Bibliography

The Logic of Relatives

A relative […] may be defined as the equivalent of a word or phrase which, either as it is (when I term it a complete relative), or else when the verb “is” is attached to it (and if it wants such attachment, I term it a nominal relative), becomes a sentence with some number of proper names left blank. A relationship, or fundamentum relationis, is a fact relative to a number of objects, considered apart from those objects, as if, after the statement of the fact, the designations of those objects had been erased. A relation is a relationship considered as something that may be said to be true of one of the objects, the others being separated from the relationship yet kept in view. Thus, for each relationship there are as many relations as there are blanks. For example, corresponding to the relationship which consists in one thing loving another there are two relations, that of loving and that of being loved by. There is a nominal relative for each of these relations, as “lover of –,” and “loved by –.” These nominal relatives belonging to one relationship, are in their relation to one another termed correlatives. In the case of a dyad, the two correlatives, and the corresponding relations are said, each to be the converse of the other. The objects whose designations fill the blanks of a complete relative are called the correlates.

An ordinary relative with an active verb as “– is a lover of –” or “the loving by – of –” has two blanks; it is a dyad, or dyadic relative.

…a dyadic relation […] is nothing but an aggregation of pairs. Now any two hecceities may in either order form a pair; and any aggregate whatever of such pairs will form some dyadic relation. Hence, we may totally disregard the manner in which the hecceities are connected in determining the possibility of a hypothesis about some dyadic relation.

Very many writers assert that everything is logically possible which involves no contradiction. Let us call that sort of logical possibility, essential, or formal, logical possibility. It is not the only logical possibility; for in this sense, two propositions contradictory of one another may both be severally possible, although their combination is not possible.

By a hecceity, I mean, some element of existence which, not merely by the likeness between its different apparitions, but by an inward force of identity, manifesting itself in the continuity of its apparition throughout time and in space, is distinct from everything else, and is thus fit (as it can in no other way be) to receive a proper name or to be indicated as this or that.

In a complete proposition there are no blanks. It may be called a medad, or medadic relative…

A non-relative name with a substantive verb, as “– is a man,” or “man that is –,” or “–‘s manhood” has one blank; it is a monad, or monadic relative.

I formerly defined the possible as that which in a given state of information (real or feigned) we do not know not to be true. But this definition today seems to me only a twisted phrase which, by means of two negatives, conceals an anacoluthon. We know in advance of experience that certain things are not true, because we see they are impossible. Thus, if a chemist tests the contents of a hundred bottles for fluorine, and finds it present in the majority, and if another chemist tests them for oxygen and finds it in the majority, and if each of them reports his result to me, it will be useless for them to come to me together and say that they know infallibly that fluorine and oxygen cannot be present in the same bottle; for I see that such infallibility is impossible. I know it is not true, because I satisfy myself that there is no room for it even in that ideal world of which the real world is but a fragment. I need no sensible experimentation, because ideal experimentation establishes a much broader answer to the question than sensible experimentation could give.

A relative […] may be defined as the equivalent of a word or phrase which, either as it is (when I term it a complete relative), or else when the verb “is” is attached to it (and if it wants such attachment, I term it a nominal relative), becomes a sentence with some number of proper names left blank. A relationship, or fundamentum relationis, is a fact relative to a number of objects, considered apart from those objects, as if, after the statement of the fact, the designations of those objects had been erased. A relation is a relationship considered as something that may be said to be true of one of the objects, the others being separated from the relationship yet kept in view. Thus, for each relationship there are as many relations as there are blanks. For example, corresponding to the relationship which consists in one thing loving another there are two relations, that of loving and that of being loved by. There is a nominal relative for each of these relations, as “lover of –,” and “loved by –.” These nominal relatives belonging to one relationship, are in their relation to one another termed correlatives. In the case of a dyad, the two correlatives, and the corresponding relations are said, each to be the converse of the other. The objects whose designations fill the blanks of a complete relative are called the correlates. The correlate to which a nominal relative is attributed is called the relate.

A relative […] may be defined as the equivalent of a word or phrase which, either as it is (when I term it a complete relative), or else when the verb “is” is attached to it (and if it wants such attachment, I term it a nominal relative), becomes a sentence with some number of proper names left blank. A relationship, or fundamentum relationis, is a fact relative to a number of objects, considered apart from those objects, as if, after the statement of the fact, the designations of those objects had been erased. A relation is a relationship considered as something that may be said to be true of one of the objects, the others being separated from the relationship yet kept in view. Thus, for each relationship there are as many relations as there are blanks.

A relative […] may be defined as the equivalent of a word or phrase which, either as it is (when I term it a complete relative), or else when the verb “is” is attached to it (and if it wants such attachment, I term it a nominal relative), becomes a sentence with some number of proper names left blank. A relationship, or fundamentum relationis, is a fact relative to a number of objects, considered apart from those objects, as if, after the statement of the fact, the designations of those objects had been erased. A relation is a relationship considered as something that may be said to be true of one of the objects, the others being separated from the relationship yet kept in view. Thus, for each relationship there are as many relations as there are blanks.

A relative […] may be defined as the equivalent of a word or phrase which, either as it is (when I term it a complete relative), or else when the verb “is” is attached to it (and if it wants such attachment, I term it a nominal relative), becomes a sentence with some number of proper names left blank.

Our European languages are peculiar in their marked differentiation of common nouns from verbs. Proper nouns must exist in all languages; and so must such “pronouns,” or indicative words, as this, that, something, anything. But it is probably true that in the great majority of the tongues of men, distinctive common nouns either do not exist or are exceptional formations. In their meaning as they stand in sentences, and in many comparatively widely-studied languages, common nouns are akin to participles, as being mere inflexions of verbs. If a language has a verb meaning “is a man,” a noun “man” becomes a superfluity. For all men are mortals is perfectly expressed by “Anything either is-a-man not or is-a-mortal.” Some man is a miser is expressed by “Something both is-a-man and is-a-miser.” The best treatment of the logic of relatives, as I contend, will dispense altogether with class names and only use such verbs. A verb requiring an object or objects to complete the sense may be called a complete relative.

A verb by itself signifies a mere dream, an imagination unattached to any particular occasion. It calls up in the mind an icon. A relative is just that, an icon, or image, without attachments to experience, without “a local habitation and a name,” but with indications of the need of such attachments.

By logical reflexion, I mean the observation of thoughts in their expressions. Aquinas remarked that this sort of reflexion is requisite to furnish us with those ideas which, from lack of contrast, ordinary external experience fails to bring into prominence. He called such ideas second intentions. It is by means of relatives of second intention that the general method of logical representation is to find completion.

In respect to the ideal world we are virtually omniscient; that is to say, there is nothing but lack of time, of perseverance, and of activity of mind to prevent our making the requisite experiments to ascertain positively whether a given combination occurs or not. Thus, every proposition about the ideal world can be ascertained to be either true or false. A description of thing which occurs in that world is possible, in the substantive logical sense. Very many writers assert that everything is logically possible which involves no contradiction. Let us call that sort of logical possibility, essential, or formal, logical possibility. It is not the only logical possibility; for in this sense, two propositions contradictory of one another may both be severally possible, although their combination is not possible. But in the substantive sense, the contradictory of a possible proposition is impossible, because we are virtually omniscient in regard to the ideal world. For example, there is no contradiction in supposing that only four, or any other number, of independent atoms exist. But it is made clear to us by ideal experimentation, that five atoms are to be found in the ideal world. Whether all five are to be found in the sensible world or not, to say that there are only four in the ideal world is a proposition absolutely to be rejected, notwithstanding its involving no contradiction.