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9224
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Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
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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.
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From:
Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
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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.
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9223
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My Proceduralism has one simple rule, and four complex rules [Fine,K]
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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).
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From:
Kit Fine (Our Knowledge of Mathematical Objects [2005], 1)
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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.
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23669
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Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid]
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Full Idea:
Those philosophers who attribute to matter the power of gravitation, and other active powers, teach us, at the same time, that matter is a substance altogether inert, and merely passive; …that those powers are impressed on it by some external cause.
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From:
Thomas Reid (Essays on Active Powers 1: Active power [1788], 6)
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A reaction:
This shows the dilemma of the period, when 'laws of nature' were imposed on passive matter by God, and yet gravity and magnetism appeared as inherent properties of matter.
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23666
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It is obvious that there could not be a power without a subject which possesses it [Reid]
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Full Idea:
It is evident that a power is a quality, and cannot exist without a subject to which it belongs. That power may exist without any being or subject to which that power may be attributed, is an absurdity, shocking to every man of common understanding.
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From:
Thomas Reid (Essays on Active Powers 1: Active power [1788], 1)
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A reaction:
This is understandble in the 18th C, when free-floating powers were inconceivable, but now that we have fields and plasmas and whatnot, we can't rule out pure powers as basic. However, I incline to agree with Reid. Matter is active.
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14080
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Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]
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Full Idea:
Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does.
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From:
report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1
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A reaction:
[Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox.
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8383
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Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane]
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Full Idea:
A famous example of Thomas Reid: day regularly follows night, and night regularly follows day. There is therefore a constant conjunction between night and day. But day does not cause night, nor does night cause day.
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From:
report of Thomas Reid (Essays on Active Powers 1: Active power [1788]) by Tim Crane - Causation 1.2.2
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A reaction:
Not a fatal objection to Hume, of course, because in the complex real world there are huge numbers of nested constant conjunctions. Night and the rotation of the Earth are conjoined. But how do you tell which constant conjunctions are causal?
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23667
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Regular events don't imply a cause, without an innate conviction of universal causation [Reid]
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Full Idea:
A train of events following one another ever so regularly, could never lead us to the notion of a cause, if we had not, from our constitution, a conviction of the necessity of a cause for every event.
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From:
Thomas Reid (Essays on Active Powers 1: Active power [1788], 5)
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A reaction:
Presumably a theist like Reid must assume that the actions of God are freely chosen, rather than necessities. It's hard to see why this principle should be innate in us, and hard to see why it must thereby be true. A bit Kantian, this idea.
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23670
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Scientists don't know the cause of magnetism, and only discover its regulations [Reid]
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Full Idea:
A Newtonian philosopher …confesses his ignorance of the true cause of magnetic motion, and thinks that his business, as a philosopher, is only to find from experiment the laws by which it is regulated in all cases.
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From:
Thomas Reid (Essays on Active Powers 1: Active power [1788], 6)
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A reaction:
Since there is a 'true cause', that implies that the laws don't actively 'regulate' the magnetism, but only describe its regularity, which I think is the correct view of laws.
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