Page:On the Fourfold Root, and On the Will in Nature.djvu/212

 indeed every hypothetical judgment is ultimately based upon that principle, and here the laws of hypothetical conclusions always hold good: that is to say, it is right to infer the existence of the consequence from the existence of the reason, and the non-existence of the reason from the non-existence of the consequence ; but it is wrong to infer the non-existence of the consequence from the non-existence of the reason, and the existence of the reason from the existence of the consequence. Now it is singular that in Geometry we are nevertheless nearly always able to infer the existence of the reason from the existence of the consequence, and the non-existence of the consequence from the non-existence of the reason. This proceeds, as I have shown in § 37, from the fact that, as each line determines the position of the rest, it is quite indifferent which we begin at : that is, which we consider as the reason, and which as the consequence. We may easily convince ourselves of this by going through the whole of the geometrical theorems. It is only where we have to do not only with figures, i.e., with the positions of lines, but with planes independently of figures, that we find it in most cases impossible to infer the existence of the reason from the existence of the consequence, or, in other words, to convert the propositions by making the condition the conditioned. The following theorem gives an instance of this: Triangles whose lengths and bases are equal, include equal areas. This cannot be converted as follows: Triangles whose areas are equal, have likewise equal bases and lengths; for the lengths may stand in inverse proportion to the bases.

In § 20 it has already been shown, that the law of causality does not admit of reciprocity, since the effect never can be the cause of its cause ; therefore the conception of reciprocity is, in its right sense, inadmissible. Reciprocity, according to the Principle of Sufficient Reason