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In Peirce's paper New List why is possible to prescind (i.e. abstract) space from color but not color from space?

Peirce mentions three types of abstraction, the relevant one being called Prescission (var. precision, precisive abstraction, precission). I believe Peirce explains everything in §5, but I need more of an eli5 explanation as I am too dumb to really understand it deeply. Here is §5:

§ 5. The terms “prescision” and “abstraction,” which were formerly applied to every kind of separation, are now limited, not merely to mental separation, but to that which arises from attention to one element and neglect of the other. Exclusive attention consists in a definite conception or supposition of one part of an object, without any supposition of the other. Abstraction or prescision ought to be carefully distinguished from two other modes of mental separation, which may be termed discrimination and dissociation. Discrimination has to do merely with the senses of terms, and only draws a distinction in meaning. Dissociation is that separation which, in the absence of a constant association, is permitted by the law of association of images. It is the consciousness of one thing, without the necessary simultaneous consciousness of the other. Abstraction or prescision, therefore, supposes a greater separation than discrimination, but a less separation than dissociation. Thus I can discriminate red from blue, space from color, and color from space, but not red from color. I can prescind red from blue, and space from color (as is manifest from the fact that I actually believe there is an uncolored space between my face and the wall); but I cannot prescind color from space, nor red from color. I can dissociate red from blue, but not space from color, color from space, nor red from color.

Prescision is not a reciprocal process. It is frequently the case, that, while A cannot be prescinded from B, B can be prescinded from A. This circumstance is accounted for as follows. Elementary conceptions only arise upon the occasion of experience; that is, they are produced for the first time according to a general law, the condition of which is the existence of certain impressions. Now if a conception does not reduce the impressions upon which it follows to unity, it is a mere arbitrary addition to these latter; and elementary conceptions do not arise thus arbitrarily. But if the impressions could be definitely comprehended without the conception, this latter would not reduce them to unity. Hence, the impressions (or more immediate conceptions) cannot be definitely conceived or attended to, to the neglect of an elementary conception which reduces them to unity. On the other hand, when such a conception has once been obtained, there is, in general, no reason why the premisses which have occasioned it should not be neglected, and therefore the explaining conception may frequently be prescinded from the more immediate ones and from the impressions.

Here is a hyperlink: (On a New List of Categories).

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    Colour is extensive and hence presupposes space and hence we can abstract space from colour. But space does not presuppose colour. A blind man cannot not see colour but can move around and feel space. Thus colour cannot be abstracted from space. Oct 2 at 0:20
  • not sure why he defines them as a new list. Dealt with ad nausem by Hindu and Buddhist philosophers. Oct 2 at 6:02
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Why can one abstract space from colour but not colour from space?

Colour is extensive and hence presupposes space and hence we can abstract space from colour. But space does not presuppose colour. A blind man cannot not see colour but can move around and feel space. Thus colour cannot be abstracted from space.

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  • I don't know if anyone here is qualified to comment on this. I was wondering if the logical/definitional concepts of extension and comprehension could help recapitulate what you (Ullah) said here. In particular there is a formalization of these concepts called Formal Concept Analysis where they represent the data table of the extension x intension as a lattice. Where a concept is situated on the lattice helps you compare the extension and intension of the concepts analyzed (some elements will be incomparable).
    – arisbe
    Oct 2 at 19:58
  • But I don't know if there is any formalization of precissive abstraction in FCA.
    – arisbe
    Oct 2 at 20:05
  • @arisbe: No, I don't think so. The term 'extensive', I use has nothing to do with the term 'extension' that you use. They mean totally different things. The former is a physical concept and the latter is a logical concept. Oct 2 at 23:02
  • @arisbe: I think it's worth noting that 'comprehension' is the same as 'intension'. The way that you've phrased it is confusing. Oct 2 at 23:06
  • Ullah, Yes I am aware of that. I guess you could say "extension" the property that you mentioned is part of the logical intension of space and color. Color has some additional properties that makes its intension "larger" than the intension of space. It is only a coincidence that we used the same word with different senses. Sorry for not being more clear.
    – arisbe
    Oct 3 at 11:09
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As defined in the passage, prescision "arises from attention to one element and neglect of the other", where "exclusive attention consists in a definite conception or supposition of one part of an object, without any supposition of the other". Murphy in his Development of Peirce's Philosophy, p.73 gives a brief explanation of the asymmetry based on it:

"Space may be prescinded from color, because it is possible to suppose a state of things in which space would not be colored; but color cannot be prescinded from space since in every state of things colors must occur in space".

A more extended explanation relies on the second part of the passage, which displays, of course, a very Kantian way of phrasing things. Kant was Peirce's predominant influence in the early period when the New List was written (1867). To make it sound even more Kantian, concepts without intuitions are empty, but can be conceived, while intuitions ("impressions") without concepts are blind, and hence "not conceivable". But concepts can unify not just intuitions, but also "lesser" concepts:"That act of understanding by which the manifold of given representations (be they intuitions or concepts) is brought under one apperception, is the logical function of judgment", Kant says.

Peirce has in mind a gradation of "conceptions" between intuitions and concepts, so "not conceivable" is softened to "not conceivable on its own", not prescindable. Prescision is a vehicle of this gradation, and the asymmetry is between what brings what "to unity":"impressions (or more immediate conceptions) [color] cannot be definitely conceived or attended to, to the neglect of an elementary conception [space] which reduces them to unity", but "the explaining conception may frequently be prescinded from the more immediate ones and from the impressions". Buzzelli highlights this point in his paragraph by paragraph commentary on the New List in The Argument of Peirce's "New List of Categories":

"Precision differs from dissociation and discrimination, which are always reciprocal. The reason is this: Conceptions arise in experience in order to unify the manifold of impressions so that it can be thought. Consequently it is not possible to attend to or suppose the concrete manifold without also supposing the conception. If that were possible, the conception would be superfluous. On the other hand, one can always think the conception without attending to the experiential conditions from which it originally arose.

For example, space can be prescinded from color, but not color from space. The reason is that the conception of space must be introduced in order to bring order to the impressions that constitute color. Color is immediately perceived, but perceived colors would not make sense unless they were arranged in space. Thus space must be thought if one is to experience color, and color therefore cannot be prescinded from it. On the other hand, once space has been introduced, it can be thought without thinking of the color impressions that were its concrete occasion, and that made it legitimate as a necessary element in some experience".

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