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Single Idea 15422
[filed under theme 10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
]
Full Idea
Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability).
Gist of Idea
Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth)
Source
John P. Burgess (Philosophical Logic [2009], 4.3)
Book Ref
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.78
Related Idea
Idea 6879
'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner]
The
34 ideas
from John P. Burgess
15404
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Technical people see logic as any formal system that can be studied, not a study of argument validity
[Burgess]
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15403
|
Philosophical logic is a branch of logic, and is now centred in computer science
[Burgess]
|
15405
|
Classical logic neglects the non-mathematical, such as temporality or modality
[Burgess]
|
15407
|
Formalising arguments favours lots of connectives; proving things favours having very few
[Burgess]
|
15406
|
'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components
[Burgess]
|
15408
|
'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics
[Burgess]
|
15409
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All occurrences of variables in atomic formulas are free
[Burgess]
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15411
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We only need to study mathematical models, since all other models are isomorphic to these
[Burgess]
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15412
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Models leave out meaning, and just focus on truth values
[Burgess]
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15413
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With four tense operators, all complex tenses reduce to fourteen basic cases
[Burgess]
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15415
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The temporal Barcan formulas fix what exists, which seems absurd
[Burgess]
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15414
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The denotation of a definite description is flexible, rather than rigid
[Burgess]
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15416
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We aim to get the technical notion of truth in all models matching intuitive truth in all instances
[Burgess]
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15418
|
Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency
[Burgess]
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15417
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Logical necessity has two sides - validity and demonstrability - which coincide in classical logic
[Burgess]
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15419
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General consensus is S5 for logical modality of validity, and S4 for proof
[Burgess]
|
15420
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De re modality seems to apply to objects a concept intended for sentences
[Burgess]
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15421
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Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them
[Burgess]
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15422
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Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth)
[Burgess]
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15423
|
It is doubtful whether the negation of a conditional has any clear meaning
[Burgess]
|
15424
|
Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths
[Burgess]
|
15426
|
We can build one expanding sequence, instead of a chain of deductions
[Burgess]
|
15425
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The sequent calculus makes it possible to have proof without transitivity of entailment
[Burgess]
|
15427
|
The Cut Rule expresses the classical idea that entailment is transitive
[Burgess]
|
15428
|
The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut'
[Burgess]
|
15429
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Relevance logic's → is perhaps expressible by 'if A, then B, for that reason'
[Burgess]
|
15430
|
Is classical logic a part of intuitionist logic, or vice versa?
[Burgess]
|
15431
|
It is still unsettled whether standard intuitionist logic is complete
[Burgess]
|
10186
|
If set theory is used to define 'structure', we can't define set theory structurally
[Burgess]
|
10187
|
Abstract algebra concerns relations between models, not common features of all the models
[Burgess]
|
10185
|
Set theory is the standard background for modern mathematics
[Burgess]
|
10184
|
Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure
[Burgess]
|
10189
|
There is no one relation for the real number 2, as relations differ in different models
[Burgess]
|
10188
|
How can mathematical relations be either internal, or external, or intrinsic?
[Burgess]
|