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PART III

On Discourse

CHAPTER 1

When the relation or connection of two ideas or terms cannot be directly perceived, the relation between them will often be able to be seen by a comparison of both of them with some third or middle [idea or term] or with several middle [ideas or terms] which are clearly connected with each other. This mental process is dianoetic judgment or discourse.

When there is only one middle, we are said to have a syllogism; when there are several middles connected with each other, by which the comparison of the terms is made, it is a sorites, or complex form of reasoning.¹ First, therefore, we must deal with the simple and categorical syllogism, for the other more complex forms may be reduced to syllogisms.

A syllogism is “discourse in which a third proposition is inferred from two propositions rightly arranged.”

Before a proof is given by means of a syllogism, there is a question or problem of showing the relationship between two terms. These terms are called the Extremes; they are the Major term and the Minor term. The Major term is “the predicate of the question” or of the conclusion, and the Minor term is “the subject of the question.” The Middle Term is that which is compared with both of the extreme terms in the premissed propositions.

Irrespective of the content of the syllogism, there are these three terms: the Major, the Minor, and the Middle Terms. Taking account of the content, there are three propositions: the Major Proposition, the Minor Proposition (these are also called the Premisses), and the Conclusion. They are distinguished not by their order but by their nature.

1. The major proposition “is that in which the major term is compared with the middle term” and is called the proposition par excellence.

2. The minor proposition is that “in which the minor term is compared with the middle term” and is called the assumption or subsumption.

3. The conclusion is that “in which the extremes are compared with each other,” and the middle term never appears here.

CHAPTER 2

The whole force of the syllogism may be explained from the following axioms.²

Axiom 1. “Those things which agree with a single third thing agree with each other.”

2. “Those of which one agrees and the other does not agree with one and the same third thing, do not agree with each other.”

3. “Those which agree in no third thing, do not agree with each other.”

4. “Those which do not disagree with any third thing, do not disagree with each other.” From these [axioms] the general rules of syllogisms are deduced. The first three are about the quality of propositions.

Rule 1. If one of the premisses is negative, the conclusion will be negative (by axiom 2).

Rule 2. If both the premisses are affirmative, the conclusion will be affirmative (axiom 1).

Rule 3. From two negative [premisses] nothing follows because those which agree with each other and those which disagree with each other may both be different from a third.

Two [rules] on the Quantity of Terms:

Rule 4. The middle must be distributed once, or taken universally; for a common term often contains two or more species which are mutually opposed to each other, and from which predication may be made according to different parts of its own extension; therefore terms do not truly agree with a third term, unless one at least agrees with the whole of the middle.

Rule 5. No term may be taken more universally in the conclusion than it was in the premisses, because an inference from particular to universal is not valid.

On the Quantity of Propositions:

Rule 6. “If one of the premisses is particular, the conclusion will be particular.” For (i) suppose the conclusion is affirmative: therefore (by rule 1) both premisses are affirmative; but no term is distributed in a particular [premiss]; therefore (by rule 4) the middle term has to be distributed in the other one; it is therefore the subject of a universal affirmative; therefore the other extreme is also taken particularly, since it is the predicate of an affirmative, ergo, the conclusion will be particular (by rule 5). (ii): Suppose the conclusion is negative: therefore, its predicate is distributed; hence (by rules 5 and 4) both the major term and the middle term have to be distributed in the premisses, but (rule 3) when one premiss is negative, the other is affirmative. If one [premiss] is particular, only these two terms can be distributed; when one premiss is affirmative, the other should be particular. Therefore the minor extreme, the subject of the conclusion, is not distributed in the premisses; therefore (by rule 5) it is not distributed in the conclusion.

Rule 7. “From two particulars nothing follows,” at least in our normal way of speaking, according to which the predicate of a negative is taken to be distributed. For (i) if the conclusion is affirmative and both premisses are affirmative, no term in the premisses is distributed (contrary to rule 4). (ii) Suppose the conclusion is negative; therefore some predicate is distributed, but the predicate is distributed only in particular premisses; it will therefore be invalid (contrary to rule 4 or 5).

Rules 1 and 7 are thus reduced to one rule. The conclusion follows the weaker side, i.e., the negative or particular. All the rules are contained in these verses:³

You must distribute the middle, and there should be no fourth term.

Both premisses should not be both negative and particular.

The conclusion should follow the weaker side;

And it may not be distributed or negative, except when a premiss is.⁴

In a curious and unusual manner of speaking, a certain negative conclusion may be reached, with the predicate undistributed, as in this example:

Certain Frenchmen are learned,

Certain Englishmen are not learned,

Therefore,

Certain Englishmen are not certain Frenchmen.

CHAPTER 3

A figure of a syllogism is “the proper arrangement of the middle in the premisses”; there are only four figures.

1. That in which the middle is the subject of the major and the predicate of the minor.

2. That in which the middle is the predicate of both.

3. That in which the middle is the subject of both.

4. That in which the middle is the predicate of the major and the subject of the minor.

In the first [the middle is] sub[ject and] pre[dicate]; in the second [it is] twice a pre[dicate]; in the third [it is] twice a sub[ject]; and in the fourth [it is] pre[dicate and] sub[ject].

The mood of the syllogism is “the correct determination 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 modes can be reduced to the four modes of the first figure, which Aristotle calls the perfect [modes].¹⁰

There are two kinds of reduction, ostensive and ad absurdum. The initial letters in each of the modes (B, C, D, and F) indicate the modes of the first figure to which the modes of the other [figures] are to be reduced, i.e., those of which the initial letter is the same.¹¹ S and P following a vowel show that that proposition is to be converted, S simpliciter, P per accidens. M shows that the propositions are to be transposed, K that the reduction is made per impossibile, of which more later. When this is done, the conclusion reached will be either the same as in reducing Cesare, Festino, etc., or [a conclusion] which implies the same conclusion, or the contradictory to the conceded premiss. The validity of an ostensive reduction is known from the rules of conversion and subalternation.

Reduction to the impossible is as follows. If it is denied that a given conclusion follows from true premisses, let the contradictory of the conclusion be substituted for the premiss whose symbol includes a K, like the major in Bokardo and the minor in Baroko; these premisses will then show in Barbara the truth of the contradictory of the premiss which was claimed to be true. If therefore the given premisses had been true, the conclusion would also have been true; for if it was not, its contradictory would have been true, and if that had been true, it will show (in Barbara) that the other premiss is false, contrary to the hypothesis.

For these rules of syllogisms to hold, we have to look carefully for the true subjects and predicates of the propositions, which are sometimes not at all obvious to beginners; and then we have to determine whether they are really affirmative or negative as they are used in the argument. For in complex [propositions], sometimes one part is negative, the other is affirmative, and occasionally it is the negative part (the less obvious part) which is chiefly in point. For example,

And the dictum de omni et nullo is so useful in proving a true argument and detecting a false one, that by its help any intelligent person may be able to see both true syllogistic force and its fallacious semblance, according to whether one of the premisses contains the conclusion or not, even before applying the special rules of syllogisms.

CHAPTER 7

With regard to the remaining forms of argument, it is evident that they are imperfect syllogisms or may be reduced to imperfect syllogisms.

1. The enthymeme¹² or rhetorical syllogism is “when one of the premisses is unspoken because it is quite obvious”; it is for this reason that an enthymematic judgment has full syllogistic force.

2. Induction is “an inference from various examples,” of which the chief use is in physics, in politics, and in household matters. It does not generate the highest credit or exclude all fears of the contrary, unless it is clear that there are absolutely no contrary examples.

3. An epicheirema¹³ is “a complex syllogism in which a confirmation is attached to one or both of the premisses.”

4. Sorites is “discourse which contains several syllogisms which are connected with each other,” or where there are several middle terms which are connected with each other or with the extremes in several propositions of which if even one is negative, the conclusion will be negative, and if two are negative or any middle term is not distributed at least once, there will be no inference.

5. A dilemma is “a kind of epicheirema, where in making a division, that which is shown about the individual parts in the premisses is concluded of the whole.”

6. A hypothetical syllogism is “one in which one of the premisses is hypothetical”; when the minor is hypothetical, so also is the conclusion; these also serve to prove the inference in an enthymeme. More frequent are those in which the major is hypothetical, for example:

	Major: If this [is], that will be	Or, If this [is], that will be,
	Minor: But this [is] (con.), therefore also that.	But not that, therefore not this either.

But since a more general predicate follows from any of the corresponding kinds (for example, If it is a man, if it is a horse, etc., it will also be an animal), but from a general predicate, no one particular species will follow (for from the fact that it is an animal, it does not follow that it will be a horse or an ass), it is evident that hypothetical syllogisms rightly proceed (1) from the positing of an antecedent to the positing of a consequent, or (2) from the removal of a consequent to the removal of an antecedent.

	If Titius is a man, he is also an animal,	2) If it were a bird, it would fly,
	But he is a man, therefore he is an animal.	But it does not fly, therefore it is not a bird.

It is a fallacious inference from the removal of an antecedent, or the positing of a consequent:

	If Titius is a horse, he is an animal,	Or, But he is an animal,
	He is not a horse, therefore he is not an animal.	Therefore he is a horse.

The positing of a negative will be a negation, and the removal of it an affirmation.

