If we say, the circle is a conic section, evidently any one ignorant of the terms, or who has not reflected on their true sense, will not think of the attribute in the subject. No addition is made to the conception of the circle; only a property not before known is discovered, and this discovery results from comparison with the cone. Is there any synthesis here? No. There is only an analysis of the two conceptions, the circle and the cone, compared. As this error destroys the foundation of Kant's doctrine on this point, we will develop it and place it on a more solid foundation.
285. Synthesis, properly so called, requires something to be added to the conception, which in nowise belongs to it, as the example brought by Kant shows. The conception, extension, is contained in the conception, body; but heaviness is an entirely foreign idea, which we can unite to the conception, body, only because experience authorizes it. Only with this addition is there properly synthesis. The union of ideas which results from the conception of the thing, although comparison may be necessary in order to fecundate them, does not make a synthesis. The conceptions are not wholly absolute, they contain relations, and the discovery of these relations does not give a synthesis, but a more complete analysis. If it be said that in this case there is something more than the primitive conception, we answer that the same thing happens in all not purely identical. We may also add that by the comparison a new total conception is formed resulting from the primitive conceptions; and the properties of the relations are then seen, not by synthesis, but by the analysis of the total conception.
According to Kant, true synthesis requires the union of things so different from one another, that the bond uniting them is a sort of mystery, an x, whose determination is a great philosophical problem. If this x is found in the essential relation of the partial conceptions constituting the total conception, the problem is resolved by a simple analysis, or, to speak more exactly, it is shown that the problem did not exist, because the x was a known quantity.
We know of no judgment more analytical than that in which we see the parts in the whole, since the whole is only the parts united. If we say, one and one are two, or, two is equal to one plus one; it cannot be denied that we have a total conception, two, in the decomposition of which, we find one plus one. If this be not an analytic conception, that is to say, if the predicate be not here contained in the idea of the subject, it will be hard to tell what is. But even here there are different conceptions, one plus one; unite them, and they form the total conception. The relation, although most simple, exists; and whether it be more or less, simple or complicated, and, consequently, seen with more or less facility, does not alter the character of the judgments, or from synthetic convert them into analytic.