Having considered issues related to individual propositions, we are now ready to turn to the combination of propositions into a syllogism.1 Here the inevitable starting point is Aristotleâs definition of the syllogism in his Prior Analytics as âan argument in which, certain things being posited, something other than what was laid down follows by necessity because these things are soâ [T1]. In the QiyÄs of his ShifÄʾ, that is, the part corresponding to the Prior Analytics, Avicenna explains and evaluates this definition nearly word for word. He adds a further qualification, namely that the following of the conclusion from the premises must be necessary and essential, not accidental [T2]. The resulting definition will hold of syllogisms in the mind and those that are actually spoken; for demonstrative science we can deal only with mental syllogisms, whereas in disciplines like rhetoric or poetics the arguments must actually be stated. The terse parallel explanation in his IshÄrÄt adds that a syllogism simply states what follows from premises: it does not require that the premises actually be accepted [T7].
As Avicenna says, the syllogism is the âunderpinning (Ê¿umda)â of all argumentation that leads to new knowledge [T6, T8, T20]. Several authors lay out its definition, often delineating its parts: the syllogism is made up of propositions or statements, which are made up of terms plus a copula [T9, T10, T11, T14, T21, T27]. Extending an idea we already saw in our chapter on the Proposition, al-SÄwÄ« extends the âhylomorphicâ analysis to the parts of the syllogism, making the propositions its âmatterâ and the syllogistic figure its âformâ [T13]. The definition and whole-part analysis are applicable to the most straightforward case of a âcombinatorial (iqtirÄnÄ«)â syllogism, where the statement in the conclusion has not yet appeared in the argument. But they also apply to what Avicenna calls a âreiterative (istithnÄʾī)â syllogism. As its name implies, the conclusion is a reiteration of something already found in a premise [T7, T15, T20, T27, T37]. This would be the case with some hypothetical syllogisms, as contrasted to categorical syllogisms [T16], because when we argue âIf A then B, but A, therefore B,â the conclusion B has already appeared as the consequent in the first premise. But as al-ḤillÄ« stresses [T37], we should not just equate combinatorial syllogisms with categorical syllogisms and reiterative syllogisms with hypothetical syllogisms. This is because, as already noted by Avicenna, a hypothetical syllogism can be combinatorial; we provide an example in a note to [T7]. One other contrast that should be mentioned here is that between a simple and compound syllogism. This is quite straightforward, as a simple syllogism is just one that is not composed of further syllogisms [T30] or more than two premises [T28].
Avicenna stipulates that a syllogism should imply its conclusion âall on its own (li-dhÄtihi)â [T6]. Part of the idea here is that no additional implicit premises should be needed in order to produce the conclusion. A popular example is that from âA is equal to Bâ and âB is equal to Câ it might seem immediately to follow that A is equal to C, but this requires a suppressed premise about the transitiveness of equality. An interesting modification is found in al-ṬūsÄ«, who in the process of critiquing al-AbharÄ« weakens the demand that the conclusion follows from the syllogism âall on its own.â The syllogism is still valid if the needed premise is present potentially, in the sense that it follows immediately from a premise that is stated [T29]. There is a further idea captured by âall on its own,â namely that the premises should be in the right form so as to produce the conclusion. For instance, we should not need to change the premise to its contraposition to get a valid argument [T21, T28, T32]. Despite his generally following Avicennaâs account, al-SÄwÄ« says that if we have this clause in our definition of the syllogism, then we do not need to follow Avicenna in adding that the syllogism yields the conclusion essentially or necessarily, rather than accidentally [T12] cf. [T11]. That would be superfluous.
If we now return to the QiyÄs of the ShifÄʾ, we find that Avicenna goes on to raise several doubts about the definition of âsyllogismâ [T3], which he resolves at [T4] and [T5]. This material is reprised by al-KhÅ«najÄ« at [T24]. Avicennaâs doubts touch on several interesting questions: does Aristotleâs canonical definition apply to non-demonstrative arguments? Do trivial, tautologous inferences count as syllogisms? These sorts of worries can already be found in the late ancient logical tradition. For example Alexander of Aphrodisias critiqued the Stoics for giving a place in logic to tautologies like âIf A, then A, but A, therefore A.â2 A new set of doubts is found in al-RÄzÄ« [T22], and these become a standard topic of discussion; Avicennaâs doubts are taken together with al-RÄzÄ«âs at [T35, T36]. Al-RÄzÄ«âs worries have to do not merely with the definition of âsyllogism,â but with the very idea of implication and inference, and are reminiscent of Lewis Carrollâs paradox.3 His first doubt is effectively that the premises of a syllogism do not yield the conclusion without being combined. To get from âA is Bâ and âB is Câ to âA is C,â I need to think about both premises together. But then I must be adding something beyond the individual premises, namely their combination. As in Carrollâs paradox, a regress looms, because I will need a second-order combination to put together the premises and the first-order combination. The second doubt transposes the point to epistemology. If I know the two premises, it would seem I should know the conclusion, but if that were so then I would immediately grasp the truth of all implications of all the propositions I know and their combinations. On the other hand, if knowing the premises is not enough for me to know the conclusion, then what do I need to add to get that further knowledge? There is a rich tradition of responding to these doubts, beginning with al-RÄzÄ« himself [T23, T25, T31, T34].
A final issue that arises in this chapter concerns Aristotleâs rejection of the fourth figure in syllogistic, which was long ago said to have provoked âperhaps the strangest controversy in the history of logic.â4 The fourth figure is just an indirect version of the first figure:
|
First figure |
Fourth figure |
|---|---|
|
AâB |
BâA |
|
BâC |
CâB |
|
AâC |
AâC |
Avicenna followed Aristotle in rejecting the fourth figure, and some authors agreed to âdiscard itâ on the grounds that it is âremote from natureâ and âtroublesomeâ to establish [T17, T20, T38]. Notice that the complaint here is not that the fourth figure is invalid, just that we can skip it, since the first figure is effectively the same and is much more intuitive. The fourth figure was however defended early on by Ibn al-á¹¢alÄḥ [T18] and Majd al-DÄ«n al-JÄ«lÄ« [T19], and then more influentially by al-RÄzÄ« and then al-KhÅ«najÄ« [T26]. This subsequently becomes the more widespread view, e.g. in al-AbharÄ« [T27], providing us with a small but telling example of al-KhÅ«najÄ«âs pivotal role in post-Avicennan logic.
Texts from: Aristotle, Avicenna, BahmanyÄr, al-SÄwÄ«, Ibn al-á¹¢alÄḥ, al-JÄ«lÄ«, al-SuhrawardÄ«, al-RÄzÄ«, al-KhÅ«najÄ«, al-AbharÄ«, al-ṬūsÄ«, al-KÄtibÄ«, al-UrmawÄ«, al-SamarqandÄ«, al-ḤillÄ«
[T1] Aristotle, Prior Analytics, 24b18â26 [trans. Striker, mod.]
[Aristotleâs definition of âsyllogismâ]
A syllogism is an argument in which, certain things being posited, something other than what was laid down follows by necessity because these things are so. By âbecause these things are soâ I mean that it results through these, and by âresulting through theseâ I mean that no term is required from outside for the necessity to come about. Now I call a syllogism perfect if it requires nothing beyond the things posited for the necessity to be evident; I call a syllogism imperfect if it requires one or more things that are indeed necessary because of the terms laid down, but that have not been taken among the premises.
[T2] Avicenna, ShifÄʾ, Maná¹iq, QiyÄs, 54.6â55.10
[Avicennaâs definition of âsyllogism,â and the distinction between spoken and mental syllogisms]
A syllogism is a discourse (qawl) in which, if more than one thing is posited, something other than what was posited follows from these things by necessity, and not accidentally, but essentially.
So discourse here is, as it were, the genus of âsyllogism.â It should be considered whether it is a genus for the syllogism that is understood and conceived in the soul, or a genus for the spoken syllogism. We say: âsyllogismâ is said indistinctly of both things. That is, it is said of the compound thoughts assembled in the soul that lead to an assent to something else in the soul, and of the statement composed of propositions from which another proposition follows, and not only insofar as it is a statement that is heard [by someone]. For statements that are heard do not at all imply another statement [being spoken and heard]. The utterance, just insofar as it is an utterance, does not necessitate that some other utterance does or does not follow it; rather, it is only insofar as it is a statement that is heard that it signifies a meaning that is understood. And this not merely insofar as it is a statement that is heard, and that signifies a meaning that is understoodâon the basis that it is a statement heard by someone who is listening to itâbut [55] simply because it is a statement that is heard, absolutely and without specification of any language. For it is not right to say that the implicand (lÄzim) and the implicate (malzÅ«m) are something that one language may signify but not another; rather, this is meant absolutely and in whichever language it may be. The meaning of âimplicandâ is: that utterance whose meaning is to be established.
Just as âsyllogismâ is said of both of these [sc. the one in the mind and the one that is spoken], the statement that is like a genus for the syllogism [i.e. Aristotleâs definition] is said of both. The syllogism that is heard, in the sense just explained, has as its genus âstatement that is heardâ; while the syllogism that is understood [in the mind] has as its genus âstatement whose meaning is understood.â
But the mental syllogism alone suffices in order to reach the aim of the syllogism, when what is sought is a demonstrative proof. As for Dialectic, Rhetoric, Sophistic, and Poetics, in these cases the heard syllogism is indispensable in order for their respective aims to be reached. And likewise with the examinations that they use. All that we shall mention in its due place. So, this is the meaning of the received opinion on the genus of the syllogism.
