Document Type : Original Article
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Introduction
What makes Suhrawardi’s logic markedly different from that of the Peripatetic logicians is his theory of modal syllogisms. Compared with Ibn Sina and his followers, Suhrawardi makes the subject extremely simple. And that is because:
i.) He Makes modality a part of the predicate and confines his modality only to the alethic ones i.e., necessity and possibility. So he writes:
لما کان الممکن امکانه ضروریا و الممتنع امتناعه ضروریا والواجب وجوبه ایضا کذا، فالاولی ان تجعل الجهات من الوجوب و قسیمیه اجزاء للمحمولات حتی تصیر القضیة علی جمیع الاحوال ضروریة. (1, p.17)
“Since the contingency of the contingent, the impossibility of the impossible, and the necessity of the necessary are all necessary, it is better to make the modes of necessity, contingency, and impossibility parts of the predicate, so that the proposition will become necessary in all circumstances.”
And he maintains that:
ولا نعنی بالضروری إلاّ ما یکون لذاته فحسب. واما ما یجب بشرط من وقت و حال فهو ممکن فی نفسه.(1, p.17)
“By ‘necessary’, we mean only that which‘is’ by virtue of its own essence. That which necessarily ‘is’ on condition of a time or a state, on the other hand, is contingent [possible] in itself.”
ii.) By making modality a part of the predicate he radically changes the notion of the predicate in modal propositions as it was common among the Peripatetic logicians.
iii.) Now by (i) the proposition ‘Every A is Mod B’; or:
"x(Ax→Mod Bx),
in which ‘Mod’ stands for ‘necessity’ or ‘possibility’ becomes:
£"x(Ax→Mod Bx)
The second innovation is the main reason for the simplicity of his modal theory. To see why, let us examine an interesting and controversial example in the Peripatetic tradition:
"x(Fx→¸Gx)
"x(Gx→£Hx)
\"x(Fx→£Hx)
This is a first figure modal BARBARA syllogism that Farabi and IbnSina argue for its validity, but among Muslim logicians perhaps it is Khunaji who for the first time rejects it, and depending on two different interpretations, he regards it either as invalid or as not known to be productive or sterile(2,xlxliv.p.270281).
For Suhrawardi such controversy over this syllogism has no significance. This is because for him this syllogism is illformed for the simple reason that in it the middle term which according to (ii) is ‘¸Gx’ is not repeated. So it is not a syllogism proper. For him the right form of the syllogism would be:
£"x(Fx→¸Gx)
£"x(¸Gx→£Hx)
\£"x(Fx→£Hx).
But as we shall see Suhrawardi’s insistence on the recurrence of the middle term leads to an inconsistency in his second figure modal syllogisms.
I shall come back to the disputed syllogism soon and show how its validity can be proven in Suhrawardi’s logic.
But let us first examine his modal syllogisms of the first figure.
First figure
As I have shown (3) Suhrawardi reduces all nonmodal moods of the first figure to:
"x(Fx→Gx)
"x(Gx→Hx)
\ "x(Fx→Hx)
Now by (i)(iii)aforementioned, in the modal cases that single mood becomes:
£"x(Fx→ModGx)
£"x(ModGx→ModHx)
\ £"x(Fx→ModHx)
‘Mod’by (ii) can be either ‘£’ in the ‘ModGx’ or ‘¸’ and in each of these two cases the’Mod’ of’‘Hx’ can be ‘£’ or ‘¸’. Given that the ‘Mod’ of ‘H’ in the major premise and the conclusion should be the same we have four modal moods altogether The validity of these moods, all in BARBARA, is obvious. Suhrawardi gives the following examples:
«کل انسان بالضرورة هو ممکن الکتابة» و «کل ممکن الکتابة فهو بالضرورة واجب الحیوانیة او ممکن المشی»، ینتج ان «کل انسان بالضرورة واجب الحیوانیة او ممکن المشی». (1, p.23)
1Necessarily every human being is a possible writer
Necessarily every possible writer is necessarily animal
\Necessarily every human being is necessarily animal
2Necessarily every human being is a possible writer
Necessarily every possible writer is a possible walker
\Necessarily every human being is a possible walker
It is worth mentioning that formally in each of the moods of this figure the subject of the minor premise may also be modalized and this would double the number of syllogisms.
Suhrawardi on Aristotle’s Controversial Syllogism
Before going to the second figure let us see how the socalled illformed syllogism mentioned earlier can be converted to the Suhrawardian form of it and then show its validity after all. Here is the proof in the quantified modal logic S5 with which I assume the reader’s familiarity.
£"x(Fx→¸Gx) 
£"x(Gx→£Hx) 
\£"x( Fx→£Hx) 
1 
£"x(Fx→¸Gx) 

