Combining Texts

All the ideas for 'Wiener Logik', 'The Laws of Thought' and 'Abstract Objects: a Case Study'

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11 ideas

2. Reason / D. Definition / 2. Aims of Definition
A simplification which is complete constitutes a definition [Kant]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives us the necessary rules which show us how we ought to think [Kant]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
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
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If we knew what we know, we would be astonished [Kant]