Cesare, Camestres, Festmo, Baroko, seeunda3. Tertia Darapti, Disannis, Datisi, Felapton, Bokardo, Ferison habet, quarta insuper addit Bmmantip, Camenes, Dimaris, Fesapo, Fresison." The first line gives the standard figure, and states the propositions entering into each syllogism. The three A's in Barbara are three universal propositions. The E, A, E, in Celarent, are a universal negative, a universal affirmative, a universal negative; in Darii, A, I, I, a universal affirmative and two particular affirmatives, etc. In the other figures the commencing letter (C, B, etc.) shows which standard syllogism each is to be reduced to (Baroko to Barbara, Cesare to Celarent, etc.). The consonant s means simple con version of the proposition marked by the preceding vowel; p means conversion by limi tation, or per accidens; m signifies the transposition of the premises; A; occurs in Baroko and Bokardo, and denotes that these are to be reduced by supposing the conclusion false, and then showing that on that supposition Barbara would be contradicted—from which it is inferred that the original form is true.
There are some species of deductive arguments that do not fall under the syllogistic figures. Thus, the major may state a conditional proposition, and the minor affirm the truth of the condition. "If the witness is to be believed, the man is guilty" (major); now " the witness' is to be believed " (minor): therefore " the man is guilty." A true conclusion would also be obtained by a minor denying the consequent, " the man is not guilty." It would then follow that the witness (who affirms his guilt) is not to be believed. But uo conclusion would follow froiu either denying the condition, "the witness is not to be believed," or affirming the consequent, "the man is guilty;" for, in the first place, the man might be guilty whether this particular witness be credible or not; and second ly, the guilt of the man does not prove the credibility of the witness. This is called the conditional syllogism.
Again, the major may be what is called a disjunctive or alternative proposition, from which also inferences may be drawn by supplying certain minors. "This was done by
either A or B;" now " it was not done by A (or by B);" therefore "it was done by 1.1 (or by A)." Should the major be understood to mean that it was done by one, and not by both, there would be two other possible inferences. "It was done by A (or by B);" therefore " it was not done by B (or byA)." There are other disjunctive pairs, as for example: " Either A is B, or C is D;" now " A. is not B, therefore C is D," etc. This is called the disjunctive syllogism.
A combination of the conditional and the disjunctive makes the dilemma. For example: If A exist, then either B or C exists.
Neither B nor C exists.
Therefore A does not exist.
The following dilemma was given to refute the practice of torturing witnesses: "A person able to endure pain will be likely to utter falsehood under torture; one unable will be equally likely; therefore, a person under torture will be likely to utter falsehood." A very great enlargement has been given to the doctrine of the syllogism by sir W. Hamilton (see QUANTn'ICATION), prof. De Morgan, and the late prof. Boole of Cork. They have shown that many more syllogistic pairs can be created, and have invented symbols for the purpose. It is, however, comparatively few, either of the old pairs or of the new, that are assumed by the ordinarily occurring arguments, either in the sci ences or in common affairs. By far the most useful part of the syllogism is contained within the limits of the first or standard figure, which shows what premises are to be looked out for to prove any conclusion; namely, some general assertion of matter of fact, affirmative or negative (major), and a particular assertion that a given thing comes under the subject of the general assertion (minor), and therefore falls likewise under its predi cate. When an argument is stated in a puzzling or perplexed form, with perhaps the omission of one of its essential propositions, it is well to know how to supply the sup pressed premises, and put the argument into regular order: the truth or fallacy of the reasoning then becomes evident at a glance.