Logic, Metaphysics, and the Natural Sociability of Mankind. Francis Hutcheson

of the propositions according to quantity and quality.”

      Sixty-four arrangements are possible of the four letters A, E, I, O; of these, fifty-two are excluded by the general rules. There remain, therefore, twelve concluding modes of which not all lead to a conclusion in every figure because of the nature of the figure; and some are not useful at all.

      CHAPTER 4

      The special rules of the figures are as follows.

      1. i. In figure 1 the minor [premiss] must be affirmative; if it were negative, the conclusion would be negative (by rule 1), and its predicate would be distributed. But the major would be affirmative (by rule 3), and its predicate would not be distributed; hence there would be a fallacy (contrary to rule 5).

      ii. The major [premiss] must be universal. For the minor is affirmative (from the former rule), and therefore its predicate is particular, namely the middle term. It must therefore (by rule 4) be distributed in the major of which it is the subject. These things will be more easily made clear by the schema below, where the letters denote distributed terms.⁵

      Here are examples of fallacies.

      N.B. Capital letters denote distributed terms; lowercase letters particular terms.

      2. Rules of the second figure:

      i. One of the premisses must be negative. For since the middle term is predicated of both, it would be distributed in neither if both were affirmative (contrary to rule 4).

      ii. The major must be universal. For the conclusion is negative, and its predicate is distributed. It must therefore (by rule 5) be distributed in the major of which it is the subject.

      3. Rules of the third figure:

      i. The minor must be affirmative, for the same reason as in the previous figure.

      ii. The conclusion must be particular. For since the minor is affirmative, its predicate, the minor term, is not distributed; therefore (by rule 5) it is not distributed in the conclusion of which it is the subject.

      Examples of fallacies:

      4. Rules of the fourth figure:

      i. “If the major is affirmative, the minor must be universal”; otherwise it will contravene rule 4.

      ii. If the conclusion is negative, the major must be universal; otherwise it will contravene 5.

      iii. If the minor is affirmative, the conclusion must be particular, for the same reason as in the third figure.⁸

      CHAPTER 5

      The concluding modes in the four figures are six.

      1. AAA, EAE, AII, EIO, *AAI, *EAO.

      2. EAE, AEE, EIO, AOO, *EAO, *AEO.

      3. AAI, EAO, IAI, AII, OAO, EIO.

      4. AAI, AEE, IAI, EAO, EIO, *AEO.⁹

      Thus there are two [modes] in the first [figure], two likewise in the second, and one in the fourth, which are useless and have no names, because they make a particular inference where the valid conclusion would be universal.

      The named modes are contained in these verses:

      Barbara, Celarent, Darii, and Ferio are of the First;

      Cesare, Camestres, Festino, Baroko are of the Second;

      The Third claims Darapti and Felapton,

      And includes Disamis, Datisi, Bocardo, Ferison.

      Bramantip, Camenes, Dimaris, Fresapo, Fresison,

      Are of the Fourth. But the five which arise from the five universal [modes]

      Are unnamed, and have no use in good reasoning.

      Here are examples of the modes according to the vowels which are contained in the words [of the mnemonic], A, E, I, O.

		FIGURE 1
	Bar	all A is b
	bA	all c is a: therefore
	rA	all c is b.
	CE	no A is B
	lA	all C is a
	rEnt	no C is B.
	DA	all A is b
	rI	some C is a
	I	some C is b.
	FEr	no A is b
	rI	some c is a
	O	some c is not b.
	Unnamed
	A	all A is b
	A	all C is A
	I	some c is b.
		(This is Subaltern 1, Barbara.)
	E	no A is B
	A	all C is A
	O	some C is not B.
		(Subaltern 2, Celarent)

		FIGURE 2
	CE	no B is A
	sA	all C is a
	rE	no C is B.
	CA	all B is a
	mEs	no C is A
	trEs	no c is B.
	fEs	no B is A
	tI	some c is a
	nO	some c is not B.
	bA	all B is A
	rOk	some c is not A
	O	some c is not B.
	E	no B is A
	A	all C is a
	O	some C is not b.
		(Subaltern Cesare)
	A	all B is a
	E	no C is A
	O	some c is not B.
		(Subaltern Camestres)

		FIGURE 3
	dA	all A is B
	rAp	all A is C
	tI	some C is b.
	fE	no A is B
	lAp	all A is C
	tOn	some c is not B.
	dI	some a is b
	sA	all A is c
	mI	some c is b.
	dA	all A is b
	tI	some a is c
	sI	some c is b.
	bO	some a is not B
	kAr	all A is C
	dO	some C is not B.
	fE	no A is B
	rI	some a is c
	sOn	some c is not B.

		FIGURE 4
	brA	all B is a
	mAn	all A is c
	tIp	some c is a.
	cA	all B is a
	mE	no A is C
	nEs	no C is B.
	dI	some b is a
	mA	all A is C
	rIs	some c is B.
	fE	no B is A
	sA	all A is C
	pO	some C is not B.
	frE	no B is A
	sI	some a is C
	sOn	some c is not B.
	A	all B is A
	E	no A is C
	O	some C is not B.
		(Subaltern Camenes)

      CHAPTER 6

      From axioms 1 and 2 (p. 32) the force of the inference in all of these modes will be clear, since both of the extremes are compared with the middle, and one of them with the distributed middle; and either both agree with it, or one only does not agree.

      The Aristotelians neatly demonstrate the force of the inference, and perfect the syllogisms, by means of reduction, since the validity of all [the syllogisms] in figure 1 is evident from the dictum de omni et nullo (see p. 26); they also give, in their technical language, the rules of conversion and opposition, by means of which all the other