1

FIGURES OF PROSLEPTIC SYLLOGISMS

IN PRIOR ANALYTICS 2.7

(number of words including notes: 5.000)

This paper is about a problematic passage from Prior Analytics 2.7 (59a32-41). The

passage is a summary of Aristotles discussion in chapters 2.5-7 of what he calls circular

proofs. It states, among other things, that certain circular proofs come about in the third figure.

These statements are incorrect if they are taken to refer to the third figure of Aristotles

categorical syllogisms. Consequently, the passage is often regarded as spurious although it is

found in all MSS.

Following Pacius, I argue that those statements refer to the third figure not of categorical

syllogisms but of what Theophrastus called prosleptic syllogisms. If interpreted in this way,

the statements are correct, and there is no reason to think that they are spurious. Thus the

passage appears to be the earliest extant evidence of the classification of prosleptic syllogisms

into three figures.

I. CIRCULAR PROOF IN PRIOR ANALYTICS 2.5-7

As is well known, Aristotles assertoric syllogistic focusses on four kinds of categorical

propositions:

AaB (A belongs to all B)

AeB (A belongs to no B)

AiB (A belongs to some B)

AoB (A does not belong to some B)

2

The syllogisms with which Aristotle is primarily concerned consist of three categorical

propositions, two of them serving as premisses and one as the conclusion. For example, here

is a syllogism in Barbara:

AaB (major premiss)

BaC (minor premiss)

AaC (conclusion)

Such syllogisms are traditionally referred to as categorical syllogisms. Aristotle distinguishes

three figures of categorical syllogisms (x, y, z are placeholders for a, e, i, o):

first figure: second figure: third figure:

AxB

ByC

AzC

BxA

ByC

AzC

AxB

CyB

AzC

Let us now turn to Aristotles discussion of circular proofs in Prior Analytics 2.5-7. Aristotle

begins by introducing the notion of circular proof:

,

(APr. 2.5 57b18-21)

In a circular proof one of the premisses of a categorical syllogism is proved by means of the

conclusion of this syllogism and the other premiss converted in predication (

3

). More precisely: given a categorical syllogism, a

circular proof is a syllogism (i) one of whose premisses is the conclusion of the original

syllogism, (ii) whose other premiss is one of the premisses of the original syllogism

converted in predication, (iii) and whose conclusion is the other premiss of the original

syllogism. Aristotle seems to take it for granted that this is a reasonable notion of circular

proof, and he relies on it in the Posterior Analytics in an argument against circular

demonstration.1 However, he does not explain or justify the details of his definition; in

particular, he does not explain why one of the premisses of the original syllogism should be

converted in predication.

The conversion which Aristotle has in mind here is different from the truth-preserving

conversions introduced in Prior Analytics 1.2, according to which AeB can be converted to

BeA, and AaB to BiA, and AiB to BiA. The kind of conversion which Aristotle employs in

2.5-7 is not in general truth-preserving. He applies it only to a- and e-propositions. When

applied to a-propositions, it consists simply in interchanging the predicate and subject term,

converting AaB to BaA. For example, here are Aristotles circular proofs of the two premisses

of a categorical syllogism in Barbara, each of them being itself a syllogism in Barbara:

original syllogism (Barbara)

circular proof of the major

premiss (2.5 57b22-5):

circular proof of the minor

premiss (2.5 57b25-8):

AaB

BaC

AaC

AaC

CaB

AaB

BaA

AaC

BaC

1 APost. I.3 73a11-16. See R. Smith, Immediate Propositions and Aristotles Proof Theory,

Ancient Philosophy 6 (1986), 47-68, at 60-1.

4

When the conversion in question is applied to e-propositions, it is more complex. Consider a

possible circular proof of the a-premiss of a categorical syllogism in Celarent. Such a circular

proof needs to deduce the a-premiss of Celarent from the e-conclusion and the converted e-

premiss. If conversion consisted in interchanging the predicate and subject term, the circular

proof would need to deduce an a-proposition from two e-propositions, which is impossible.

