Combining Texts

All the ideas for 'fragments/reports', 'Remarks on axiomatised set theory' and 'Il Saggiatore ('The Assayer')'

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10 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879

Axiomatising set theory makes it all relative [Skolem]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880

Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881

Mathematician want performable operations, not propositions about objects [Skolem]

12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities

7401	Heat and colour don't exist, so cannot mislead about the external world [Galileo, by Tuck]

5454	Tastes, odours and colours only reside in consciousness, and would disappear with creatures [Galileo]

14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism

16560

Galileo introduced geometrico-mechanical explanation, based on Archimedes [Galileo, by Machamer/Darden/Craver]

25. Social Practice / E. Policies / 5. Education / b. Education principles

13304

Learned men gain more in one day than others do in a lifetime [Posidonius]

26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature

3645	To understand the universe mathematics is essential [Galileo]

27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure

20820

Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]