[T3] Avicenna, ShifÄʾ, Maná¹iq, QiyÄs, 66.4â67.2
[Avicennaâs doubts regarding Aristotleâs definition of âsyllogismâ]
But some doubts may apply to what has been said above [sc. the definition of syllogism discussed in T2]. (a) One of them is that sometimes the implications are not necessary, but rather contingent, but [such a] syllogism is still a syllogism. (b) Another is that dialectical syllogisms are syllogisms, but what is implied in them is not implied with necessity; rather it [just] prevails in terms of belief (áºann). Nor is the implication of what follows in rhetorical [syllogisms] necessary. (c) Again, in hypothetical syllogisms the conclusion may be something that was already in the premises. So if you were to say: âIf the sun is up, then it is day; but the sun is up; therefore, it is day,â then what follows was already included in the premises that were posited; so you would make the hypothetical syllogism fall outside this definition. Likewise, when you say: âEither motion exists, or does not; but motion does exist,â then the conclusion is the contrary of the second disjunct, and the same as what was said in the first disjunct. This is why when you say: âMotion does existâ the conclusion follows: âTherefore, motion exists.â (d) Even worse than this example is the following: âIf motion exists, then motion exists; but motion exists; therefore, motion exists.â They also said: if there is an automatic inference (muqÄyÄ«s), the conclusion is made necessary by a [67] single statement, like when someone says: âSo-and-so moves [of his own accord]; therefore, he is aliveâ or âÊ¿AbdullÄh is writing; therefore, his hand is moving.â
[T4] Avicenna, ShifÄʾ, Maná¹iq, QiyÄs, 67.3â68.5
[Avicennaâs solutions to the three doubts in T3]
(a) Concerning the first doubt, it may be resolved by recalling what we said: that the meaning of âfollows necessarilyâ is not that what follows is itself a necessary statement, but that its following from the syllogism is necessary. This is so whether it is false in itself, or necessarily true, or contingent rather than necessary. Even something absurd or something contingent may follow necessarily from something else, once that thing is conceded, without being in itself necessary.
(b) Concerning the second doubt, it might be said that what is meant by âfollowing (lÄzim)â is either what really (bi-l-ḥaqÄ«qa) follows, or what does so in a persuasive manner. But this is not correct, for what is meant by âfollowingâ is the concept of real, not metaphorical, following. Even so, the doubt is resolved, because dialectical and other such syllogisms are still syllogisms. For the conclusion will follow from whatever [the premises] include, once that is conceded, even though what they include is itself doubtful, because such premises are doubtful by the very nature of the case (fÄ« amrihÄ). But when it comes to the syllogism being a statement such that a conclusion necessarily follows from what it includes, this is a feature shared by all of them.
(c) Concerning the third doubt, it is resolved by realizing that âsomething other than what was posited results from these thingsâ does not refer to [premises] that have been accepted. It is the accepted [premises] in which there is truth and falsity. When we say âthen it is dayâ [i.e. the consequent of the hypothetical premise] this is not in itself accepted or rejected because it is true or false. [68] Rather, what was accepted is something of which this is just a part. When we say âif the sun is up, then it is dayâ this as a single whole is what is accepted, and for the time being there is no accepting of any of its parts; it may indeed be that in isolation, none of the parts are accepted. So when you say âif man is a stone, then he is an inorganic object,â neither of the two is accepted, but the premise [as a whole] is, because the accepting here concerns the way the two statements are related (ḥÄl al-nisba bayna al-qawlayn).
[T5] Avicenna, ShifÄʾ, Maná¹iq, QiyÄs, 68.13â71.4
[Avicennaâs solutions to the last doubt]
(d) Concerning the last doubt, where we say: âIf motion exists, then motion exists; but motion exists; therefore, motion existsââthis doubt may be resolved in several ways.
First, this statement is not a syllogism at all, for a syllogism is something that is of use to induce acceptance, but this [statement] is of no use whatsoever. Not everything from which something follows is a syllogism, whatever it may be. Rather, [69] what follows from it must be something for which it was useful to yield acceptance. One will not accept, on the basis of the whole [statement], something that was only posited as an assumption within that whole. Since then this is not a syllogism, we need not even say that if something is a syllogism, then what follows from it is something different from what was posited [i.e. since this is already implied by the notion of a syllogism anyway].
Second, neither is what is accepted a conclusion. For what is accepted is âbut motion exists,â which is connected [to the rest] by the utterance âbut.â Likewise, âtherefore, motion existsâ is connected by âthereforeâ (al-fÄʾ al-wÄá¹£ila). So what is put as the conclusion, i.e., that there is motion, is part of what was accepted, not the same as what was accepted. The proof for this is that if someone says: âmotion existsââbut without deploying a conjunction (Ê¿alÄ sabÄ«l al-Ê¿aá¹f) that signifies the repetition, so that itâs tantamount to saying âAnd along with that, it is true that motion exists,â so that âMotion existsâ is like a subject, and one may predicate of itâit will then furthermore be true that nothing follows from these two statements. If something does follow, then it will do so together with a realization that this [part] is being repeated, and the fact that motion exists is, in the mind, made part of the proposition whose predicate is the repetition. So in this case, what follows does indeed follow.
This is also how things stand with the example that involved disjunction [i.e. in T3: âEither motion exists, or does not; but motion does exist â¦â]: the same sorts of answer will work here. But the truth is that this is not even a syllogism. I do not say that the disjunctive premise, both affirmative and negative, is not syllogistic, for it may indeed be included in syllogisms. But I do say that their use for connecting them to the repetition of the contrary, as was said in the doubt above, does not lead to a syllogism. When someone says âeither motion exists, or does not,â then he has put forth [70] these words to clarify by them something that is not known, or to obtain something unknown that was not established before. When he then says: âbut motion does exist,â he makes this a part of the syllogism in order to make clear that motion exists. But this is still not a syllogism, because the intended conclusion is already clear and has been accepted, even before the syllogism is put together for it. If the syllogism is for the sake of clarifying something, [in this case] it can be dispensed with. But if it aims to infer something that has been denied, then the interlocutor will not accept that motion exists, just because it has been reiterated. Since he will not accept this, it also cannot be reached [as a conclusion] from such a syllogism. Furthermore, if this is not a straightforward negation, but rather some sort of metathesis, then in that case the conclusion will not be what was mentioned, but instead âmotion is not non-existent (al-ḥaraka laysat ghayr mawjÅ«da)ââwhich is not the same as âmotion exists (al-ḥaraka mawjÅ«da).â If this was [however actually] implied, then the two implications would have to be interchangeable in meaning, as you have learned several times.
As for the other examples [at the end of T3], they are complete only with a hidden premise that is understood implicitly, so that in one of them [the premise] âwhatever moves is aliveâ is hidden, in the other âwherever there is a lamp, there is light,â which is a hypothetical. And in the third, âwhoever writes, moves his hand.â
This all is in accordance with the definition of the syllogism. Now you should know that a syllogism may be perfect, [71] in which case it is obvious from its form that the acceptance of the conclusion follows from it, or it may be imperfect, in which case it is not clear what follows from it. It becomes clear only once it is changed in such a way that it becomes a perfect syllogism. This change is applicable to it by itself and to its terms, not to anything else that enters into it. This change conserves the truth of what was originally accepted in it.
[T6] Avicenna, IshÄrÄt, 138.9â139.6 [trans. Inati, mod.]
[definition and terminology of the syllogism]
The syllogism is the underpinning (Ê¿umda). It is a statement composed of [sub-]statements such that, if the propositions brought forward in it are accepted, then this all on its own leads to another statement. If the propositions are given in something like what is called âsyllogism,â âinduction,â or âanalogy,â then they are called âpremises.â The premise, therefore, is a proposition which has become part of a syllogism or argument.
The essential parts of what is called the âpremise,â which are what remains after the analysis into primary single elements, and which are the smallest parts of which the proposition is composed, are called âterms.â [139] For example: from âEvery J is Bâ and âEvery B is Aâ follows âEvery J is A.â [Here] each of our statements âEvery J is Bâ and âEvery B is Aâ is a premise, while J, B, and A are terms, and the statement âEvery J is Aâ is a conclusion. What is composed of two premises, in the manner just illustrated, so that it necessarily leads to this conclusion, is the syllogism.
It is not a condition of [this kind of proof] that propositions be accepted, in order that it be a syllogism. Rather, the condition for it is that, if its propositions are accepted, then another statement follows from them. This is the condition for its being a syllogism (qiyÄsiyya).
[T7] Avicenna, IshÄrÄt, 139.22â140.12 [trans. Inati, mod.]
[the two types of syllogism: combinatorial and reiterative]
The syllogism as determined by us, is of two kinds, combinatorial and reiterative.
The combinatorial syllogism is one in which there is no explicit mention of either one of the two contradictory sides contained in the conclusion. Rather, this will be [present] in it only potentially, as in the abovementioned example [sc. in T6].
Whereas in the reiterative syllogism, this is explicitly mentioned. For instance when you say, âIf Ê¿AbdullÄh is rich, he is not unjust; but he is rich; therefore: he is not unjust.â Thus, you find in this syllogism [an explicit mention of] one of the two contradictory sides contained in the conclusionâin fact it just is the conclusion [i.e., âhe is not unjustâ]. Another example would be if you say, âif this [140] fever is a one-day fever, it does not produce a great change in pulse; but it has produced a great change in pulse; therefore: it is not a one-day fever.â Again, you find in this syllogism [an explicit mention] of one of the two contradictory sidesâwhich in this case is the contradictory of the conclusion [i.e., âit is a one-day feverâ].
Combinatorial syllogisms may consist of simple categorical propositions, simple hypothetical propositions, or they may be composed of the two. Those which consist of simple hypothetical propositions may be formed of simple connective propositions, simple disjunctive propositions, or they may be composed of the two. Most logicians have only paid attention to categorical propositions, thinking that hypothetical syllogisms must be reiterative.5
We will mention categorical syllogisms with their various types. This will be followed by [a discussion of] some hypothetical combinatorial syllogisms, the ones that are most useful and which have the strongest hold on our natures. After that we will [treat] reiterative syllogisms. Finally, we will mention some states which the syllogism undergoes, and the syllogism that is a reductio ad absurdum. We will limit ourselves in this summary to this much.
[T8] BahmanyÄr, Taḥṣīl, 106.1â107.15
[the art of proof and the parts of the syllogism]
You should know that proof (istidlÄl) is an art that leads to a goal, and every art is connected to some matter and form. The subject-matter of an art varies in virtue of the difference of its matter and form. Likewise, proof may differ either with regard to differences in what it is composed of, or differences in how it is composedâthat is, whether it is composed well or not. The goal of proof is the obtaining of knowledge, or put alternatively, reasoning (áºann) in such a way as to acquire [new knowledge]. The underpinning in all this is the syllogism. The matter of the syllogism is what [was introduced above] and to which assent is given, while its form is the description and composition that apply to it.
