The Scottish Philosophy [271]
Hamilton's two volumes to state and examine it in detail, but I may notice some of the fundamental points.
. It proceeds on the distinction between the extension and comprehension of a term or notion. He makes no pretensions to the discovery of this principle. He knew that it was stated in the "Port Royal Logic," and that it was taught in Glasgow University by Hutcheson. Professor Baynes has shown in his translation of the "Port Royal Logic" that there were anticipations of it in earlier works. Hamilton carries out the distinction more thoroughly than it had ever been before. " The comprehension of a concept is nothing more than the sum or complement of the distinguishing characters or attributes of which the concept is made up; and the extension of a concept is nothing more than the sum or complement of the objects themselves, whose resembling characters were abstracted to constitute the concept." (Vol. I., P. 148.) If we except his exposition of this distinction, he does not seem to me to throw much light, otherwise, on the first part of logic, -- the part as it appears to me which has most need to be cleared up. He draws no distinction between the general notion and the abstract notion, but treats of both under the one designation, concept. But surely there is a distinction between two such notions as "animal" on the one band, embracing an indefinite number of objects, and " life," which has not a complement of objects, but is only an attribute of objects. {450}
. He claims originality chiefly for his doctrine of the thorough quantification of the predicate. "Touching the principle of an explicitly quantified predicate, I bad by 1833 become convinced of the necessity to extend and correct the logical doctrine on this point." " Before 1840 I had become convinced that it was necessary to extend the principle equally to negatives." (Vol. "., P. 209.) This doctrine, as Professor Baynes shows, had been partially anticipated, but had never been fully carried out. I am inclined to admit that the credit, if there be any credit, in the thorough quantification of the predicate belongs to Hamilton. But I set no value on the supposed improvement. It proceeds on the simple logical postulate, "to state explicitly what is thought implicitly." I admit the principle, but deny that it requires the predicate to be universally quantified. When we say "the dog barks," we make the predication, without inquiring in thought whether there are or are not other dogs that bark, whether dogs are all or only some barking animals. When we say " man is rational," we do not determine whether or no there are other creatures that are rational; whether, for example, angels may be called rational, whether men are "all" or only "some" rational. As the predicate is not always or even commonly quantified in spontaneous thought, so we do not require always to quantify it in the logical enunciation. At the same time, it is of importance to be able to quantify it on demand, and thus to see reflectively what is involved in every proposition. In carrying out his principles, he adds to the four classes of propositions acknowledged in the received logic A, E, I, 0, other four,
U. Common salt is chloride of sodium. Y. Some stars are all the planets. n. No birds are some animals. w. Some common salt is not some chloride of sodium.
I do regard it as of moment to place in a distinct class those propositions which assert the equivalence of subject and predicate (U). But the others seem to me to be converted or rather perverted forms that never do present themselves in spontaneous thought: in which we say instead " all the planets are stars," and " some animals are not birds," and that " chloride {451} of sodium in this cellar is not the same as chloride of sodium in that salt-cellar."
It is one of the supposed advantages of his analytic that it reduces the conversion of propositions from three species to one, -- that of simple conversion. This holds true after we have converted the proposition
U. Common salt is chloride of sodium. Y. Some stars are all the planets. n. No birds are some animals. w. Some common salt is not some chloride of sodium.
I do regard it as of moment to place in a distinct class those propositions which assert the equivalence of subject and predicate (U). But the others seem to me to be converted or rather perverted forms that never do present themselves in spontaneous thought: in which we say instead " all the planets are stars," and " some animals are not birds," and that " chloride {451} of sodium in this cellar is not the same as chloride of sodium in that salt-cellar."
It is one of the supposed advantages of his analytic that it reduces the conversion of propositions from three species to one, -- that of simple conversion. This holds true after we have converted the proposition