Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Morality and the emotions' and 'The Laws of Thought'

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13 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
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 / H. Proof Systems / 2. Axiomatic Proof
Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
Reference to a person's emotions is often essential to understanding their actions [Williams,B]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Moral education must involve learning about various types of feeling towards things [Williams,B]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
Emotivism saw morality as expressing emotions, and influencing others' emotions [Williams,B]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
An admirable human being should have certain kinds of emotional responses [Williams,B]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B]