 Hi, I'm Peter Adamson and you're listening to the History of Philosophy podcast, brought to you with the support of King's College London and the LMU in Munich. Online at www.historyofphilosophy.net. Today's episode… Proof Positive – The Logical Tradition In the Islamic world, many humorous stories are told featuring the Sufi folk hero Mullah Nasruddin. For example, Nasruddin turns up at a border crossing, and the customs officer searches him, his donkey and his empty basket, for contraband. He finds nothing and waves him through. The next week the same thing happens, and again the following week, and so on, but the customs officer can find nothing hidden on the donkey or in the basket. This goes on for years. The customs officer eventually retires. He runs into Nasruddin at the market and says, I'm retired now you can tell me. I know you must have been smuggling something all those years. What was it? Donkeys and baskets, replies Nasruddin. Or how about this one. Nasruddin is sitting by a river and sees a traveler arrive at the far shore. The traveler looks around and then calls out, how do I get across? What do you mean? asks Nasruddin. You're already across! And here's a third one, more germane to the topic of this week's episode. A king declares that he will tolerate no deviations from the truth, and that anyone who tells a lie in his city will be executed. Nasruddin goes to the city, presents himself at the gates, and is asked what his business is. I'm here to be executed, he explains. What should the guard do? If he executes Nasruddin, then he makes him a truth teller so he is innocent and should not have been killed. But if he lets him go, then Nasruddin is guilty of lying and should have been put to death. This is a picturesque version of one of the most famous logical puzzles, the liar paradox. It can be formulated in various ways, but the basic idea is that somebody makes a statement that will be true if it is false and false if it is true. For instance, this sentence is a lie. If that sentence is true, then it is a lie, so it is false. But if the sentence is false, it isn't a lie, so it is true. I referred to this paradox many episodes ago when talking about the Stoics. The great Stoic logician Chrysippus wrote about the liar, but his treatments of the problem are lost. It also received considerable attention in Latin medieval philosophy, and philosophers are still interested in the paradox today. Less well known is the fact that many thinkers of the Islamic world were fascinated by the liar paradox. The first discussions were not produced by philosophers engaged with the Greek tradition—no surprise there, since Aristotle never discusses it and Chrysippus's works did not make it into the Arabic-speaking world. Rather, it was the theologians of the kalam tradition who first dealt with it in about the 9th and 10th centuries. Interest in it becomes truly obsessive though in the period we're dealing with now, the 12th century onwards. Over the course of generations, considerable progress was made with the formulation of the paradox. The first attempts focused on something that is actually a distraction, namely the status of the person who is making the paradoxical utterance—is he lying or not? We thus find theologians imagining a scenario where someone has never spoken a lie in his life and then suddenly says, I have told a lie. This will only be true if this very sentence is a lie, but then of course it must be false. Alternatively, they imagine someone saying, everything I say is a lie. These early discussions tend to accept the simplest but least satisfying solution. You would think that every meaningful assertion must be either true or false. Philosophers often call this the principle of bivalence. One way to deal with the liar is to bite the bullet and make it an exception to this principle, that is to admit that it is neither true nor false. Like I say, simple but not very satisfying. A philosopher we've covered recently achieved some advances concerning both the formulation and the solution to the paradox. I have in mind Nasir ad-Din Atouzi. He had the insight that the liar paradox is really a problem about self-reference. In other words, it arises because we are making a statement that is about itself. Atouzi explained this very clearly by pointing out that a statement can be about anything at all, not just about things like giraffes and silent film stars, but also about other statements, as when I say, the statement giraffes are tall is true. And once we've allowed this, then we can hardly ban statements that are about themselves like the one in the liar paradox. Thus his formulation of the paradoxical utterance is simply, this statement is false. That zeroes in on the real problem, which is not whether the person making the statement is lying or not, but whether the statement itself is true or not. And of course, if it is true, then it is false, but if it is false, then it is true. Of course it's one thing to state the paradox clearly and quite another to solve it. Atouzi tried to pull off that second trick by considering what it means for a statement to be true in the first place. A true statement, he argued, is one that describes something else as being the way it really is. But this can't happen with a self-referential statement, because it is