Nevertheless, Aristotle wants to give a circular proof of the a-premiss of Celarent. To this end,

he converts the e-premiss, AeB, to a more complex proposition, namely to:

whatever A belongs to none of, B belongs to all of it

, (APr. 2.5 58a29-30)

We know from Alexander that Theophrastus called such propositions prosleptic propositions

( , Alexander in APr. 378.14).2 In modern notation they can be

expressed as follows:

(1) for any X, if AeX then BaX

Aristotle does not explain the conversion from AeB to (1). But according to an anonymous

scholiast, the conversion consists of two steps ( 190a5-8 Brandis). First, AeB is transformed

into this prosleptic proposition:

(2) for any X, if BaX then AeX

2 See also 189b43-4 Brandis. Aristotle does not use the term prosleptic, unless one accepts

the phrase in APr. 2.5 58b9, which is attested by some MSS but is generally

regarded as spurious.

5

Theophrastus maintained that (2) is equivalent to AeB ( 190a1-4 Brandis), and it is

reasonable to accept this equivalence.3 In the second step, the two categorical propositions

which occur in (2), BaX and AeX, are interchanged. The result of this non-truth-preserving

conversion is the prosleptic proposition in (1). This may help to explain why Aristotle

thought that AeB can be converted to (1). A similar explanation can be given for the

conversion from AaB to BaA. In a first step, AaB can be taken to be transformed into this

prosleptic proposition:

(3) for any X, if BaX, then AaX

Again, Theophrastus maintained that this is equivalent to AaB ( 190a4-5 Brandis), and it is

reasonable to accept this equivalence.4 In the second step, the two categorical propositions in

(3) are interchanged, which leads to:

(4) for any X, if AaX, then BaX

And this is equivalent to BaA. Thus Aristotles special conversions of a- and e-propositions in

circular proofs can be viewed as instances of the same kind of conversion.

3 That AeB implies (2) is a consequence of Celarent, and that (2) implies AeB follows from

BaB. It is reasonable to think that BaB is always true for any term B; Aristotle appears to state

this in APr. 2.15 64b713 (in conjunction with 64a47, 2330); see J. ukasiewicz,

Aristotles Syllogistic from the Standpoint of Modern Formal Logic (Oxford, 19572), 9; P.

Thom, The Syllogism (Munich, 1981), 92.

4 That AaB implies (3) is a consequence of Barbara, and the converse follows from BaB.

6

Aristotles circular proof of the a-premiss of Celarent is:

original syllogism (Celarent): circular proof of the minor premiss (2.5 58a26-32):

AeB

BaC

AeC

for any X, if AeX then BaX

AeC

BaC

The circular proof is an argument which consists of a prosleptic premiss, a categorical premiss,

and a categorical conclusion. According to a scholium entitled On all the kinds of syllogism

( ), Theophrastus called such arguments prosleptic

syllogisms ( CAG 4.6 XII.4 Wallies).

Now, Aristotle converts AeB not only to (1), but also to each of the following two

prosleptic propositions:

(5) for any X, if BoX then AiX (2.6 58b36-8)

(6) for any X, if AoX then BiX (2.5 58b7-10, 2.7 59a25-9)

These two conversions can be justified by means of the conversion from AeB to (1), given

some truth-preserving transformations. Aristotle holds that a-propositions are contradictory to

o-propositions, and e- to i-propositions. So by contraposition, (5) is equivalent to (1). Given

that AeB can be converted to (1), it can therefore also be converted to (5). In the same way,

BeA can be converted to (6). But AeB is equivalent to BeA, according to the truth-preserving

conversions from Prior Analytics 1.2. So, given that BeA can be converted to (6), AeB can

also be converted to (6).

In chapters 2.5-7 Aristotle examines the (valid) syllogisms of the assertoric syllogistic,

and determines whether circular proofs of their premisses are possible. Sometimes he applies

7

an extended version of circular proof, in which the conclusion of a circular proof such as

described so far is converted by means of one of the truth-preserving conversions from

chapter 1.2 (for example, in the circular proof of the major premiss of Cesare).

