of its Subject. As when we say that Men are Creatures, the word Creature signifies no more all sorts of Creatures, but only such Creatures as are Men.

CHAP. XIV.

Of the Conversion of Affirmative Propositions.

WE call that the Conversion of a Proposition, when the Subject is changed into the Predicate, and yet the Proposition holds true, if it were so before: Or rather that it necessarily follows to be true by the Conversion, supposing that it were such before.

Now from what we have said, it may be easily understood how this Conversion is to be made. For as it is impossible that one thing should be joined and united to another; but that the other must be joined to the first; and that it follows of course, if A be joined to B, B is also joined to A, it is evident that it is impossible, that two things should be conceived as Identified, which is the most perfect of all Unions, but that the said Union must be reciprocal, that is, unless it may be affirmed of both Terms, that they are united in the same manner as they are said to be. Which is called Conversion.

Therefore as in particular Affirmative Propositions for example, when it is said, some Man is just the Subject and the Predicate are both Particular; for that the Predicate just being restrained by the extent of the Subject, signifies only that particular justice which is in some one Man; it is evident that if some one Man be Identified with just, somewhat of just is also Identified with some one Man. And therefore there needs no more than simply to change the Attribute into the Subject, observing the same particularity, to convert these sorts of Propositions,

We cannot say the same thing of Universal Affirmative Propositions, because that in those Propositions the Subject is only Universal, that is, is taken in its full extent, and the attribute on the other side is limited and restrained. And therefore when it is to be made the Subject by Conversion, the same restriction is to be observed, and the mark which determines it, must be added, lest it should not be taken generally. Thus when I say, that Man is a Creature, I unite the Idea of Man with that of a Creature, restrained and limited only to Men. And therefore if I would invert this Union, by beginning from a Creature, of which may afterwards be predicated, the same restriction of the first Term is to be observed, and for fear of being deceived, some note of determination must be added,

However, because Affirmative Propositions cannot be converted, but into particular Affirmatives, that they are less properly converted than others. But as they are composed of a general Subject, and a restrained Predicate, it is evident when they are converted, by changing the Attribute into the Subject, they ought to have a restrained or limited Subject.

Whence we deduce these two Rules.

1. RULE.

Universal Affirmative Propositions may be converted, by adding a mark of Particularity to the Attribute, and become the Subject. 2. RULE.

Particular Affirmative Propositions are to be converted without any addition, or any change. That is, retaining only for the Attribute, become the Subject, the Mark of particularity that belonged to the first Subject.

But these two Rules may be reduced to one that shall com prehend both.

The Attribute being limited by the Subject, in all affirmative Propositions, if the predicate is to be changed into the Subject, the Restriction must be observed: And by consequence it must have a mark of particularity annexed, whether the first Subject were Universal or Particular.

Nevertheless it often happens, that Universal Affirmative Propositions, may be converted into others that are Universal. But this is only when the Attribute is of itself no larger in extent than the Subject, as when difference or property are affirmed of the Species, or the definition of the thing defined. For then the Attribute not being restrained, may be taken in the Conversion, as generally as the Subject, all Men are Rational, all Rational Creatures are Men.

But these Conversions not being true, unless upon particular occasions, they are regarded as true Conversions, which ought to be certain and infallible, by the Disposition of the Terms.

CHAP. XV.

Of the Nature of Negative Propositions.

THE nature of a Negative Proposition cannot be more clearly expressed than by saying, that one thing is conceived not to be another.

But to the end one thing may not be another, it is not necessary that it should have nothing common with it; it being sufficient that it has not all which the other has; as it is sufficient for a

Beast not to be a Man, that he has not all that a Man has, not but that he may have something common with Man. From whence this Axiom follows.

5. AXIOM.

A Negative Proposition does not separate from the Subject all the parts contained in the Comprehension of the Attribute; but it only separates the total Idea composed of all the united Attributes.

If I say that Matter is not a thinking Substance, yet do I not deny it to be a Substance, but I say it is not a Thinking Substance, which is the total and entire which I deny of the Matter.

