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All the ideas for 'Mathematics without Numbers', 'Scientific Attitude and Fallibilism' and 'works'

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17 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
10153 In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19141 Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10048 There is no clear boundary between the logical and the non-logical [Tarski]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10694 Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
10479 Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
14775 Numbers are just names devised for counting [Peirce]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10157 Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8698 Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
9557 Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
10263 Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
14776 That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
14770 Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
14774 Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce]
12. Knowledge Sources / E. Direct Knowledge / 3. Inspiration
14773 A truth is hard for us to understand if it rests on nothing but inspiration [Peirce]
14772 If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce]
14771 Only reason can establish whether some deliverance of revelation really is inspired [Peirce]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
14769 Only imagination can connect phenomena together in a rational way [Peirce]