A 
2 
£"x(Gx→£Hx) 

A 
3 
"x£(Gx→£Hx) 

2,Ibn Sina Barcan (3) 
4 
£(Gx→£Hx) 

3,UE 
5 
¸Gx→¸£Hx 

4,ML 
6 
¸Gx→£Hx 

5,Axiom 5 
7 
"x(Fx→¸Gx) 

1,£E 
8 
Fx→¸Gx 

7,UE 
9 
Fx→£Hx 

6,8,PL 
10 
"x(Fx→£Hx) 

9,UI 
11 
£"x(Fx→£Hx) 

10,£ I 
If we accept Suhrawardi’s embedding the premises in the necessary modality, which I regard it as a metaphysical thesis, and apply it to the controversial modal syllogism, Suhrawardi’s derivation would become a shortcut proof. In fact Suhrawadi goes from the first line of the above derivation right to the line (6).
Here are the proofs of some other mixed syllogisms of the first figure found in Ibn Sina. For brevity I only mention those axioms used in some lines in the following proofs. It was Paul Thom who for the first time interpreted IbnSina’s modal syllogistic somehow in the line with Suhrawardi by embedding IbnSina’s premises of modal syllogisms within a necessity modality(4):
£"x(Fx→¸Gx) 
£"x(Gx→¸Hx) 
\£"x( Fx→¸Hx) 
1 
£"x(Fx→¸Gx) 

2 
£"x(Gx→¸Hx) 

3 
"x£(Gx→¸Hx) 

4 
£(Gx→¸Hx) 

5 
¸Gx→¸¸Hx 

6 
"x(Fx→¸Gx) 

7 
Fx→¸Gx 

8 
Fx→¸¸Hx 

9 
Fx→¸Hx 
8, Axiom 4 
10 
"x(Fx→¸Hx) 

11 
£"x(Fx→¸Hx) 

