(b) Formal Logic clearly will not quail before the charge of uselessness.  But on its own principles it ought to be consistent.  But by this test also, when it is rigorously judged by it, it fails completely.  Its inconsistencies are many and incurable.  It cannot even be consistent in its theory of the simplest fundamentals.  It is found upon some occasions to define judgment as that which may be either true or false; and upon others as that which is ‘true’ (formally)—­i.e., it cannot decide whether or not to ignore the existence of error.

(c) The Formal view of inference regards it as a ‘paradox.’  An inference is required on the one hand to supply fresh information, and on the other to follow rigorously from its premisses; it must, in a word, exhibit both novelty and necessity.  It would seem, however, that if our inference genuinely had imparted new knowledge, the event must be merely psychological; for how can any process or event perturb, or add to, the completed totality of truth in itself?  On the other hand, if the ‘necessity’ of the operation be taken seriously, the ‘inference’ becomes illusory; for if the conclusion inferred is already contained in the premisses, what sense is there in the purely verbal process of drawing it out?

(d) Most glaringly inadequate of all, however, is the Formal doctrine of ‘Proof’ contained in its theory of the Syllogism.  A Formal or verbal syllogism depends essentially on the ability of its Middle Term to connect the terms in its conclusion.  If, however, the Middle Term has not the same meaning in the two premisses, the syllogism breaks in two, and no ‘valid’ conclusion can be reached.  Now, whether in fact any particular Middle Term bears the same meaning in any actual reasoning Formal Logic has debarred itself from inquiring, by deciding that actual meaning was ‘psychological.’  It has to be content, therefore, with an identity in the word employed for its Middle, But this evidence may always fail; for when two premisses which are (in general) ‘true’ are brought together for the purpose of drawing a particular conclusion, a glaring falsehood may result. E.g., it would in general be granted that ‘iron sinks in water,’ yet it does not follow that because ’this ship is iron’ it will ‘sink in water,’ Hence syllogistic ‘proof’ seems quite devoid of the ‘cogency’ it claimed.  After a conclusion has been ‘demonstrated’ it has still to come true in fact.  This flaw in the Syllogism was first pointed out by Mr. Alfred Sidgwick.

(e) The formal Syllogism, moreover, conceals another formal flaw.  An infinite regress lurks in its bosom.  For if its premisses are disputed, they must in turn be ‘proved.’  Four fresh premisses are needed, and if these again are challenged, the number of true premisses needed to prove the first conclusion goes on doubling at every step ad infinitum.  The only way to stop