In the first of these logically differentiated cases, the transformation into the speech of formulated thought leads to the following inference from analogy:
Fire A burned.
Fire B is similar to fire A.
Fire B will burn.
In the second case there arises a syllogism of some such form as:
All fire causes burning upon contact.
This present phenomenon is fire.
This present phenomenon will cause burning upon contact.
Both premises of this syllogism are inductive inferences, whose implicit meaning becomes clear when we formulate as follows:
All heretofore investigated instances of fire have burned, therefore all fire burns.
The present phenomenon manifests some properties of fire, will consequently have all the properties thereof.
The present phenomenon will, in case of contact, cause burning.
The first syllogism goes from the particular to the particular. The second proves itself to be (contrary to the analysis of Stuart Mill) an inference that leads from the general to the particular. For the conclusion is the particular of the second parts of the major and minor premises; and these second parts of the premises are inferred from their first parts in the two possible ways of inductive inference. The latter do not contain the case referred to in the conclusion, but set forth the conditions of carrying a result of previous experience over to a new case with inductive probability, in other words, the conditions of making past experience a means of foreseeing future experience. It would be superfluous to give here the symbols of the two forms of inductive inference.
We remain within the bounds of logical analysis, if we state under what conditions conclusions follow necessarily from their premises, viz., the conclusions of arguments from analogy and of syllogisms in the narrower sense, as well as those of the foregoing inductive arguments. For the inference from analogy and the two forms of inductive inference, these conditions are the presuppositions already set forth in the text of the present paper, that in the as yet unobserved portion of reality the like causes will be found and they will give rise to like effects. For the syllogism they are the thought that the predicate of a predicate is the (mediate) predicate of the subject. Only the further analysis of these presuppositions, which is undertaken in the text, leads to critical considerations in the narrower sense.
[12] A System of Logic, Ratiocinative and Inductive, bk. III, ch. v, § 6.
[13] This doctrine began in the theological evolution of the Christian concept of God. It was first fundamentally formulated by Leibnitz. It is retained in Kant's doctrine of the harmonia generaliter stabilita and the latter's consequences for the critical doctrine of the mundus intelligibilis. Hence it permeates the metaphysical doctrines of the systems of the nineteenth century in various ways.