Talk:Law of thought
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Notes & Queries
Jon Awbrey 22:16, 18 January 2006 (UTC)
Formal logic is NOT "how we think"
Where does the following statement in the first paragraph come from?
"...which collectively prescribe how a rational mind must think. To break any of the laws of thought (for example, to contradict oneself) is to be irrational."
"Law of thought" is a misnomer, in the first place, because the 3 "laws" listed are just parts of an axiom-system (= set of Assumptions), and not valid as general "laws of human thinking", since it is easy to demonstrate, by example, natural language statements that violate "law of noncontradiction" and/or "law of excluded middle", such as: "This statement is false." We can clearly grasp the meaning of it, but still, it is neither true nor false.
Axiom systems are not necessarily related to anyone's mind. They are not laws of thought. They exist in a timeless, spaceless realm of being, much like Platonic Ideas or Forms. If there were no humans, axiom systems would still exist in their universe of pure logic. We don't create them in our thoughts. We discover them as something that already existed but had been concealed from our knowledge. To say that formal logic is "how we think" is to commit the unpardonable, unspeakable sin of psychologism.Lestrade (talk) 02:14, 27 July 2008 (UTC)Lestrade
To the user above, above: 'laws of thought' are not assumptions, nor are they to be interpreted as assumptions (or taken lightly for that matter). This is a poor misunderstanding of their purpose. The 'laws of thought' are indeed the axiomatic principles for a rational mind, and to not use them is to deny reality, and thus irrational, because they are based on nature, and reality. Existence vs. non-existence is the central point behind the law of non-contradiction, and the others follow suit. Either something exists, or it does not exist. To deny the laws, you would have to use them.
Also, the sentence "this statement is false" is riddled with fallacies. First, it's ambiguous, and sophistic. Second, there are no premises that demonstrate your conclusion, which not only begs the question, it also doesn't follow. Third, 'natural language' is not in itself contradicting, or sloppy, the user of it can be, though. The laws of thought are the basis for all rational thinking, and the article had it correct the first time -- as stated above, to deny the laws, you would have to use them, which is contradicting, concluding that the assertion/claim is necessarily false. Source: http://www.thelogician.net/5b_ruminate/5b_chapter_01.htm#3.%C2%A0%C2%A0%C2%A0%C2%A0%C2%A0%C2%A0%C2%A0%C2%A0_Paradoxical_Propositions
There is a wealth of information on that page, for the editor of this page, if you wish to add further information. I would suggest the editor add back the original assertion that they are indeed the axiomatic principles for rational thinking. In-fact, it's not even possible to not use them. 13:09, 5 January 2010 (UTC) —Preceding unsigned comment added by 220.127.116.11 (talk)
- Heaven forbid that there should be a relation between laws of thought and psychology. That would be the most mortal of all sins. We are here talking about logic and logic alone, that is, mere abstract, disembodied forms. It must be intuitively obvious to any thinking person that thinking does not require a brain or mind in order to occur.Lestrade (talk) 14:47, 5 January 2010 (UTC)Lestrade
This article should be called "Laws of Thought," not "Law of Thought." The George Boole article should be called "Laws of Thought (Book)."Lestrade 19:22, 27 July 2006 (UTC)Lestrade
- I renamed the article on Boole's book and I heartily agree with User:Lestrade's comment about the improper naming of this article. Academic philosophers speak of the laws of thought as a group. The term is standard. I think this page should be moved back to laws of thought. Perhaps this question should be put to a survey on this talk page. - WikiPedant 05:31, 7 August 2006 (UTC)
JA: No, in WP the use of singular is standard for a class of related things. Hence, law of thought. You can still have laws of thought redirect here, so no big problem. Boole's book title Laws of Thought needs no extra dab, since the plural Laws and the capitalized Thought already dab it, and this follows the rule of many similar cases in WP. Jon Awbrey 07:08, 7 August 2006 (UTC)
- Hello JA -- I can understand why you want to adhere closely to WP standards, but the fact is that the WP standards are more flexible and complex than you say. The guidelines do allow plural article names in cases just like this one, where the article is about the whole set of things (that is, the things considered as a collective) and where the collective term is itself standard usage. See Wikipedia:Naming_conventions_(plurals) which recognizes exceptions to the use of singular names, such as "articles on groups of specific things" (for example, articles on particular language families, such as Romance languages and Afro-Asiatic languages). See also Wikipedia_talk:Naming_conventions/archive5#SOME_article_titles_should_be_plural. Furthermore, the list of exemplary featured articles contains a number of plural titles, including Médecins Sans Frontières,€2 commemorative coins, Microsoft Data Access Components, Black Seminoles, Domestic AC power plugs and sockets, National parks of England and Wales, Three Laws of Robotics, The Beatles, The Supremes, The Temptations, The Waterboys, End times, Shakers, Olympic Games, Indian Railways. And specifically with respect to history and philosophy articles, the list of good articles includes Zeno's paradoxes, Khazars, and Knights Hospitaller. So there is (a) good reason, (b) allowance within the wiki guidelines, and (c) precedent for changing the name of this article back to Laws of thought. - WikiPedant 05:26, 8 August 2006 (UTC)
