[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 23

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Let us backtrack a few years, and consider how Boole explained his
twin conceptions of "selective operations" and "selective symbols".

| Let us then suppose that the universe of our discourse
| is the actual universe, so that words are to be used in
| the full extent of their meaning, and let us consider the
| two mental operations implied by the words "white" and "men".
| The word "men" implies the operation of selecting in thought
| from its subject, the universe, all men;  and the resulting
| conception, 'men', becomes the subject of the next operation.
| The operation implied by the word "white" is that of selecting
| from its subject, "men", all of that class which are white.
| The final resulting conception is that of "white men".
|
| Now it is perfectly apparent that if the operations above described
| had been performed in a converse order, the result would have been the
| same.  Whether we begin by forming the conception of "'men'", and then by
| a second intellectual act limit that conception to "white men", or whether
| we begin by forming the conception of "white objects", and then limit it to
| such of that class as are "men", is perfectly indifferent so far as the result
| is concerned.  It is obvious that the order of the mental processes would be
| equally indifferent if for the words "white" and "men" we substituted any
| other descriptive or appellative terms whatever, provided only that their
| meaning was fixed and absolute.  And thus the indifference of the order
| of two successive acts of the faculty of Conception, the one of which
| furnishes the subject upon which the other is supposed to operate,
| is a general condition of the exercise of that faculty.  It is
| a law of the mind, and it is the real origin of that law of
| the literal symbols of Logic which constitutes its formal
| expression (1) Chap. II, [namely, xy = yx].
|
| It is equally clear that the mental operation above described is of such
| a nature that its effect is not altered by repetition.  Suppose that by
| a definite act of conception the attention has been fixed upon men, and
| that by another exercise of the same faculty we limit it to those of the
| race who are white.  Then any further repetition of the latter mental act,
| by which the attention is limited to white objects, does not in any way
| modify the conception arrived at, viz., that of white men.  This is also
| an example of a general law of the mind, and it has its formal expression
| in the law ((2) Chap. II) of the literal symbols [namely, x^2 = x].
|
| Boole, 'Laws of Thought', pp. 44-45.
|
| George Boole,
|'An Investigation of the Laws of Thought,
| On Which are Founded the Mathematical
| Theories of Logic and Probabilities',
| Reprinted, Dover, New York, NY, 1958.
| Originally published, Macmillan, 1854.

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