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Single Idea 13236

[filed under theme 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth ]

Full Idea

If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting.

Gist of Idea

Logical truth is much more important if mathematics rests on it, as logicism claims

Source

JC Beall / G Restall (Logical Pluralism [2006], 2.2)

Book Ref

Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.13

A Reaction

Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic.

The 23 ideas from 'Logical Pluralism'

13232 Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]
13233 Propositions commit to content, and not to any way of spelling it out [Beall/Restall]
13235 Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
13234 The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
13236 Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]
13237 Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall]
13238 Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
13239 Judgement is always predicating a property of a subject [Beall/Restall]
13240 A sentence follows from others if they always model it [Beall/Restall]
13241 The model theory of classical predicate logic is mathematics [Beall/Restall]
13243 Excluded middle must be true for some situation, not for all situations [Beall/Restall]
13242 It's 'relevantly' valid if all those situations make it true [Beall/Restall]
13244 Relevant necessity is always true for some situation (not all situations) [Beall/Restall]
13245 Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall]
13246 Relevant logic does not abandon classical logic [Beall/Restall]
13247 A truthmaker is an object which entails a sentence [Beall/Restall]
13248 We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall]
13249 (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall]
13250 Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall]
13252 Some truths have true negations [Beall/Restall]
13254 A doesn't imply A - that would be circular [Beall/Restall]
13255 Relevant logic may reject transitivity [Beall/Restall]
13253 There are several different consequence relations [Beall/Restall]