not about something else at all, it is about itself. Thus, issues of truth and falsehood don't even arise for it. Basically, this is just an advanced version of the bullet-biting solution of his predecessors with the improvement that he now gives a reason why the problematic statement is neither true nor false. Unless the statement is about something else, it just can't be true or false, for that matter. Unfortunately, this solution is not a particularly good one. Other statements that are about themselves certainly seem to be true or false. I would be speaking the truth if I were to say, this sentence I'm now uttering is in English. And I'd be saying something false if I said, this sentence I'm now uttering is in German. So, banning truth and falsehood in the case of self-referential statements looks not just arbitrary, but downright wrong. Further attempts at a solution will be made in centuries to come though, as we'll see in a future episode. Another puzzle is why these theologian-philosophers would be spending so much effort on something like the liar paradox. Or perhaps it isn't a puzzle. Starting in the 11th century, and for centuries thereafter, the Islamic world saw a golden age of logic. This was not the logic of the formative period, when Al-Farabi and the Baghdad school were still writing commentaries on Aristotle's logical treatises. Instead, just as we've been seeing in the areas of metaphysics and philosophical theology, Avicenna was now the indispensable man. Post-Avicenna and logicians worked within Avicenna's new system, even when they disagreed with him and made further adjustments to that system. Just what was new about Avicenna? I can't answer that question fully here, but I'll give you an example. Like Aristotle's logic, Avicenna's logic is still concerned with syllogisms made up of two premises and a conclusion, where both premises and the conclusion involve something being predicated of a subject. To take an example of which, like a beloved stuffed animal is by now well-worn but still does its job admirably, all giraffes are animals. Hiawatha is a giraffe, therefore Hiawatha is an animal. What's going on here is that animal is being predicated of all giraffes, while giraffe is being predicated of Hiawatha. The argument form is A is said of all B, B is said of C, therefore A is said of C. Avicenna is happy with all this, but observes that all such predications can be taken in two ways, either essentially or under a certain description. For instance, it is essentially true of humans that they can laugh, but if we stipulate that a certain human is asleep, then the human cannot laugh. In other words, laughing is impossible for humans under the description that they are asleep. Avicenna also explains more clearly than Aristotle what it means for something to be said essentially of a subject. Laughing is said of human is going to be true as long as at some time, some human or other laughs. It only has to happen once. Laughing is said of all humans will be true as long as every human laughs at least once. And this sounds about right. It would be unreasonable to insist that laughing is said of all humans only if everyone is laughing all the time. After all, you can only tell so many jokes about Mullah Nasruddin. Now, looking ahead to the post-Efsenan period, we find his successors operating with the same distinction between essential predications and predications that are only true under a description. But again, that didn't mean they agreed with everything he said. A nice example here is Najm ad-Din Akat B. al-Kazwini, a member of the group of pioneering scientists and philosophers gathered around D'Atouzi at the Mar'aga Observatory. We met al-Khatibi briefly three episodes ago when we looked at the debates over essence and existence. Writing in the middle of the 13th century, al-Khatibi applied another Avicenna distinction to these predications that are studied in logic. It's an idea we're seeing more and more often as we move into this later period – the distinction between mental and concrete existence. We might wonder whether Avicenna is right to say that animal is said of giraffe only if there is at some point a giraffe that is an animal. What if we lived in a world where there are no giraffes out there in concrete reality? In this horrible yet perfectly possible world, Avicenna could not accept the truth of the statement animal is said of giraffe because there would be no giraffes to do the job of being animals. Al-Khatibi agrees that it would be false as concerns concrete reality, but it would remain true as concerns mental existence – even if giraffe exists only in my mind, I could still understand giraffes to be animals. A related point had been made in the previous century by another thinker we've already met, Fakhradin Arazi. Fakhradin too was interested in whether truth is tied to the frequency with which things happen. In this case, the question was whether things that are eternal are thereby necessary. We know that Aristotle would say yes to this question. For instance, the heavenly spheres, being in his opinion eternal, exist necessarily. Exploiting ideas he finds in Avicenna, Fakhradin now moves decisively away from this Aristotelian position. For him, whether something is always the case has nothing to do with its being necessary. The