Aristotles results can be summarized as follows:

Original syllogism in the first figure (2.5)

original syllogism: circular proof of the major

premiss:

circular proof of the minor

premiss:

Barbara:

AaB

BaC

AaC

first figure (57b22-5):

AaC

CaB

AaB

first figure (57b25-8):

BaA

AaC

BaC

Celarent:

AeB

BaC

AeC

first figure (58a23-6):

AeC

CaB

AeB

prosleptic syllogism (58a26-32):

for any X, if AeX then BaX

AeC

BaC

Darii:

AaB

BiC

AiC

not possible (58a36-b2)

first figure (58b2-6):

BaA

AiC

BiC

8

Ferio:

AeB

BiC

AoC

not possible (58b6-7) prosleptic syllogism (58b7-12):

for any X, if AoX then BiX

AoC

BiC

Original syllogism in the second figure (2.6)

Camestres:

AaB

AeC

BeC

not possible (58b13-18) second figure (58b18-22):

BaA

BeC

AeC

Cesare:

AeB

AaC

BeC

first figure (58b22-7):

BeC

CaA

BeA

AeB additional conversion

not possible (58b13-18)

Baroco:

AaB

AoC

BoC

not possible (58b27-9) second figure (58b29-33):

BaA

BoC

AoC

Festino:

AeB

not possible (58b27-9) prosleptic syllogism (58b33-8):

for any X, if BoX then AiX

9

AiC

BoC

BoC

AiC

Original syllogism in the third figure (2.7)

Darapti:

AaC

BaC

AiB

not possible (58b39-59a3) not possible (58b39-59a3)

Felapton:

AeC

BaC

AoB

not possible (58b39-59a3) not possible (58b39-59a3)

Datisi:

AaC

BiC

AiB

not possible (58a36-b2,

58b27-9)

first figure (59a3-14):

CaA

AiB

CiB

BiC additional conversion

Disamis:

AiC

BaC

AiB

third figure (59a15-18):

AiB

CaB

AiC

not possible (58a36-b2, 58b27-9)

10

Bocardo:

AoC

BaC

AoB

third figure (59a18-23):

AoB

CaB

AoC

not possible (58a36-b2, 58b27-9)

Ferison:

AeC

BiC

AoB

not possible (58a36-b2,

58b27-9)

prosleptic syllogism (59a24-31):

for any X, if AoX then CiX

AoB

CiB

BiC additional conversion

There is an issue with Camestres and Cesare in the second figure. Aristotle states that there is

no circular proof of their a-premiss. But Pseudo-Philoponus argues that their a-premiss can be

proved by means of a prosleptic syllogism; for example, his circular proof of the a-premiss of

Cesare is:5

original syllogism (Cesare): circular proof of the minor premiss:

AeB

AaC

BeC

for any X, if BeX then AaX

BeC

AaC

5 Pseudo-Philoponus in APr. 420.1-3 (CAG 13.2); see also Cz. Lejewski, On Prosleptic

Syllogisms, Notre Dame Journal of Formal Logic 2 (1961), 158-76, at 167.

11

This proof assumes that the e-premiss of Cesare, AeB, can be converted to this prosleptic

proposition:

(7) for any X, if BeX then AaX

By contraposition, (7) is equivalent to (6). Since Aristotle accepts that AeB can be converted

to (6), he should also accept that it can be converted to (7). So Pseudo-Philoponus circular

proof of the a-premiss of Cesare appears to be in accordance with Aristotles standards. A

similar proof can be given for the a-premiss of Camestres.6 Thus, Aristotles claim that there

is no circular proof of the a-premiss of Camestres and Cesare is not true without qualification.

It should be understood to apply only to circular proofs by means of categorical syllogisms,

not to those by means of prosleptic syllogisms. This is in accordance with some passages

from chapters 2.6-7, which suggest that for Aristotle only circular proofs by means of

categorical syllogisms are circular proofs in the proper sense.7

In all other cases where Aristotle states that a circular proof is not possible the original

syllogism has a non-universal conclusion. Aristotle states that if the original syllogism has an

i- or o-conclusion, there is no circular proof of its a- or e-premiss. Pseudo-Philoponus argues

that even in these cases it is possible to construct circular proofs by means of suitable

6 Pseudo-Philoponus in APr. 419.16-19. As in the case of Cesare, the e-premiss of Camestres,

AeC, is converted to for any X, if CeX then AaX. The conclusion of Camestres is BeC,

which is equivalent to CeB. So for any X, if CeX then AaX and CeB allow us to infer AaB.

