head of head step and middle step, allsome,

Lo. head of upshot, somely.

'Every two-horned beast-is cud-chewsome,'
'Every two-horned beast-is grass-eatsome,'
'Some grass-eatsome beast-is cud-chewsome.'

5. Shape-shifting (reductio). Shape-shifting of a redeship or thought-putting is a bringing of it over into another shape, by a shifting of some ends of its steps:

3 Ho.
Ma.

Lo.

Ho., 'Some dog-is a greyhound.'

Ma., 'Every dog-is barksome.'

Lo., 'Some barksome (beast)—is a dog.'

Take the step Ma. and put it first:

'Every dog is barksome.'

Take the step Ho. and make it Mo., with the ends 'dog' and 'greyhound' shifted each into the place of the other :

'Some greyhound-is a dog.'

Turn Ma. into Lo., putting the ends 'dog' and 'barksome (beast)' each into the place of the other:

'Some barksome (beast)—is a dog.'

Ha. 'Every dog-is barksome.'

Mo. 'Some greyhound-is a dog.'

Lo. 'Some barksome (beast)-is a dog.'

6. The finding of the middle step-end (inventio medii termini). A man may sometimes want to find whether he can bring from a given head-thought-putting an upshot of a needed form, and so must seek a so-called middle term, middle step-end, or a step-end between the two ends of the first step or thought-putting.

If he wants to bring out an unstraitened ayesome upshot, the middle step-end may be the fore-end to the

higher step, and hinder end to the lower step. Call it the 'What is it,' and so write the rede-ship as of the B.headed shape:

"Every "What is it"—is cloven-hoofed.'

'Every two-horned beast-is "What is it."
Question: What will do in the stead of 'What is it'?
Answer: Cud-chewsome beast.

'Every cud-chewsome beast-is cloven-hoofed.'
'Every two-horned beast-is cud-chewsome.'
'Every cloven-hoofed beast-is two-horned.'

If he wants a straitened ayesome upshot, the middle term must be fore-end to the higher step, and hinder end to the under step of the rede-ship, which is of the shape

"Every "What is it'-is two-horned.'

'Some one grass-eatsome beast-is "What is it."
'Some one two-horned beast-is grass-eatsome.'
Question: What will do for 'What is it'?
Answer: Cud-chewsome.

If he wants an unstraitened naysome upshot, the middle term must gainsay the higher step, and be hinder end to the under step, and may be of the shape

C.e

s.a

th.e

'No good man-is "What is it."'

'Every miser-is "What is it."
'No miser-is a good man.'

Question: What will do for 'What is it'?
Answer: Selfish.

If he seeks a straitened nay, the middle term may thwart the higher step and be hinder end to the under one, and the rede-ship may be of the shape

F.e

though it

s.i

th.o

may take one of two or three other shapes.

7. A single-headed rede-ship is one with the same foreend to the two fore-steps, as

'Alfred-was good.'

‘Alfred—was king;' so

'Some king-was good.'

8. In-lurking rede-step (enthymeme) is a rede-ship of only two rede-steps, as one of the three lurks unworded in the mind of the speaker, as

'My starling has only one leg,' and so
'She cannot run.'

Put in the higher rede-step, which may be

1. 'A starling with only one leg cannot run.
2. 'My starling has only one leg;' therefore
3. 'She cannot run.'

A rede-ship with an in-lurking thought (the enthymeme) is not unwisely very rife in our common talk since the head step is so fully understood and allowed that there is no call for the wording of it. If I say 'my tub leaks, because it has a hole in the bottom of it,' the truth of the step of the reasoning which words the cause of the upshot, ‘a tub with a hole in the bottom of it will leak,' is already in the hearer's mind.

It is not, however, always thus with the in-lurking step of rede-ship, as it may be a belief only of the speaker's mind, and may lack proof, or may be too strongly put to be fully true; as, if Tom should say, 'John holds such or such opinions and must be a fool,' the head step would be that every man who holds those opinions must be a fool, which wants proof and may not be true. He might say on a call for a proof, 'They are opinions which I feel sure are wrong, and which every body but himself knows to be wrong;' the first of which propositions is of no weight as a proof, and the other wants proof which, most likely, no man could find.

The head step which may lurk in the mind may be true, but the middle one may be untrue, as—

'John cannot understand that, for he does not understand anything at all.'

The full rede-ship would be

'A man who cannot understand anything at all cannot understand that.'

'John cannot understand anything at all'; therefore 'John cannot understand that.'

But the middle step might be open to a very unwelcome challenge for proof.