CHAPTER VIII.-OPPOSITION AND TRANSFORMATION OF CATEGORICAL

PROPOSITIONS

51. KNOWLEDGE VALUE OF THE FOUR CATEGORICAL JUDGMENTS.-At this point we must determine exactly what amount of knowledge respecting each concept in its relation to the other the four categorical judgments convey. It must be borne in mind that the judgment states our experience respecting the subjectmatter under consideration, and is conveyed in appropriate propositional form with the purpose of gaining the assent of others. We are supposing here that we strive to render judgments which are true to our actual experience, and that the several propositions in which we couch those judgments are so framed as to render our full knowledge in standard logical form.

We shall consider first the knowledge that we feel warranted in asserting in a judgment which we state as an A proposition. Take, for instance, the proposition, All amphibians in the adult form breathe by lungs. An instant's thought shows that an assertion is here made respecting each and every individual belonging to the class indicated by the term amphibians in the adult form; the assertion, namely, that they breathe by lungs. In other words, the full denotation of the subject-term is meant. On the other hand, no assertion is intended

respecting each and every individual belonging to the class indicated by the term breathers by lungs. So far as the judgment under consideration is concerned, our knowledge does not allow us to predicate anything universally respecting the predicate-term. This may be summed up by saying that the A proposition asserts the predicate-term respecting each and every individual (the full denotation) of the subject-term, whereas the subject-term does not convey any knowledge respecting each and every individual (the full denotation) of the predicate-term.

Next let us consider the E proposition. As an instance let us take the proposition, No bats are birds. In this proposition we give voice to a judgment that gives negative knowledge regarding each and every individual belonging to the class signified by the term bat, for it tells us one thing that each and every bat is not, viz., a bird. The proposition also gives negative knowledge respecting each and every individual referred to by the predicate-term bird, for in denying that bats are birds we also necessarily preclude the possibility of maintaining that birds are bats. That is to say, by severing all possibility of relationship between the two concepts represented by the terms bat and bird, negative knowledge is conveyed respecting each and every individual referred to by either concept.

As an example of the I proposition may be taken the judgment that we feel warranted in asserting in the sentence, Some dogs are hounds. It is evident that nothing is asserted about each and every individual included in the concept referred to by the term dog, for we qualify

our affirmation by the word some, with the special intention of referring only to an indefinite part of the class dogs. We only mean to say what some dogs are, viz., hounds. And in this proposition we do not assert anything regarding each and every individual referred to by the term hound. For although it chances that our experience tells us that all hounds (each and every hound) are dogs, we have to frame another proposition to express such a judgment. Another example will better illustrate how erroneous it would be to maintain that the predicate-term is employed universally in the I proposition. Take the sentence, Some pupils in this class are bright girls. It would certainly do violence to the facts of experience to claim that here some one assertion is made regarding each and every individual symbolized by the predicate-term bright girl; for as the only concept which is related to the predicate-term in this proposition is the subject-term pupils in this class, we should fall into the absurdity of maintaining the judgment that each and every bright girl is a pupil in this class.

The following proposition illustrates the O form of judgment: Some educated men are not moral. Here we are not asserting any one thing respecting each and every individual of the class referred to by the term educated men, for we qualify that term by the indefinitely limiting word some. Hence the subject-term is not taken universally. The predicate-term, on the other hand, has something told respecting it that refers to each and every individual falling within the class denoted by it. One item of (negative) information is conveyed

to the mind respecting every moral being in existence, viz., that he is not one of the group of some educated men indicated by the subject-term. This is summed up by saying that the subject-term of the O proposition does not furnish the mind with any one item of knowledge regarding its full denotation, whereas the predicateterm of the O does supply such knowledge.

The whole of this subject of the knowledge value of the several categorical propositions may be briefly stated as follows: Our problem is to tell how complete is the knowledge vouchsafed us in regard to each term. The universal propositions A and E are so called because their subject-terms are used in full denotation, that is, are meant to refer to each and every individual belonging to the class symbolized by the term. In contradistinction to them, the I and O propositions are called particular because their subject-terms are not used in full denotation, as is indicated by the word some, or its equivalent, prefixed to them. Hence it is clear that the subject-terms of universal propositions are meant in full denotation, while those of particular propositions are not so meant. But so far nothing is shown respecting the predicate-terms. A moment's thought shows us that the negative propositions E and O indicate a complete severance of relation between the subject and predicate terms; hence they must necessarily furnish us with knowledge of a negative character affecting every individual falling within the denotation of the predicateterms; for we know in these two propositions at least one thing that the individuals denoted by the predicateterms are not, viz., the individuals referred to or such

part as is meant by the subject-term. The predicateterms of the affirmative propositions A and I make no such complete contribution to our knowledge, for they are left entirely indefinite, so that from the propositions as they stand we cannot tell whether all or only a part of the denotation is intended.

The subject that has just been discussed is technically referred to in logic as distribution of terms, which means the character of their denotation, i. e., whether all the individuals belonging to the concept, or only some indefinite part of them, are meant. Distribution is an abstract noun; corresponding to it are the two adjective forms distributed and undistributed. A term is said to be dis

tributed when used in a proposition to refer to the full denotation of (each and every individual in) the class which it symbolizes. A term is said to be undistributed if used in a proposition to refer to only some indefinite part of its full denotation, i. e., to some only of all the individuals of the class which it symbolizes.

The results of the above discussion may be expressed in this table:

Of course only two distributions are possible in a given proposition. Remembering this, we can also summarize as follows: E distributes both; I distributes