Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'Constructibility and Mathematical Existence' and 'Rules for the Direction of the Mind'

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9 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
8758 We could talk of open sentences, instead of sets [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10265 Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
8759 We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10580 Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
10579 Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
10264 Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
10577 Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
10578 We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9807 In pursuing truth, anything less certain than mathematics is a waste of time [Descartes]