Combining Texts

All the ideas for 'Mechanisms', 'Remarks on the Foundations of Mathematics' and 'The Art of the Infinite'

expand these ideas     |    start again     |     specify just one area for these texts


15 ideas

3. Truth / H. Deflationary Truth / 1. Redundant Truth
'It is true that this follows' means simply: this follows [Wittgenstein]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Two and one making three has the necessity of logical inference [Wittgenstein]
14. Science / B. Scientific Theories / 2. Aim of Science
Empiricist theories are sets of laws, which give explanations and reductions [Glennan]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Modern mechanism need parts with spatial, temporal and function facts, and diagrams [Glennan]
Mechanistic philosophy of science is an alternative to the empiricist law-based tradition [Glennan]
Mechanisms are either systems of parts or sequences of activities [Glennan]
17th century mechanists explained everything by the kinetic physical fundamentals [Glennan]
Unlike the lawlike approach, mechanistic explanation can allow for exceptions [Glennan]
26. Natural Theory / C. Causation / 4. Naturalised causation
Since causal events are related by mechanisms, causation can be analysed in that way [Glennan]