more on this theme
|
more from this text
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
31 ideas
from JC Beall / G Restall
10688
|
'Equivocation' is when terms do not mean the same thing in premises and conclusion
[Beall/Restall]
|
10690
|
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought
[Beall/Restall]
|
10695
|
Logical consequence is either necessary truth preservation, or preservation based on interpretation
[Beall/Restall]
|
10689
|
A step is a 'material consequence' if we need contents as well as form
[Beall/Restall]
|
10691
|
Logical consequence needs either proofs, or absence of counterexamples
[Beall/Restall]
|
10693
|
Models are mathematical structures which interpret the non-logical primitives
[Beall/Restall]
|
10692
|
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite
[Beall/Restall]
|
10696
|
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
[Beall/Restall]
|
13233
|
Propositions commit to content, and not to any way of spelling it out
[Beall/Restall]
|
13232
|
Logic studies arguments, not formal languages; this involves interpretations
[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The view of logic as knowing a body of truths looks out-of-date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]
|
13239
|
Judgement is always predicating a property of a subject
[Beall/Restall]
|
13238
|
Syllogisms are only logic when they use variables, and not concrete terms
[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]
|