Combining Texts

All the ideas for 'Reply to Fourth Objections', 'Our Knowledge of Mathematical Objects' and 'Predest.,God's foreknowledge and contingents'

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5 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
9224 Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
     Full Idea: My Proceduralism offers axiom-free foundations for mathematics. Axioms give way to the stipulation of procedures. We obtain a form of logicism, but with a procedural twist, and with a logic which is ontologically neutral, and no assumption of objects.
     From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
     A reaction: [See Ideas 9222 and 9223 for his Proceduralism] Sounds like philosophical heaven. We get to take charge of mathematics, without the embarrassment of declaring ourselves to be platonists. Someone, not me, should evaluate this.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
9222 The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
     Full Idea: I call my new approach to mathematics 'proceduralism'. It agrees with Hilbert and Poincaré that the objects and truths are postulations, but takes them to be imperatival rather than indicative in form; not propositions, but procedures for construction.
     From: Kit Fine (Our Knowledge of Mathematical Objects [2005], Intro)
     A reaction: I'm not sure how an object or a truth can be a procedure, any more than a house can be a procedure. If a procedure doesn't have a product then it is an idle way to pass the time. The view seems to be related to fictionalism.
9223 My Proceduralism has one simple rule, and four complex rules [Fine,K]
     Full Idea: My Proceduralism has one simple rule (introduce an object), and four complex rules: Composition (combining two procedures), Conditionality (if A, do B), Universality (do a procedure for every x), and Iteration (rule to keep doing B).
     From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
     A reaction: It sounds like a highly artificial and private game which Fine has invented, but he claims that this is the sort of thing that practising mathematicians have always done.
7. Existence / E. Categories / 5. Category Anti-Realism
16654 Our words and concepts don't always correspond to what is out there [William of Ockham]
     Full Idea: It should not be said that as distinct words and intentions or concepts are distinct from one another, so too the corresponding things are distinct. Those distinctions do not always line up with distinctions among things that are signified.
     From: William of Ockham (Predest.,God's foreknowledge and contingents [1320], 7.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.2
     A reaction: [compressed] This is the great nominalist opponent of the idea that Aristotle's ten categories give an accurate map of reality. He proposed just substance and accidents, and based categorisation on the questions we ask.
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
3643 The concept of mind excludes body, and vice versa [Descartes]
     Full Idea: The concept of body includes nothing at all which belongs to the mind, and the concept of mind includes nothing at all which belongs to the body.
     From: René Descartes (Reply to Fourth Objections [1641], 225)
     A reaction: A headache? Hunger? The mistake, I think, is to regard the mind as entirely conscious, thus creating a sharp boundary between two aspects of our lives. As shown by blindsight, I take many of my central mental operations to be pre- or non-conscious.