§6 - Concluding reflection

Summary

Our discussions have established the following points: that the supreme rules governing all syllogisms lead directly to that order of concepts which is called the first figure; that all other transpositions of the middle term only yield valid inferences if, by means of easy and immediate inferences, they lead to such propositions as are connected in the simple order of the first figure; that it is impossible to draw simple and unmixed inferences in more than one figure, for it is only ever the first figure which, concealed in a syllogism by means of covert inferences, has the power to generate the conclusion, with the changed position of the terms merely occasioning a deviation, shorter or longer as the case may be, which has to be followed if one is to understand how the conclusion has been reached; and that the division of the figures in general, in so far as they are supposed to contain inferences which are pure, unmixed and free from interpolated inferences, is false and impossible. It is easy to see from our explanations – and for that reason I do not propose to dwell on it – that the universal fundamental rules which govern all syllogisms contain the special rules of the so-called first figure; it is also easy to see that, given the conclusion and the middle term, one can instantly convert any syllogism belonging to one of the other figures into the first simple figure, without the futile tediousness of the formulae of reduction, so that either the conclusion itself or a proposition from which the conclusion follows by immediate inference, can be inferred.

I do not wish to conclude this reflection without adding some remarks which may be of some considerable use in other connections.

Firstly, then I would say: a distinct concept is only possible by means of a judgement, while a complete concept is only possible by means of a syllogism.