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Rule VI. From two negative premises nothing can be concludeil
. For they separate the middle term both from the subject and predicate of the conclufion, and when two ideas disagree to a third, we cannot infer that they either agree or disagree with each other.
Yet where the negation is a part of the middle term, the two premises may look like negatives according to the words, but one of them is affirmative in sense ; as,, what has no thought cannot reason; but a worin has. no thought; therefore a worm cannot reason. The minor proposition does really affirm the middle term concerning the subject. (viz. ) a worm is what has no thought, and thus it is properly in this fyllogism an afofirmative propofition.
Rule VII. From two particular premises nothing can be concluded. This rule depends chiefly on the first axiom.
A more laborious and accurate proof of these rules,, and the derivation of every part of them in all possible cases, from the foregoing axioms, require so much time,, and are of so little importance to allilt the right use of reason, that it is needless to infift longer upon them here. See all this done ingeniously in the Logic, calleed the Art of Thinking, Part III. Chap. III. &c.
Of the Modes and Figures of simple Syllogifmis.".
IMPLE syllogisms are adorned and surrounded in
the common books of Logic with a variety of inventions about modes and figures, wherein by the artiaficial contexture of the letters A, E, I, and O, men have endeavoured to transform Logic, or the Art of Reasoning, into a sort of mechanism, and to teach boys to syllogize, or frame argument and refute them, with. out any real inward knowledge of the question. This is almost in the same manner as school-boys have been .
taught perhaps in their trifling years to compofe Latin verfes; that is, by certain tables and squares, with a variety of letters in them, wherein by counting every Exth, seventh, or eight letter, certain Latin words should be framed in the form of hexameters or pentameters; and this may be done by those who know nothing of Latin or verses.
I confess, some of these logical subtleties have much more use than those verifying tables, and there is much ingenuity discovered in dleterinining the precise number of fyllogilms that may be formed in every figure, and giving the reasons of them ; yet the light of nature, a good judgment, and due consideration of things tend more to true reasoning, than all the trappings of modes, and figures.
But left this book be charged with too great defects and imperfections, it may be proper to give short hints of that which some logicians have spent so much time and paper upon:
All the possible combinations of three of the letters, A, E, I, O, to make three propositions amount to Gxty. four, but fifty four of them are excluded from form. ing true syllogisms, by the seven rules in the foregoing section : the remaining ten are variously diversified by figures and modes into fourteen fyllogisms..
The figure of a syllogism is the proper disposition of the middle term with the parts of the question.
A mode is the regular determination of propositions according to their quantity and quality, that is, their universal or particular affirmation or negation ; which are signified by certain artificial words wherein the confonants are neglected, and these four vowels A, E, I, O; are only regarded.
There are generally counted three figures.
In the first of them the middle term is the subject of the major propofition, and the predicate of the minor. This contains four modes (viz.). Barbara, Celarent, Darii, Ferio. And it is the excellency of this figure that all sorts of questions or conclusions may be proved by it, whether A, E, I, or O, that is, universal or par. ticular, afirmative or negative, as,
Bar- Every wicked man is truly miserable ; ba.. All tyrants are wicked men :
Therefore all tyrants are truly miserable.
Ce- He that is always in fear is not happy ;
Da- Whatsoever furthers our salvation is good for us ; ri- Some afflictions further our salvation : i. Therefore forne afilictions are good for us.
Fe. Nothing that must be repented of is truly desirable ; ri- Some pleasures must be repented of: Therefore there are some pleasures which are not
In the second figure the middle term is the predicate of both the premises; this contains four modes, (viz.) Cæfare, Camcitres, Festino, Baroco, and it admits only of negative conclusions ; as,
Cæ- No liar is fit to be believed;
Therefore no good christian is a liar.
The reader may easily form examples of the rest. The third figure requires that the middle term be the subject of both the premises. It has fix modes, (viz.) Darepti, Felapton, Disamis, Datis, Bocardo, Ferison; and it admits only of particular conclusions : as,
Da- Whosoever loves God shall be faved ;
I leave the reader to form examples of the rest.
The modes of these three figures are comprised in four Latin verses.
Barbara, Celarent, Darii, Ferio quoque prima.
In the first figure the major proposition must always be universal, and the minor affirmative.
In the second figure also the major must be univer-fal, and one of the premises, together with the conclusion, must be negative.
In the third tigure the minor must be affirmative, and the conclusion always particular.
There is also a fourth figure, wherein the middle term is predicated in the major proposition, and subjected in the minor : but this is a very indirect manner of concluding, and is never used in the sciences, nor in human life, and therefore I call it useless. Some logicians will allow it to be nothing else but a mere inversion of the first figure; the modes of it, (viz ) Baralipton or Barbari, Celantes, Dabitis, Fapismo, Ferifon, are not worthy to be explained by one example.
Of complex Syllogismsó.
T is not the mere use of complex terms in a syllo
gism that gives it this name, though one of the terms is usually complex: but those are properly called complex syllogisms, in which the middle term is connected with the whole subject, or the whole predicate in two distinct propofitions, but is intermingled and compared with them by parts, or in a more confused manner, in different forms of speech; as,
The sun is a senseless being :
Here the predicate of the conclusion is worshipped, a senseless being, part of which is joined with the middie term, fun in the major proposition, and the other part in the minor.
Though this fort of argument is confefled to be entangled, or confused, and irregular, if examined by the rules of fimple fyllogisms; yet there is a great variety of arguments used in books of learning, and in common life, whose consequence is strong and evident, and which must be ranked under this head; as,
I. Exclusive propofitions will form a complex argument; as pious men are the only favourites of heaven; true christians are favourites of heaven : therefore true christians are pious men. Or thus, hypocrites are not pious men; therefore hypocrites are no favourites of heaven.
II. Exceptive propositions will make such complex fyllogisms; as, none but physicians caine to the confultation ; the nurse is no physician ; therefore the nurse came not to the consultation.
III. Or, comparative propofitions ; as, knowledge is better than riches ; virtue is better than knowledge : therefore virtue is better than riches. Or thus, a dove will fly a mile in a minute : a swallow flies swifter than a dove; therefore a swallow will fly more than a mile in a minute.
IV. Or inceptive and defitive propositions ; as, the fogs. vanish as the sun rises : but the fogs have not yet ben gun to vanish : therefore the sun is not yet risen.
V. Or modal propositions ; as, it is necessary that a General understand the art of war: but Caius does not understand the art of war; therefore it is necesary Caius should not be a General. Or thus, a total eclipse of the fun would cause darkness at noon ; it is possible that the moon at that time may totally eclipse the sun : therefore it is pofsible that the moon may cause darkness at noon.
Beside all these, there is a great number of complex fyllogisms which can hardly be reduced under any particular titles, because the forms of human language are fo exceeding various; as,
Christianity requires us to believe what the Apostles