heavenly spheres may indeed exist eternally, as Aristotle and Avicenna claimed, but they are certainly not necessary, since it is up to God whether they exist. In a way, this is just good Avicennism. Avicenna would agree that the spheres are in themselves only contingently existent. They must indeed exist, but only because God is causing them to exist. Their eternity is borrowed from God's, not the result of any intrinsic necessity. Yet, Fakhradin's firm insistence that eternity doesn't imply necessity is probably more motivated by theological considerations. He was not only a master of philosophical argument, but also an Asherite theologian, and the Asherites always stressed that all things are subject to God's will. And God's will might have been different, had he seen fit. By finally making a clean break between eternity and necessity, Fakhradin is able to say that eternal things are just as contingent on God's free choices as things that do start and stop existing. Even though logic in this later period was always done within the framework laid down by Avicenna, his works were not necessarily on the standard reading list. As often as not, students of logic would be reading a book by someone like Al-Khatibi, rather than by Avicenna himself. Al-Khatibi's logical textbook, Ar-Risālā al-Shamsīya, was studied in logic classes in the madrasas for many centuries. He was only one of several authors working around the time of At-Tūzī, in other words during and after the Mongol invasions, who produced such summaries of logic for the beginning reader. Another was Al-Khatibi's teacher Al-Abhārī, and in the same period we might also mention Sirajādīn al-ʿOrmāwī. All these men wrote advanced works on philosophical theology, not only logic textbooks for beginners. But, if I may indulge in a self-referential statement, here's a sentence that was true then and is still true today. If you want to impress your fellow philosophers, you should write ambitious theoretical treatises, but if you want to be read, you should write a textbook for the general reader. In a pinch, a podcast will do just as well. When I say that these textbooks have been influential, I mean it. This is a tradition that still lived on in Egypt, Persia, and India as late as the 20th century. And the textbooks of Al-Khatibi and his contemporaries were not only studied by students, they were also made the subject of commentaries, just like Avicenna's own works. It all confirms a parallel I've drawn in past episodes between the role of Aristotle in late antiquity and the role of Avicenna in later Islamic intellectual history. By writing a useful introduction to Aristotle's logic, a late ancient Platonist like Porphyry could be read by many generations of students, not only in Greek, but also through Latin and Arabic translation. And, he could become an object of commentary in all these languages. With their handy introductions to Avicenna's logic, the 13th century authors accomplished more or less the same thing. More than the late ancient commentators on Aristotle, the logicians in the Islamic world were ready to challenge and openly criticize their indispensable author Avicenna. This goes against an assumption that has been made even by experts in the history of Arabic logic. It has often been taken for granted that the later centuries were a time of unoriginality and stagnation. Scholars were led to this assumption by the fact that, in the wake of the 13th century textbooks, most writing on logic took the form of either commentaries or glosses, in other words, marginal notations on earlier works. Yet again, there's a parallel here to late antiquity. Nowadays, everyone admits that the late ancient commentators on Aristotle showed great originality in the interpretive texts they wrote in places like Alexandria. But only recently has it started to emerge that the same is true of logical works written in places like Maragha from the 13th century onwards. As logicians reacted to Avicenna and the textbooks he inspired, they took up new issues like the liar paradox, they questioned Avicenna's opinions, and they patched holes in the Avicennan logical system. Research on all this is in its infancy, but here are a couple of examples that have come to light. First let's consider the question of what logic is even about. What is its subject matter? Avicenna, true to form, had an excellent answer to this question. So excellent was his answer, in fact, that it came to be the standard view in the Latin Christian tradition too. His answer was that logic is about second intentions. A first intention is a concept in our minds like the concept of giraffe. This is a concept that is about something, namely giraffes out in concrete reality. A second intention is about one of these first-order concepts. For instance, I might see that giraffe is a species and that it belongs to the genus animal. Species and genus are, then, concepts about concepts, rather than being directly about things in the outside world. And logic deals with this meta-level of concepts. Clever though Avicenna's answer is, it was rejected by yet another logician of the 13th century whose name was Aftal-ad-din al-khunajji. Sorry, I know I'm throwing a lot of names at you, but hopefully it will at least convey the overall point that this was, if anything, a period