7 2.6 58b33-8, 2.7 59a24-6, 59a41 (for the last passage, see n. 9 below); see also Pseudo-

Philoponus in APr. 419.16-17, 420.22, 422.6-7.

12

prosleptic propositions.8 However, it is not clear whether such circular proofs would still be in

accordance with Aristotles standards; for it is not in general clear what Aristotles standards

are. For example, consider Pseudo-Philoponus circular proof of the a-premiss of Baroco (in

APr. 420.11-13):

original syllogism (Baroco): circular proof of the major premiss:

AaB

AoC

BoC

for any X, if XoC then AaX

BoC

AaB

The prosleptic proposition used in this proof is of the form for any X, if XyB then AzX.

This is not in accordance with the prosleptic propositions used by Aristotle, which are all of

the form for any X, if ByX then AzX. Similar problems arise also in the other cases where

the original syllogism has an i- or o-conclusion: there is no circular proof of an a- or e-premiss

of such a syllogism by means of a prosleptic proposition of the latter form.

II. THE PROBLEMATIC PASSAGE

The problematic passage occurs at the end of chapter 2.7. It is intended to be a summary of

chapters 2.5-7:

8 Pseudo-Philoponus in APr. 418.3, 418.16-20, 420.11-13, 421.5-6, 422.1-2; T. Waitz,

Aristotelis Organon graece, vol. 1 (Leipzig, 1844), 498; Lejewski (n. 5), 167.

13

'

. ,

, , .

' ,

' , ' . ' .

'

9 (APr. 2.7 59a32-41)

The passage contains a number of references to figures of syllogisms. The default assumption

is that such references are, as everywhere else in the Prior Analytics, to figures of categorical

syllogisms. This assumption is correct for many references in our passage, but some

references are problematic.

The passage begins with the cases where the original syllogism is in the first figure (of

categorical syllogisms). It states that in the case of Barbara and Darii circular proofs are

through the first figure. This is correct, those circular proofs being categorical syllogisms in

9 The ' referred to in the last sentence are those circular

proofs which are not in the same scheme as the original syllogism. For example, when the

original syllogism is in the scheme Camestres, the circular proof of the e-premiss is also in the

scheme Camestres; and likewise for the circular proofs of the i- or o-premiss of Baroco,

Disamis, and Bocardo. This is not true when the original syllogism is in the scheme Cesare,

Festino, Datisi, or Ferison. In the case of Festino and Ferison the circular proofs are prosleptic

syllogisms and are therefore regarded as (cf. n. 7 above). In the case

of Cesare and Datisi the circular proofs involve an additional truth-preserving conversion and

are therefore regarded as (cf. 2.7 59a3-14). See D. Ross, Aristotles Prior and

Posterior Analytics (Oxford, 1949), 444.

14

the first figure. But the passage also states that in the case of Celarent and Ferio circular

proofs are through the third figure. There are two problems with this: (i) the circular proof of

the major premiss of Celarent is a categorical syllogism in the first figure, and (ii) the circular

proofs of the minor premiss of Celarent and Ferio are not categorical syllogisms at all, but

prosleptic syllogisms.

As to the second figure, the passage states that in the case of Camestres and Cesare

circular proofs are through the second and first figure respectively, and in the case of Baroco

and Festino through the second and third figure respectively. There is one problem with this:

(iii) while the passage states that the circular proof of the minor premiss of Festino is through

the third figure, this circular proof is not a categorical but a prosleptic syllogism.

As to the third figure, the passage states that all circular proofs are through the third

figure. There are two problems: (iv) the circular proof of the minor premiss of Datisi is a

categorical syllogism in the first figure, and (v) the circular proof of the minor premiss of

Ferison is not a categorical but a prosleptic syllogism.

Ross argues that the problems in (i) and (iv) are less serious and might be a mere

oversight.10

The problem in (i) might also be solved by taking the passage in 59a34-5 to mean

that in the case of Barbara and Darii circular proofs are only through the first figure while in

the case of Celarent and Ferio they are not only through the first but also through the third

figure.

