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 ****** conversion.This holds true after we have converted the proposition into the form in which Hamilton has put it.When we say, "The bird sings,"which is the form in spontaneous thought, Hamilton insists that logically it is, " The bird is some singing animal; "and after we have thus converted it once, the second conversion follows simply, " Some singing animals are birds." But there is nothing saved by requiring us to put every proposition in a form so different from that which it assumes in spontaneous thought.
Hamilton has done service to logic by unfolding more fully than had been done before what Kant called "syllogisms of the understanding," and which he calls immediate inferences, that is, inferences without a middle term, as when, from the proposition " All men have a conscience," we infer that some men have a conscience.He includes very properly under this head every form of conversion and opposition; and it has been shown by him and others that it includes other immediate inferences which it is important to spread out to view.But instead of placing them under reasoning, they might be allowed to remain where conversion and opposition have usually been placed, in the second part of logic.
<Reasoning>.It is an alleged advantage of his analytic that it is ,the revocation of two terms of a proposition to their true relation; a proposition being always an equation of its subject and predicate." So he says the proposition all men are mortal, means "all men = some mortal." That in some propositions the subject and predicate are equivalent may be allowed; and in such cases there may be no impropriety in using the mathematical equation, though generally it is better to allow mathematicians to keep their own symbols, as in their science they have a definite meaning, a meaning in regard to quantity; and if we introduce symbols into logic, let us introduce new symbols appropriated to the ideas.Human thought is employed about a great many other objects as well as quantity.When we say, "Virtue leads to happiness," we are not uttering a quantitative {452} statement, "Virtue = some things that lead to happiness; " but primarily an attributive assertion, that virtue has the attribute of leading to happiness, and by implication in extension, "among the things that lead to happiness is virtue."The new analytic claims that it reduces all the general laws of categorical syllogisms to a single canon.But what is that canon? I confess I have difficulty in finding it.
Mr.Baynes states it " A syllogism is the product of that act of mediate comparison " by which we recognized that two notions stand to each other in the relation of whole and part, through the recognition that these notions severally stand in the same relation to a third.This canon is vague enough till it is explained what is meant by the relation of whole and parts.There is valid ratiocination where the relationship does not seem that of whole and parts.
Chloride of sodium is not common salt;
Pepper is not chloride of sodium;
Therefore pepper is not common salt.
In many cases the relation is one of whole and parts.
But of what kind of whole? Hamilton says that it is first one of comprehension, and complains that logicians have overlooked it.Thus (Vol.I., P.272): --Every morally responsible agent is a free agent;Man is a morally responsible agent;
Therefore man is a free agent, --
which is thus explained: The notion man comprehends in it the notion responsible agent; but the notion responsible agent comprehends in it the notion free agent; therefore, on the principle that a part of a part is a part of a whole, the notion man also comprehends in it the notion free agent.
But it is clear to me that in every one of these propositions there is generalization or extension implied.
We have " every responsible agent," "every man," and in the class of "free agents," or "some free agents." I acknowledge that there is also comprehension involved, for all extension involves comprehension.But the uppermost thought seems to me to be in extension: Man is in the class responsible;which again is in the class free agent; consequently man is in the class free agent.Unless our knowledge of attributes is such as to enable us {453} thus to form classes, the reasoning is not valid; and the best form in which to brand out the principle involved is, All responsible agents are free agents;But man is a responsible agent Therefore he is a free agent.
But if this be so, then we are back to the <dictum>, "Whatever is true of a class is true of all the members of the class." But as all extension involves comprehension, it is of moment to be able on demand to put reasoning in the form of comprehension.
It is urged in favor of the practical value of the analytic, that it makes figure unessential and reduction unnecessary.But it enlarges the number of legitimate moods, ****** them 36 under each figure, or in all 108, -- a number which is apt to frighten the student.
