Combining Texts

All the ideas for 'works', 'Models and Reality' and 'fragments/reports'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13655 The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]
     Full Idea: Putnam claims that the Löwenheim-Skolem theorems indicate that there is no 'fact of the matter' whether all sets are constructible.
     From: report of Hilary Putnam (Models and Reality [1977]) by Stewart Shapiro - Foundations without Foundationalism
     A reaction: [He refers to the 4th and 5th pages of Putnam's article] Shapiro offers (p.109) a critique of Putnam's proposal.
9915 V = L just says all sets are constructible [Putnam]
     Full Idea: V = L just says all sets are constructible. L is the class of all constructible sets, and V is the universe of all sets.
     From: Hilary Putnam (Models and Reality [1977], p.425)
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
9913 The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam]
     Full Idea: The Löwenheim-Skolem Theorem says that a satisfiable first-order theory (in a countable language) has a countable model. ..I argue that this is not a logical antinomy, but close to one in philosophy of language.
     From: Hilary Putnam (Models and Reality [1977], p.421)
     A reaction: See the rest of this paper for where he takes us on this.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9914 It is unfashionable, but most mathematical intuitions come from nature [Putnam]
     Full Idea: Experience with nature is undoubtedly the source of our most basic 'mathematical intuitions', even if it is unfashionable to say so.
     From: Hilary Putnam (Models and Reality [1977], p.424)
     A reaction: Correct. I find it quite bewildering how Frege has managed to so discredit all empirical and psychological approaches to mathematics that it has become a heresy to say such things.
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
22511 Some reasonings are stronger than we are [Philolaus]
     Full Idea: Some reasonings are stronger than we are.
     From: Philolaus (fragments/reports [c.425 BCE]), quoted by Aristotle - Eudemian Ethics 1225a33
     A reaction: This endorses the Aristotle view of akrasia (as opposed to the Socratic view). This isolated remark seems to imply that we are more clearly embodiments of will than of reason.
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
     Full Idea: Philosophers are the forefathers of heretics.
     From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]
     Full Idea: I believe because it is absurd ('Credo quia absurdum est').
     From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
     A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.