Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'Maths as a Science of Patterns' and 'Interview with Baggini and Stangroom'

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


15 ideas

1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Formal logic struck me as exactly the language I wanted to think in [Williamson]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
There are too many mathematical objects for them all to be mental or physical [Resnik]
Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson]
12. Knowledge Sources / B. Perception / 1. Perception
How can one discriminate yellow from red, but not the colours in between? [Williamson]