You should know that it is not possible to acquire knowledge of something [as yet] unknown from just any anything whatever that is already known; rather, the knowledge [one already has] has a specific relation to what is [as yet] unknown. And likewise, a specific composition. In general, there must inevitably be primary assents which are not acquired by reflection; otherwise there would be no way to [107] acquire secondary [assents], and everything that one seeks to acquire through the syllogism would become a premise in another syllogism, so that one would be devoting oneâs effort to a task that might be endless.
Custom has it that the syllogistic science is called âconverse analysis (al-taḥlÄ«l bi-l-Ê¿aks),â which is the same as composition (tarkÄ«b). For a syllogism is only a syllogism when you have a defined object of inquiry, and you seek it by [figuring out] what produces this object as a conclusion. What shows this object of inquiry for you has parts, which are called the middle term and the extreme terms; so [the procedure] is really a converse analysis [i.e. one works backwards from what one wishes to prove to the syllogism that proves it]. In the same way, its opposite is called synthesis (tarkÄ«b). If a syllogism is assembled in a chance way and leads to a conclusion that was not sought beforehand, it is not really a syllogism.
A premise is a declarative statement that is made part of a syllogism. [Being part of a syllogism] is however not a specific difference that attaches to the premise; otherwise, if I were to remove this attribute from the premise, its essence would perish, and it would no longer be a declarative statement. Just as this applies to quantified, unquantified, and particular propositions, so it does to the premises.
The definition of that into which the premise is analyzed, I mean if the premise is broken up so that nothing but the subject and the predicate remain, this (once the analysis is performed) is called a âterm.â As for the copula, it does not remain, as it is in general not something into which a premise is analyzed. In hypothetical [premises] it is the conditional and the disjunctive particles [that are analogous to the copula].
[T9] BahmanyÄr, Taḥṣīl, 108.1â111.5
[on the definition of âsyllogismâ]
A syllogism is a statement in which, if more than one thing are posited, something other than what was posited follows from these things by necessity, and not accidentally, but essentially. [â¦]
[109.15] You should know that the meaning of âfollowingâ is that if you accept these things, then you must accept the second statement [sc. the conclusion]. But this does not require that the second statement be true. To say âfrom this, that followsâ is more general than saying, âwhat follows from it is true.â [â¦]
[111.1] In hypothetical syllogisms what is accepted in them is not the conclusion. What is accepted in them is the truth or falsity that accrues to the hypothetical premise, as it is [stated]. What is accepted here is only the state of the relation between the antecedent and the consequent, not one of the parts, which is the conclusion. Thus when we say âIf the sun is up it is day,â it is this that is accepted, whereas the conclusion is one of its two parts [sc. âit is dayâ]. So what is accepted here is not the conclusion.
[T10] Al-SÄwÄ«, Baá¹£Äʾir, 139.3â140.1
[how the study of the syllogism fits into logic]
Knowledge of the argument (ḥujja) is the most important goal in logic. The [argument] itself is composite, and knowledge of a composite arises only once there is knowledge of that of which it is composed. The argument is composed of propositions, which are in turn composed of simple [utterances]. This is why the beginning of our exposition was about simple meanings and simple utterances, and the composition of propositions in their [different] types, so that we could provide a clear account of all this. Now, we ought to take stock, so as to make known the argument and its divisions.
The argument is a statement composed of [sub-]statements which aim at the production of assent to some other statement, to which one did not [previously] assent. There are three types: syllogism, induction, and analogy. Each of those has [forms] that are close to it, like enthymeme, [140] proof, opinion, and sign. In general, what underpins conviction in all of them is the syllogism.
[T11] Al-SÄwÄ«, Baá¹£Äʾir, 140.1â140.11
[explanation of the definition of the syllogism]
[The syllogism] is a statement composed of propositions such that, if they are accepted, another statement follows from it all on its own. âComposed of propositionsâ serves to distinguish the syllogism from a single proposition, whose truth implies the falsity of its contradictory and the truth of its conversion, and other such immediate implications. By âif they are acceptedâ we do not mean that the accepted premise is in itself true. Indeed, unbeknownst to us, it may be false in itself; but even so, if it is accepted, once it is composed [in a syllogism] there follows from it another statement. âThere follows from itâ serves to distinguish between syllogisms and inductions and what is counted together with them, since upon verification nothing follows from these. âAll on its ownâ tells us that the things that follow do so not because of a specific matter [i.e. content], so that if something else were substituted [for that content] what follows would no longer follow. For example: âNo human is a horse; all horses neigh.â What follows with regard to âhumanâ and âneighingâ is that neighing is denied of humans. But now, if something that is not coextensive with âhorseâ is substituted in the predication, that denial might not follow anymore. For example, when âneighingâ is replaced by âanimal,â then what follows is that âanimalâ is affirmed of âhuman.â The expression ânecessarilyâ has been added to the definition [of the syllogism by some people] to exclude such [cases], but it is superfluous.
[T12] Al-SÄwÄ«, Baá¹£Äʾir, 140.11â141.4
[omitted and implied premises]
In some cases, what follows does so with no need for any connection to another thing which would ensure that it does indeed follow, whether this be entirely omitted without anything standing in for it, or a stand-in that has the same force [as what would complete the implication]. A prime example for [complete] omission is âA is equal to B; B is equal to J; therefore, A is equal to Jâ: it does not follow from this statement alone that A is equal to J. Rather, this only follows [with the addition of] something else that has been omitted, namely âA is equal to the equal of J; and the equal of an equal is equal.â From this it now does follow that A is equal to J. According to the aforementioned account, there was no syllogism for what was taken to follow, since it did not follow from it âall on its own.â
As for the stand-in that has the same force [an example would be]: âRemoving a part of a substance necessarily removes the substance; the removal of something that is not a substance does not remove the substance; therefore, a part of a substance is a substance.â The conclusion does not follow from what is explicitly said here. Rather, [the conclusion is implied] by another premise that is omitted and needs to be connected to the first premise, namely âThat whose removal necessarily removes the substance is a substance.â But the [explicitly] mentioned premise, namely that âthe removal of something that is not a substance does not remove the substance,â has the same force as the omitted premise. One might easily suppose that the conclusion does follow when [the second, actually mentioned premise] is connected to the first premise, but this is not so.
In order to hedge [the definition] against such specific cases, he [Avicenna, in T2] adduced an addition to the definition, namely âall on its own, and not [141] accidentally.â But this addition would only be needed if it were possible that something followed from it all on its own, but accidentally; then one would need to hedge the definition against such a case. But in fact this is not possible. In the example we just mentioned nothing follows from what is explicitly stated all on its own, so the phrase âall on its ownâ already excludes that, without adding âand not accidentally.â
[T13] Al-SÄwÄ«, Baá¹£Äʾir, 141.6â9
[form and matter of the syllogism]
You should know that these propositions are called the âmatterâ of the syllogism, and the specific composition in which they are arranged the âformâ of the syllogism. Syllogisms are classified as demonstrative, dialectical, sophistical, rhetorical, and poetic, due to their variation in matter; but they all share a single form. Since there is a specific matter for each [type of syllogism] but the form is shared in general by all, and it is more appropriate for inquiry to proceed from the general to the specific, let us begin by first explaining the form of the syllogism.
[T14] Al-SÄwÄ«, Baá¹£Äʾir, 141.13â21
[terminology and examples for the parts of a syllogism]
When propositions are composed to form a syllogism, they become its parts and are then called premises. The essential parts of the premises that remain after analysis are called terms. When the categorical premise is analyzed into its essential parts, [only] subject and predicate remain; the quantifier and modal operator are not essential to the proposition. As for the copula, even though it is essential [to the proposition], it is an utterance signifying the connection [between subject and predicate], and this connection no longer remains after analysis.
Let us then give examples for syllogism, premise, and terms: from âEvery body is composite; every composite is createdâ it follows that âevery body is created.â âEvery body is compositeâ is one premise, âEvery composite is createdâ the other premise. Their parts are âbody,â âcomposite,â and âcreatedâ which are the terms. Both premises together, in the order in which we presented them, are the syllogism. What follows from it is âEvery body is createdâ and this, once it is shown to follow, is called the conclusion. Before its following is grasped by the mind in the arrangement and setting up of the syllogism, [this same proposition] is called the object of inquiry (maá¹lÅ«b).
[T15] Al-SÄwÄ«, Baá¹£Äʾir, 141.22â142.2
[combinatorial and reiterative syllogisms]
If what follows, or its contradictory, is not actually mentioned in the syllogism but only contained potentially, then such syllogisms are called combinatorialâas in the above example [in T14]. What follows, namely âEvery body is created,â or its contradictory, is not actually explicitly mentioned in [the syllogism], but is contained in it potentially, because [âbodyâ] falls under âcomposite,â and this is made explicit by âevery composite is created.â If, on the other hand, [the conclusion] or its contradictory is actually mentioned in [the syllogism], then it is called reiterative. For instance, from âIf this number is odd, then it cannot be divided into equal [numbers]; but it is oddâ there follows âIt cannot be divided into equal numbers,â [142] which has actually been mentioned in the same form in the syllogism. Likewise, if you repeat in this example âbut it can be divided into two equal numbers,â there follows that âIt is not odd.â The contradictory of this implicationââThis number is oddââis actually mentioned in the [syllogism].
[T16] Al-SÄwÄ«, Baá¹£Äʾir, 142.3â11
[categorical and hypothetical syllogisms]
Combinatorial syllogisms may consist of categorical premises only, or of hypothetical premises only, or may be put together from both categorical and hypothetical premises. Let us begin with the simple categorical ones. They are inevitably composed of two premises that share a middle term. In the above example [in T14] it is âcomposite,â and it is called the middle term. Each of the premises has another term specific to it, like âbodyâ in the first premise of the example, and âcreatedâ in the second. The conclusion obtains from both premises together. What is the subject in the conclusion is called the minor term, while the predicate in it is called the major term. The premise containing the minor term is called the minor premise, and the premise containing the major term is called the major premise. The composition of both premises is called the combination. Those combinations that produce a conclusion all on their own are called syllogisms, and the form of the syllogism in terms of the relation of the middle term to the extreme terms is called a figure.