But the problems in (ii), (iii), and (v) are more serious. It is remarkable that they

concern precisely the four cases where Aristotle gives a circular proof by means of a

prosleptic syllogism. In each case the passage states that the circular proof is a syllogism in

the third figure, which is incorrect if the reference is to the third figure of categorical

syllogisms. Ross and others conclude from this that the whole passage is a gloss which should

10

Ross (n. 9), 444.

15

be excised.11

However, the passage is found in all MSS, and also the context of Prior

Analytics 2.2-14 suggests that the passage is authentic. In 2.2-14 Aristotle discusses five

topics, each of them for each of the three figures of categorical syllogisms: true conclusions

from false premisses (2.2-4), circular proofs (2.5-7), a certain kind of conversion of

deductions (2.8-10), reductio ad impossibile (2.11-13), the relation between direct deductions

and reductio ad impossibile (2.14). At the end of each of these five treatments Aristotle gives

a summary, and each of these summaries begins with the words .12 In view of

this context, it seems unlikely that Aristotle did not give such a summary at the end of the

second treatment in chapter 7. So it is natural to conclude that the summary in 2.7 59a32-41 is

authentic.

Some commentators accept that the passage is authentic, but argue that Aristotle made

an error in (ii), (iii), and (v).13

On the other hand, Pacius argues that Aristotle did not make an

error here, but had in mind the third figure of hypothetical syllogisms: cave intelligas tertiam

figuram syllogismorum categoricorum ... efficitur hypotheticus: qui dicitur esse in tertia

11

Ross (n. 9), 444; M. Mignucci, Aristotele: Gli Analitici Primi (Naples, 1969), 622-3; J.

Barnes (ed.), The Complete Works of Aristotle: The Revised Oxford Translation (Princeton,

1984), 1.94; R. Smith, Aristotle: Prior Analytics (Indianapolis, Cambridge, 1989), 78.

12 2.4 57a36-57b17 (only 57a36-40 is a summary of 2.2-4, the rest is an explanation of what

Aristotle says in 57a40), 2.7 59a32-41, 2.10 61a5-16, 2.13 62b25-8, 2.14 63b12-21.

13 Waitz (n. 8), 498; J. H. von Kirchmann, Erluterungen zu den ersten Analytiken des

Aristoteles (Leipzig, 1877), 191. Tricot, Maier???

16

figura.14

The term hypothetical syllogism is usually used to refer to certain arguments

studied by the Stoics, such as:

if A then B (premiss)

A (premiss)

B (conclusion)

Aristotles prosleptic syllogisms are not instances of this kind of hypothetical syllogism,

although they are not dissimilar from it. But Pacius makes clear that by hypothetical

syllogisms he means prosleptic syllogisms: hic est syllogismus hypotheticus

.15 So Pacius thinks that Aristotle takes his prosleptic syllogisms to be in the third

figure. It is true that there is no trace of figures of prosleptic syllogisms in the rest of the

Analytics and the Organon. But as I shall argue, Aristotle is not unlikely to have known a

classification of prosleptic syllogisms into three firgures, so that Pacius interpretation should

be accepted.

III. FIGURES OF PROSLEPTIC SYLLOGISMS

The Greek commentators did not deem it necessary to explain the references to the third

figure in our passage at least there is no indication of it in Pseudo-Philoponus commentary

14

J. Pacius, Aristotelis Stagiritae Peripateticorum Principis Organum (Frankfurt, 15972), 335;

similarly O. F. Owen, The Organon, or Logical Treatises, of Aristotle, vol. 1 (London, 1889),

198-9.

