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Single Idea 13233
[filed under theme 19. Language / D. Propositions / 1. Propositions
]
Full Idea
Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out.
Gist of Idea
Propositions commit to content, and not to any way of spelling it out
Source
JC Beall / G Restall (Logical Pluralism [2006], 2.1)
Book Ref
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.12
A Reaction
As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I.
The
31 ideas
from JC Beall / G Restall
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10688
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'Equivocation' is when terms do not mean the same thing in premises and conclusion
[Beall/Restall]
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10690
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Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought
[Beall/Restall]
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10695
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Logical consequence is either necessary truth preservation, or preservation based on interpretation
[Beall/Restall]
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10689
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A step is a 'material consequence' if we need contents as well as form
[Beall/Restall]
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10691
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Logical consequence needs either proofs, or absence of counterexamples
[Beall/Restall]
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10693
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Models are mathematical structures which interpret the non-logical primitives
[Beall/Restall]
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10692
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Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite
[Beall/Restall]
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10696
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A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
[Beall/Restall]
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13233
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Propositions commit to content, and not to any way of spelling it out
[Beall/Restall]
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13232
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Logic studies arguments, not formal languages; this involves interpretations
[Beall/Restall]
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13235
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Logic studies consequence; logical truths are consequences of everything, or nothing
[Beall/Restall]
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13234
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The view of logic as knowing a body of truths looks out-of-date
[Beall/Restall]
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13236
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Logical truth is much more important if mathematics rests on it, as logicism claims
[Beall/Restall]
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13237
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Preface Paradox affirms and denies the conjunction of propositions in the book
[Beall/Restall]
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13239
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Judgement is always predicating a property of a subject
[Beall/Restall]
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13238
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Syllogisms are only logic when they use variables, and not concrete terms
[Beall/Restall]
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13240
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A sentence follows from others if they always model it
[Beall/Restall]
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13241
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The model theory of classical predicate logic is mathematics
[Beall/Restall]
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13243
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Excluded middle must be true for some situation, not for all situations
[Beall/Restall]
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13242
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It's 'relevantly' valid if all those situations make it true
[Beall/Restall]
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13244
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Relevant necessity is always true for some situation (not all situations)
[Beall/Restall]
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13245
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Relevant consequence says invalidity is the conclusion not being 'in' the premises
[Beall/Restall]
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13246
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Relevant logic does not abandon classical logic
[Beall/Restall]
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13247
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A truthmaker is an object which entails a sentence
[Beall/Restall]
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13248
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We can rest truth-conditions on situations, rather than on possible worlds
[Beall/Restall]
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13249
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(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically
[Beall/Restall]
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13250
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Free logic terms aren't existential; classical is non-empty, with referring names
[Beall/Restall]
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13252
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Some truths have true negations
[Beall/Restall]
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13254
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A doesn't imply A - that would be circular
[Beall/Restall]
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13255
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Relevant logic may reject transitivity
[Beall/Restall]
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13253
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There are several different consequence relations
[Beall/Restall]
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