£"x(Fx→£Gx) 
£"x(Gx→£Hx) 
\£"x( Fx→£Hx) 
1 
£"x(Fx→£Gx) 
A 
2 
£"x(Gx→£Hx) 
A 
3 
£"x(Fx→Gx) 
1,£E 
4 
Fx→£Gx 
3,UE 
5 
Fx→Gx 
4,Axiom T 
6 
"x(Gx→£Hx) 
2,£E 
7 
Gx→£Hx 
3,UE 
8 
Fx→£Hx 
5,7 Barbara 
9 
"x(Fx→£Hx) 
8,UI 
10 
£"x(Fx→£Hx) 
9,£I 
£"x(Fx→£Gx) 
£"x(Gx→¸Hx) 
\£"x( Fx→¸Hx) 
1 
£"x(Fx→£Gx) 
A 
2 
£"x(Gx→¸Hx) 
A 
3 
"x(Fx→£Gx) 
1,£E 
4 
Fx→£Gx 
3,UE 
5 
Fx→Gx 
4,Axiom T 
6 
"x(Gx→¸Hx) 
2,£E 
7 
Gx→¸Hx 
3,UE 
8 
Fx→¸Hx 
5,7 Barbara 
9 
"x(Fx→¸Hx) 
8,UI 
10 
£"x( Fx→¸Hx) 
9,£I 
Second figure
Suhrawardi’s single pattern for this figure is:
£"x(Fx→ModGx)
£"x(Hx→~ModGx)
\£"x(Fx→~¸Hx)
Here ‘Mod’ may be either ‘£’ in the both premises or ‘¸’. So we have only two modal syllogisms provided the subject of each premise is not modalized. Suhrawardi’s example is the following:
«کل انسان بالضرورة ممکن الکتابة» و «کل حجر بالضرورة فهو ممتنع الکتابة». فنعلم انّ الانسان بالضرورة ممتنع الحجریة. (1, p.23)
Necessarily every human being is a possible writer
Necessarily every stone is not a possible (is an impossible) writer
\Necessarily every human being is not a possible (is an impossible) stone.
Or,in modern symbolism:
£"x(Hx→¸Lx)
£"x(Sx→~¸Lx)
\£"x(Hx→~¸Sx)
Here in this syllogism we are faced with two problems.
1 Despite Suhrawardi’s insistence that the middle term should remain the same in the premises (1,p.21), in this syllogism, by turning both negation and modality into parts of the predicate, the middle term of one of the premises has become the negation of the other.
2 What is the justification for adding modality to the predicate of the conclusion?
As to the first problem, after mentioning the example quoted above he says:
وحینئذ لایشترط اتحاد المحمول ایضا فی جمیع الوجوه فی هذا السیاق خاصة، بل إنّما تعتبر الشرکة فیها وراء الجهة المجعولة جزء المحمول، ویجوز تغایر جهتی القضیتین فیه. (1, p.23)
So, in this specific mood, it is not a condition that the predicates [middle terms] be the same in every respect. They need only be the same in what comes after the mode that is made part of the predicate [middle term], it being permissible for the two modes of the two premises to be different in it (i.e. this syllogism)
So, in fact, he makes an exception to his rules for the predicates and consequently allows the change of the middle term in this mood.
As to(2) he maintains that since in this mood what is possible for the subject of one is impossible for the subject of the other "their two subjects are necessarily incompatible"(1,p.23).
Here Suhrawardi introduces two more rules. One rule is logical and concerns the changing of the middle term from one of the premises to the other. The other rule is a metaphysical one, allowing for the addition of the modality of necessity to the predicate of the conclusion.
In this figure too, the subject of the two premises can in theory also be modalized. Suhrawardi does not mention this possibility.
Suhrawardi’s second rule justified
Interestingly there is a derivation of Suhrawardi’s common pattern for the second figure with the same modal conclusion without using his rule in quantified modal logic S5 which shows Suhravardi’s sound intuition behind his second rule for that figure. This is the rule IbnSina also used for that figure before Suhravardi. Here is the derivation[1]:
£"x(Hx→¸Lx)
£"x(Sx→~¸Lx)
\£"x(Hx→~¸Sx)
1 
£"x(Fx→¸Lx) 

A 
2 
£"x(Sx→~¸Lx) 

A 
3 
"x£(Sx→~¸Lx) 

2,Ibn Sina Barcan (3) 
4 
£(Sx→~¸Lx) 

3,UE 
5 
¸Sx→¸~¸Lx 

4,ML 
6 
~¸~¸Lx→~¸Sx 

5, Contraposition 
7 
£¸Lx→~¸Sx 

6, 
8 
"x(Fx→¸Lx) 

1,£E 
9 
Fx→¸Lx 

8,UE 
10 
Fx→£¸Lx 

9,Axiom 5 
11 
Fx→~¸Sx 

7,10,PL 
12 
"x(Fx→~¸Sx) 

11,UI 
13 
£"x( Fx→~¸Sx) 

