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ment that "All men are mortal" has the effect of including men in the class of mortal beings, which would be represented by a small circle for "men," in a large one for "mortal." The annexed diagram exhibits (1) the Mood A A A, (11) E A E, (ш) A I I, and (iv) E I O, all of the first Figure.*

§ 105. Inference in Intension, Extension, and Denomination.

That a judgment may be interpreted either in its extension, or intension, or denomination, has been already shown (§ 78.). Every syllogism has the same property. Thus,

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The class of metals are some lustrous things,
Iridium is in the class of metals;

.. Iridium is among lustrous things—

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* The system of symbolical notation of Professor Boole, of Cork, ought not to be passed over. But it is so intimately connected with his whole work, " An Investigation of the Laws of Thought," that an attempt to compress it into a paragraph would only do an injustice to a thoughtful and profound writer.

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or in intension

The notion of some lustrous things attaches to the notion of

all metals,

The notion of some metal is implied in Iridium;

.. The notion of some lustrous thing attaches to that of Iridium

or in less uncouth, but at the same time, less accurate form

Lustrousness belongs to our notion of metals, Being a metal is part of the notion of Iridium; .. Lustrousness belongs to our notion of Iridium :

or lastly, in denomination

Metals may be called lustrous, Iridium has the name of metal ; .. Iridium may be called lustrous.

Although any argument may be so expressed as to give one or other capacity greater prominence, it is at all times possible to read an argument in any of the three powers, preserving of course the distribution of terms unchanged. The most important term in the extensive point of view is the least in the intensive, because it embraces most objects, but we know least of its nature; in the example, "lustrous" contains the other terms under it, and more, but "iridium" implies in it the notion of lustrous and much more; "lustrous" therefore has the greatest extension, "iridium" the greatest intension.

Where

the terms are equal, as in U U U of all Figures, ex tension and intension are in æquilibrio.

§ 106. Conditional Syllogisms.

A syllogism in which there is one pure conditional judgment or more (see § 71.) is called a Conditional Syllogism. All arguments of this class come into the scheme of syllogisms already given, when they are properly exhibited. The principal forms are here annexed.

1. In cases where M is N, C is D,

In cases where A is B, M is N; .. In cases where A is B, C is D.

II. In cases where C is D, M is N,

In cases where A is B, M is N; .. In cases where A is B, C is D. III. In cases where M is N, C is D, In cases where M is N, A is B; .. In cases where A is B, C is D.

These three forms are composed entirely of conditional propositions. They are in the three different figures; and examples of them will be correct or incorrect according as they do or do not conform to the principles of the syllogism already laid down, as to affirmation and negation, distribution of terms, &c,

Iv. In cases where M is N, C is D,
But in the given cases M is N;
Therefore in these cases C is D.

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v. In cases where M is N, C is not D,
But in the given cases M is N;

Therefore in the given cases C is not D.

VI. In all cases where M is N, and in no others, C is D,
In the given cases, M is not N;

Therefore in the given cases C is not D.

VII. In all cases where M is N, and in no others, C is D,
In the given case C is D;

Therefore M is N.

VIII. In all cases where A is B, M is N,
In the given cases M is not N;
Therefore in the given cases A is not B.

It

IX. In all the cases where A is B, M is not N,
In the given cases M is N;

Therefore in the given cases A is not B.

may facilitate the use of these formulæ if concrete examples of them are added, expressed in the form of ordinary categorical syllogisms.

I. (A A A. FIG. 1.)

All cases where law prevails, are cases where the rights of the weaker are secured,

All well-ordered states exhibit such cases;

Therefore in all well-ordered states the rights of the weaker are secured.

II. (A EE. FIG. II.)

All cases where rain falls are cases where clouds obscure the sky, All cases of heavy dew are cases where there are no clouds; Therefore cases of heavy dew are not cases of rain.

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