Im right your wrong.

We are the same and we are diffrent.

We agree to disagree. No We agree to agree.


The voice of Neutrality speakes out.

Naruto episode 107 part 2 English Dub

Naruto episode 108 part 1 English Dub

--Gjeremy (talk) 02:13, 28 April 2009 (UTC)


Tears of Neutrality

Naruto episode 109 part 2 English Dub

--Gjeremy (talk) 04:17, 28 April 2009 (UTC)

I think you need a better understanding of the issues involved before you edit the article. A university course in logic would help. Rick Norwood (talk) 18:07, 28 April 2009 (UTC)


Thanks for the advice but dont underestamate me. I could be eccentric.

--Gjeremy (talk) 22:02, 28 April 2009 (UTC)

You might be god or a brain in a vat (BOV), but you still you still need a better understanding of the issues involved before you edit the article. This particular issue is normally addressed in chap 1 of introductions to Logic. The points you raise invariably come up in intro logic classes, and none the worse for that. However before you can make a useful contribution to an article it is necessary to have a knowledge of at least the basics. Otherwise you might as well edit a Chemistry article to say that an acid is somethings that burns, or a maths article saying that there we cannot know if infinity exists 'cos we cannot count that high, or a Physics article saying that Newton's laws are undemocratic because they were not passed in parliament.--Philogo (talk) 22:28, 28 April 2009 (UTC)


I may not have a P.H.D. in Logic. and I may not Know everything a P.H.D. does but I have something better. I think Like a P.H.D.


Here is a stratigy for defeating Deep Blue (2,800) if your score is 400.

And it only took me 10 minutes to think about it.


1. Memorize the moves of two difrent cheess matches.

One where you win if you start first. The other where you win if you start second.

2. If a person by luck loses to Deep Blue on the 45th or 46th (Step 1) move (Deep Blue problely only thinks 15 moves ahead).

Then memorize those moves. Back up a cuple of moves. Then use the stratigy in step 1. Starting at that move.

3. Dumb Luck.

--Gjeremy (talk) 22:53, 28 April 2009 (UTC)

This is not a chat room--Philogo (talk) 23:58, 28 April 2009 (UTC)


Have a tast of your own medicien. —Preceding unsigned comment added by Gjeremy (talkcontribs) 00:57, 29 April 2009 (UTC)

Quote de jour It is all the same to me...whether it is your own opinion or not. It is the argument itself that I wish to probe, though it may turn out that both I who question and you who answer are equally under scrutiny.

Plato, Protagoras, 333c -

--Gjeremy (talk) 00:55, 29 April 2009 (UTC)

Gjeremy: I don't think their is a place in this article for a discussion of theological arguments against classical logic, although certainly there is encyclopedic value in some of these arguments, eg. cf. Pavel Florensky's trinitarian argument for true contradictions [5].
It seems to me that your argument would find a better home on many-valued logic: that's also a better article to work on, since this article has had a fair bit of effort put into figuring out what should go into this article, and so you can expect quite a bit of intereference with your edits to this article. Your argument is certainly WP:OR: the crucial thing is to document work in logic that has been published and whose merit has been tested.
If you are going to make a useful contribution to wikipedia, you need to work alongside the other editors here: Philogo has done much work on the logic articles, and he was not deliberately riling you. — Charles Stewart (talk) 08:35, 29 April 2009 (UTC)


You are not the first person to mention WP:OR to me.


In the article Love I gave an argument in my own words useing the terms of pain and plesure. Love is a philosophy article so I thought other philosophers would recognize this ancient Greek Philosophy of Good and Evil and improve the article. Sadly my comments were removed from the discussion page.


On the Discussion page of Free will. In the heading Biblical definition wich I started I gave these camments.


I may not know who said it and I may say it in my own words and I am sorry if I violated the standard, but As long as I ask help from others on Wikipedia to find the author then it dosent matter.

A refrence is a refrence is a refrence.

I will no longer refer to my user page as a refrence apropriate by Wikipedia standards (until those standard change). But if it becomes well known and is published by a major source. Then I can make referance to it idirectly. Thereby not violating Wikipedias standards.


I have been saying things in my own words. It is not WP:OR.


Here is a heading on my user page.


Discussion topics I created on other articles



I believe that Disproving The Law of Non-Cotrodiction will improve the article Logic.

It is a topic worthy of discussion.