[T17] Al-SÄwÄ«, Baá¹£Äʾir, 142.12â22
[the fourth figure rejected]
This relation falls in its correct classification into four types. (a) If the middle term is the predicate in the minor premise and the subject in the major premise it is called the first figure. It may also be (b) the subject of the minor premise and the predicate of the major premise, or (c) a predicate in both, or else (d) a subject in both. (b) But the second class, even if it must be included in the classification, is not [usually] expressed, because it is remote from nature and to make conspicuous what follows from it, one has to apply a troublesome inquiry, even though one can do without it. As for the remaining two figures (c) and (d), what follows from them may not be clear by itself, but it is nevertheless close to nature. A person of astute understanding might show that these two are [validly] syllogistic, prior to showing something else, but still his mind will more readily come to this thing that is shown [than to accept these two figures]. This is why the two are not considered to be on a par, insofar as one discards what is opposed to the first figure.
Hence, the categorical figures that are used are three. They all share in the fact that there is no syllogism consisting of two particular [premises] absolutely, no syllogism consisting of two negations, and no syllogism with a negated minor premise and a particular major premise, except in the case of contingent de re modality, as you will learn, and that the conclusion follows the weaker of the premises in quantity and quality, unless they fall under the exceptions we are going to make.
[T18] Ibn al-á¹¢alÄḥ, MaqÄla fÄ« l-shakl al-rÄbiÊ¿, fol. 122v4â123r3 [trans. Sabra 1965, 17â18, mod.]
[history of the debate over the fourth figure]
We have found most logicians omit this figure and fail to mention it, so that the large commentaries on the Prior Analytics do not refer to it at all. The exceptions which do mention it either discard it, for the reason that it is remote from natureâas we find in the greatest book which the Master Avicenna has composed and called The Cure, in the fourth section of the first treatise on the syllogismâor completely reject it, saying that it is not required by the division [of the figures], as we find in the commentary of AbÅ« l-Faraj ibn al-Ṭayyib on the Book on the Syllogism. Thus he criticizes Galen and accuses him of error, not by producing any evidence whatsoever, but by merely saying that while Galen distinguished himself in medical matters, he is not to be trusted in matters of logic. Aḥmad ibn al-Ṭayyib al-SarakhshÄ« said in his Abridgement of the Analytics that a man mentioned to his teacher YaÊ¿qÅ«b ibn IsḥÄq al-KindÄ« that he possessed a Syriac treatise of Galenâs expressing the same opinion. But al-KindÄ« denied that, and said a rational division requires only three figures, no more: he did not recognize a fourth figure. It has also been related that AbÅ« Naá¹£r al-FÄrÄbÄ« has a discussion (kalÄm) of the invalidation and rejection of this figure, which I have not seen. These, then, are the books we have found which refer to this figure. As for the other books and commentaries which have come down to us from Aristotle, Alexander, Porphyry and others among the ancients and moderns, we have not found them referring to it. Rather, they divide the figures into three, and state that there is no fourth. We have found that Galen did the same in the ninth section of [his] Book on Demonstration. For he divided the categorical figures into three only and asserted that there is no fourth; he did the same in book On the Enumeration of the Syllogisms. These are the only two of his logical books that we have seen, in spite of their large number indicated in the Fihrist. Now there came our way a treatise by a man called Diná¸¥Ä the priest, entitled The Fourth Figure of Galen. When we looked into it we found it defective in the enumeration of its moods, and in his regarding some sterile moods as productive and in [his] badly understanding [123r] the first figure to which this figure is reduced. When we noted this, we inquired into this figure and into the conditions for the three known figures and what distinguishes it from them. [We have also inquired into] the enumerations of its moods one by one, and we have proved those that are productive and have shown those that are sterile and pointed them out.
[T19] Al-JÄ«lÄ«, al-LÄmiÊ¿ fÄ« l-shakl al-rÄbiÊ¿, 220.8â12 [trans. El-Rouayheb 2019, 26]
[an early rehabilitation of the fourth figure]
I have seen that the notable among philosophers and the great among scholars have omitted the fourth figure from their books, and have considered it among the futile and insignificant matters, claiming that it is too intricate for natural disposition and too remote from satisfactory investigation. Into my soul came an urge to look into extracting it, and an inclination to contemplate it with a view to presenting its proofs. I found it not to be so remote as they described, and have discovered things the like of which they have not seen. I will therefore make clear its conditions of productivity, and give the details of its moods and their conclusions.
[T20] Al-SuhrawardÄ«, Maná¹iq al-TalwīḥÄt, 46.6â48.6
[the formal argument and the definition of the syllogism]
You should know that an argument is a statement composed of [sub-]statements, which aims at the occurrence of assent to another statement. There are different types, but the underpinning of all types is the syllogism. We shall mention the remaining types, God willing.
A syllogism is a statement composed of propositions such that if they are accepted, there follows from itâall on its ownâanother statement. If it were not for the specification that the composition consists of [multiple] propositions, then a single proposition from which, all on its own, there follows the truth of its converse and the contraposition,6 would not fall outside the definition [of the syllogism]. âAll on its ownâ serves to exclude the sterile case where its conclusion happens to be true due to special features of the matter, or other such cases, like when the conclusion of the syllogism does not follow as a conclusion except by means of another premise that has not been not mentioned. [â¦]
[reiterative syllogisms]
[47.7] A syllogism must be either such that the conclusion or its contradictory is mentioned in it, or not. If it is, then it is called reiterative, as in âIf the sun is up, it is day; but the sun is up; therefore, it is day.â Here, one of the contradictory pair of the conclusion is mentioned, namely the conclusion itself. [â¦]
[rejection of the fourth figure]
[48.5] [The fourth figure] which is the opposite of the first, is remote from nature and intuitively does not seem to be a syllogism, and requires troublesome elucidation, which is why it was dropped.
[T21] Al-RÄzÄ«, Maná¹iq al-Mulakhkhaá¹£, 243.1â245.4
[comments on the definition of âsyllogismâ]
A syllogism is a statement composed of propositions such that if they are accepted, another statement follows from it all on its own.
âOf propositionsâ is meant to distinguish it from a simple premise from which follow its converse, its contraposition, and the falsity of its contradiction, whereas a syllogism is always composed of two premises. Let no one say: this is wrong, [in light of examples like] âSo-and-so moves [voluntarily], so he is alive,â or âWhen the sun is up, it is day,â because we reach a conclusion from the first [part of each statement]. For here the syllogism is only made complete with another implicit premise, which would be âEverything that moves [voluntarily] is alive.â The same answer applies to the second [example], because the conclusion only follows from it, so long as one believes that the presence of day does follows from the fact that the sun is up; then [244] one will believe that the sun is [actually] up.
By âwhen [the premises] are acceptedâ we do not mean that they are accepted in themselves, but that they are such that if they were accepted, then what is sought would follow from them. In that way any type of syllogism is included [in the definition].
âFollows from itâ is more general than âfollowing evidently (al-luzÅ«m al-bayyin),â which is why both the perfect [syllogism] and others [where the inference is not evident] are subsumed under the definition.
âAll on its ownâ distinguishes [the syllogism] from two other things. First, [cases in which] those propositions do not necessarily conclude in another proposition when they are the case. If you say âA is equal to Bâ and âB is equal to J,â then it is thought to be obvious that it produces the conclusion âA is equal to J.â But upon closer inspection (taḥqÄ«q), this conclusion does not follow from them. Rather, the implication is âA is equal to what is equal to Jâ; only then, if you say âwhat is equal to the equal is equal,â does the conclusion follow. Second, [cases in which] this implication is not due to a premise being among the concomitants of the mentioned premises, like when you prove that a part of a substance is a substance: âEliminating part of a substance eliminates the substance; and what is not a substance will not necessarily eliminate substance when it itself is eliminated; therefore, a part of a substance is a substance.â This does follow from what was said, but not on account of the major premise that was actually mentioned, but because of the contraposition, namely âThat whose elimination necessarily eliminates a substance, is itself a substance.â
And we also have to say [in the definition] âanother statement,â that is, a conclusion distinct from the premises.
This then is the well-known explication for the description [of the syllogism]. I say: What is intended by the âstatement,â [245] from which the acceptance of the conclusion follows once its premises are accepted, is not the linguistic statement (al-qawl al-lisÄnÄ«). Someone who utters the premises is under no obligation to utter the conclusion. [What is intended] are rather thoughts in the soul (al-afkÄr al-nafsÄniyya). And a thought is nothing but the co-presence of items of knowledge or beliefs, ordered in a specific way such that from their occurrence there follows, in the mind, the occurrence of knowledge or belief about something else.
[T22] Al-RÄzÄ«, Maná¹iq al-Mulakhkhaá¹£, 245.5â247.12
[two doubts about the syllogism]
Now, someone might raise doubts, as follows.
[First doubt]: what is required for the occurrence of a conclusion in the mind is either (a) those items of knowledge taken together, or (b) each one of them [individually]. This first [option] is false, for three reasons.
(a1) Two items of knowledge cannot exist in the mind [together], so there will be no cause for anything. As for the first [claim, that two items of knowledge cannot exist together in the mind], this is because we find through introspection (min anfusinÄ) that, when we turn our mind towards the knowledge of something, it is impossible for us in that same moment to turn to another item of knowledge. Once one tries it out, one knows necessarily that this is so. As for the second [claim, that there will be no cause for the conclusion], this is because if something has no existence in itself, it cannot cause the existence of anything else.
(a2) Whatever makes something exist must itself exist when its effect occurs. Now, if the thought (fikr) comes down to these items of knowledge as being ordered so as to make the conclusion exist, it would follow that the sought item of knowledge would [already] occur when thought is seeking it, which is absurd. For we find [246] necessarily through introspection that, when we are thinking, we do not have knowledge of the sought [conclusion] yet. This is because thought is seeking knowledge, and it is absurd to seek what is already there.
(a3) If each of these two items of knowledge does not cause the conclusion individually, then once they are put together, either (a3a) some change occursâthat is, either something happens that hadnât yet, or something that was there ceasesâor (a3b) no [change] occurs.
If the former (a3a), then what is required for this change is either (a3a1) each of the two individually, or (a3a2) their combination.
