Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Merely Possible Propositions' and 'Our Knowledge of Mathematical Objects'

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6 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.

9. Objects / A. Existence of Objects / 4. Impossible objects

14617	Predicates can't apply to what doesn't exist [Stalnaker]
	Full Idea: Nothing can be predicated of something which does not exist.
	From: Robert C. Stalnaker (Merely Possible Propositions [2010], p.28)
	A reaction: [He says he is 'agreeing with Plantinga' on this] This seems very puzzling, as you can obviously say that dragons do not exist, but they breathe fire. Why can't you attach predicates to hypothetical objects?

19. Language / D. Propositions / 3. Concrete Propositions

14616	A 'Russellian proposition' is an ordered sequence of individual, properties and relations [Stalnaker]
	Full Idea: A 'Russellian proposition' is an ordered sequence containing the individual, along with properties and relations.
	From: Robert C. Stalnaker (Merely Possible Propositions [2010], p.22)
	A reaction: Since Russell took properties and relations to be features of reality, this made the whole proposition a feature of reality. This is utterly different from what I understand by the word 'proposition', which is a feature of thought, not of the world.

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').