JA: Let's put aside the temptations to exploit proper namess that are plural, please. As a general rule, it just makes sense use the stem word, say, logic, as the main article title if there is any occasion at all to use the stem word in text, as the regular derivatives, say, logics, logical, logicality, etc. can all be linked without having to bother with redirects. Of course, law of thought is a special case, since the law is embedded in the phrase, but the criterion of convenience here is whether one ever finds occasion to use the singular term in text, amd one often does, since law of thought, like national park, is a class name, and is often used in the singular. Jon Awbrey 19:42, 8 August 2006 (UTC)
Leibniz's assertion of the Identity of indiscernibles is not a law of thought. The article is mistaken by including Leibniz's assertion as one of the laws of thought.18.104.22.168 17:27, 3 August 2006 (UTC)Lestrade
- I tend to agree, and the classic Aristotelian law of identity is missing. I addressed this (diplomatically) in my edit today. - WikiPedant 05:31, 7 August 2006 (UTC)
JA: I reverted the following addition to the lead because it lends itself a bit too easily to a purely psychological reading, whereas it needs to be made more clear that logical laws are normative principles.
The laws of thought are the traditional, fundamental rules which collectively define how a rational mind must think. To break any of the laws of thought (for example, to contradict oneself) is to be irrational.
JA: Given the proper explanation beforehand, though, it looks like it would be pretty easy to fix it. Jon Awbrey 13:42, 7 August 2006 (UTC)
- Who was it that first judged that the laws of thought are not related in any way to dreaded psychology and its description of brains or minds and their acts of thinking? Was he the same man who claimed that the laws of thought are pure logical principles that would exist somewhere separately even if there were no humans who had thoughts running through their heads? 22.214.171.124 02:57, 6 January 2007 (UTC)Benighted—The preceding unsigned comment was added by 126.96.36.199 (talk) 04:41, 3 January 2007 (UTC).
Why are these called 'laws of thought' (over and above the fact that it is traditional to do so)? Does anyone seriously think that people actually cogitate in syllogisms, or that they use the formal calculi found in Principia Mathematica when they reason?
If logic were the science of what went on in people's heads, then logicians would busy themselves with brain scans, surveys, psychometric tests, and the like. They certainly would not bother with all those useless theorems and proofs.
Of course, this is not to endorse the opposite extreme rehearsed at the top of this page, that is, that the theorems and axioms of logic exist in a sort of quasi-Platonic realm.
Reply to Rosa Lichtenstein:
- Hell yeah I do! If it’s worth the effort. I don’t use mathematical symbolism, since when you use descriptive identifiers, you can be much more efficient in processing things. But I use cold hard logic to reason, and can usually spot every logical failure my dialog partners’ use. (Even when I don’t go all the way myself.) I became this way, because I grew up with people that were infected by religious schizophrenia, and had to *properly* prove (for myself anyway) what was ultimately right. But I think, if you don’t use proper logic in your reasoning, you’re a retard and unworthy of vocalizing any arguments (since they wouldn’t actually be arguments). Of course, the ultimate problem is, that without a proper set of common paradigms, you would have to have such a long string of arguments, that they could go right down to explaining the beginning of the big bang. I can do that, nowadays, due to a deep understanding for physics, logic and psychology. But usually it’s just not worth it, since your parter wouldn’t even remotely be able to comprehend what it means. So in a way, you may still be right in that it’s not very common. ;) I guess(!) most people are just “cattle” anyway. — 188.8.131.52 (talk) 06:37, 8 December 2010 (UTC)
Reply to 184.108.40.206 etc.:
Thanks for those thoughts, during the expression of which, by the way, you did not use even so much as one syllogism or a single wff from Principia, but you will note that I in fact said this:
"Does anyone seriously think that people actually cogitate in syllogisms, or that they use the formal calculi found in Principia Mathematica when they reason?"