If the former (a3a1), then each of the two will independently ensure that this change takes place. So, since this change independently ensures the conclusion, and [on the current assumption] each of the premises independently ensures the conclusion, each of them will be productive of the conclusion [which is absurd]. But if they are not independent [in yielding the conclusion], then the argument is the same as before.
If the latter (a3a2), then inevitably something beyond each of the two [premises] in themselves must happen once they are together, so that from their being together it follows that this additional thing happens. But then the argument is the same as before, and a regress follows.
(a3b) If, now, their being together does not lead to the occurrence of any change whatsoever, then the situation of the two premises when they are together is the same as their situation on their own. If neither of the premises independently yields the conclusion when it is on its own, neither will it do so when they are together.
(b) Now someone might say: âwhat ensures the occurrence of this conclusion is each single one of these [247] two items of knowledge.â But this [too] is false. First, one knows necessarily that neither of the premises independently ensures the conclusion. Second, if each of them ensured [the conclusion] independently, then multiple independent causes would come together to produce a single effect. But this is absurd. And if the independent [cause] is just one [of the premises], then mentioning the other would be superfluous (ḥashwan).
[Second] doubt: knowledge of the conclusion either (a) follows from knowledge of the two premises, or (b) does not.
(b) If the latter, then the following [of the conclusion] is undermined, in which case your claim [as to the definition of the syllogism] is wrong.
(a) If the former, then either (a1) knowledge of the premises is necessary, or (a2) it is not.
(a1) If it is, then what necessarily follows from what is necessary is itself necessary; so all items of knowledge into which we inquire would have to occur [straightaway]. (a2) If it is not, then this ensures that the knowledge of the premises is a matter of inquiry. Then, the argument is the same as the first case [where the knowledge of the premises was insufficient for producing knowledge of the conclusion]. This either leads to a regress, which is absurd, or to necessary premises, which brings us back to the [problem that everything will necessarily] follow, or to premises that are unknown; but in that case the items of knowledge that follow from them will also be unknown.
[T23] Al-RÄzÄ«, Maná¹iq al-Mulakhkhaá¹£, 247.13â248.7
[Al-RÄzÄ«âs solutions to both doubts in T22]
Response to the first [doubt]: what makes the conclusion necessary is [in fact] those items of knowledge taken together. When [the objector] says âthe items of knowledge are not together [in the mind],â [step (a1) of the first doubt in T22], we respond that we do not concede this, and we will produce the explanation for this in the part on philosophy (fÄ« l-ḥikma).7 When he says, âit follows that thought is linked to knowledge of the sought conclusionâ [step (a2)], we respond that these items of knowledge are only a thought on account of their occurring in a temporal sequence. Insofar as they are such, they do not make knowledge of the conclusion necessary. But [248] insofar as they are what they are, with a view to their true realities, they are knowledge of the premises. It is not impossible that they be together with knowledge of the conclusion. As for his saying that either [the conclusion] occurs once these items of knowledge are together, as something that had not yet occurred when they were separate, or this is not the case [step (a3)], we reply that doubtless a form (hayʾa) of togetherness does occur for them, but in such a way that you [first] understand their having occurred, and then they make you understand the conclusion.
As for the second doubt, the response to it is that inquiry only concerns those primary items of knowledge [insofar as they are] arranged in a temporal succession. If distinct causes in the mind entail their occurrence, then the occurrence of derivative knowledge is necessary; otherwise it is not.
[T24] Al-KhÅ«najÄ«, Kashf al-AsrÄr, 235.12â238.4
[restatement of the doubts raised by Avicenna in T3]
[Avicenna] advanced some doubts concerning the description [of the syllogism] mentioned above.
First: the implication [contained in a syllogism] may not be necessary, as is the case with a conclusion that is [merely] contingent, or absolute. Likewise, what follows in rhetorical and dialectical [arguments].
[236] Second: what follows may be part of what was posited in the syllogism, as in the reiterative syllogism, from which one seeks to obtain the consequent, which is however already present in the hypothetical premise of the syllogism.
Third: when we say âeither motion exists or it does not,â and then âbut it does exist,â it follows that âmotion exists,â here [the conclusion] is the same as one of the premises. Likewise, when we say âif motion were to exist, then motion would exist,â and then âbut in fact, motion exists,â then there follows âmotion exists.â Furthermore the patterns in combinatorial syllogisms behave the same way, like âEvery J is B, every B is B, therefore, every J is B,â or âEvery J is J, every J is B, therefore, every J is B,â and so forth for the remaining forms. Similar examples can be devised in hypothetical combinatorial syllogisms, and generally whenever the middle term coincides with one of the [other] terms.
Fourth: there are simple propositions from which the intended conclusions follow [immediately], so that they are already syllogistically productive, as when we say âSo-and-so says the sun is up, hence he speaks trulyâ and âÊ¿AbdullÄh is writing, so he is moving his hand,â and the like.
[solutions to the doubts]
Response to the first: the necessity is a quality of the inference (al-luzÅ«m), not what follows from the inference (al-lÄzim), and the difference between the two is clear. For what follows, and that from which it follows, might not be necessary, even though the inference between them is necessary; and vice-versa.
[237] As to the second: what is stated in [the hypothetical premise of a hypothetical] syllogism is that the consequent is implied by the antecedent. That is not the same positing [the consequent], which is in the conclusion; nor does [the consequent] follow from [the hypothetical premise just by itself].
Response to the third: in some cases it can be ruled out that the examples given are syllogisms. For a statement is only a syllogism if something is deduced from it, and what is mentioned in the [third] objection is not like that. Then it can be ruled out that what is sought in one of the premises is the same as that sought in another, because the word âbut (lakin)â and the particle âfa-â [i.e. âthereforeâ] imply some difference; if these were not included, or there were no connection to signify the conjunction and link between one premise and the other, nothing would follow [from them]. In disjunctive [propositions] there is an additional solution available, namely that what follows is âIt is not the case that motion does not exist,â which is distinct from âMotion exists,â which was one of the premises. [â¦]
[238.3] The solution to the fourth question is obvious, because the mentioned propositions do not yield the conclusions that follow from them insofar as they are statements, but by means of other premises that are omitted at the level of utterances but implicitly affirmed at the level of the intellect.
[T25] Al-KhÅ«najÄ«, Kashf al-AsrÄr, 240.6â243.11
[restatement of al-RÄzÄ«âs doubts in T22]
The ImÄm [al-RÄzÄ«] mentioned in the Mulakhkhaá¹£ two doubts that would reject the syllogism altogether.
(a) First: what ensures the conclusion [of a syllogism] is either (a1) the items of knowledge taken together, or (a2) each of them singly, or (a3) only some of them. (a1) The first is false, because it is impossible that they all exist together in the mind at the same time, for when we know something we must turn our minds towards an object of knowledge, so that it is impossible for us that the mind turns to another object of knowledge at this very time; but so long as [the premises] are not together at all, there is no cause for the existence of the conclusion. For the items of knowledge will be together in order only while thinking it over (fikr) and thinking about something is incompatible with knowledge of it, so that the two do not happen together. Also, the existence of the cause must be at the same time as the existence of the effect. For if none of [the premises] individually necessitates [the conclusion], and [241] nothing additional arises once they are taken together, it is impossible that [the conclusion] be necessitated once they are taken together. If, on the other hand, some [additional thing] does arise, the argument reverts to [the question of] what is required for that, and a regress follows. (a2) The second option is false too; otherwise two independent causes would together give rise to [a single] effect; also, because the necessary knowledge would arise even when one of the premises that independently [necessitate] the conclusion is missing. (a3) The third option is false for the same reason, and because adducing something not necessary [for the conclusion] would be superfluous.
(b) Second: (b1) if knowledge of the conclusion necessarily requires knowledge of the premises, and knowledge of the premises is necessary, everyone must have [knowledge of the conclusion], because what necessarily follows from the necessary is [itself] necessary. Thus every [person] will share in [knowledge of the conclusion]. (b2) If on the other hand the inference, or the knowledge of the premises, are a matter of inquiry, or if at least one of them is, then the same argument applies again, yielding a regress. Or else it stops at necessary [premises], in which case the consequence [of (b1)] recurs.
[reaction to al-RÄzÄ«âs responses in T23]
(a) [Al-RÄzÄ«âs] reply to the first: [a conclusion] does requires that the items of knowledge be taken together; but they are together as soon as we find ourselves to have knowledge of things in our souls at the same time. To his saying, âone thinks something over while pursuing knowledge of itâ we respond: those items of knowledge are but the thought of their arising in a specific order, and considered as such, they do not necessitate a conclusion. Rather, they do so in consideration of their true realities.
But this calls for further inquiry. For these very items of knowledge, by their true realities, only necessitate knowledge of the conclusion when they are ordered in a specific way, as has been stated several times. But he explained âthinkingâ in terms of these items of knowledge being put in order. So it is not right for him to say that they do not necessitate knowledge when considered as such.
The truth is that âthinkingâ is just the intention [242] of moving from those items of knowledge, and by means of them reaching the intended [conclusion], or whatever gives rise to this intention; or the very arrangement of these items of knowledge as a means [to this end]. So the necessitating element would be the ordered items of knowledge, which are doubtless different from the thinking process, on any of these three interpretations.
[Quotation from al-RÄzÄ«:] âAs for his saying that either [the conclusion] occurs once these items of knowledge are together, as something that had not yet occurred when they were separate, or this is not the case, we reply that doubtless a form (hayʾa) of togetherness does occur for them, but in such a way that you [first] understand their having occurred, and then they make you understand the conclusion.â
This is a comprehensive critique [of the syllogism as such]. Verification lies in blocking [the argument] by uncovering the false premise. We do this by saying: when [the items of knowledge] come together, something does arise that was not there when they were separate, and necessarily so. There is no need to belabor the necessity that their being together arises, once they are brought together, or that this is different from each one of the parts, and was not yet existent when they were separate.
He said: the necessitating element for that is either each of the parts, or some of them, or their totality. We say: these are not the only options. Rather, the reasons could be external, because [the syllogism] taken together is compounded from two things whose complete cause is those two parts, these being the material cause, plus an efficient cause which is external, with the upshot that neither of the parts is independent of the other in necessitating [the conclusion]. We say this because nothing here is independently [necessitating] apart from [the syllogism] taken together, since an external cause ensures the togetherness of its parts.
