Bibliography

On the Logic of Quantity

The first prime division [of science] consists of Mathematics, which merely frames hypotheses and traces out their consequences, and alone of all the sciences does not concern itself with positive truth.

The second prime division of the sciences consists of Philosophy, which concerns itself, indeed, with positive truths but only with such as would manifestly remain true whatever observation might reveal. Even if it be denied that there is any such truth, a place in the scheme of the sciences must be accorded to this inquiry. For a department of science is not a body of truth but a group of possible researches after truth.

A term may conform to the reality or not; that is, it may signify a kind of which there are examples in the universe of discourse or it may not. It is therefore not accurate to define a proposition as which is either true or false. A proposition should be defined as that which professes to be true, or assigns a logical value to itself. The Truth is defined as that logical value which a proposition assigns to itself. Whether or not there really is such value, whether there is any truth is a question, not of definitions, but of fact.

Dual relations, – facts about pairs of subjects, – are of two types, first those which imply no more about their subjects that that they have certain qualities between which some comparison is made; and secondly, those which imply more about their subjects than is true of them in their separate existences, something real and positive which could not be true of one if the other did not exist to enable it to be true, in other words a real action and reaction between the individuals. This is the old distinction between real relations and relations of reason. Real relations exhibit the fully developed type of duality. In this case, it is what happens to the individuals, the actions of them, which pairs them.

Dual relations, – facts about pairs of subjects, – are of two types, first those which imply no more about their subjects that that they have certain qualities between which some comparison is made; and secondly, those which imply more about their subjects than is true of them in their separate existences, something real and positive which could not be true of one if the other did not exist to enable it to be true, in other words a real action and reaction between the individuals. This is the old distinction between real relations and relations of reason. Real relations exhibit the fully developed type of duality. In this case, it is what happens to the individuals, the actions of them, which pairs them. Relations of reason imply no other facts than the possession of two qualities severally by two individuals; and it is primarily the qualities that are paired.

A proposition should be defined as that which professes to be true, or assigns a logical value to itself. The Truth is defined as that logical value which a proposition assigns to itself. Whether or not there really is such value, whether there is any truth is a question, not of definitions, but of fact.