I did not speculate whether or not there were maverick individuals on the planet who might at least claim they think in syllogisms (a remarkably useless and inefficient way to think, anyway) or the calculii of Principia (but I retain a healthy scepticism that you actually think using symbols like this: ~[(P→Q)v(P→R)↔(P→(QvR))], or this ~[~(Ex)(Fx&~Gx)↔(x)(Fx→Gx)]), but whether "people" do this, i.e., the majority of the population. And if they don't, then logic can't express 'laws of thought', otherwise we'd all be at it, and we'd have been doing it for thousands of years before Russell and/or Aristotle were thought of.
But, and more importantly, even if everyone on the planet thought in syllogisms etc., that would still not make logic the study of the 'laws of thought' -- as I also pointed out:
"If logic were the science of what went on in people's heads (or the study of the 'laws of thought' -- added comment), then logicians would busy themselves with brain scans, surveys, psychometric tests, and the like. They certainly would not bother with all those useless theorems and proofs."
My comments still stand, therefore.
The article tells us that Aristotle accepted the so-called 'Law of Identity'. But, what later came to be known as the 'Law of Identity' is absent from Aristotle's work.
The quotation from the Metaphysics does not support the conclusion that he accepted this 'law'. If anything, it shows he was dissmissive of it -- that is, if he was referring to it in the first place!
- A large part of the problem is that we are not sure what we mean by the ambiguous word "thought." Does "thought" mean any brain activity or any mental activity? Does thought mean "unspoken language"? If all thought is discursively related to words, then it is related to grammar and what can be said. This would include the laws of identity, contradiction, excluded middle, sufficient reason, etc. In this way, all thought is connected to verbal judgments, propositions, and Kantian Categories. If all thought, however, is intuitively related to imagination, willing, emotion, sensation, etc., then it may not be related to those laws. We can then ask, with Rosa Lichtenstein, "Does anyone seriously think that people actually cogitate in syllogisms, or that they use the formal calculi found in Principia Mathematica when they reason?" She assumes here that all thought is equivalent to cogitation and reasoning.Lestrade (talk) 03:33, 26 November 2010 (UTC)Lestrade
Thank you for those comments Lestrade, and you are quite right to point out that how we interpret this question does depend on what we mean by 'thought'. But, my general point still stands, for even if you are right about the other things you say (but, I am sceptical even of that -- however, we can put that to one side for now), logicians would surely throw away their definitions, proofs and rules of inference, and conduct surveys about how people actually think, or, how they actually use words/language (to put this in the way you chose to frame this question). Logic would then become a sub-branch of Psycholinguistics.
But, this isn't correct:
"She assumes here that all thought is equivalent to cogitation and reasoning."
I was in fact addressing a traditional view of 'thought' associated with this view of logic. It is undeniable that psychologism dominated the interpretation of logic until quite recently, and this view (that logic is the study of the 'laws of thought') dates back to this outmoded conception of 'thought' and its relation to logic.
This article simply re-inforces that misguided view.
While we are at it, what can this possibly mean?
"The law of identity states that an object is the same as itself: A ≡ A."
If "A" is an object, or the name of an object, then the equivalence sign "≡" is surely misplaced. While Socrates might or might not be identical with himself, there is no way he is truth-functionally equivalent to himself, since he isn't a proposition, statement or indicative sentence. "Socrates if and only if Socrates" is unvarnished nonsense.
And this can't be correct, either:
"The law of non-contradiction and the law of excluded middle are not separate laws per se, but correlates of the law of identity. That is to say, they are two interdependent and complementary principles that inhere naturally (implicitly) within the law of identity, as its essential nature."
The Law of Identity (LOI) and the other two 'laws' are in no way linked, as the above suggests.
The problem is that if the LOI concerns the identity of objects, or their names (depending on how we read it), that is, if the "A"s used in the article are the names of objects, or stand for objects, then the LOI can't be connected with the 'Law of Non-contradiction' [LOC] or the 'Law of Excluded Middle' [LEM]. That is because the "A"s used in the article in relation to the LOC and the LEM stand for propositions, statements or predicables, not objects or their names.
And this reasoning is defective too:
"In other words, the proposition, “A is A and A is not ~A” (law of identity) intellectually partitions a universe of discourse (the domain of all things)into exactly two subsets, A and ~A, and thus gives rise to a dichotomy. As with all dichotomies, A and ~A must then be 'mutually exclusive' and 'jointly exhaustive' with respect to that universe of discourse. In other words, 'no one thing can simultaneously be a member of both A and ~A' (law of non-contradiction), whilst 'every single thing must be a member of either A or ~A' (law of excluded middle)."