(b) [Al-RÄzÄ«âs] reply to the second: the inquiry only concerns those primary items of knowledge [insofar as they are] arranged in a temporal succession. If distinct causes in the mind ensure their occurrence, then the occurrence of knowledge by inquiry is not impossible; otherwise it is.
[243] Verification of this reply: we do not concede that if the knowledge of the two premises is necessary, and likewise the fact that the intended conclusion follows from them, then knowledge by inquiry occurs for each of them. For what it means for each of the premises to be necessary is that, if we conceive of their terms and of the nexus (nisba) of their predicates to their subjects, we know that this nexus is necessary. What it means for it to be necessary that the conclusion follows is that, if we conceive of the two premises and the intended [conclusion] and the relation (nisba) of the intended [conclusion] to the two [premises], the former is known to follow from the latter. Someone might conceive each of the terms in both premises and the terms of the intended [conclusion], without conceiving the premises and intended [conclusion], because the occurrence of that depends on external causes, which themselves may occur or fail to occur. When [the objector] says, âwhat necessarily follows from the necessary is [itself] necessary,â this is wrong, because all matters of inquiry are like that. The necessary [proposition] is one such that the conception of its two terms suffices to assent to it, whereas the fact that something necessarily follows from something necessary does not suffice for assenting to it; an intermediary necessity, from which this follows, is needed. So it is not necessary [knowledge], but [knowledge] by inquiry.
[T26] Al-KhÅ«najÄ«, Kashf al-AsrÄr, 247.12â248.9
[defense of the fourth figure]
Some have omitted the [fourth] figure from this classification, and made the figures only three, because they said: the middle term is either a predicate in both premises or a subject in both, or else a predicate in one of them and a subject in the other, the latter being the first figure. Then, when they mentioned the first figure, they mentioned it as being more specific than this, in that the middle term in it is a predicate in the minor premise and a subject in the major premise. On this basis they proclaimed its perfection, under the condition that the minor premise be affirmative and the major premise universally quantified. But if the first figure is explained in its more general meaning, then none of these features holds true. Hence, they were forced either to maintain a defective classification [of syllogistic figures] or to a false explanation of the first figure, as just mentioned.
As for [248] the excellent al-FÄrÄbÄ« and the Master [Avicenna], they abandoned [the fourth figure]âafter affirming its place in the classificationâbecause it is remote from nature, difficult to reduce to the first figure (as this requires applying changes to all its premises), and unsuitable for the habits of theoretical inquiry and deliberation. And finally, because it is not needed, given the other three figures. The Master [Avicenna] said: therefore, it is most appropriate for it, in its own right and for the relevant positions (bi-hi wa bi-mÄ huwa fÄ« madhhabihi), that it be abandoned.8 We, however, follow the later logicians in what they have said, since the logician investigates everything by whose means it is possible to reach something [as yet] unknown from what is already known, and [investigates] how one is to order what leads to this, regardless whether it is an ordering reached by means of another ordering, or notâwhatever it may be. If one certain arrangement was made superfluous by another, that would mean that the second and the third figure should also be abandoned. The usefulness ascribed to the other two figures is present for the fourth figure as well, as will be shown.
[T27] Al-AbharÄ«, ĪsÄghÅ«jÄ«, 21.1â25.15 [trans. Salem, mod.]
[definition and terminology]
The syllogism is a statement composed of [sub-]statements such that, if these are accepted, then this all on its own leads to another statement. It can be a combinatorial syllogism, as when we say âEvery body is composed (muʾallaf); everything composed is created; therefore, every body is created.â Alternatively, it can be a reiterative syllogism, as when we say âIf the sun is up, then it is day; but, it is not daytime; therefore, the sun is not up.â
What is repeated between the two premises of the syllogism is referred to as the âmiddle term.â The subject of the conclusion is referred to as the minor term and its predicate is the major term. The premise that contains the minor term is referred to as the minor premise and the one that contains the major term is known as the major premise. The structural composition (hayʾa al-taʾlÄ«f) of the major and minor premises of the syllogism is called a figure.
[figures of the syllogism: preference for the first figure]
There are four figures. If the middle term is the predicate in the minor premise and the subject in the major premise, then it is the first figure. If it is the other way around, then it is the fourth figure. If the middle term is the subject in both premises, then it is the third figure. If the middle term is the predicate in both premises, then it is the second figure. These are the four figures mentioned in logic.
The fourth figure is exceedingly distant from what is natural. No one with a sound mind and a steady disposition needs to reduce the second figure to the first figure. The second figure is derived when there is a contradiction between the two premises, whether by affirmation or negation. The first figure is the one that has been laid down as the standard (miÊ¿yÄr) for the sciences. We present it here as a paradigm, and from it derive what is sought.
[moods of the syllogism]
There are four productive moods. First: as when we say, âEvery body is composed; everything composed is created; therefore, every body is created.â Second: as when we say, âEvery body is composed; nothing composed is eternal; therefore, no body is eternal.â Third: as when we say, âSome bodies are composed; everything composed is created; therefore, some bodies are created.â Fourth: as when we say, âSome bodies are composed; nothing composed is eternal; therefore, some bodies are not eternal.â
[two types of syllogism]
Combinatorial syllogisms may be composed (murakkab) from (a) two categorical propositions, as happened [in the examples just given]; or (b) two conjunctive propositions, as when we say, âIf the sun is up, then it is day; whenever it is daytime, the earth is illuminated; therefore, if the sun is up, the earth is illuminatedâ; or (c) two disjunctive propositions, as when we say, âEvery whole number is either even or odd; every even number is either the double of an even number or the double of an odd number; therefore, every number is either odd, or the double of an even number, or the double of an odd numberâ; (d) or a categorical proposition and a conjunctive proposition, as when we say, âAs long as this is a human, it is an animal; every animal is a body; therefore, every being that is a human is also a bodyâ; (e) or a categorical proposition and a disjunctive proposition, as when we say, âEvery number is either even or odd; and every even number is divisible into two equals; therefore, every number is either odd, or can be divided into two equalsâ; (f) or a conjunctive proposition and disjunctive proposition, as when we say, âAs long as this is a human, it is an animal; every animal is either white or black; therefore, as long as this is a human, it is either white or black.â
[T28] Al-AbharÄ«, TanzÄ«l, quoted from al-ṬūsÄ«, TaÊ¿dÄ«l, 201.4â204.1
[some doubts about the definition of âsyllogismâ dispersed]
When we said that [the syllogism produces the conclusion] âall on its own,â we were guarding against two things.
First, [to ensure] that for the intended [conclusion] to follow, there is no need to bring in anything beyond the premises of the composite statement.9 [â¦]
[202.3] Second, [to ensure] that the conclusion be not by means of an [additional] premise that follows from some of the premises.10 [â¦]
[202.20] Someone might say: if it is a condition of the syllogism that the intended [conclusion] does not follow by means of some other premise, which itself follows some of the premises that were mentioned, then composites from which the intended [conclusion] follows by means of the converse do not fall under [the definition of] syllogism.
We say: the meaning of saying âwhat follows does not do so by means of what follows from some of the premises,â is [203] that it is not by means of something that follows from them insofar as one changes their parts from the parts of the original premises. But in the case of the converse, its parts are not different from the original parts of the premises; unlike in the case of the contraposition, for here its predicate and subject are different from the predicate and subject of the original premise. [Cf [T21].]
[203.13] Someone might say: if what you have mentioned is a condition for the syllogism, it follows that âwhenever A is B, every C is D, and every D is Hâ is not a syllogism productive of the conclusion âeither A is not B, or every C is H.â For the first part of the disjunction is different from the first part of the connective [premise].
We say: what was meant by âoriginal partsâ are the simple [elements] which remain after the analysis of the premises, I mean the predicates and subjects. [â¦]
[204.1] If the syllogism is composed of two premises only, it is called simple; if not, [it is called] composite.
[T29] Al-ṬūsÄ«, TaÊ¿dÄ«l, 203.4â11
[commentary on T28: critique of AbharÄ«âs comments on implied premises]
This response [by al-Abharī] is not correct, if one takes the objection in the right way. The correct response would be that the converse is not needed for the inference itself; it is needed only in the science of inferences. It is not a condition of the syllogism that the conclusion be known to follow without the mediation of any statement apart from the premises. Rather, it would be correct to say that a condition of [the syllogism] is [simply] that the conclusion does [in fact] follow without the mediation of any statement apart from the premises.
The correct [response] is: it is a condition of the syllogism that the intended [conclusion] does not follow through the mediation of any statement that is not actually contained in the premises in actuality, and not potentially either. For we do not rule out that a composed [premise] involving a negation that follows from an affirmation may be required for the conclusion; however, we would say that this affirmation has been mentioned, but potentially. When [al-AbharÄ«] says âin the case of the contraposition, its predicate and subject are different from the predicate and subject of the original premise,â this is taking it at the level of utterance.
[T30] Al-ṬūsÄ«, TaÊ¿dÄ«l, 204.2â5
[commentary on T28: the simplicity of the syllogism]
The syllogism is simple not in consideration of the number of the premises, but of the state of the conclusions: it will be simple if only a single conclusion follows, without first having to produce another conclusion which serves as a premise for that conclusion. It doesnât matter whether there are two premises or more. For a syllogism is composed due to its being composed of [other] syllogisms, not of premises.
[T31] Al-KÄtibÄ«, Munaṣṣaá¹£, Fols. 110r8â110v14
[commentary on al-RÄzÄ«âs solutions to his own doubts in t23]
[Al-RÄzÄ«] said: âthe response to the first doubt11 is that what makes the conclusion necessary is those items of knowledge taken together,â etc.
I say: the strategy of this response is as follows. [The objector] says under the first option [(a) in T22], regarding the idea that what makes the conclusion necessary is those items of knowledge taken together, that first of all two items of knowledge cannot exist in the mind [together]. But we say: we do not concede this. He will provide an explanation in [his treatment of] metaphysics, as to how the two can exist together. What he says here is that we judge a hypothetical proposition in terms of whether one proposition follows from the other, or does not. And this can be conceptualized only when both premises are known together. Secondly, [the objector] said: if these ordered items of knowledge necessitate that the knowledge of the conclusion arises, it follows that the thought [process] is linked to the knowledge of the intended [conclusion]. [Al-RÄzÄ«] said in answer that insofar as these items of knowledge are a thought [process] that arises in temporal sequence, they do not necessitate the knowledge of the conclusion. But insofar as they are what they are, that is, with a view to their true realities, they are items of knowledge about the premises, and it is not impossible that these and knowledge of the conclusion be together.