15 Pacius (n. 14), 327, see also 329.

17

(CAG 13.2 422) or in Brandiss scholia (190). They seem to have taken it for granted that

Aristotles prosleptic syllogisms are in the third figure:

(i.e. the minor premiss of Celarent),

(Pseudo-Philoponus, in APr. 417.27-9, cf. also 418.19-20)

, ( 190b7 Brandis)

According to the scholium On all the kinds of syllogism, there are three kinds of syllogisms:

categorical, hypothetical, and prosleptic syllogisms. The scholiast writes that prosleptic

syllogisms were so called by Theophrastus, and that they are divided into three figures:

, ( CAG 4.6

XII.3-5 Wallies)

As the scholiast goes on to explain, the three figures are (y and z are placeholders for a, e, i, o):

first figure: second figure: third figure:

for any X, if XyB then AzX

CyB

AzC

for any X, if XyB then XzA

CyB

CzA

for any X, if ByX then AzX

ByC

AzC

This corresponds to a classification of prosleptic propositions into three figures: a prosleptic

proposition belongs to the figure to which the prosleptic syllogisms in which it can serve as a

18

premiss belong. For example, prosleptic propositions of the form for any X, if XyB then

AzX belong to the first figure, and so on.16

But Aristotle uses exclusively third figure

prosleptic propositions in the Prior Analytics.

Now, the problems in (ii), (iii), and (v) discussed above can be solved by taking the

passage to refer to the third figure of prosleptic syllogisms. Consider the problem in (ii): the

passage states that the circular proofs of the minor premiss of Celarent and Ferio are through

the third figure ( , 59a35), and both circular proofs are

prosleptic syllogisms in the third figure. The passage goes on to restate the prosleptic premiss

of the circular proof of the minor premiss of Celarent: , ,

(59a35-6). This clause indicates that the author was aware that

the circular proof under consideration is not a categorical syllogism but a prosleptic syllogism,

whether or not he knew the term prosleptic ( ). In fact, the author might have

added the clause in order to make clear that he is referring to the third figure not of

categorical but of prosleptic syllogisms. At any rate, it seems unlikely that he erroneously

referred to the third figure of categorical syllogisms.

The problem in (iii) can be solved in the same way, by taking the reference in question

to be to the third figure of prosleptic syllogisms.17

As to the problem in (v), the passage states

that in the third figure all circular proofs are through the third figure ( '

, 59a39). The circular proofs for Disamis and Bocardo are categorical syllogisms in the

third figure, and that for Ferison is a prosleptic syllogism in the third figure. Thus one and the

16

189b44-8 Brandis; Anon. CAG 4.6 69.30-3; Lejewski (n. 5), 159-60.

17 Some MSS read after in 2.7 59a38. If this phrase is accepted,

it can also be taken to refer to the third figure of prosleptic syllogisms, indicating prosleptic

circular proofs of the a-premiss of Camestres and Cesare. Aristotle does not mention these

circular proofs, but as discussed above, they are possible.

19

same general reference to the third figure includes a reference to both the third figure of

categorical syllogisms and that of prosleptic syllogisms. This might seem unusual and

confusing, but we have to take into account that there is a close connection between the three

figures of categorical syllogisms and the three figures of prosleptic syllogisms or propositions.

The connection in question can be described as follows. A prosleptic proposition

contains two categorical propositions, one in the antecedent and one in the consequent.

Together they constitute the premiss pair of a categorical syllogism, with the categorical

proposition in the consequent being the major premiss. This categorical syllogism is in the

same figure as the prosleptic proposition. For example, a first figure prosleptic proposition of

the form for any X, if XyB then AzX contains the two categorical propositions AzX and

XyB, which constitute the premiss pair of a categorical syllogism in the first figure; and

likewise for the other two figures. This suggests that the three figures of prosleptic

propositions and syllogisms were derived from Aristotles three figures of categorical

syllogisms.18

In an appendix to Ammonius commentary on the first book of the Prior Analytics

there is a short section entitled On prosleptic syllogisms, whose author states that prosleptic

syllogisms are similar to categorical ones in that they fall into the three figures:

(sc. )

(Anon. CAG 4.6 69.30)

18

Cf. 190a22-4 Brandis; W. and M. Kneale, Prosleptic Propositions and Arguments, in: S.

Stern et al. (edd.), Islamic Philosophy and the Classical Tradition (Oxford, 1972), 189-207, at

194.

20

(Anon. CAG 4.6

69.38)19

The author appears to think that prosleptic syllogisms belong to the same three figures as

categorical ones.

