Then putting A., S., N., or all, some, or none for the fore-end of the thought-puttings, and so or not so for the latter-end or time-taking of it, we shall have patterns of sundry forms of propositions:

(1) and (2) which are flatly gainsaying (contradictoria), as 'all men are wise,' 'no man is wise.' So (2), (3), ‘no man is wise,' 'some man is wise,' and (1), (4), ‘all men are wise,' 'some man is not wise' are flatly gainsaying (contradictoria).

(3) and (4), 'some men are wise,' 'some men are not wise,' are underthwartsome (subcontraria).

(1), (3), 'all men are wise,' 'some man is wise,' undermatchsome (subalterna).

(2), (4), 'no man is wise,' 'some man is not wise,' under-matchsome.

6. Even-mightedness of thought-puttings (æquipollentia), Thought-puttings may be unlike in shape or in their two ends, and yet may be of one might in meaning. The ends may shift their shape or wording by the intaking or outleaving of fornaying words, no, not, ne, and others,

as

'Not every horse is black; some horse is not black.' 'It is not that no horse is black; some horse is black.' "There is not any horse which has not been a colt; every horse has been a colt.'

'It is not every man who has not been sick; some man has been sick.'

Two nays make an ay, as—

'It is not John who is not at school; It is John who is at school.'

'I am not unmindful of your kindness; I am mindful of &c.'

7. Shifting (conversio).

End-shifting. End-shifting is the setting of each of the two ends of a thought-putting in the stead of the other, as

'A triangle-is a three-sided figure.'
Shiftedly :

A three-sided figure-is a triangle.'

There are three kinds of end-shiftings:

Simple:

I. Simple.

2. By hap, and

3. By with-setting.

'No man-is a stone,' 'no stone-is a man.'

Not every true thought-putting is true with its ends shifted, as―

as

'Every soldier-is a man.' But it is not true that
'Every man-is a soldier.' But if

'Every soldier is a man': then by hapsomeness
'Some man is a soldier.'

Shifting of the head-end by hapsomeness (accidens),

'Every soldier-is a man.'

'Some (not every) man-is a soldier.'

Shifting by thwart-putting.

Shifting of the ends and changing of the straitened end into an unstraitened shape, as—

'Every soldier-is a man.'

'Every one not a man-is not a soldier.'

8. Mood thought-putting (propositiones modales), are such as are put in some wider shape under a new heading, or those in which the whole thought-putting is put as an under-end to a new head-end, of

Needsomeness, or

Hapliness, or

Mayliness, or

Unmightsomeness, as—

Simple:

'Man is breathesome.'

With a mood heading of needsomeness:

'(It must be that) a man is breathesome.'

Simple:

'John is learned.'

With a mood heading of hapsomeness:

'(It is open to) John to become learned.' Simple:

'Some water is hot.'

By a heading of mayliness:

'(It can or may be that) some water is hot.'

Simple:

'Offences will come.'

'(It must be that) offences will come.'

'He goes through Samaria.'

'(He must needs) go through Samaria.'

Let a mean aye (affirmatio), to both mood and timetaking,

u-unaye or nay (negation) to both.

Let m stand for mood,

am-aye to the mood, and nay to the time-taking, um—unaye or nay to the mood, and aye to the time-taking,

Thence we may form tables of the moods: