Peirce’s 1870 “Logic of Relatives” • Comment 9.1

Peirce’s 1870 “Logic of Relatives”Comment 9.1

Perspective on Peirce’s use of the comma operator at CP 3.73 and CP 3.74 can be gained by dropping back a few years and seeing how George 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, [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 [x^2 = x] of the literal symbols.

(Boole, Laws of Thought, 44–45)


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6 Responses to Peirce’s 1870 “Logic of Relatives” • Comment 9.1

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