Aristotle probably used certain diagrams to represent categorical syllogisms. We do

not know what kind of diagrams he or the early Peripatetics used. But it might be worth

noting that the later scholiasts used the same diagrams to represent categorical and prosleptic

syllogisms of the third figure. For example, in the scholium On all the kinds of syllogism the

third figure prosleptic syllogism

For any X, if animal belongs to all X then rational belongs to all X (prosleptic premiss)

Animal belongs to all man (categorical premiss)

Rational belongs to all man (conclusion)

is represented by the following diagram:20

19

See also Pseudo-Philoponus in APr. 417.13-15.

20 CAG 4.6 XII.9-10 Wallies; the first premiss of this valid prosleptic syllogism is

apparently false, see Kneale & Kneale (n. 18), 206. The same kind of diagram is used by a

scholiast in the 10th

century MS Vaticanus Barberinianus gr. 87 (102v) to represent the third

figure prosleptic syllogism in Aristotles circular proof of the minor premiss of Ferio (APr.

2.5 58b7-12).

21

The same kind of diagram is typically used by scholiasts to represent categorical syllogisms in

the third figure, such as the following syllogism in Darapti:

Rational belongs to all man (major premiss)

Animal belongs to all man (minor premiss)

Rational belongs to some animal (conclusion)

If the author of our passage from Prior Analytics 2.7 also used the same diagrams to represent

the third figure of categorical and prosleptic syllogisms, he might have thought that both kinds

of syllogisms belong to the same third figure. This may help to explain the double function of

references to the third figure in that passage.

It is not clear when and by whom the three figures of prosleptic syllogisms were first

introduced. But Lejewski and the Kneales think it probable that they were introduced by

Theophrastus.21

As mentioned above, Theophrastus used the term prosleptic (

).22 And he wrote on prosleptic propositions in his work On Assertion, arguing that

21

Lejewski (n. 5), 167; Kneale & Kneale (n. 18), 205; Cz. Lejewski, On Prosleptic

Premisses, Notre Dame Journal of Formal Logic 17 (1976), 1-18, at 1. However, P. M. Huby

challenges this view, see her Theophrastus of Eresus, Commentary, vol. 2, Logic (Leiden,

2007), 133-4.

22 Alexander in APr. 378.14; 189b43-4 Brandis; CAG 4.6 XII.4 Wallies.

rational

man

animal

22

they are equivalent to categorical ones.23

Given that Theophrastus studied prosleptic

propositions and syllogisms, he may also divided them into three figures in a similar way in

which he also divided what are known as wholly hypothetical syllogisms into three figures

(Alexander in APr. 326.20-22, 328.2-5).

In her paper Did Aristotle Reply to Eudemus and Theophrastus on Some Logical

Issues? P. Huby argues that Aristotle knew Eudemus and Theophrastus logical work, and

that the answer to her question is affirmative.24

So Aristotle may also have been familiar with

Theophrastus work on prosleptic propositions, and may have discussed it with him. In fact,

as suggested by Lejewski, Theophrastus work on prosleptic propositions may have been

influenced by Aristotle, either by the discussion of circular proof in Prior Analytics 2.5-7 or

by a discussion of prosleptic propositions in Prior Analytics 1.41.25

It might even have been

Aristotle who introduced the idea that prosleptic propositions and syllogisms can be classified

into three figures. But in any case, Aristotle could have been familiar with this classification

so as to refer to it in our passage from Prior Analytics 2.7.

Thus, the passage may well have been written by Aristotle, and there is no reason to

think otherwise. Of course, it is also conceivable that the passage was written by another

author of the early Peripatetic school; but if I am correct, there is no compelling reason to

think so. In any case, the passage appears to be the earliest extant evidence of the

classification of prosleptic syllogisms into three figures.

23

Alexander in APr. 378.18-20; 190a1-4 Brandis. However, the details of this equivalence

remain unclear.

24 P. M. Huby, Did Aristotle Reply to Eudemus and Theophrastus on Some Logical Issues?,

in I. Bodnr and W. W. Fortenbaugh (edd.), Eudemus of Rhodes (New Brunswick, 2002), 85-

106, at 90.

25 See Lejewski (n. 5), 164-7.