It is quite otherwise with the Extension of an Idea. For the Negative Proposition separates from the Subject the Idea of the Attribute in its full extent. The reason of which is evident. For to be the Subject of an Idea, and to be contained in its extension is no more than to include that Idea, consequently when we say, that one Idea does not include another, which may be called denying, we say that it is not one of the subjects of the Idea.

Thus when I say that a Man is not an Insensible Being, I say at the same time that Man is none of the Insensible Beings, and by consequence I deny all things Insensible of Man, whence we may derive this Axiom.

6. AXIOM.

The Attribute of a Negative Proposition is always taken generally. Which may be expressed more distinctly. All the Subjects of an Idea, which are denied of another Idea, are also denied of the former Idea. If a Triangle be denied of Squares, whatever `is Triangular shall be denied of a Square. In the Schools they usually say, what is denied of the Genus, is denied also of the Species. For the Species is the Subject of the Genus, as Man is the Subject of Creature, being contained in the Extension of Creature.

Not only Negative Propositions separate the Attribute from the Subject according to the full Extension of the Attribute; but they separate that Attribute also from the Subject, according to the full extension which the Subject has in the Proposition. That is, it separates universally, if the Subject be universal; particularly, if particular. As if I say, No vicious Man is happy, I separate all vicious persons from happy persons. And if I say, Some one Doctor is not learned, I separate learned from some Doctor. From whence we draw this Axiom.

7. ΑΧΙΟΜ.

Every Attribute denied of a Subject, is denied of all that is cóntained in the extent which the Subject has in the Proposition.

CHAP. XVI.

Of the Conversion of Negative Propositions.

AS it is impossible to separate two things totally, but that the separation must be mutual and reciprocal, it is evident that if I say, No Man is a Stone, I can likewise say, No Stone is a Man. For if any Stone were a Man, that Man would be a Stone, and by consequence it would not be true that no Man was a Stone. Hence this Rule.

3. RULE.

Universal Negative Propositions may be converted simply, by changing the Attribute into the Subject, and by preserving the Attribute, become the Subject, the same Universality which the former Subject had.

In Negative Propositions, the Attribute is always taken Universally; as being denied according to its full extent.

But the same Reason will not allow the Conversion of particular Negative Propositions. For example, we cannot say that some one Physician is not a Man, because we may say that some one Man is no Physican. Which proceeds from the nature of the Negation itself, that in negative Propositions the Attribute is always taken Universally, and according to its full Extension. So that when a particular Subject becomes an Attribute by Conversion in a Negative particular Proposition, it becomes Universal, and changes its nature, contrary to the Rules of true Conversion; which ought not to change the restriction of the Terms. So in this Proposition, Some one Man is no Physician, the term Man is taken particularly. But in the false Conversion, Some one Physician is no Man, the word Man is taken Universally.

Now it no way follows, that because the quality of the Physician is separated from some one Man in this Proposition, Some one Man is no Physician; or because the Idea of a Triangle is denied of some other Figure, as in this Proposition, Some one Figure is no Triangle, I say it does not follow hence, that there are any Physicians that are not Men, nor any Triangles that are not Figures

No. 15.

THE END OF THE SECOND PART,

THE

ART OF THINKING.

PART THE THIRD.

Of Discourse or Ratiocination.

THIS Part of which we are now to treat, containing the Rules of Discourse, is deemed the most important Part of the Art of Thinking, and is almost the only Part which ought to be treated most accurately. But we have some reason to suspect whether it be altogether so useful. For the greatest Part of the Errors among men, as we have already said, arises from hence, that they build their discourses upon false Principles, rather than from their drawing false conclusions from their Principles. It rarely happens that we are imposed upon by such discourses which are therefore only false, because the consequences are ill drawn. Seeing they who are not able to discover those falsities by the light of Nature, will for the most part be as unable to understand, much less to apply the Rules which are laid down for discourse. Nevertheless should these Rules be looked upon only but as speculative Truth, they would be very useful for the exercise of the Wit. And moreover it cannot be denied but that they be of some use upon several occasions, especially to such who being of a quick and lively apprehension, never suffer themselves to be deluded by false Consequences, but for want of heed and attention, which a due reflection upon these Rules would easily rectify. However it be, we here present you with what has been usually said concerning this matter, and with something more than has hitherto yet been discovered,