12,£ I 
This derivation provides us with an additional support for accepting quantified modal logic S5 as probably the best modal logic representing metaphysical necessity. (9,pp. 257273)
Third figure
Suhrawardi’s treatment of the third figure is even briefer than the first and the second and gives no modal example. But from what I said on his non modal cases (3, pp. 811) his single mood for this figure is:
£"x (Gx→ ModFx)
£"x (Gx→ ModHx)
\£$x (ModFx & ModHx)
Obviously in this mood according to whether ‘Mod’ in each of the premises represents possibility or necessity, we would have four modal moods. In these moods too we need the following additional necessary existential premise for each mood to get the modality de dicto for the conclusion:
£$xGx
So, all in all, we have the following four possible conclusions:
£$x (¸/£Fx&¸/£Hx)
Some of these conclusions, namely the ones that are in the modality of necessity, can be simplified by elimination of that modality. The only conclusion that cannot be simplified and that has no counterpart in IbnSina’s tradition is:
£$x(¸Fx&¸Hx)
This ends my exposition of Suhrawardi’s modal syllogisms. I think that the following additional points are worth mentioning:
1 Given the semantics of modality in terms of possible worlds Suhrawardi’s making modality a part of the predicate of modal propositions can have two readings with different truthconditions. For example‘¸Fa’, in particular where ‘a’ is a definite description, can be read as ‘¸(Fa)’ or ‘(¸F)(a)’. Now if we take ‘a’ as ‘The author of Hamlet’, then in the first reading and at the possible world w ‘The author of Hamlet’ refers to whoever at that possible world has this description whether Shakespeare or not. But in the second reading ‘F’ applies only to Shakespeare at w, if he exists in w at all. The question is how to read Suhrawardi’s de re modality. Now according to the second interpretation the proposition:
Every man is a possible writer
is to be symbolized as:
"x (Mx→((¸W)(x))
Here x refers to an actual man to whom writing as a possible natural capacity applies and Suhrawardi takes this application true , not only as a matter of fact, but also as a matter of necessity, so:
£"x(Mx→((¸W)(x)).
2 Suhrawardi’s rule for the second figure goes back to IbnSina. IbnSina maintains that in this figure the two subjects of each mood are essentially different, so it is not possible to predicate the major term to the minor.
Ibn Sina writes:
فالحق یوجب فیها ما لایجب أن نستحیی منه وهو أن النتیجة دائما سالبة ضروریة. (6. p.38)
And the truth about it [the conclusion] demands not to be ashamed of the truth that the conclusion is always necessary negation.
IbnSina by ‘not being ashamed’is referring to his disagreement with Aristotle’s view on this point in the Prior Analytics (7, 1011) where he discusses the modal syllogisms. Ibn Sina also takes up this subject in more detail in his so far unpublished book on logic: AlMukhtasar alAwsat (8, Manuscript, no.2763, p.54, Nour Uthmaniyah Library in Istanbul).
Conclusion
The theory of modal syllogisms in the Islamic logical tradition is a very complicated and controversial subject. But as we have seen, Suhrawardi gives a very simple version of the subject. He has done it by:
1 confining it to alethic modality;
2 turning modality and negation into parts of the predicate of modal propositions;
3 reducing all moods of each figure to a single universal affirmative pattern;
4 embedding all the premises of the syllogisms in the necessity modality;
5 introducing for each of his second and third figure syllogisms only one rule for deduction and so dispensing with the rule of conversion and the other rules that are traditionally used for reducing the latter figures to the first;
Suhrawardi’s de dicto necessity reading of all premises and de re necessity rule for the second figure discussed above makes his theory committed to essentialism.
I would like to thank Professor Joep Lameer and Professor Paul Thom and Dr. Assadollah Fallahi for comments on the final version of this paper.
Bibliography
1 Suhrawardi, The philosophy of Illumination, ed. and trans. J Walbridge and H. Ziai, Provo 1999.
2 Afdal alDin Khunaji, Kashf alAsrar ^{c}an Ghawamid alAfkar, ed. Khaled ElRouayheb, Iranian Institute of Philosophy, Tehran, 2010.
3 Zia Movahed ‘Suhrawardi on Syllogisms’, in: Sophia Perennis, Iranian Institute of Philosophy, Tehran, vol.2, no.4, 2010, pp. 518.
4 P.Thom. "Logic and Metaphysics’ in Avicenna’s Modal Syllogistic", in S. Rahman, T.Street, and H.Tahiri(eds), The Unity of Science in the Arabic Tradition: Metaphysics, Logic and Epistemology and their Interactions (Dordrecht: Springer 2008),pp.36176.
5 Zia Movahed, ‘IbnSina’s Anticipation of the Formulas of Buridan and Barcan’Lecture Notes in Logic 26, Association for Symbolic Logic, 2003.pp.24856.
6 IbnSina, Kitab alNajat, ed. M.S.Kurdi, second edition, Cairo, 1937, A.H., p.38.
7 Aristotle, Prior Analytics, trans. Hugh Tredennick, in The Loeb Classical Library,1973.
8 IbnSina, AlMokhtasar alAwsat (Manuscript, no.2763, p.54, Nour Uthmaniyah Library, Istanbul).
9 For defending quantified modal logic S5 as logic for metaphysical necessity see: Timothy Williamson.‛Bare Possibilia’ Erkenntnis, 48, 4, 1998, 257273.