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.
|
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.
|
19729
|
'Modal epistemology' demands a connection between the belief and facts in possible worlds [Black,T]
|
|
Full Idea:
In 'modal epistemologies' a belief counts as knowledge only if there is a modal connection - a connection not only to the actual world, but also to other non-actual possible worlds - between the belief and the facts of the matter.
|
|
From:
Tim Black (Modal and Anti-Luck Epistemology [2011], 1)
|
|
A reaction:
[Pritchard 2005 seems to be a source for this] This sounds to me a bit like Nozick's tracking or sensitivity theory. Nozick is, I suppose, diachronic (time must pass, for the tracking), where this theory is synchronic.
|