Combining Texts

All the ideas for 'The Value of Science', '10: Ephesians' and 'Philosophy of Mathematics'

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6 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
23766 Don't be tossed to and fro with every wind of doctrine, by cunning deceptive men [Paul]
     Full Idea: Henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive.
     From: St Paul (10: Ephesians [c.55], 4:14)
     A reaction: One quoted to me by a learned religious friend, in response to Idea 23767. I sympathise. I find it extraordinary the nonsense that students of philosophy can be led into, when they swallow some specious argument.
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)
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
15877 The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
     Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
     From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
     A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.