--Gjeremy (talk) 09:52, 29 April 2009 (UTC)

The exact arguments that you give are WP:OR because your writings on this subject, like mine, have not been absorbed into the record of logic and been responded to and counter-responded to. Also your arguments are all over the place: it is not a bad thing to have lots of unorthodox ideas, but you have to get some focus if you want to work with other editors here.
But you are quite right: there are antecedents to your arguments, and as I said, you are welcome to document these kind of arguments for neutrality (i.e. against bivalence), and against the law of non-contradiction. If you care enough about making this information available to the public, you can do so, but it is work, both for you alone, in terms of researching well-documented antecedents for these views, and for both of us, in terms of working together.
I don't think there is a place for this kind of argument on this page, because logic is a big subject and the topics on this page have tight space constraints: the general area of non-classical logic is well represented in the article, and I don't think deserves more space. But the various articles to do with non-classical logic do have space.
If you are interested in doing the research, Theodor W. Adorno wrote some stuff on non-propositional content that might appeal to you; Adorno comes from aesthetics, and there seems to be some parallels between theological and aesthetic criticisms of mainstream logic. Pavel Florensky, who I mentioned before, did both theology & aesthetics. I would certainly like to see good content documenting this area. — Charles Stewart (talk) 10:28, 29 April 2009 (UTC)


You are completely right. I was blind and now I see. Was lame and now can walk.

--Gjeremy (talk) 10:37, 29 April 2009 (UTC)

Intent to rework article before submitting for 2nd peer review

I'll be away from WP for a few days, on my return I expect to have some time to do some serious work on the article. Two things to emphasise: 1. I don't think the current article is really an improvement on what I submitted for peer review on the 18th November 2005 [6], despite the article having received over 1000 edits in that time. 2. I think that all of the criticisms from the peer review still apply, and that Peter Damian's idea for how to introduce the idea of logic still provides the best way to go ahead with fixing the peer review criticisms. I'll post a plan when I have time to make a real start, hopefully next Tuesday. — Charles Stewart (talk) 13:42, 27 May 2009 (UTC)

It's probably worth pointing out that I have no plans to do this kind of substantial work on Wikipedia in the forseeable future; cf. my user page. — Charles Stewart (talk) 10:08, 10 February 2010 (UTC)

The first sentence of the article is incorrect

Logic as it is taught and studied in the university, is a mathematical kind of model that seeks to pick some of certain important characteristics of the things mentioned in the first sentence, but does not seek to do so in the most descriptive manner possible. It just wants to know that if a computer knows one scientifical kind of fact, what can it deduce from it. What we with pictures of the world, enormous amounts of experience, with a nature that has instinctual wisdom, what we humans can deduce from the same facts is an entirely different thing. Logic in the university is calculations, it is not understanding. It gets its spirit from copying from the computers! InsectIntelligence (talk) 19:25, 30 May 2009 (UTC)

Logic is much more than just computers. Historically, it began in philosophy, and the editors currently think that the reference to computer science is currently sufficient. If you like, you can propose a new first sentence here and we all could discuss it. JEN9841 (talk) 07:20, 8 June 2009 (UTC)

Some things

1. I've reworded the lede, which is bound to be controversial, but WP:BOLD. I think it is good to cite some definitions of logic that "cover the bases", rather than make up our own. I've not asserted any branchhood, but have emphasised the subjects affinity for philosophy.

2. I think this article would benefit from being presented in a "notes+references" style, where all the texts are given in a references section, but we use notes to indicate the place that such citations are made, and where cites to non-peer reviewed web sites are left in notes forms. Does anyone have a strong opinion against this?

3. Someone has made the effort to convert the references section over from "." separated fields (ie. AUTHORLIST (DATE). TITLE. SOURCE. PUBLISHER.) to "," separated. Please don't do this again: I've converted this back because it is a marginal style for lists of references, and it is against the style used by the citation templates. I don't like the citations templates: they make references hard to read and they don't handle everything they should, but they do indicate a sort of house style. — Charles Stewart (talk) 09:43, 11 June 2009 (UTC)


Next task: I'm going to merge 3 sections from User:Renamed user 4/logic (Peter Damian's old proposal) into the Nature of logic section, and I'll delete much of what is currently there to make room. This is the biggest change I plan to do to the article & is intended to change it from an article that says some things about logic to one that explains what it is. The sections are the ones on Logical Form, Semantics, and Inference.

Entire Article

Its a shame that this article sucks, there should be an explanation of what deduction is how its linked to proof (a complete and sound deduction system) with a basic basic truth functional and monadic overview. Also something on the importance of algorithms and interpretation. Finally an explanation of a set theory or polyadic system, say its incomplete and undeciabable, and leave syllogism, recursion, notation and etc. for history of philosophy and computer science or mathematical logic subsections. —Preceding unsigned comment added by 67.165.86.4 (talk) 07:45, 15 November 2010 (UTC)

Lede

Can we puleez change the first sentence of the lede? Right now it is wrong and gross. First of all, it has an inactive link to the Penguin Encyclopedia, and I think the definition of logic is not as accurate as it should be. Saying that it studies "valid inference and correct reasoning" makes it seem that only arguments that can be valid are the ones that logic studies. This would exclude inductive arguments. And since when did the Penguin Enclyclopedia become the end all of philosophy authorities? I think something like this, which is from a prior archived discussion of the same topic would be better:

Logic is the art and science of reasoning which studies the principles of valid demonstration and inference.

