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All the ideas for 'Symposium', 'Behaviorism' and 'Philosophy of Mathematics'

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6 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)
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
7517 I could take a healthy infant and train it up to be any type of specialist I choose [Watson,JB]
     Full Idea: Give me a dozen healthy infants, and my own specified world to bring them up in, and I'll guarantee to take any one at random and train him to become any type of specialist I might select - doctor, artist, beggar, thief - regardless of his ancestry.
     From: J.B. Watson (Behaviorism [1924], Ch.2), quoted by Steven Pinker - The Blank Slate
     A reaction: This was a famous pronouncement rejecting the concept of human nature as in any way fixed - a total assertion of nurture over nature. Modern research seems to be suggesting that Watson is (alas?) wrong.
22. Metaethics / B. Value / 2. Values / h. Fine deeds
5845 Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
     Full Idea: Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'.
     From: Xenophon (Symposium [c.391 BCE], 3.5)
     A reaction: This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue