Gold is a shining, fusible, ductile, simple body. Metals are shining, fusible, ductile, simple bodies. But to say from these premises, "Gold and metal are similar in what is signified by the middle term," is a mere repetition of the premises; to say, further, that "Gold may be a metal" is a _non-sequitur_, because, the middle being undistributed, the logical conclusion is the contingent "Gold may or may not be a metal," which leaves the question quite open, and therefore there is no syllogism. Wundt, who is again followed by Bosanquet, also supposes another syllogism in the third figure, under the title of "Inference by Connexion" (_Verbindungsschluss_), to be useful for induction. He proposes, for example, the following premises:-- Gold, silver, copper, lead, are fusible. Gold, silver, copper, lead, are metals. Here there is no syllogistic fallacy in the premises; but the question is what syllogistic conclusion can be drawn, and there is only one which follows without an illicit process of the minor, namely, "Some metals are fusible." The moment we stir a step further with Wundt m the direction of a more general conclusion (_ein allgemeinerer Satz_), we cannot infer from the premises the conclusion desired by Wundt, "Metals and fusible are connected"; nor can we infer "All metals are fusible," nor "Metals are fusible," nor "Metals may be fusible," nor "All metals may be fusible," nor any assertory conclusion, determinate or indeterminate, but the indifferent contingent, "All metals may or may not be fusible," which leaves the question undecided, so that there is no syllogism. We do not mean that in Wundt's supposed "inferences of relation by comparison and connexion" the premises are of no further use; but those of the first kind are of no syllogistic use in the second figure, and those of the second kind of no syllogistic use beyond particular conclusions in the third figure. What they really are in the inferences proposed by Wundt is not premises for syllogism, but data for induction parading as syllogism. We must pass the same sentence on Lotze's attempt to extend the second figure of the syllogism for inductive purposes, thus:-- S is M. Q is M. R is M. :. Every [Sigma], which is common to S, Q, R, is M. We could not have a more flagrant abuse of the rule _Ne esto plus minusque in conclusione quam in praemissis_. As we see from Lotze's own defence, the conclusion cannot be drawn without another premise or premises to the effect that "S, Q, R, are [Sigma], and [Sigma] is the one real subject of M." But how is all this to be got into the second figure? Again, Wundt and B. Erdmann propose new moods of syllogism with convertible premises, containing definitions and equations. Wundt's _Logic_ has the following forms:-- (1) 1st Fig. | (2) 2nd Fig. | (3) 3rd Fig. Only M is P. | x = y. | y = x. No S is M. | z = y. | y = z. :. No S is P. | :. x = z. | :. x = z.