If the negative particle attaches to singular terms, so that it is interpreted as an operator mapping singular terms onto 'negative' singular terms (whatever they are!), then it can't also be a sentential operator mapping a sentence or proposition onto its negation, which it has to be in relation to the LEM and the LOC.
In the above the sign "~" slides effortlessly between the following roles: an operator on names (or objects!), an operator on ill-defined classes (so that it seems to resemble a class exclusion operator), and a sentential modifier.
This is a dodge Hegel also tried to pull in his badly mis-named books on 'logic' -- meaning that his 'dialectic' can only be kick started by the use of sloppy semantics/syntax like this.
In tandem with this, these "A"s also slide between several distinct roles -- one minute "A" is an object (or its name), the next it's a class (or its name), then it's a proposition, sentence, or statement (depending on one's philosophical logic).
From sloppy semantics and syntax like this nothing but confusion can follow.
Or, maybe not; as Bertrand Russell remarked: "The worse a man's logic, the more interesting the results to which it gives rise".
The article needs to be completely re-written, or deleted.
I disagree; WIkipedia should not be promoting such sloppy logic. This is one of the first places novices look for advice and information. Filling their heads with defective semantics and syntax is no way to educate them.
And I have rehearsed these ideas elsewhere, and in more detail at my site:
Lacking the core thing!
The article lacks the single most important thing it could contain: An explanation for why exacly these and no others are the rules that be. Instead they are presented as unquestioned, and even unquestionable. Adding “long tradition” as a filler term typical for things that nobody actually thinks about (which usually are bullshit) does not make it better.
— 220.127.116.11 (talk) 06:26, 8 December 2010 (UTC)
Plainly, any explanation is going to have to be non-contradictory, use terms that maintain their identity throughout that explanation, and is either correct or not. In which case, anything that counts as an explanation will have to take these 'laws' (but I prefer to call them rules of language) for granted.
On the other hand, anyone who attacks these rules is going to find it impossible to explain themselves without also implicitly accepting/using/applying these rules, thus nullifying their attack. [This was, essentially, Aristotle's defence, even if he worded it differently.]
2nd & 3rd corollaries of the first??
So the rationale section of the article seems to be implying that the second and third laws are corollaries of the first. The article doesn't actually use the word 'corollary' though; it leaves the reader confused as to weather the second and third laws can be inferred from the first or not.
I think this needs clearing up. I'm not sure exactly what the edit should be, so I'm hoping an expert in the area can help out.
Well, as I have shown above, the 'Law of Non-contradiction' [LOC] and the 'Law of Excluded Middle' [LEM] cannot be derived from the 'Law of Identity', and neither are they corollaries.
However, by De Morgan's Laws, it is easy to inter-derive the LOC and the LEM (if we also allow ¬¬p ↔ p):
(1) ¬(p & ¬p) ↔ ¬p v ¬¬p
(2) ¬p v ¬¬p ↔ ¬p v p
(3) Ergo: ¬(p & ¬p) ↔ p v ¬p
Agreed; the example given regarding the "+" symbol is nonsensical. The article seems to indicate that there can't be ambiguity in symbols? Sometimes, in maths, a "." is used to denote multiplication - so I fail to see what on Earth the author(s) point is. They then go on to say that 7 is 7; yes, that's true. But it's the same as simply invoking a number (deflationary theory).
I fail to see how the two latter "laws" are derived from the "law of identity" (which is actually simply called the axiom of equality, pertaining to the Peano Axioms). It does not follow that A = A implies that the "universe is partitioned into two subsets of A and ~A." This is just baffling. All the axiom of equality denotes is that a thing is itself a time t -- and I'm quite happy that this is linguistically self-evident...but why's it even a "law" ?
Not to mention that the Copenhagen interpretation of quantum mechanics, viz. Schrödinger's cat (or the double slit theory, etc) obliterates the latter two "laws." If the response to this is to simply move the goalposts and argue that "a thing is either in a superposition of states or it isn't" , that's frankly amusing and demonstrates the lack of utility in these "laws."
The entirety of this article needs to be scrapped if these concepts keep being spouted off as "absolutely true." Did I miss that memo in philosophy that anything can be considered as such? — Preceding unsigned comment added by 18.104.22.168 (talk) 16:33, 16 July 2013 (UTC)
Quantum mechanics has in fact no implications for the 'Law of Excluded Middle' [LEM] or the 'Law of Non-Contradiction' [LOC], since if it is unclear what scientists are proposing (or putting forward for logicians to consider), then what they have to say can't be put into propositional form. Since the LEM and the LOC deal only with propositions, and since scientists have yet to propose something clear (or refrain from equivocating), these 'laws' remain unscathed.
