I.
Cloven feet inhere with horns
Fossil animal appears to
have had cloven feet
it is probable he
had horns

When an architect, contemplating the fragments of a building, restores it in imagination after the analogy of similar buildings, we have an argument in inherence. Such speculations are generally too long and complex for analysis, but an instructive example occurs in Canon Rawlinson's Seventh Oriental Monarchy, which I will venture to quote, marking the phrases that introduce or express the rational idea. Observe the difference of style between this, which is real practical reasoning, and the trivial certainties of Syllogistic.

'What remains of this massive erection [the Takht-i-Khosru, or palace of Chosroës Anushirwan, at Ctesiphon] is a mere fragment, which, to judge from the other extant Sassanian ruins, cannot have formed so much as one fourth part of the original edifice. Nothing has come down to our day but a single vaulted hall on the grandest scale, together with the mere outer wall of what no doubt constituted the main facade of the building. The apartments, which, according to all analogy, must have existed at the two sides, and in the rear, of the great hall, some of which should have been vaulted, have wholly perished. Imagination may supply them from the Firuzabad, or the Mashita palace; but not a trace, even of their foundations, is extant; and the details consequently are uncertain, though the general plan can scarcely be doubted. At each side of the great hall were probably two lateral ones, communicating with each other, and capable of being entered either from the hall or from the outer air. Beyond the great hall was probably a domed chamber equalling it in width, and opening upon a court, round which were a number of moderate-sized apartments. The entire building was no doubt an oblong square, of which the shorter sides seem to have measured 370 feet. It had at least three, and may not improbably have had a larger number of entrances, since it belongs to tranquil times and a secure locality.'

***

The most notable argument in the category of concretion is undoubtedly the inference as to the sphericity of the earth. Next is the sub-inference by Columbus that China could be reached by sailing westward from Portugal. If the syllogistic opinion were valid—that a conclusion must be absolutely true or absolutely false—the expedition of Columbus was based on a fallacy. Most people think it was eminently rational.

No one has seen the north or the south poles, and the conviction that they could be realised, if certain difficulties of transport were overcome, is a sub-inference of the same character.

Here is a common type of inference in perspection—

III.
That church is 100 yards off
A man appears on
the roof of the ch.
he is 100 ys. off

And this—