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All the ideas for 'fragments/reports', 'Anti-Semite and Jew' and 'Philosophy of Mathematics'

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7 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
541 Virtue comes more from habit than character [Critias]
     Full Idea: More men are good through habit than through character.
     From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41
23. Ethics / F. Existentialism / 6. Authentic Self
22232 Authenticity is taking responsibility for a situation, with all its risks and emotions [Sartre]
     Full Idea: Authenticity consists in having a true and lucid consciousness of the situation, in assuming the responsibilities and risks that it involves, in accepting it in pride of humiliation, sometimes in horror and hate.
     From: Jean-Paul Sartre (Anti-Semite and Jew [1946], p.90), quoted by Christine Daigle - Jean-Paul Sartre 2.4
     A reaction: [Not sure what 'pride of humiliation' is, so it may be a typo for 'or']
28. God / C. Attitudes to God / 5. Atheism
542 Fear of the gods was invented to discourage secret sin [Critias]
     Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret.
     From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54