Some Remarks on Logical Form: Difference between revisions

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-about it, ''e.g.'', P is red, by the symbol "[6–9, 3–8] R", where "R" is yet an unanalyzed term ("6–9" and "3–8" stand for the continuous in terval between the respective numbers). The system of co-ordinates here is part of the mode of expression; it is part of the method of projection by which the reality is projected into our symbolism. The relation of a patch lying between two others can be expressed analogously by the use of apparent variables. I need not say that this analysis does not in any way pretend to be complete. I have made no mention in it of time, and the use of two-dimensional space is not justified even in the case of monocular vision. I only wish to point out the direction in which, I believe, the analysis of visual phenomena is to be looked for, and that in this analysis we meet with logical forms quite different from those which ordinary language leads us to expect. The occurrence of numbers in the forms of atomic propositions is, in my opinion, not merely a feature of a special symbolism, but an essential and, consequently, unavoidable feature of the representation. And numbers will have to enter these forms when—as we should say in ordinary language—we are (167) dealing with properties which admit of gradation, ''i.e.'', properties as the length of an interval, the pitch of a tone, the brightness or redness of a shade of colour, etc. It is a characteristic of these properties that one degree of them excludes any other. One shade of colour cannot simultaneously have two different degrees of brightness or redness, a tone not two different strengths, etc. And the important point here is that these remarks do not express an experience but are in some sense tautologies. Every one of us knows that in ordinary life. If someone asks us "What is the temperature outside?" and we said "Eighty degrees", and now he were to ask us again, "And is it ninety degrees?" we should answer, "I told you it was eighty." We take the statement of a degree (of temperature, for instance) to be a ''complete'' description which needs no supplementation. Thus, when asked, we say what the time is, and not also what it isn't.
+about it, ''e.g.'', P is red, by the symbol "[6–9, 3–8] R", where "R" is yet an unanalyzed term ("6–9" and "3–8" stand for the continuous interval between the respective numbers). The system of co-ordinates here is part of the mode of expression; it is part of the method of projection by which the reality is projected into our symbolism. The relation of a patch lying between two others can be expressed analogously by the use of apparent variables. I need not say that this analysis does not in any way pretend to be complete. I have made no mention in it of time, and the use of two-dimensional space is not justified even in the case of monocular vision. I only wish to point out the direction in which, I believe, the analysis of visual phenomena is to be looked for, and that in this analysis we meet with logical forms quite different from those which ordinary language leads us to expect. The occurrence of numbers in the forms of atomic propositions is, in my opinion, not merely a feature of a special symbolism, but an essential and, consequently, unavoidable feature of the representation. And numbers will have to enter these forms when—as we should say in ordinary language—we are (167) dealing with properties which admit of gradation, ''i.e.'', properties as the length of an interval, the pitch of a tone, the brightness or redness of a shade of colour, etc. It is a characteristic of these properties that one degree of them excludes any other. One shade of colour cannot simultaneously have two different degrees of brightness or redness, a tone not two different strengths, etc. And the important point here is that these remarks do not express an experience but are in some sense tautologies. Every one of us knows that in ordinary life. If someone asks us "What is the temperature outside?" and we said "Eighty degrees", and now he were to ask us again, "And is it ninety degrees?" we should answer, "I told you it was eighty." We take the statement of a degree (of temperature, for instance) to be a ''complete'' description which needs no supplementation. Thus, when asked, we say what the time is, and not also what it isn't.
 One might think—and I thought so not long ago—that a statement expressing the degree of a quality could be analyzed into a logical product of single statements of quantity and a completing supplementary statement. As I could describe the contents of my pocket by saying "It contains a penny, a shilling, two keys, and nothing else". This "and nothing less" is the supplementary statement which completes the description. But this will not do as an analysis of a statement of degree. For let us call the unit of, say, brightness ''b'' and let E(''b'') be the statement that the entity E possesses this brightness, then the proposition E(2''b''), which says that E has two degrees of brightness, should be analyzable into the logical product E(''b'') & E(''b''), but this is equal to E(''b''); if, on the other hand, we try to distinguish between the units and consequently write E(2''b'') = E(''b''<nowiki>'</nowiki>) & E(''b''"), we assume (168) two different units of brightness; and then, if an entity possesses one unit, the question could arise, which of the two—''b''<nowiki>'</nowiki> or ''b''"—it is; which is obviously absurd.