, 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 the process that occurred to logicians was an appeal to
the 'self-evident' truth of 'intuitions'; but this has been shown to be
argumentatively worthless. From this difficulty the pragmatist alone
escapes, by assuming his premisses _provisionally_ and arguing
_forwards_, in order to test them by their consequences. If the deduced
conclusion can be verified in fact, the premisses grow more assured.
Thus every real inference is an experiment, and 'proof' is an affair of
continuous trial and verification--not an infinite falling back upon an
elusive 'certainty,' but an infinite reaching forwards towards a fuller
consummation.

(_f_) So long as the logician regards his premisses not as hypotheses to
be tested, but as established truths, he must condemn the Syllogism as a
formal fallacy. It is inevitably a _petitio principii_. If the argument
'All men are mortal; S