Rational or Logical ?
The article begins by asserting: 'The laws of thought are fundamental axiomatic rules upon which rational discourse itself is based.'
As a mere layperson who has no wish to get into an edit-war against actual or alleged experts, I am reluctant to correct what nevertheless seems to me to be a common abuse of language in that statement (which seems acceptable in everyday speech but arguably not in an encyclopedia article about logic), namely the use of the word 'rational' when one means 'logical'.
For instance self-delusion through wishful thinking is illogical, in that it violates rules of logic, but it may well be perfectly 'rational' if it fulfils the person's rational desire to remain happy or to become happier, or even it doesn't but if the person mistakenly thinks that it will, or hopes that it might, or whatever. Discourse intended to achieve such a rational objective is then arguably 'rational discourse', no matter how much it violates rules of logic. Much the same can probably also often be said of much discourse in pursuit of a rational motive to deceive others (which arguably means something like almost half of all discourses in almost any debate on almost any subject).
Need for some mention of Fuzzy Logic and/or of the real world
The article begins by asserting: 'The laws of thought are fundamental axiomatic rules upon which rational discourse itself is based.'
It seems to me that it should be prominently stated that the real world arguably doesn't work like that, and that a whole branch of computer science called Fuzzy Logic has been created in a partial attempt to deal with this problem. In computing, Fuzzy Logic uses Truth values between 0 and 1 to reflect this, in effect saying statements can be 'truish' (or, for instance, '87% true and 13% false') and 'falsish' and 'in-betweeenish' as well as 'true' and 'false'. For example 'that thing is big' can be true relative to some things and false relative to other things. And 'I am tlhslobus' is true in some senses, and false in other senses (because tlhslobus is obviously only a pen-name). 'There's no such person as Santa Claus' seems true until you consider that there's one in every major department store in the run-up to Christmas, let alone how many might 'exist' in dreams and/or might exist in any parallel subuniverses that the universe may contain if it is in fact a Multiverse. 'This chair is solid' - well, yes, I'm sitting on it, but it's basically almost nothing but empty space from the perspective of the zillions of neutrinos passing through it every second (at least if science is to be believed). And so on ad infinitum.
I may eventually try to amend the text myself (if I remember), but first I'd prefer to wait and see if somebody with more expertise than me can amend it better. Tlhslobus (talk) 13:22, 11 October 2012 (UTC)
If that chair is 'mostly empty space', then why don't you fall through it? An appeal to 'forces' (or particles that 'carry forces') would be to no avail, since, if you are to make sense of their capacity to resist motion, you are going to have to use words that depend on everyday notions of solidity, undermining the point you wish to make.
Furthermore, what are those 'items' that aren't empty space made of? Energy? But that can't resist motion, either. So, where does solidity come from? It can't be from 'forces', for the above reasons.
In other words, we have no good reason to give up our ordinary ideas of solidity. They underpin science and so cannot be challenged by any scientific theory, no matter how successful it might be, without that theory undermining itself.
[For anyone interested, this debate has been continued over at my 'talk' page -- link below.]
about the "The Three Classical Laws" section; and the quality of this page in general
This section is overly opinionated (non-neutral) and lacking references to back up it claims. It seems, furthermore, to be the product of own research by a user with IP 22.214.171.124 who made several edits to this page in March. Although that user's comments may have improved parts of the page, too much of what has been inserted seems to reflect that person's opinions and research, and much of the page needs to be rewritten in a more neutral tone. The "The Three Classical Laws" is the worst in this sense (i.e. by Wikipedia standards), but I also have my doubts about (the neutrality of) the section "Contemporary developments". Lajib (talk) 00:56, 9 May 2013 (UTC)
Also, in that section it is asserted that Russell & Whitehead wrote "For any proposition A: A = A" I have serious doubts about this. First R&W use : in a special sense, and I guess the WP-editor added this theirself. Second = means "is identical to", but "A is identical to A" is NOT the same as "if A then A" (or 'if A exists then A exists' or 'given that A exists then we can conclude that A exists'). I assert, but without much confidence since I am neither an expert in the field nor have I studied Principia, that R & W wrote something along the lines of "given A then A" or "A implies A" = A → A. Could someone check this?126.96.36.199 (talk) 22:23, 5 May 2015 (UTC)
- I'm not seeing where Russell and Whitehead aka "Principa Mathematica" assert "For any proposition A: A = A". Russell alone, in his philosophical text 1912:72, is quoted as stating "whatever is, is". Here's a specific example: Given the proposition "this dog is black": "this dog is black" is identical to "this dog is black". Is this false? Thus when extended over all propositions, the sentence "For any proposition A: A = A" does not seem incorrect; for why, see the section titled "Tarski (1946): Leibniz's Law" and then sub-section titled "Law of identity (Leibniz's Law, equality" where the matter of "equality" -- "identical in all respects" -- is discussed in detail; here the exact, formal definition of equality (identicality over all assertions (functions)) from PM is quoted. BillWvbailey (talk) 15:52, 6 May 2015 (UTC)
"A = A" can't be the equivalent of "If A then A", anyway, since the "A"s in "A = A" are singular terms, not propositions, whereas the "A"s in "If A then A" are propositional variables. "If Socrates then Socrates" is unvarnished nonsense.