You should know that the strategy of this response is to say: what you mentioned in [your] proof does show that these items of knowledge, insofar as they arise in a temporal sequence, do not, considered in that light, necessitate the existence of the knowledge of the conclusion. We then say that this is not what ânecessitating itâ means. They ânecessitate itâ only when considering their true realities. [â¦]
[110r22] But this calls for further inquiry. For if it were like this, it would obviously be false, since in respect of their true realities, these items of knowledge do not necessitate the knowledge of the conclusion, so long as they are not ordered in a specific way (as will be made clear to you later). The ImÄm [al-RÄzÄ«] interprets âthoughtâ as either these ordered items of knowledge, or the ordering itself of these items of knowledge. But how could this be? Given that thought is involved in the inference (istilzÄm) from these items of knowledge to the conclusion. If it is as [al-RÄzÄ« claims], then there will follow what we said [in the objection, step (a2)]: that the thought of something will come together with the arising of the knowledge of that thing.
The correct solution is to say: we do not concede the truth of what you said about hypothetical propositions. [Al-RÄzÄ«] said in his explanation of them that âthoughtâ comes down to these ordered items of knowledge. We say: we do not concede this. Rather, in our view, âthoughtâ comes down to the intention to make a transition (qaá¹£d al-intiqÄl) from these items of knowledge, by means of which one is led, to the intended [conclusion]; and whatever follows from this aim. If this is the case, then what you [sc. the objector] mentioned does not follow, on the assumption that these ordered items of knowledge are what necessitates the existence of the conclusion.
And [the objector] said, thirdly [in step (a3)], that these items of knowledge may arise differently when they do so together or individually. In his answer [al-RÄzÄ«] said, âdoubtless a form of togetherness does occur, but in such a way that you [first] understand their having occurred, and then they make you understand the conclusion.â
You should know: this was a general criticism. His intended strategy is to say: if you were right in what you said about the premises arising together, it would follow that no form of togetherness occurs when these items of knowledge are actually together. The consequent is obviously false, so the antecedent likewise. The verification of the answer is simply: rule this out, and reveal the false premise. This is done by taking the first alternative [i.e. (a3a)], which was that when they come together, something does occur that was not there when they were present individually, and this is indeed how things must be. [The objector] said that what is required for that is a change, either of each of them individually or of both together. But we say: we do not concede that this is an exhaustive set of options. Rather, [it might also be] their being together, together with some external causes. If the composition is a complete cause, the material cause and something external requires that the parts be brought together, which is the efficient cause.
[Al-RÄzÄ«] said: âAs for the second doubt, the response to it is that inquiry only concerns those primary items of knowledge [insofar as they are] arranged in a temporal succession. If distinct causes in the mind ensure their occurrence, then the occurrence of inquiry is not impossible; otherwise it is.â
I say: the strategy of this response is to say, we do not concede that if the knowledge of the conclusion necessarily follows from knowledge of the two premises, then the knowledge of the premises is also like that. For each of them, there must be items knowledge reached through inquiry. For what is meant by âfollowing necessarilyâ is that, when we conceptualize two premises, the conclusion, and the relation (nisba) of the conclusion to the [premises], the mind is sure that the conclusion follows from the premises. What is meant by the premises being necessary is that, when we conceptualize their terms and the nexus (nisba) of the predicate to the subject in them, the mind is sure that this nexus is necessary. This being so, it could be that someone fails to conceptualize each of the terms in the premises and the nexus of the predicate to the subject in them, and so does not conceptualize the premises and the conclusion either. For these are distinct causes, and these causes may occur or fail to occur.
[Al-RÄzÄ«] is wrong to say that what necessarily follows from something necessary is itself necessary. For the necessary is that whose terms, on their own, suffice for assent. Whereas what follows from the necessary is not itself necessary, but rather a matter of inquiry.
[T32] Al-UrmawÄ«, Maá¹ÄliÊ¿, 64.15â65.13
[definition of syllogism]
[A syllogism] is a statement made up of propositions such that when they are accepted, another statement follows from it just by itself. In âfollows from it,â by âitâ we mean the statement made up [of propositions]. And by âjust by itselfâ we mean that it does not follow by means of a further premise or an implicit premise.
[additional and implied premises]
[An example] of the first [needing another premise] is this. When we say âA is equal to B; B is equal to J,â from this it follows that âA is equal to J,â by means of the [additional premise] âeverything that is equal to B is equal to everything to which B is equal.â When we say [65] âB is equal to J,â this implies âJ is equaled by Bâ and becomes the minor premise for âeverything to which B is equal A is equal to as wellâ which then implies âJ is something A is equal toâ implying âA is equal to J.â Some people made that [additional] premise to be: âwhat is equal to something equal is equal.â But you will notice that with this premise [the syllogism] does not produce a conclusion âby itself,â for the middle term is not repeated.
[An example] of the second [needing an implied premise] is this. When we say âRemoving part of a substance necessarily removes the substance; the removal of what is not a substance does not necessarily remove the substance,â this implies âa part of a substance is a substanceâ by means of the contraposition, namely âthat whose removal necessarily removes the substance is [itself] a substance.â This would require a change in the terms of the syllogism, lest it fall outside proof by straight conversion.
By âanother statementâ we mean: [one that is] distinct from both of the premises. [â¦]
The syllogism may be intellectual (maʿqūl), composed in the intellect in such a way as to leads to assent of another thing; or it may be heard, as we said earlier.
[T33] Al-UrmawÄ«, Maá¹ÄliÊ¿, 66.3â13
[al-UrmawÄ« responds to al-RÄzÄ«âs doubts in T22]
Response to the first: if what necessitates [the conclusion] is [both items of knowledge] being together, and this has existence in the mind, which [al-RÄzÄ«] calls the âthought,â we say: no, rather âthoughtâ is the intention to make a transition from those ordered items of knowledge, or what follows from this [intention], or their arrangement, right up to the attainment of the object of inquiry. As for his saying [in step (a3a2)], âif, when they are together, something occurs that did not yet occur when they were on their own, the same argument recurs,â we reply: we do not concede that a regress will follow. Rather it ends in distinct reasons, which are the efficient causes.
Response to the second: we do not concede that everyone shares [knowledge of the conclusion, as inferred in (a1) of the second doubt], if [knowledge of] the two [premises] is necessary. For what it means for a premise to be ânecessaryâ is that when we conceptualize both its terms and ascribe a nexus of one of them to the other, then we have knowledge of this nexus. The meaning âfollows necessarilyâ is that, if we know the two premises and we relate the intended [conclusion] to them, then we know that [the conclusion] follows from the two [premises], even if one of the two sides of the proposition or one of the two premises of the syllogism may not be conceived. When [al-RÄzÄ«] says, âwhat necessarily follows from something necessary is itself necessary,â we say: we do not concede this, rather it is reached by inquiry (naáºarÄ«).
[T34] Al-SamarqandÄ«, Qisá¹Äs, 321.8â323.7
[answer to al-RÄzÄ«âs first doubt in T22, as restated by al-KhÅ«najÄ« in T25]
Response to the first: what necessitates [the conclusion] is the [items of knowledge] being together, and that they come together in the mind, because we judge whether the consequent follows from the antecedent, or whether the predicate holds of the subject, and so on, by means of relations, which is impossible without intellectually grasping both relata together. When [al-KhÅ«najÄ«] says, âfor the [items of knowledge] will be together in order only while thinking it over (fikr) and thinking about something is incompatible with knowledge of it,â we say: we do not concede that their being together in order is thought; rather thought is the ordering of this aggregate in order to reach the intended conclusion. When [al-KhÅ«najÄ«] says, âwhen they come together, if something occurs that was not there before, then what necessitates that is either each of the [premises], or some, or all together,â we say: when they come together, a form of togetherness necessarily arises, which is different from each of the parts and which does not exist while they are [still] separate. What necessitates this is something external, namely the intellectual faculty, just as in the other composites, because the efficient cause is not part of the effect. [â¦]
[answer to al-RÄzÄ«âs second doubt, cf. T33]
[323] Response to the second: if what is meant by ânecessaryâ is its general meaning, then we do not concede that every [person] would share in [this necessary knowledge]. For in this case, the meaning of the premises being ânecessaryâ is that if their terms and the nexus of one of them to the other are conceptualized, then it is known that this nexus obtains. The meaning of âfollowing necessarilyâ is that if the two premises are conceptualized together with the intended [conclusion], and the relation of the intended [conclusion] to them, it is known that it follows from them. Whenever these conceptualizations are not taking place, the arising of the intended [conclusion] does not follow, so it will not follow that all [people] share it. If on the other hand what is meant by ânecessaryâ is the specific meaning, then we do not concede that a regress follows, because it may end with something that is necessary in the general sense. But God knows best.
[T35] Al-ḤillÄ«, MarÄá¹£id, 238.5â239.12
[objections drawn from Avicenna in T3 and al-RÄzÄ« in T22]
Several objections have been leveled [against the definition of the syllogism].
(a) In âOne who walks about by night is a thiefâ or âWhen the sun is up, it is dayâ a single premise produces a conclusion, so there is no need for several premises in a syllogism.
(b) You say âEvery J is B; every B is B,â and conclude âevery J is B,â but that is the same as the minor premise. Or you say âEvery J is J; every J is Bâ and conclude âevery J is B,â which is the same as the major premise. So it is a syllogism from which no âother statementâ follows. Likewise, you may say: âIf there is movement, then there is movement; but in fact, there is movement; therefore, there is movementâ and âEither there is movement or not; but in fact, there is movement; therefore, there is movement.â
(c) If in a reiterative syllogism what is reiterated is the same as the premise, what follows [i.e. the conclusion] is the same as the consequent [of the hypothetical premise]. So this [too] is a syllogism from which no other statement follows.
