Talk:Classical logic

2005
The list of non-classical logic, as far as I can see, was initially supposed to be in order of properties of classical logic that are not satisfied. However, some non-classical logic are considered so also because they are syntactically different from classical logic (besides, S1-S5 are also mentioned as classical logics). I propose to reshape the list so that it has one item for family of non-classical logic. Paolo Liberatore (Talk) 16:28, 28 September 2005 (UTC)

Non-classical logics
Shouldn't Jaynes' model of probability theory as an extension of classical logic be included in the article? 62.179.244.231 02:00, 28 November 2005 (UTC)ragnar

Which non-classical logic denies commutativity of conjunction? Panu Kalliokoski

Non-classical arithmetic/algebra?
It would be useful to clarify what happens to arithmetic & algebra in the face of non-classical logics. Can one have non-classical arithmetic & algebra? Sholto Maud 11:02, 6 June 2006 (UTC)

See Heyting arithmetic for arithmetic (more broadly, algebra in the context of the natural numbers) with intuitionistic logic. &mdash;Toby Bartels 00:52, 31 July 2006 (UTC)

An explanation of how second-order and other higher-order logics depart from classical logic would be welcome. rgfuller

two-valued
The principles 1-5 are valid in any boolean algebra. So why is classical logic per se two-valued? —Preceding unsigned comment added by 84.172.47.229 (talk • contribs)
 * Because boolean algebra is two-valued. Simões ( talk/contribs ) 18:04, 28 October 2006 (UTC)
 * It's not, which you can see in boolean algebra ;) —The preceding unsigned comment was added by 89.12.23.84 (talk) 13:31, 29 March 2007 (UTC).

The situation with Boolean algebra is that it could mean either two-element Boolean algebra or any of the other Boolean algebras (note the plural). I've fixed the two-valued logic article though, so at least that is clear now. :-) Tijfo098 (talk) 11:59, 28 March 2011 (UTC)

Default logic?
Does default logic belong to classical logics? Pgr94 07:53, 16 May 2007 (UTC)
 * Nope, it's a Non-monotonic logic. Tizio 13:46, 16 May 2007 (UTC)
 * Thanks, re-reading the article it is quite clear. Pgr94 14:30, 16 May 2007 (UTC)

Truth function, truth condition, bivalance
Modal logic is currently grouped among the non-classical logics. Kripkean modal logic does, however, satisfy the five conditions from the article, and admits a bivalent, truth-conditional semantics in terms of Kripke structures.

Likewise, there is an issue in interpreting predicate logic in terms of compositional truth conditions: $$\exists x.\phi(x)$$ is true when there is some t for which $$\phi(t)$$ is true. But for the terms $$(\bar{a})$$ of the language$$\phi(a)$$ is not, in general, a subformula of $$\exists x.\phi(x)$$, so what is the truth function associated with $$\exists$$ supposed to be a truth function of? The simplicity of the T-schema for the quantifiers should not blind us to the fact that the quantifiers act on predicates, not propositions, and so are not the kind of thing that can be expressed as first-order functions on truth values.

And a last comment: the article talks of the five conditions, and of truth functions and bivalence, but does not discuss the relationship between them. And, in fact, I know of no work that relates them, though they are the kind of properties one needs for a Gödel-style completeness proof to yield a bivalent interpretation for the language.

I propose dropping talk of truth functions from the discussion of what a classical logic is in favour of truth conditions, calling (Kripkean) modal logic classical. And I'd be delighted if anyone could give more of a connection between the inferential and model-theoretic conditions for a logic to be classical; failing this we need to list the two side by side. And we need some discussion of the issues about when a many-valued logic can be considered classical or not. &mdash; Charles Stewart (talk) 09:04, 29 April 2009 (UTC)
 * Perhaps a separate section is needed for those logics that contain the classical one as a fragment in some sense. But it would need to be sourced, not written off the top of the head. Tijfo098 (talk) 11:54, 28 March 2011 (UTC)

Removed two entries
I've removed two entries added by Jagged 85. I WP:AGF that he misunderstood "classical" to mean "old" or something like that, instead of the technical way in which it is used here. Tijfo098 (talk) 11:52, 28 March 2011 (UTC)

Introductory Jargon
The introduction to the article contains a lot of jargon terminology, which is not even slightly understandable to the average reader. Please would someone with a talent for teaching and simplification re-write it in plain English ? Many thanks ! Darkman101 (talk) —Preceding undated comment added 23:03, 31 May 2013 (UTC)