Talk:Logical truth

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fundamental concept in logic[edit]

The article says

Logical truth is one of the most fundamental concepts in logic,

Why is it fundamental to logic? I'm no expert but I thought that concepts like "truth" mostly belong to classical logic, which these days is just one particular logical system. I went and changed "logic" to "philosophical logic" since I think it identifies the article's general subject matter a little more precisely. I also don't think "logical truth" is a fundamental concept in mathematical logic. I could be wrong though. (talk) 12:03, 13 February 2010 (UTC)

Its fundamental because almost everything that logicians do (including mathematical logicians) can be expressed as accounting for logical truth. They just do it using different methods. I understand your impression, and I certainly believe that your edit was good faith. However it really does consist in a POV edit.Greg Bard (talk) 18:46, 13 February 2010 (UTC)

Contentious why?[edit]

"The concept of a rule of inference is very closely connected to the concept of logical truth. Usually when a logical system is constructed, it is constructed so that every rule of inference is equivalent to a logical truth and every logical truth of the system can be transformed into a rule of inference consistent with the others."

There has been a long discussion at Talk:Rule of inference. But no actual question has come up over this language (other than Ghouse calling it "mealymouthed" which is just rhetoric.) What exactly is the controversy with this? Greg Bard 22:57, 23 February 2010 (UTC)

Are you being intentionally deceptive, or did you not read the discussion there? Carl pointed out on Jan 21 that your source was speaking only of the Principia Mathematica, not of logical systems in general. On Jan 22 he pointed out that the terms were not usual for formal systems generally, and gave the obvious counterexample. Later that day, he pointed out that your formulation at that time was a category mistake; though your current formulation avoids this, it does so by not specifying how to convert between logical truths and rules of inference. (This unfortunately robs it of all semantic content; I'm surprised the discussion continued after that point.) Emil J. gave an (excellent, IMO) example of why truths and rules of inference cannot be equated except in special cases. I pointed out on Feb 14 that the source you used as reference was extremely dated: a statement true of most of the formal systems known at the time need not be at all representative of the logical systems known today, let alone of all logical systems across all time. The following day I pointed out that you didn't have sources backing your now-expanded claim regarding most constructed systems. The next day Carl and Emil suggested that Ayers was referring to the deduction theorem. This, unlike your proposed addition, is well-defined; I (later) agreed that, if this was the intent, the section could be reworded to become true -- though it's not obvious to me that it would be relevant here at logical truth. (I take no position on that at this time.) I gave an example that same day showing why (a particular interpretation of) your statement is uninteresting. The following day, Carl suggested that the deduction theorem was the intended interpretation of the statement, and (curiously, considering *this* discussion had not yet begun) said that it should not be cast "as a statement about 'logical truth'".
That's a great number of serious objections from almost every editor posting in that discussion (notable exception: Arthur Rubin). At the risk of slight redundancy, I will note that your current statement is unsourced (it's certainly not what Ayers said). I'm usually quite tolerant of unsourced material (relative to other admins), but in a case as clearly contentious as this, you would be remiss to make a claim without good backing!
CRGreathouse (t | c)

00:06, 24 February 2010 (UTC)

Please offer a counter-proposal before a more 'mealy' formulation is proposed. So far I have been doing all the work of collaboration.
I would like to include
Daffy Duck is an excellent actor.
to the article. Is this good? If not, please offer an alternate wording.
CRGreathouse (t | c) 01:03, 24 February 2010 (UTC)
That is not good faith collaboration is it? Do you see that as equivalent? Really? I think you need to take a break.Greg Bard 01:08, 24 February 2010 (UTC)
Funny, I feel just that way about you. CRGreathouse (t | c) 01:29, 24 February 2010 (UTC)
But consider my perspective for a moment. You add something to an article; someone removes it. You put it back up; it's removed again, and many editors explain why it's not appropriate. You persist in adding it, the arguments continue, and it's removed again. The selection you suggest never changes much, and the changes do not address the fundamental issues pointed out. You wait a week and post the same flawed content to a different article, while denying that any issues were raised against it. I wade through *over a month's worth* of discussion and summarize all the issues with it, including several that show that it's essentially irreparable. You then say that, by not suggesting a change to it, I'm the one acting in bad faith?
CRGreathouse (t | c) 01:37, 24 February 2010 (UTC)

Logic bias?[edit]

I thought Greg would get a kick out of that title. :) The article has, in section Logical truths and tautologies, two types of tautologies: those formulas or propositions that are true under every assignment of truth values, and truth-functional tautologies. These exclude intuitionistic logic (and probably most paraconsistent logics). Why?

CRGreathouse (t | c) 00:27, 24 February 2010 (UTC)

It should be explicit in the MOS that exceptions caused by appeals to non-classical, non-standard interpretations, and very esoteric counterexamples should be held as special exceptions, not deal-breakers for the whole article. If you want to elucidate on those distinctions, they should be in a separate section. Greg Bard 00:45, 24 February 2010 (UTC)
I don't consider that esoteric at all. It [that is, intuitionistic logic] is an extremely popular logic, often used in many fields outside of logic proper. (I grant that paraconsistent logics are niche, though.) CRGreathouse (t | c) 01:19, 24 February 2010 (UTC)

Rule of inference[edit]

The latest version seems not incorrect, at least for classical logic. I'm not sure that it needs a section*, but as this article is quite short that doesn't seem to hurt. I would like a better source, if at all possible; if anyone comes across one, feel free to add it. (The current source is quite dated; the majority of work in formal logic has been done since it was published!) Also, there's no mention of where in the source the connection is made, which makes using the reference inconvenient.

* Actually, I don't really see a need for this sentence at all. This seems a quite tenuous tie to rules of inference; many more closely related things are not mentioned at all. But since the sentence is clearly very important to User:Gregbard I'm happy to oblige him, as long as the sentence is correct. :)

CRGreathouse (t | c) 17:19, 24 February 2010 (UTC)


"A logical truth was considered by Ludwig Wittgenstein to be a statement which is true in all possible worlds."

I understand the point that is made here but Wittgenstein mentions neither possible worlds nor logical truths in the Tractatus directly, so this statement is at best anachronistic. Possible world semantics were developed in the 50s by Saul Kripke. Larion Garaczi (talk) 19:10, 8 March 2013 (UTC)

I agree and I don't remember any discussion of logical truth in the technical sense of this article in Tractatus. (talk) —Preceding undated comment added 16:33, 13 May 2013 (UTC)

evident circularity?[edit]

"A logical truth is considered by some philosophers to be a statement which is true in all possible worlds."

How is possible world defined? Can one define it in a substantially different way than:

A pssible world (for me) is a world (?) in which all necessary truths (in my view) hold.

Subsidiary question: what is a world here?

denis 'spir' (talk) —Preceding undated comment added 13:03, 12 September 2013 (UTC)

"Just in case"[edit]

On behalf of the general audience, I have replaced the misleading and confusing expression "just in case", with its correct, and easily understood equivalent, "if, and only if" (also, in more technical writing, "if and only if"). The following explains the error: