# Talk:Symbolic logic

Currently we have Mathematical logicSymbolic logic and First-order logicFirst-order predicate calculus. I want to make the arrows point in opposite directions. From where I stand, "symbolic logic" and "predicate calculus", while certainly valid terms, are old-fashioned and more likely to be used by philosophers rather than mathematicians.

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I think logic is every bit a branch of philosophy as of mathematics...but I don't really care where the articles live, as long as the titles are precise and accurate. --LMS

It certainly is, Larry, and I wish there were more articles about philosophical logic in Wikipedia (I'm gonna act on that wish too ;)), currently the balance is in favor of mathematical logic. But "symbolic logic" is really just an alias for "mathematical logic" and "first-order logic" is of primary technical importance in mathematical logic as well, so using the modern mathematical names as defaults seems justified to me, for these two concepts. --AV

I understand the term First Order Predicate Calculus as being the language used in First Order Predicate Logic, and therefore the two terms are not stictly synonymous. Similarly the Sentential Calculus (Propositional calculus) is the language used in Sentential (Propositional) Logic --Philogo 00:09, 28 September 2007 (UTC)

The article states that we want the set of axioms to be recursively enumerable. Is that enough, or do we want the set to be recursive? --AxelBoldt

I don't mind changing 'symbolic logic' to 'mathematical logic', but personally I wouldn't replace 'first order predicate calculus' with 'first order logic'.

As to AxelBoldt's question, you'd have to remind me of what the difference is. The basic idea is that for any wff, a turing machine should be able to determine whether or not that wff is an axiom, the turing machine being guaranteed to halt. -- SJK

That would make the set of axioms a recursive set. A recursively enumerable set is one where the accepting turing machine is not required to stop, or equivalently a set whose elements can be produced one after the other on the tape of a turing machine. --AxelBoldt

The point is that for many purposes recursively enumerable is enough. However the article is wrong as it is now, i.e. its "explanation" of what r.e. is is actually about recursive sets. So maybe we should change the requirements to recursive and add in parentheses that sometimes even r.e. is enough, or something. --AV

Notice the above is rather historical discussion. (according to history, it is mainly 2001!)

Anyway, I moved the article to logic of mathematics. The title is a synthesized one rather than actually used widely today. In my understanding, termiology is a kind of confusion. In mathematics, mathematical logic or symbolic logic is simply referred as logic. People use more complex word simply to disambiguate stuff. In other words, the title simple "logic" seems fine but the trouble there is also logic as a branch of philosophy. Because I think logic article should contain not just current usage but also history, logic article should cover rather philosophical logic or history and logic of mathematics should be dedicated to more formal definition stuff. -- Taku 15:39 18 May 2003 (UTC)

About definition. I will rather move formal definition stuff or system discussion in the below because I believe first we should talk about basic knowledge such as proposition, true, false. I know they are defined formally for example by logical calculus. But for example, even if you don't know BNF specification of Java language, you can make a Java program and we should not start first definition. The article should be understandable without knowledge of a lot of math stuff. -- Taku 15:46 18 May 2003 (UTC)

I think (from my limited knowledge) that what Taku added is an attempt to show the basic steps demonstrating the binary logic. I think this should have its own article (but I'm not sure). Also the language used made it very hard to understand what it was talking about, I tried to figure out and hopefully improved a bit, but unfortunatly I have not taken courses about symbolic logic yet, So I'm actually clueless, Anyone to shed light over this? It seems that other articles Taku wrote suffer from the same problems I mentioned, I will try to rescue these from the "All your base are belong to us" Engrish style, but I doubt I'll succeed (because of lack of math understanding) -- Rotem Dan 11:04 21 May 2003 (UTC)

I know I am not qualified to write this sort of article but since no one starts to write a really basis. We don't need a kind of course catalog in college. I tried to explain how mathematicians use symbolic logic as language to express ideas logically maybe in vain? It is true that sometimes my writing doesn't make sense. -- Taku 15:15 21 May 2003 (UTC)
No, it wasn't what I meant :) I couldn't understand it because I haven't learned anything related to symbolic logic yet. (I don't take a course on Dicrete Mathematics cause that's for CS students, rather take an expanded course on Mathematical logic). And fixing engrish is fun, by the way, though sometimes hard to read.. I usually have problems of limited thesarous, rather than spelling or grammer (though everything I write, including what you see now, is dropped into a spell-checker, "my pal" spellonline (: --Rotem Dan 15:23 21 May 2003 (UTC)
Umm, I see so maybe my knowledge is logic in cs courses rather than that treated in math courses. I can understand why you are confused because even I was not so sure what I was talking about. We can keep research or hopefully someone knowledgable in symbolic logic can will help us.. -- Taku 16:22 21 May 2003 (UTC)
Hehe :), see a similar clueless n00b entry in Axiomatic system (summarised and translated from all sorts of undergraduate textbooks ,in hebrew!) -- Rotem Dan 16:59 21 May 2003 (UTC)