of feverish philosophical activity, rather than one of decline. On this question of the subject matter of logic, al-khunajji insisted that logic is a proper philosophical science. But philosophical sciences do not study second-order concepts, they study the essential properties of things. For instance, giraffeology, if it is a science, and who would dare to deny this, deals with the essential properties of giraffes. Likewise, logic should deal with the essential properties that belong to our first-order concepts. This is the right way to think about such things as species and genera, they are essential features of notions like giraffe, not a second order of notions laid on top of our basic concepts. The later tradition also had the admirable goal of ensuring that logic was without gaps. And here they noticed a serious problem. The systems of Aristotle and Avicenna are fine and good if you want to focus on arguments that consist of nothing but predications, like animal is said of giraffe, but there are plenty of valid arguments that are not of this form. One example had already been pointed out by the Stoics, conditional inferences, like if it is day, then there is light. That sort of case was already noted by Al-Farabi and Avicenna, and continued to be discussed in the later period. Another exception was the so-called relational syllogism. The standard example here concerned the relation of equality. If I say that A is equal to B and B is equal to C, you'll have no trouble in seeing that A is equal to C. Or, we might consider the relation of being in something. If the mouse is in the box and the box is in the house, obviously the mouse is in the house. Even Dr. Seuss could tell you that. Like conditional if-then arguments, the relational syllogisms do not quite fit into the Aristotelian and Avicenna syllogistic. This problem, pointed out forcefully by Fakhradi Narazi, provoked solutions in commentaries and glosses at the time of the Mongols and thereafter into the Ottoman, Safavid, and Mughal periods. As I've already hinted, the reason logic was such a fixture of intellectual activity in these centuries is that it had been integrated into the educational system. The madrasas that were set up under the Seljuks survived the Mongol invasions. The beginner jurists and theologians at these institutions cut their teeth on logic, usually using the sort of textbook I mentioned before. If the students became particularly interested in logic, they could then use those teeth to bite the bullet of denying the principle of bivalence to solve the liar paradox. But of course, most students were content to do their exercises and move on to theology or the law. There is perhaps no simple answer to the question of why logic became so widespread an aspect of the education of religious scholars. Al-Ghazali can take some of the credit, or blame, since alongside his criticisms of Avicenna and the other philosophers, he poured scorn on anyone who dismissed the validity and utility of logic. Other theologians agreed, and went so far as to begin general works on the religious sciences with the treatment of logic. A good example is yet another author I haven't mentioned yet, Saif ad-Din al-Ahmadi. He died in 1233 as the Mongols were on the horizon, so to speak. He contributed to the discussion of various logical issues, including the liar paradox, and was among the first to integrate logic into writing on what was called usul ad-Din, or principles of religion. Thanks to thinkers like al-Ahmadi, logic became so pervasive that even vigorous critics of Avicenna would usually try to show their mastery of this science, sometimes making the odd innovation of their own in the process. In the 12th century, Suhrabadi, the founder of illuminationism, criticized Avicenna in the first, logical, section of his most important work, The Philosophy of Illumination. We already saw him arguing that the philosophical goal of providing definitions is misguided and in fact impossible. He also made technical proposals in the direction of simplifying Avicenna's system, consistently with his rhetoric that the so-called peripatetics are always overcomplicating things. He suggested, for example, that we don't need to consider both affirmative and negative propositions. Rather, any negative proposition can be rephrased as an affirmation with a negative predicate. For instance, instead of negating the proposition all men fly, we could just affirmatively say all men are non-flying. Not earth-shattering, perhaps, but it shows he is playing the Avicenna logical game. Yet, it would be an exaggeration to say that everyone was keen to take part in this game. Some thinkers did firmly reject the utility of logic as practiced by Avicenna and his heirs. One of them wrote that the philosophers' theories and I quote, These are the words of the most famous, or perhaps I should say notorious, intellectual of the Mongol period. The mere mention of his name still has the power to make some people like an irate camel, spitting mad. But his reputation for anti-intellectualism and fundamentalism underestimates the subtlety and argumentative skill shown by one of the greatest ever Muslim religious scholars. It's only logical that you should join me next time as I discuss Ibn Taymiyya, Hereon, the History of Philosophy, Without Any Gaps.