Convoluted quote without clarification
The Third Law of Rational Thought is given as a direct quote that reads incredibly poorly in English, strewn with double negatives and run-ons. I imagine this amounts to a bad translation of a valid idea. Either way, cleaning that bit up would be beneficial. — Preceding unsigned comment added by 188.8.131.52 (talk) 22:12, 20 August 2013 (UTC)
Rationale needs to be re-written.
The writer seems to deem it necessary to describe that symbols hold meanings. More specifically using the statement of "2+2=4" to convey that one requires knowledge that the addition operation has the meaning that it does. For such information to be relevant the section should conclude that the origins of predicate or first-order logic was driven by notation used to not only describe but to demonstrate consistency in relationships between statements primarily in the context of arguments. This statement is also not related to material implication since they are not synonymous and the only similarity is that they are functions.
Furthermore, considering the statement "The law of non-contradiction and the law of excluded middle are not exactly separate laws; rather, they are correlates of the law of identity." They are not 'correlates' of the law of identity. The axiom A is A is provable from its negation assuming A implies A, see Contradiction. Also, saying that they are or are not separate laws is irrelevant. Their identity is proven through the material implication of axioms and therefore, being separate laws is false since they are defined as such. We are not speculating about the way things are defined, especially in such an manner.
"Furthermore, we cannot think conceptually without making use of some form of language (symbolic communication), for thinking conceptually entails the manipulation and amalgamation of simpler concepts in order to form more complex concepts" Further describing the need for symbols. This could even be the start of the article.
I believe that what is discussed here is of both obvious and irrelevant components. The title suggests origin rather than explanation and needs to take a more chronologically historical stance. — Preceding unsigned comment added by Lethalattraction (talk • contribs) 10:11, 7 July 2014 (UTC)
- I've emended the important section that defines the "traditional" three laws of thought by means of quotes etc from Bertrand Russell 1912 and removed its "original research" tag, which I thought was unnecessary to begin with. I agree that the lead paragraphs need honing; the LoEM and law of (non-)contradiction are distinctl -different; that's why disallowal of the LoEM in intuitionistic logic historically made some people's blood boil (e.g. David Hilbert).
- By the way, fuzzy logic and "alternative logics" (e.g. intuitionistic logic) is not appropriate here.
This about the three traditional "laws of thought".[but see comments in next section]. That these three have historically been singled out from some others is appropriate, but that discussion should probably stop there (unless someone can find a historical reason why these three are the chosen ones; maybe with reference to alternative logics, but just a reference, not clutter). I'd like to see this be a solid reference article on the topic of the traditional laws of thought, and that's it. BillWvbailey (talk) 15:41, 8 September 2014 (UTC)
- But we need a definitive source for this "classical" section that lists three laws. Remember, before this edit this section had a "original research" tag on it. My readings (they go back until the writings turn to Greek) have indicated that the "schoolmen" couldn't decide which "laws" (principles) should be included in the general heading. Russell gives us the three. So at least we should keep the three as Russell states them. I'll move the other paragraph to a new section. There's a deeper problem here, but I'll come back to discuss it here after I've moved the Russell paragraph. BillWvbailey (talk) 19:30, 8 September 2014 (UTC)
This is in response to the comments posted above by 'Lethalattraction':
As I have pointed out above (in the section entitled 'Problems'), the so-called 'Law of Identity' [LOI] and the other two 'laws' are in no way related (nor are they inter-derivable), but this can't be right:
"The axiom A is A is provable from its negation assuming A implies A".
That is because, in the LOI, "A" stands for a singular term, not a proposition or indicative sentence -- in which case, "A" can't imply anything. "Socrates implies Socrates" makes no sense.
On the other hand, if "A implies A" were the case, then "A" would have to be a propositional or sentential variable. In that case, "A" (so interpreted) can't appear in the LOI. "Socrates was Plato's teacher is identical to Socrates was Plato's teacher" is unvarnished nonsense, since it treats a proposition as a singular term, object, or name thereof.
