Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'Predest.,God's foreknowledge and contingents' and 'Gentzen's Analysis of First-Order Proofs'

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

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8 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

13831

Logic is based on transitions between sentences [Prawitz]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

13825

Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

13823

In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]

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]

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]

7. Existence / E. Categories / 5. Category Anti-Realism

16654

Our words and concepts don't always correspond to what is out there [William of Ockham]