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Single Idea 7800
[filed under theme 10. Modality / A. Necessity / 3. Types of Necessity
]
Full Idea
It has been customary to see analytic truths as dividing into the logically necessary and the conceptually necessary.
Gist of Idea
Analytic truths are divided into logically and conceptually necessary
Source
Rod Girle (Modal Logics and Philosophy [2000], 7.3)
Book Ref
Girle,Rod: 'Modal Logics and Philosophy' [Acumen 2000], p.114
A Reaction
I suspect that this neglected distinction is important in discussions of Quine's elimination of the analytic/synthetic distinction. Was Quine too influenced by what is logically necessary, which might shift with a change of axioms?
The
15 ideas
from Rod Girle
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7786
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Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations
[Girle]
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7787
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Possible worlds logics use true-in-a-world rather than true
[Girle]
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7788
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Modal logic has four basic modal negation equivalences
[Girle]
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7789
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Necessary implication is called 'strict implication'; if successful, it is called 'entailment'
[Girle]
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7790
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If an argument is invalid, a truth tree will indicate a counter-example
[Girle]
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7792
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A world has 'access' to a world it generates, which is important in possible worlds semantics
[Girle]
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7793
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◊p → □◊p is the hallmark of S5
[Girle]
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7795
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S5 has just six modalities, and all strings can be reduced to those
[Girle]
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7794
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There are seven modalities in S4, each with its negation
[Girle]
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7796
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Modal logics were studied in terms of axioms, but now possible worlds semantics is added
[Girle]
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7798
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There are three axiom schemas for propositional logic
[Girle]
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7799
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Proposition logic has definitions for its three operators: or, and, and identical
[Girle]
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7797
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Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems
[Girle]
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7800
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Analytic truths are divided into logically and conceptually necessary
[Girle]
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7801
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Possibilities can be logical, theoretical, physical, economic or human
[Girle]
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