On why propositions (and/or indicative sentences) aren't singular terms, objects, or the names thereof, see here:
[If you are using Internet Explorer 10 (or later), the above link won't work properly unless you switch to 'Compatibility View' (in the Tools Menu); for IE11 select 'Compatibility View Settings' and then add my site, which is where the above link will take you.]
Scope of this article
The title of this article "Law of thought" is peculiar. What first comes to my mind is the question: "What 'law of thought'?" . Are we talking about a generalization to the plural "traditional laws of thought", or about the generalized notion "law of thought" or what? the reason why defining what a "law of thought" is important, is that the three "laws of thought" are insufficient by themselves to form a "logical system" that we can use in "argumentation". We need more than these -- we need the idea of "connectives", substitution and detachment (modus ponens) and some axioms that allow us to do things such as put an & between two propositions. See Goedel 1930a in van Heijenoort 1967:584. Here Goedel lists a few "primitive symbols" (OR, NOT, "for all"), 6 "formal axioms" and 4 "rules of inference" (modus ponens, substitution, + two more) from which he proves that "every valid formula of the restricted functional calculus is provable".
Inclusion of "implication" and "modus ponens": I noticed in the Schopenhauer section the inclusion of "implication" as expressed (sort of) by Russell's primitive proposition" "*1.1 Anything implied by a true elementary proposition is true". But Russell followed this up with another primitive proposition *1.11 [modus ponens] that gave him such fits he completely rewrote the section, eliminating *1.11 in the 1927 second edition of Principia Mathematica. The text of his rewrite appears on page 9 (1962 Edition) and it describes what we now think of modus ponens:
- "Accordingly whenever, in symbols, where p and q have of course special determinations,
- "⊦p" and "⊦(p ⊃ q)"
- have occurred, then "⊦q" will occur if it is desired to put it on record. The process of the inference cannot be reduced to symbols. Its sole record is the occurrence of "⊦q"."
Observe also another "law of thought" -- that of the notion of "assertion of a proposition" symbolized with the mark ⊦ before the proposition. In other words given our assertion of a statement p [⊦p] and the truth of the implication "p implies q", we can "detach" q and throw away the assertion of p and the implication "p implies q", and just proceed with "⊦q", the assertion of q.
If assertion plus implication plus "modus ponens" isn't a "law of thought", I'm at a loss to know what it is. Ditto for "substitution". Is this stuff supposed to be in the article? Just what is this article supposed to be about? What should it include and not include? BillWvbailey (talk) 21:08, 8 September 2014 (UTC)
--- RE Interested editors can find a huge trove of historical sources that I located and cc'd into a "user" page in 2009, at User:Wvbailey/Law of Excluded Middle. Most of this includes direct quotations from Hamilton's lectures published in 1860: ON THE FUNDAMENTAL LAWS OF THOUGHT-THEIR CONTENTS AND HISTORY (1830's). Hamilton died in 1856, so this is an effort of his editors Mansel and Veitch. Most of the footnotes are additions and emendations by Mansel and Veitch -- see the preface for background information. Hamilton's book is in the public domain at googlebooks.
Hamilton discusses at great length four laws, the 4th of which we know as "connection" in particular implication + modus ponens (his is an informal description compared to Russell in PM). Also of particular interest here is the attribution of the "principles of Contradiction and Excluded Middle" to Plato as well as Aristotle, and his assertion of the late development of the law of identity that he attributes to Antonius Andreas. Bill Wvbailey (talk) 15:27, 9 September 2014 (UTC)
from Hamilton LECT. V. LOGIC. 62:
The principles of Contradiction and Excluded Middle can be traced back to Plato: The principles of Contradiction and of Excluded Middle can both be traced back to Plato, by whom they were enounced and frequently applied; though it was not till long after, that either of them obtained a distinctive appellation. To take the principle of Contradiction first. This law Plato frequently employs, but the most remarkable passages are found in the Phœdo, in the Sophista, and in the fourth and seventh books of the Republic.2
2 See Phœdo, p. 103; Sophista, p.252; Republic, iv. p. 436; vii. p. 525. – ED.
from Hamilton LECT. V. LOGIC. 65:
Law of Excluded Middle: The law of Excluded Middle between two contradictories remounts, as I have said, also to Plato, though the Second Alcibiades, the dialogue in which it is most clearly expressed, must be admitted to be spurious.1 It is also in the fragments of Pseudo-Archytas, to be found in Stobraeus.2
- 1 Second Alcibiades, p. 139. See also Sophista, p. 250 – ED.
