The Philosophical Review/Volume 1/Summary: Erhardt, F - Der Satz vom Grunde als Princip des Schliessens
The purpose of this paper is to show how all the forms of conclusion formulated by Logic can be reduced to the Principle of Reason and Consequent. The Progressive Conclusion is the conclusion of the consequent from the reason: the Regressive Conclusion is the conclusion of the non-existence of the reason from the non-existence of the conclusion. Only in the case of the sole and exclusive reason can we infer from the existence of the conclusion to the existence of the reason; and only when there is one definite condition of a consequence given can we infer from the non-existence of the reason the non-existence of the consequent. As to Conversion: we infer here regressively from the consequence to the reason; in the case of the converse of an A and an I, we infer from the existence of the consequence the existence of the reason; and in the case of the converse of an E we infer from the removal of the consequence the removal of the reason. As to Contraposition: in the case of the contraposition of an A, we infer from the removal of the consequence the removal of the reason; in the contraposition of an E, from the existence of the consequence to the existence of the reason; in the contraposition of an O, we conclude from the consequent to the reason, as in the conversion of an I. It is thus evident that the traditional separation of Conversion and Contraposition rests on grammatical and not on logical grounds. As to Opposition: that one contradictory should be false when the other is true is a consequence from the very meaning of ‘all’ and ‘some’ and negation. The reasoning termed Modal Consequence is manifestly based on the Principle of Reason and Consequent. In the first syllogistic figure we conclude from the reason to a consequence of the consequence; in the second figure we have a mixed or a regressive-progressive conclusion, for in the major premise we argue from the reason to the consequence and in the minor from the consequence to the reason; in the third figure we have also a mixed conclusion, for in the minor we conclude from the consequence to the reason and in the major from the reason to the consequence; in the fourth figure we have to do with a doubly-regressive reasoning, for we conclude from the consequence to the reason of the reason. Through all this we see what the middle term really is: a syllogism is only possible where two premises are given with a common concept which is logically consequence in the one premise and reason in the other. Then when we compare syllogism with induction through analogical reasoning we see that the inference process in its last resort is always the deduction of a logical conclusion from its logical ground. What really distinguishes the analogical from the syllogistic inference is not so much the progress from the particular to the particular in contradistinction to the descent from the general to the particular, as the difference in the certainty about the inner connection of the conceptions that are given in the premises. When one instance (as in a geometrical figure) really gives us the inner connection between certain attributes and certain others, we do not need any more an analogical inference to conclude about the connection of these attributes in other or new instances, but may do this syllogistically. The Inductive conclusion does not present us with anything new in relation to the analogical inference; it only extends the consequence which analogy draws for one case to the whole class of objects which agree with the former objects in the definite relation which made the analogical inference possible.