Combining Texts

All the ideas for '', 'Mathematics without Foundations' and 'Wittgenstein on Rules and Private Language'

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16 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
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 / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
18. Thought / A. Modes of Thought / 10. Rule Following
No rule can be fully explained [Kripke]
'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A]
If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
19. Language / F. Communication / 4. Private Language
The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna]