Combining Texts

All the ideas for 'Realism in Mathematics', 'The Emergence of Probability' and 'Intensions Revisited'

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18 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
Gassendi is the first great empiricist philosopher [Hacking]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Quantified modal logic collapses if essence is withdrawn [Quine]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essences can make sense in a particular context or enquiry, as the most basic predicates [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
Necessity is relative to context; it is what is assumed in an inquiry [Quine]
10. Modality / B. Possibility / 6. Probability
Probability was fully explained between 1654 and 1812 [Hacking]
Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking]
Epistemological probability based either on logical implications or coherent judgments [Hacking]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds are a way to dramatise essentialism, and yet they presuppose essentialism [Quine]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
A rigid designator (for all possible worlds) picks out an object by its essential traits [Quine]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Beliefs can be ascribed to machines [Quine]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
In the medieval view, only deduction counted as true evidence [Hacking]
Formerly evidence came from people; the new idea was that things provided evidence [Hacking]
14. Science / A. Basis of Science / 3. Experiment
An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking]