Combining Texts

All the ideas for 'Mind and Its Place in Nature', 'Conditionals' and 'Constructibility and Mathematical Existence'

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14 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
We could talk of open sentences, instead of sets [Chihara, by Shapiro]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
'¬', '&', and 'v' are truth functions: the truth of the compound is fixed by the truth of the components [Jackson]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
Possible worlds for subjunctives (and dispositions), and no-truth for indicatives? [Jackson]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Modus ponens requires that A→B is F when A is T and B is F [Jackson]
When A and B have the same truth value, A→B is true, because A→A is a logical truth [Jackson]
(A&B)→A is a logical truth, even if antecedent false and consequent true, so it is T if A is F and B is T [Jackson]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
In the possible worlds account of conditionals, modus ponens and modus tollens are validated [Jackson]
Only assertions have truth-values, and conditionals are not proper assertions [Jackson]
Possible worlds account, unlike A⊃B, says nothing about when A is false [Jackson]
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
We can't insist that A is relevant to B, as conditionals can express lack of relevance [Jackson]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
Broad rejects the inferential component of the representative theory [Broad, by Maund]