Chance, Love, and Logic · Charles S. Peirce
I
The chief business of the logician is to classify arguments; for all testing clearly depends on classification. The classes of the logicians are defined by certain typical forms called syllogisms. For example, the syllogism called _Barbara_ is as follows: S is M; M is P: Hence, S is P. Or, to put words for letters— Enoch and Elijah were men; all men die: Hence, Enoch and Elijah must have died. The “is P” of the logicians stands for any verb, active or neuter. It is capable of strict proof (with which, however, I will not trouble the reader) that all arguments whatever can be put into this form; but only under the condition that the _is_ shall mean “_is_ for the purposes of the argument” or “is represented by.” Thus, an induction will appear in this form something like this: These beans are two-thirds white; But, the beans in this bag are (represented by) these beans; ∴ The beans in the bag are two-thirds white.
But, because all inference may be reduced in some way to _Barbara_, it does not follow that this is the most appropriate form in which to represent every kind of inference. On the contrary, to show the distinctive characters of different sorts of inference, they must clearly be exhibited in different forms peculiar to each. _Barbara_ particularly typifies deductive reasoning; and so long as the _is_ is taken literally, no inductive reasoning can be put into this form. _Barbara_ is, in fact, nothing but the application of a rule. The so-called major premise lays down this rule; as, for example, _All men are mortal._ The other or minor premise states a case under the rule; as, _Enoch was a man._ The conclusion applies the rule to the case and states the result: _Enoch is mortal._ All deduction is of this character; it is merely the application of general rules to particular cases. Sometimes this is not very evident, as in the following: All quadrangles are figures, But no triangle is a quadrangle; Therefore, some figures are not triangles. But here the reasoning is really this: _Rule._—Every quadrangle is other than a triangle. _Case._—Some figures are quadrangles. _Result._—Some figures are not triangles. Inductive or synthetic reasoning, being something more than the mere application of a general rule to a particular case, can never be reduced to this form.
So that induction is the inference of the _rule_ from the _case_ and _result_. But this is not the only way of inverting a deductive syllogism so as to produce a synthetic inference. Suppose I enter a room and there find a number of bags, containing different kinds of beans. On the table there is a handful of white beans; and, after some searching, I find one of the bags contains white beans only. I at once infer as a probability, or as a fair guess, that this handful was taken out of that bag. This sort of inference is called _making an hypothesis_.[52] It is the inference of a _case_ from a _rule_ and _result_. We have, then— _Rule._—All the beans from this bag are white. _Case._—These beans are from this bag. ∴ _Result._—These beans are white. _Case._—These beans are from this bag. _Result._—These beans are white. ∴ _Rule._—All the beans from this bag are white.
Ideas discussed in this chapter
Text from Project Gutenberg, public domain in the United States.