The Commens Dictionary

Quote from ‘Letters to Mario Calderoni’

… there are but three elementary kinds of reasoning. … The second kind of reasoning is deduction, or necessary reasoning. It is applicable only to an ideal state of things, or to a state of things in so far as it may conform to an ideal. It merely gives a new aspect to the premisses. It consists in constructing an image or diagram in accordance with a general precept, in observing in that image certain relations of parts not explicitly laid down in the precept, and in convincing oneself that the same relations will always occur when that precept is followed out. For example, having convinced ourselves of the truth of the pons asinorum with the aid of a diagram drawn with a common lead pencil, we are quite sure it would be the same with a diagram drawn in red; and a form of syllogism which is certain in black is equally so in red. A phenomenon having been observed in a laboratory, though we may not know on what conditions it depends, yet we are quite sure that it would make no difference whether the number of degrees of the longitude of the planet Eros just one week previous were a prime or composite number. [—] Deduction is certain but relates only to ideal objects.