Combining Texts

All the ideas for '', 'Five Milestones of Empiricism' and 'Constructibility and Mathematical Existence'

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13 ideas

2. Reason / D. Definition / 7. Contextual Definition
Contextual definition shifted the emphasis from words to whole sentences [Quine]
Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine]
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 / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
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]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine]
Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Holism in language blurs empirical synthetic and empty analytic sentences [Quine]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]