(d) What is required for the conclusion is not that the premises be together, because this cannot exist in the mind. We find in our souls that when we turn with our minds to seeking an object of knowledge, it is impossible for us to turn our attention to [239] another item of knowledge at the same time. And what has no existence in its own right cannot possibly be the cause for the existence of something else, because it is the existence of the cause that necessitates the effectâs occurrence. Now if it is the thought, which comes down to these ordered items of knowledge, that necessitates the existence of the conclusion, then it would follow that knowledge of the object of inquiry would occur as soon as the thought does. But this is false, because we know for sure that, when we are in the state of thinking, we are not yet knowing. Also, because thinking is seeking [new knowledge], and seeking what has [already] occurred would be absurd. And, because if these items of knowledge are not each the cause for the conclusion singly, but when they come together nothing additional occurs, either by something happening that had not been there before, or because something ceases, then no cause for the conclusion occurs. But if something [new] does occur, we direct the argument to the cause of this occurrence. What ensures [the conclusion] is not all of the premises taken singly: we know necessarily that this option must be discarded, and besides we would have an aggregate of several causes for a single effect [i.e. there would be overdetermination]. Nor is what ensures [the conclusion] just one [of the premises], for the first reason [i.e. it is obviously false] and because neither [premise] would have precedence [over the other, i.e. neither has a better claim to be the cause].
(e) If knowledge of the conclusion necessarily presupposes knowledge of the premises, then so long as knowledge of [the premises] is necessary, that would imply that [all] intellects would share in [the knowledge of the conclusion]. Alternatively, if knowledge of the implication or the premises (or just one of them) is a matter of inquiry, then a regress follows. Or else the regress ends with a necessary [premise] and the difficulty returns.
[T36] Al-ḤillÄ«, MarÄá¹£id, 239.13â242.3
[replies to doubts about the syllogism]
Response to (a): in each of the examples there are two premises producing the conclusion, but one of them is implicit: either because it is known, or because there is something indicating it. So when we say âSomeone walking about by night is a thief,â the major premise is implied because it is obvious: âeveryone who walks about by night is a thief.â And when we say âWhen the sun is up, it is day,â the other premise is implied [240] because the utterance âwhen,â once connected, indicates the presence of the [other] premise.
Response to (b): in âEvery B is Bâ the subject and predicate are the same, so nothing is [really] made subject or made predicate, so there is no premise and no syllogismâexcept on the level of utterances, which are however nonsensical. If one takes it to be a syllogism, the inference from it is likewise nonsense, albeit that [the conclusion] is true. But if [the nonsensical premise] is altered, the objection disappears.
Response to (c): when the consequent that is part of a conditional proposition is reiterated, its status (ḥÄl) changes: for first it is not a complete statement, and does not bear truth or falsehood, unlike in its second [appearance as the conclusion].
Response to (d): what produces the conclusion is [indeed] the two premises being together, and we do not concede that their being together in the mind is impossible. For we find in our souls that we know many items of knowledge at the same time, and know the implications between the propositions. And this is possible only once there is knowledge of the two at the same time. When [the objector] says that thought does not constitute knowledge, because thought [still] seeks [that knowledge], and thought is the premises being together, we reply: if thought is made out to be the same thing as seeking [knowledge], then it is wrong to make it come down to the premisesâ being together. Alternatively, if it is made out to be the same as the premises, then can it be together with knowledge. As for his saying that one of [the premises] is not a cause [separately], so neither are they when taken together, [241] we reply: this is ruled out, in the sense that when we understand the attribute of âtogethernessâ to occur [for the premises], we [also] understand them to have causal efficacy (wujÅ«d al-Ê¿illiyya) [to produce the conclusion]. It might be said that this could occur as something additional. As to his saying that what necessitates [the conclusion] is either each of the parts [of the syllogism] or some of them, or all of them together, we reply: we deny that the set of options is exclusive, because there could also be reliance (isnÄd) on something external. What is composed from two things may well have as its complete cause these two parts as the material cause, plus an efficient cause which is external. The upshot will be that neither of the parts is independently responsible for causing [the conclusion]. Our reason for saying this is that [the syllogism] taken together is independently [able to produce the conclusion] only when an external cause ensures that its parts are together.
But this argument [sc. the response just given to objection (d)] is extremely weak, because the questioner [who posed objection (d)] denied that the premisesâ being together is a complete cause, and this argument [in response] admits his claim. For the additional thing that occurs when [the premises] are together, just insofar as they are together, is a cause. Then [the response] makes that additional thing reliant on something external; therefore something external is involved in reaching the conclusion. The conclusion is thus not exclusively reliant on [the premises] being together, but also on something external. So the problem reappears.
[242] [Response] to (e): necessary [items of knowledge] must indeed be shared. With respect to those that rely on the bodily faculties, this is obvious. With respect to those that are immediate (badÄ«hiyyÄt), it may be that [this sharing] ought to occur, but then either the sound natural disposition is contaminated, preventing the intellect from judging [as it should], or some kind of defect befalls the intellectual faculty.
[T37] Al-ḤillÄ«, MarÄá¹£id, 119.5â10
[reiterative and combinatorial syllogisms]
Secret: when a syllogism somehow contains the sought [conclusion] or its contrary, it is called reiterative, like âWhenever A is B, J is D; but A is B; therefore, J is Dâ or â[Whenever A is B, J is D; but] J is not D; therefore, A is not B.â If by contrast [the conclusion] is not contained [in the syllogism], it is called combinatorial, like âEvery J is B, and every B is Aâ and âWhenever A is B, then J is D; and whenever J is D, then H is R.â The earlier logicians assimilated the combinatorial syllogism to the categorical, and the reiterative to the hypothetical. They did not realize that combinatorial syllogisms may [also be] hypothetical. The Master [Avicenna] explained this [cf. T7].
[T38] Al-ḤillÄ«, AsrÄr, 119.12â120.9
[the four figures of the syllogism]
Secret: the combinatorial syllogism is composed of two premises. One contains the subject of the conclusion or similar: it is called the minor premise. The other contains the predicate of the conclusion or similar: it is called the major premise. For example âEvery human is an animal, and every animal is a body.â âHumanâ is the minor because of its specification, while âbodyâ is the major, because of its generality; âanimalâ is the middle. [â¦]
[120] All three of them are called by the name âterm.â What is sought is called the âconclusion,â the composition of premises âcombination,â the form in which they are composed âfigure,â and that which produces the conclusion âsyllogism.â
The figures are four, because if the middle term is a predicate in the minor premise and a subject in the major premise, then this is the first figure. This is the clearest and noblest of all the figures, because it is productive in the universal affirmative and all four quantifications. If it is the other way around, then this is the fourth figure, but the ancients omitted it because it is so remote from nature. And if [the middle term] is a predicate in both premises, then this is the second [figure], and this one follows the first [figure] in that it is productive in the universal and in that it is used in the sciences. If the [middle term] is the subject in both [premises], then it is the third [figure].
For medieval reactions to this definition see more generally K. El-Rouayheb, Relational Syllogisms and the History of Arabic Logic, 900â1900 (Leiden: 2010), 116â¯ff. and P. Thom, âThe Syllogism and Its Transformations,â in C. Dutilh Novaes and S. Read (eds), The Cambridge Companion to Medieval Logic (Cambridge: 2016), 290â315.
See T.-S. Lee, Griechische Tradition der aristotelischen Syllogistik in der Spätantike (Göttingen: 1984), K. Ierodiakonou, âAristotleâs Logic: an Instrument, Not a Part of Philosophy,â in N. Avgelis and F. Peonidis (eds), Aristotle on Logic, Language and Science (Thessaloniki: 1997), 33â53, at 36.
For a more detailed discussion, see D. Klinger, âForms of Carrollâs Paradox in Postclassical Arabic Logic,â History and Philosophy of Logic 44 (2023), 1â16.
P. Henle, âOn the Fourth Figure of the Syllogism,â Philosophy of Science 16 (1949), 94â104. For the issue in our period see A.I. Sabra, âA Twelfth-Century Defence of the Fourth-Figure of the Syllogism,â Journal of the Warburg and Courtauld Institutes 28 (1965), 14â28.
For the ways in which hypothetical propositions may feature in combinatorial syllogisms, see IshÄrÄt, p. 157â¯ff. An example of a mixed categorical-hypothetical combinatorial syllogism is:
If A is B, then J is D | e.g. | If a dog is a poodle, its hair is curly |
Every D is H | All curly hair is hard to clean | |
Therefore: If A is B, then every J is H | Therefore: If a dog is a poodle, its hair is hard to clean. |
In a âcontraposition (Ê¿aks al-naqÄ«á¸),â what contradicts the subject is made the predicate, and what contradicts the predicate is made the subject. Thus âNo odd numbers are evenly divisibleâ has both the implications âNothing evenly divisible is an odd numberâ (the converse) and âNothing that is not evenly divisible is an even numberâ (the contraposition).
There, he states: âOn the possibility of jointly grasping several objects at a single stroke. Concerning conceptions, [this is possible] because if it werenât, then no assent would ever come about. For the relation (nisba) between one thing and another is only possible if both things are grasped. The falsity of the consequent here indicates the falsity of the antecedent. Moreover, one may conceptualize a compound by means of its definition, and this is only possible when all its parts are conceptualized at once. Concerning assents, [this is possible] because if it werenât, then only a single premise could ever occur in the mind. If this were the case, no conclusion would ever occur, for we know by necessity that no single premise is ever productive of a conclusion. The falsity of the consequent here indicates the falsity of the antecedent. Anyone who says that when we turn our mind to an object of knowledge, it is impossible for us to turn to another object of knowledge [at the same time], must be referring to our imagination (khayÄl), not to our intellect with which we may well [do these things].â F. al-RÄzÄ« (2021). al-Mulakhkhaá¹£ fÄ« al-maná¹iq wa-l-ḥikma. 2 vols. Ed. Ä°. HanoÄlu (Amman: 2021), 379.9â380.2.
Avicenna, ShifÄʾ: QiyÄs, 111.
Al-AbharÄ« illustrates with the example about A being equal to B, for which see al-SÄwÄ« in [T12].
Al-AbharÄ« illustrates with the example about parts of a substance being substances, for which see al-SÄwÄ« in [T12].
Al-KÄtibÄ« has just restated the doubts at fol. 110r1â14.