Descartes and Infinate Sets

Descartes makes statements in the Meditations on First Philosophy with respect to the 5 senses being valid proof that something truly exists, as the basis of scientific method.

During this process, he outlines an experiment with wax. At the beginning of the experiment, the hunk of wax is identifiable by all 5 senses: it has a certain shape and colour, faintly smells of honey, tastes sweet, makes a certain sound when rapped, has a certain texture when touched. The lump of wax is placed near the fire, and melts. Subsequently, all 5 attributes have changed: the sweet taste and smell have boiled away, the was is no longer hard, making only a gloopy sound when hit, and feels much more pliable, and certainly appears in a different shape. Dispite these changes, we understand it to still be the same lump of wax. This is because of understanding that wax has certain properties; it is flexible, infinately transmutable, and extended in space.

To know wax, one makes the leap of cognition from a finite set of examples of wax, to understanding the function used to generate an infinate set of wax-objects. The same applies to any field, be it class definitions or real numbers. This is not entirely dissimilar to Plato’s declaration that one does not know physical objects, but only the unchanging Forms or mathematical objects birthed therin.

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Published:: 10.19.05 / 12pm

Category:: Uncategorized

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Alan J Castonguay is from Ontario, Canada. Interested in philosophy, animation, serial art, and mixing bleeding-edge technology with doing things the old fashioned way. Works in tech support, but dreams of going back to the theatre.

A resume is available for your perusal, should you be interested in bribing me to do work.

_quinn at livejournal.com 10.20.05 / 12am

[Revenge-of: the Language-Oriented]It’s “infinite” and “therein.”[/Revenge-of]

Spelling, words, and sentences form an interesting case to consider in these terms. What is a word? It is not any of its representations, however mis-spelled or mis-pronounced. Is a word a pure Platonic concept, and its forms generated by an understanding of its “rule”? Most characterize words as symbols, but symbols don’t have any particular “rule” relating concept to expression. The mappings are arbitrary, although (mostly) codified as languages — which leads us to sentences. Is the (effective) infinitude of (sensible) sentences compelling evidence of a generator in the abstract rule sense you postulate above?

To know “wax” is an interesting question, actually: do you know a “true” abstraction of wax, or some set of “truly” disconnected things connected by the word? It seems odd to answer this by appealing to reductionism: a division of waxes into their constituent parts will reveal certain commonalities, and the sets of things you know as wax are the entailed consequences of those commonalities, and (to some extent) the enviroment. It seems odd, both as kind of philosophical reversal, and in the case of conceptual knowing, like the (common-English) concept of a group. Or is that those things which are reduced to find their abstraction are physical things, and those which are … simplified? there’s a sense of leaving detail behind, instead of exploring it — are nonphysical things?

Also, it would be nifty to be able to quote Descartes whilst discussing such as this. *Sigh.*

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Descartes and Infinate Sets

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