It seems Rosen would be concerned with incomplete mapping for categories of things in relation to categories of reason. Take the ideal condition: assume that nature is completely consistent with her categories and people are perfectly self-consistent in using theirs, will it then be possible to arrange a correspondence between the two?
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Nicholas Thompson Sent: Saturday, August 09, 2008 10:58 PM To: [email protected] Subject: [FRIAM] Rosen, and mapping Roseners, and anybody else vaguely interested in category theory. Rosen seems to be interested in situations in which A maps to B but not all the values in B can be generated by the mapping. this is a lot like the Intension and the Extension of an utterance. I say with assurance that Mrs. Vanderbilt wished to sail on the Titanic. In this case, Mrs Vanderbilt's "wanting" is a function (mathematical sense) that maps from her wants to a subset of the properties of the Titanic. All the properties of the Titanic constitute (in philosophic lingo ) it's extension. The subset, the "image" of Mrs Vanderbilt's wanting , constitutes the intension of her utterance, "I want to sail on the Titanic." Among the titanic's attributes, but outside that image, is the property "hit an iceberg in the North Atlantic and sank." I guess the question is whether there is a less tortured mathematics than category theory that would allow one to talk about these things. N Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([EMAIL PROTECTED])
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