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Single Idea 13250
[filed under theme 4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
]
Full Idea
A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain.
Gist of Idea
Free logic terms aren't existential; classical is non-empty, with referring names
Source
JC Beall / G Restall (Logical Pluralism [2006], 7.1)
Book Ref
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.75
A Reaction
My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse.
The
23 ideas
from 'Logical Pluralism'
13232
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Logic studies arguments, not formal languages; this involves interpretations
[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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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The view of logic as knowing a body of truths looks out-of-date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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13238
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Syllogisms are only logic when they use variables, and not concrete terms
[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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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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