Combining Texts

All the ideas for 'fragments/reports', 'Mathematics without Foundations' and 'Proper Names'

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13 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 / F. Referring in Logic / 1. Naming / b. Names as descriptive
We don't normally think of names as having senses (e.g. we don't give definitions of them) [Searle]
How can a proper name be correlated with its object if it hasn't got a sense? [Searle]
'Aristotle' means more than just 'an object that was christened "Aristotle"' [Searle]
Reference for proper names presupposes a set of uniquely referring descriptions [Searle]
Proper names are logically connected with their characteristics, in a loose way [Searle]
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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]