I moved the article to "symbolic logic" ("mathematical logic" would have been another choice; the two terms are largely synonymous). The term "Logic of mathematics" is not used for this field and has a different connotation. AxelBoldt 18:24 29 May 2003 (UTC)

I don't mean to complain but can you tell the connotation of "Logic of mathematics"? -- Taku 19:20 29 May 2003 (UTC)
I can try: one sees phrases like "the logic of language", "the logic of science" or even "the logic of modern warfare". None of these refer to logic as in symbolic logic; instead, the word seems to be used to describe a set of basic underlying principles, assumptions or rules. When I saw the title "logic of mathematics", I immediately assumed it to be a treatment of philosophy of mathematics. AxelBoldt 15:18 30 May 2003 (UTC)
I see now. But I am not still satisfied with the current title. It seems to limit the scope of logic. I mean I think logic in mathematics is actually more broad and covers set theory, proof and many. By saying symbolic logic, set theory, for example, seems off. I am not sure but that is my impression. For example, Google directory uses

which has model theory, set theory and proof theory. But as I discussed above before this discussion, I don't know a good name actually. Since a disambiguation logic of mathematics can be misleading, so how about:

• Logic and Foundations - as is in Google directory
• Logic in mathematics
• or even discard this article by moving materials to logic and spliting off each sub-topic such as propositional logic, predicate logic and so on.

-- Taku 15:29 31 May 2003 (UTC)

Set theory or model theory are usually not considered part of mathematical logic. All three are part of foundations of mathematics (which could be expaned a bit), and I think each should also be covered in their own article. We also should maintain separate articles for logic and symbolic logic, since the former is much broader. AxelBoldt 17:18 31 May 2003 (UTC)

The fact is I am so confused with termiologies and to me, it seems also the case in this article. As you see the article is such a mess. I started to what is logic in my understanding to this article. According to Rotem Dan, it is called binary logic. Are propositional logic, predicate logic, logical calculus, classical logic, etc. are part of symbolic logic or mathematical logic? I think the problem is when mathematicians talk about logic, it is not synonymous with symbolic logic, but the article seems assert that. What about rename foundations of mathematics to Logic and foundations of mathematics as is in Google directory. Do I misunderstand something? -- Taku 18:17 31 May 2003 (UTC)

It may be that I don't understand what has gone on - but a 'merge' announced of the symbolic logic with the logic pages seems to have been a deletion of the entire content of the former.

Charles Matthews 09:02 30 Jun 2003 (UTC)

Reincarnation of article:

It seems reasonable to me that this article should have at least some content. This article redirects to mathematical logic which makes a linked reference to symbolic logic (which redirects back to mathematical logic) ad infinitum. Therefore, I saw fit to create this stub. If anyone wants, change this back to a redirect, but remove the hyperlink from mathematical logic.

--69.145.79.115 00:47, 15 Mar 2005 (UTC)

Perhaps this should be reverted to the Revision as of 10:35, 10 Jun 2003, which does not seem to be a rehashing of the mathematical logic article. --209.137.247.194 19:31, 15 Mar 2005 (UTC)

## new work

I'm wrestling with the current state of articles in Wikipedia that fall under the general topic of logic. Many of these articles are quite good. Some are not. But most are a hodge podge, with conflicting definitions and notation.

I want to avoid people working on A changing B, people working on B changing C, people working on C changing A, and around and around the merry-go-round. To avoid this, we need a tree structure, something with logic at the top. But what comes next? Does the next level contain philosophical logic and mathematical logic? If so, then were does symbolic logic go? I'm trying to fix the state of affairs where "symbolic logic" is just an outdated word for "mathematical logic", because I think there is today a stronger distinction between the two.

Several appeals on the logic project page have gone unanswered, so I'm trying to do something myself, but it is a big job, and I could really use some help. Rick Norwood 18:39, 3 August 2007 (UTC)