Hypothetical [syllogisms] are reduced to categorical [syllogisms] by this general method: “every case which posits that Titius is a man, posits that he is an animal; but every case, or some case, posits that he is a man; therefore, etc.” But often it may be more easily and briefly done when there is either the same subject or the same predicate to the antecedent and the consequent; for example:

If man is an animal, he has sensation,

But every man is an animal, therefore he has sensation.

Every animal has sensation.

Every man is an animal; therefore,

Every man has sensation.

If every animal has sensation, every man has sensation;

But every animal has sensation; therefore,

Every man has sensation.

7. Disjunctive syllogisms are “those in which the major is disjunctive, [whether] affirmative or negative.” Either it is day, or it is night; but it is not day, therefore it is night. Or, it is not both night and day, but it is day; therefore it is not night. The force of the inference is obvious enough, when by positing an affirmative disjunctive major, an affirmative conclusion is drawn from a negative minor; or from a copulative negative major and an affirmative minor, the conclusion is negative. For in the former case the syllogism will be reduced to Barbara.

All time different from daytime is night;

But this time is different from daytime.

Therefore …

In the other case.

No daytime is night,

But this time is day.

Therefore …

There is no inference from an affirmative minor, in the former, or from a negative [minor] in the latter.

CHAPTER 8

As far as content is concerned, syllogisms are either certain or probable depending on their premisses.

A demonstration is “an argument duly reaching a conclusion from certain premisses,” and it is either ostensive, or leading to absurdity; the latter is the case when the contradictory of a proposition is shown to be false, from which it will be clear that it is itself true. The former is either a priori, or of a cause,14 “when an effect is shown from a known cause.” But there are causes of being and causes of knowing. The former are prior by nature and per se; the latter [are prior] in being known and in relation to us. Demonstrations drawn from both kinds of causes are called a priori, but especially those which are drawn from things prior by nature.¹⁵

“The discipline which relies on demonstrations” is science. The general rules of science are

1. “All terms must be accurately defined,” nor is their meaning ever to be altered.

2. “Certain and evident axioms are to be posited.”

3. “One must proceed from the better known to the less known by demonstrations step by step,” and premisses which go beyond axioms and propositions previously demonstrated are not to be admitted.

Demonstrations only deal with abstract propositions, especially in geometry and arithmetic.

There is no single principle of human knowledge which you may rightly say is prior to the rest. There are many evident principles apart from the most general axioms. Nor will any syllogism carry full credence unless both terms of the conclusion are found connected with the middle term in evident propositions. In demonstration, therefore, through several syllogisms which are connected in a continuous series, the number of evident propositions will exceed the number of middle terms by one.

In absolute propositions, and in those which are chiefly useful in life, there is another way of knowing which has its own proper evidence, albeit different from demonstrative [evidence]. Absolute propositions asserting that things exist are known (1) by consciousness, (2) by sense, (3) by reasoning, or by an observed link with existing things, or (4) by testimony. Other experiential truths about the powers and qualities of things are chiefly learned by experience, and by a varied acquaintance with life, and by induction; and whenever any example is similar, it should, other things being equal, be included with the larger rather than the smaller number. For rarely can men see any connection among the actual powers and qualities of things.

There are innumerable degrees of likelihood, from the slightest probability to full and stable assent; from the judicious appreciation [of their degrees] grave men are more likely to earn a reputation for prudence and wisdom than from cleverness in the sciences.

“Assent given to arguments which are probable but do not achieve the highest likelihood” is called opinion. Where either of the premisses is uncertain, there is only a probable conclusion; hence in a long chain of arguments, the result will be a very weak assent.

Arguments which create belief are either artificial and involve the use of reasoning, or inartificial, from testimony. “In recent [writers]¹⁶ assent resting on testimony is belief (par excellence).” Belief is either divine or human, depending on whether the assent rests on the testimony of God or of men.

Divine belief will be a fully firm assent when it is clearly established that God has revealed something, since a superior nature cannot deceive or be deceived.

Human belief too, although often hazardous, may sometimes attain full certainty, when it is clear that the witnesses could not have been deceived, and could not have intended to deceive others, so that neither their knowledge nor their reliability nor their truthfulness is in doubt.

Sometimes the knowledge of witnesses will be evident from the nature of the matter in hand; and their reliability will be established if they have not been induced to give testimony about the question in hand by any reward or other inducements; even more so when they testify to their own peril or loss, and could not expect to persuade others, if they themselves knew that the thing was otherwise.

If testimony is not liable to any suspicion of fraud or ignorance, belief may be given (1) to facts which cannot be known in any other way; (2) also to things totally different from what we have previously observed, if indeed there are no internal arguments that prevent belief; (3) and third, even to things that are strange and contrary to all our experience or observation, provided the testimony deals with material and circumstances that are different and remote from our own affairs.