Sagan666 (talk) 05:38, 19 August 2009 (UTC)

The def you provide is unsourced, and as the footnote from the lede says, the issue of the definition of logic is fraught, cf. Definitions of logic and footnote #2. The Penguin definition is chosen for being modern and mainstream, and it is suggested as just one of mane, fn #2 gives some others. The Penguin Encyclopedia certainly deserves an article, so someone should WP:SOFIXIT. — Charles Stewart (talk) 09:40, 19 August 2009 (UTC)
And the present source, found by googling the phrase, dates from 1896, when Logic was something different than it is today - as reading Lewis Carroll on the subject will show. Tagged accordingly. Septentrionalis PMAnderson 04:40, 10 November 2009 (UTC)
...and in 2009 people getting degrees studying logic are still getting B.A.'s. The reason it is an art is because it is the art of giving logical examples. This is still the case today. Pontiff Greg Bard (talk) 05:03, 10 November 2009 (UTC)
This asserts that Latin ars and English art are coterminous. They were once; they are not now: to use art as though it were ars is bad style; to do so without making clear to the reader what you are doing is bad content. Septentrionalis PMAnderson 15:44, 10 November 2009 (UTC)

Some people today get a degree studying logic of Ph.D. in mathematics. Rick Norwood (talk) 14:44, 10 November 2009 (UTC)

What?

I'm just pointing out that this article is written like a lecture, complete with rhetorical questions, not like an entry in an encyclopedia. I'm simply not knowledgable enough to rewrite this myself, but I thought I would throw the idea out to anyone who might want to fix it up a little bit. 68.215.72.31 (talk) 08:01, 23 August 2009 (UTC)

Penguin Encyclopedia

There is no reason to cite this minor, popular work when there are many better references. Rick Norwood (talk) 14:46, 11 November 2009 (UTC)

Better references? Providing better definitions? Name one! — Charles Stewart (talk) 10:04, 10 February 2010 (UTC)

Automate archiving?

Does anyone object to me setting up automatic archiving for this page using MiszaBot? Unless otherwise agreed, I would set it to archive threads that have been inactive for 30 days.--Oneiros (talk) 13:17, 24 January 2010 (UTC)

This talk page has fairly low traffic, so I think archiving after 6 months would be appropriate. If threads on this talk page would be archived after 30 days, the only thread here would be this one. There is no need to archive that aggressively. Svick (talk) 22:07, 24 January 2010 (UTC)
Sorry, I forgot to mention that I'd configure MiszaBot to keep the last ten threads. Thus it will be a while before it kicks in.--Oneiros (talk) 22:27, 24 January 2010 (UTC)
Yes check.svg Done--Oneiros (talk) 23:07, 3 February 2010 (UTC)

Logikos or logos

Sorry to post anonymously, it has been awhile seen I'd last participated and I need to recover my password. Anyway, I was actually trying to find the root of logic and naturally ended up here, as well as several other sites. I noticed that wikipedia and sites that link its material list 'logikos' as the Greek root of logic, however others say it is 'logos'(ex. http://www.wordiq.com/definition/Logic and http://www.newworldencyclopedia.org/entry/Logic). I will have to verify this offline to be sure for myself, but if someone could confirm the correct Greek derivative in the meantime it may help. Thank you. —Preceding unsigned comment added by 75.93.220.117 (talk) 21:06, 10 February 2010 (UTC)

History of logic

After some years of gestation, this article is now largely finished. I am thinking of taking it to FA but would like some thoughts from people first, as I have heard such bad things about this process. It should go there one day, the history of logic is one of the top 50 articles that should be in an encyclopedia. I welcome any thoughts.HistorianofLogic (talk) 20:43, 23 February 2010 (UTC)

  1. ^ Cite error: The named reference Marshack was invoked but never defined (see the help page).
  2. ^ Zaslavsky, Claudia: Africa Counts: Number and Pattern in African Culture, L. Hill, 1979.
  3. ^ Zaslavsky, Claudia: "Women as the First Mathematicians", International Study Group on Ethnomathematics Newsletter, Volume 7 Number 1, January 1992.
  4. ^ David J. Darling. The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes. John Wiley and Sons, 2004 (ISBN 0471270474)