Thus, in analogical reasoning, whether concerning sensory matters or anything else, if we know that one thing is like another, we know that what holds true of one holds true of the other, even if we do not know the cause of that judgment. If we do know its cause, we infer the judgment’s applicability from the presence of that cause. A judgment can therefore be known through either analogical reasoning or causal inference.

Causal inference is, in reality, a form of logical syllogism. Its distinguishing feature, however, is that its middle term—which serves as the evidence—is the cause of the judgment. It is called a “causal syllogism” and a “causal demonstration.” That is called an “evidential syllogism” and an “evidential demonstration.” If, however, we do not know the similarity and the cause with certainty, but merely consider them probable, then the judgment is likewise probable.

The same applies to the logical syllogism: if both premises are known with certainty, the conclusion is known with certainty; otherwise, the conclusion follows the weakest premise.

As for their claim that analogical reasoning does not yield certain knowledge, this is an outright error, demonstrably so. Indeed, most of humanity’s purely rational knowledge derives from analogical reasoning.

Moreover, as for the sciences for which they primarily intended this discipline to serve as a criterion, this logical discipline is of very little use in them.

For it is well known that those who have engaged in the mathematical sciences—arithmetic and the calculation of magnitude, whether conceived in the mind or existing externally—both ancient and modern, have been able to pursue them independently, without reference to this