Combining Texts

All the ideas for 'Conditionals', 'Method and Results' and 'Our Knowledge of Mathematical Objects'

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9 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.

10. Modality / B. Possibility / 8. Conditionals / a. Conditionals

13768	Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
	Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required.
	From: Dorothy Edgington (Conditionals [2001], 17.2.1)

10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional

13770	There are many different conditional mental states, and different conditional speech acts [Edgington]
	Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc.
	From: Dorothy Edgington (Conditionals [2001], 17.3.4)

10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals

13764	Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
	Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'?
	From: Dorothy Edgington (Conditionals [2001], 17.1)
	A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional.

13765	'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
	Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B).
	From: Dorothy Edgington (Conditionals [2001], 17.1)
	A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true.

17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism

3157	T.H.Huxley gave the earliest clear statement of epiphenomenalism [Huxley, by Rey]
	Full Idea: T.H.Huxley gave the earliest clear statement of epiphenomenalism.
	From: report of T.H. Huxley (Method and Results [1893]) by Georges Rey - Contemporary Philosophy of Mind 3.1.1
	A reaction: This is, of course, impossible, because there can't be a clear statement of epiphenomenalism.

3154	Brain causes mind, but it doesn't seem that mind causes actions [Huxley]
	Full Idea: All states of consciousness are caused by molecular changes of brain substance. It seems to me there is no proof that any state of consciousness is the cause of change in the motion of the matter of the organism.
	From: T.H. Huxley (Method and Results [1893], p.244), quoted by Georges Rey - Contemporary Philosophy of Mind 3.1.1
	A reaction: This sounds odd. Most people would say there is nothing more obvious than mental events causing actions. It certainly seems undeniable that actions are cause by the contents of thoughts, so a molecular account of intentional states is needed.