- 2 Eclogœ.. 1. ii. c. 2, p. 158, Ed. Antwerp, 1575; Part ii. tom. 1, p. 22, ed. Heeren. Cf. Simplicius, In Arist. Categ., pp. 97, 103, ed. Basil, 1551. –ED.
from Hamilton LECT. V. LOGIC. 65, re Law of Excluded Middle:
Explicitly enounced by Aristotle: It is explicitly and emphatically enounced by Aristotle in many passages both of his Metaphysics (l. iii. (iv.) c.7.) and of his Analytics, both Prior (l. i. c. 2) and Posterior (1. i. c. 4). In the first of these, he says: "It is impossible that there should exist any medium between contradictory opposites, but it is necessary either to affirm or to deny everything of everything."
Law of Identity
Hamilton also calls this "The principle of all logical affirmation and definition":
From Hamilton LECT. V. LOGIC. 65-66
Law of Identity. Antonius Andreas: The law of Identity, I stated, was not explicated as a coordinate principle till a comparatively recent period. The earliest author in whom I have found this done, is Antonius Andreas, a scholar of Scotus, who flourished at the end of the thirteenth and beginning of the fourteenth century. The schoolman, in the fourth book of his Commentary of Aristotle's Metaphysics,6 - a commentary which is full of the most ingenious and original views, - not only asserts to the law of Identity a coördinate dignity with the law of Contradiction, ¶ but, against Aristotle, he maintains that the principle of Identity, and not the principle of Contradiction, is the one absolutely first. The formula in which Andreas expressed it was Ens est ens. Subsequently to this author, the question concerning the relative priority of the two laws of Identity and of Contradiction became one much agitated in the schools; though there were also found some who asserted to the law of Excluded Middle this supreme rank." [there's more]
Hamilton's 4th law, what we know as Implication + modus ponens
Here's Hamilton's fourth law from his LECT. V. LOGIC. 60-61:
"I now go on to the fourth law.
Par. XVII. Law of Sufficient Reason, or of Reason and Consequent:
¶ XVII. The thinking of an object, as actually characterized by positive or by negative attributes, is not left to the caprice of Understanding – the faculty of thought; but that faculty must be necessitated to this or that determinate act of thinking by a knowledge of something different from, and independent of; the process of thinking itself. This condition of our understanding is expressed by the law, as it is called, of Sufficient Reason (principium Rationis Sufficientis); but it is more properly denominated the law of Reason and Consequent (principium Rationis et Consecutionis). That knowledge by which the mind is necessitated to affirm or posit something else, is called the logical reason ground, or antecedent; that something else which the mind is necessitated to affirm or posit, is called the logical consequent; and the relation between the reason and consequent, is called the logical connection or consequence. This law is expressed in the formula - Infer nothing without a ground or reason.1
Relations between Reason and Consequent: The relations between Reason and Consequent, when comprehended in a pure thought, are the following: 1. When a reason is explicitly or implicitly given, then there must ¶ exist a consequent; and, vice versa, when a consequent is given, there must also exist a reason.
- 1 See Schulze, Logik, §19, and Krug, Logik, §20, - ED.
2. Where there is no reason there can be no consequent; and, vice versa, where there is no consequent (either implicitly or explicitly) there can be no reason. That is, the concepts of reason and of consequent, as reciprocally relative, involve and suppose each other.
The logical significance of this law: The logical significance of the law of Reason and Consequent lies in this, - That in virtue of it, thought is constituted into a series of acts all indissolubly connected; each necessarily inferring the other. Thus it is that the distinction and opposition of possible, actual and necessary matter, which has been introduced into Logic, is a doctrine wholly extraneous to this science.
Contrast to fourfold/tetralemma logics
I feel the section "https://en.wikipedia.org/wiki/Law_of_thought#Indian_logic" as currently written is misleading: not only does it not adequately present the history of how the rational discourse of Russel and early 20th century logicians differ from historical systems of Indian logic/tetralemma logics (or most recently paraconsistent logic)- it makes the implication that these early systems contained the same ideas.
While I'm not an expert, reading on this leads me to think simply stating this idea was present in older system may be accurate from the references, but it misrepresents the situation. The Law of Thought, derived from the three traditional laws are much more recent, much stronger in their logical power, but constrain the applicability to rationally consistent outcomes. The "Indian logic" systems with four-fold states instead of two-fold states produced results wholly different, and supported inconsistent outcomes. It wasn't until much later in the late 1970's and after that these became formalized and studied in the west. 184.108.40.206 (talk) 06:44, 11 November 2014 (UTC)