10 ideas
| 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. |
| 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. |
| 10938 | The extremes of essentialism are that all properties are essential, or only very trivial ones [Rami] |
| Full Idea: It would be natural to label one extreme view 'maximal essentialism' - that all of an object's properties are essential - and the other extreme 'minimal' - that only trivial properties such as self-identity of being either F or not-F are essential. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008]) | |
| A reaction: Personally I don't accept the trivial ones as being in any way describable as 'properties'. The maximal view destroys any useful notion of essence. Leibniz is a minority holder of the maximal view. I would defend a middle way. |
| 10940 | An 'individual essence' is possessed uniquely by a particular object [Rami] |
| Full Idea: An 'individual essence' is a property that in addition to being essential is also unique to the object, in the sense that it is not possible that something distinct from that object possesses that property. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §5) | |
| A reaction: She cites a 'haecceity' (or mere bare identity) as a trivial example of an individual essence. |
| 10939 | 'Sortal essentialism' says being a particular kind is what is essential [Rami] |
| Full Idea: According to 'sortal essentialism', an object could not have been of a radically different kind than it in fact is. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §4) | |
| A reaction: This strikes me as thoroughly wrong. Things belong in kinds because of their properties. Could you remove all the contingent features of a tiger, leaving it as merely 'a tiger', despite being totally unrecognisable? |
| 10934 | Unlosable properties are not the same as essential properties [Rami] |
| Full Idea: It is easy to confuse the notion of an essential property that a thing could not lack, with a property it could not lose. My having spent Christmas 2007 in Tennessee is a non-essential property I could not lose. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §1) | |
| A reaction: The idea that having spent Christmas in Tennessee is a property I find quite bewildering. Is my not having spent my Christmas in Tennessee one of my properties? I suspect that real unlosable properties are essential ones. |
| 10933 | Physical possibility is part of metaphysical possibility which is part of logical possibility [Rami] |
| Full Idea: The usual view is that 'physical possibilities' are a natural subset of the 'metaphysical possibilities', which in turn are a subset of the 'logical possibilities'. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §1) | |
| A reaction: [She cites Fine 2002 for an opposing view] I prefer 'natural' to 'physical', leaving it open where the borders of the natural lie. I take 'metaphysical' possibility to be 'in all naturally possible worlds'. So is a round square a logical possibility? |
| 10932 | If it is possible 'for all I know' then it is 'epistemically possible' [Rami] |
| Full Idea: There is 'epistemic possibility' when it is 'for all I know'. That is, P is epistemically possible for agent A just in case P is consistent with what A knows. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §1) | |
| A reaction: Two problems: maybe 'we' know, and A knows we know, but A doesn't know. And maybe someone knows, but we are not sure about that, which seems to introduce a modal element into the knowing. If someone knows it's impossible, it's impossible. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |