 Hi, I'm Peter Adamson and you're listening to the History of Philosophy podcast brought to you with the support of the philosophy department at King's College London and the LMU in Munich, online at www.historyoffilosophy.net. Today's episode, Trivial Pursuits – 14th Century Logic When I arrived at the University of Notre Dame as a graduate student, I was asked to take a course on formal logic. I'll admit that I had some mixed feelings about it. On the one hand, I appreciated that logic is foundational to philosophy. It was with good reason that the medievals made their trivium of logical and linguistic arts foundational to university study. You can't do philosophy without reasoning well, and how can you do that without knowing the rules of reasoning? On the other hand, I couldn't help feeling that if I had wanted to take courses involving proofs and blackboards full of symbols, I could have just studied math instead. I suspect some listeners may feel the same and are coming to this episode on logic in 14th century scholasticism not so much with a degree in mathematical logic as with a degree of trepidation. So let me offer the reassuring observation that in a way we've already been exploring medieval logic in considerable depth without even realizing it. When we examined the debate between Occam's nominalism and Burleigh's realism, discussed mental language, and asked whether acknowledging truths about the future leads to determinism, we were discussing problems raised in treatises on logic. Take the nominalism-realism debate. This was really a controversy about logical issues, namely the categories, universals, and supposition theory. We were trying to decide whether general terms in our language, and especially in the propositions that make up a valid syllogism, stand for, or supposit for, something real in the external world or merely universal concepts. But of course, supposition theory was not only devoted to this sort of question, which we today would consider as belonging to metaphysics rather than logic. What our medieval logicians really wanted was to determine the range of things a given term might stand for. Sometimes, of course, this is quite straightforward. In the sentence, Groucho smokes cigars, the term Groucho stands for Groucho Marx. But we need only go as far as the rest of this sentence to see that things can get trickier. What does the term cigars stand for? The particular cigars that he in fact smokes during his life, or perhaps cigars in general? To say nothing of sentence is like, every farmer who has a donkey beats it, a famous example found in Walter Burley and still discussed by philosophers of language today who call a whole class of propositions donkey sentences in honor of Burley's example. Again, the statement looks straightforward at first glance, but what does the word it refer to at the end of the sentence? Let's imagine a farmer who has two donkeys. It follows from our sentence, every farmer who has a donkey beats it, that this farmer must beat at least one of them. But it seems to be an open question what the word it refers to. Would the sentence be true if the farmer only beats one donkey and leaves the other alone? Or must both donkeys be subject to the As this example shows, the lurking threat here is ambiguity. To avoid such unclarities, the medievals distinguish different types of supposition, as we've mentioned numerous times already. A word like cigar might be said to supposit personally when it stands for a specific cigar and simply when it stands for the very notion of cigars. To understand how the word cigar is being used in a given context requires knowing which sort of supposition it has, and the point of this, in turn, is to avoid making fallacious inferences. For instance, you might argue, Groucho is a human. Human is a kind of animal, therefore Groucho is a kind of animal. This sophisticated argument trades on the ambiguity of human, which in the first premise has personal supposition, it stands for Groucho, and in the second premise, simple supposition, it stands for the universal, human, which is indeed a kind or species of animal. Sensitivity to ambiguity is also important in the interpretation of texts, including authoritative texts such as the writings of the Church Fathers or the Bible itself. This is one topic on which Burleigh and Ockham agree. They both contrast the use of words in their strict meaning with using figures of speech or other kinds of equivocation. So common did this technique become that in 1340, a statute was passed down in Paris forbidding instructors from condemning an authoritative text as false according to strict meaning without carefully explaining the alternative interpretation on which the text turns out to be true. Are there no limits to the significations that a given word can take on over and above its strict meaning? Consider that in the 1980s, the word bad was used to mean something pretty close to the usual meaning of good. When Michael Jackson sang, I'm bad, I'm bad, you know it, this was not an expression of low self-esteem. Yet there must be some constraints to the meanings of terms if communication is to be possible. John Burritton achieves this with his proposal that signification is determined not only by the intention of the speaker but by the conventions agreed between two or more speakers in a given context. If you intend to mean good when you say bad, that is fine so long as the person you're talking to is up to speed on 1980s slang. Such concerns had already animated terminus logic in the 13th century, and figures like Burleigh and Ockham look back to terminism more than to the modism of the speculative grammarians in the late 13th and early 14th centuries. There is, however, a shift insofar as 14th century logic becomes particularly concerned with the ambiguity at the level of entire propositions and not just individual terms. The mid-century logician William Hatesbury wrote a whole treatise exploring this topic. Some of his examples will remind us of our discussions about contingency and free will. Take a sentence like Elvis can be alive and dead. To decide whether this is true or false, we have to tease apart its two possible meanings. If it means that the sentences Elvis is alive and Elvis is dead can both be true at the same time, it is false. But, if it just means that at one and the same time either Elvis is alive could be true or Elvis is dead could be true, then this is perfectly unobjectionable, which is why all those Elvis sightings may be ridiculous but are not logically incoherent. Having noticed that propositions, just like individual terms, can be ambiguous, we might wonder whether entire propositions can have a signification, just like terms do. If the word Groucho in Groucho Smokes Cigars signifies Groucho, what does the whole sentence signify? We mentioned before that Walter Burley answered this question with his typical realist approach arguing that there is something real out there in the outside world, a state of affairs that the proposition represents. A similar view was taken by Occam's student Adam Wodham, who was troubled by Occam's idea that when we know something, what we are knowing is simply the true proposition that we affirm. Wodham thought that this cannot be right. When I know that Groucho smokes cigars, the target of my knowledge is not a proposition, but Groucho and a fact about him. This suggestion was taken up by Gregory of Rimini, a major theologian of the Augustinian order and another figure who worked in the middle of the century dying in 1358. Gregory was active in Paris and Italy but responded to the English philosophers who have dominated our recent episodes, weighing in on such debates as the problem of divine foreknowledge. He also had a distinctive view on this question of the proposition holding that there is a complex object of signification which is a real and even eternal thing. The idea here then is that Groucho smoking cigars is an abstract state of affairs that may or may not be realized at some point in the history of the world. When it does come about, because Groucho is alive and habitually smokes cigars, the proposition, Groucho smokes cigars, is true. It signifies that the state of affairs is currently actual. Needless to say, thinkers of a more nominalist bent, like John Buridan, were stridently opposed to this, but it's a proposal that has found adherence among some modern day philosophers. Another interesting point made by Gregory, which also has its roots in earlier debates, concerns the intellectual act by which we grasp a proposition. The question here is, how many things are we doing with our mind when we assent to a sentence? Durand of Saint-Porissant believed that the mind can only do one thing at a time. Just as nothing can be simultaneously hot and cold, so the human intellect cannot simultaneously have two acts, one that grasps heat and another that grasps coldness. So we must have a single holistic grasp of each sentence when we think about it. But this view was criticized by another scholastic named Thomas Wilton. He pointed out that when we draw the conclusion of an argument, we cannot be thinking only about the conclusion, but must also still bear in mind the premises of the argument. Otherwise, we would not be drawing the conclusion on the basis of those premises, but would just be making an unjustified assertion. So, the mind must simultaneously have different acts directed towards the premises and the conclusion. Gregory of Rimini comes down on Durand's side of the debate on the basis that the intellect is immaterial and hence simple. A piece of paper is a physical object, so when you write down a sentence on it, you can distribute the terms across different parts of the paper, but the intellect has no distinct parts and must therefore grasp each whole proposition all at once. With this debate, we're moving on from individual terms and propositions to the complexities of entire arguments. Starting in the early 14th century, logicians began to write treatises about the inferences we make when we produce such arguments. They called this branch of logic the study of consequences, because a conclusion of an argument is the consequence of or follows from its premises. We can capture this relation of consequence by saying with John Buridan that a valid argument is one in which it is impossible for the antecedent to be true while the consequent is false. In other words, the truth of the premise or premises guarantees the truth of the conclusion. The easiest case is where the basis of the inference is obvious and explicit. As with the classic and, thanks to the citizen jurors of Athens, empirically verified example, Socrates is a human, all humans are mortal, therefore Socrates is mortal. But you can bet that our medieval logicians have thought about more difficult cases too. For starters, inferences may be good, even if not everything is explicitly spelled out. Take the simpler argument, Socrates is human, therefore Socrates is mortal. By Buridan's definition, this is a valid inference because if it is true that Socrates is human, it cannot be false that he is mortal. It's just that the linking premise of the inference, that all humans are mortal, is not stated explicitly. Thomas Bradwardine, whom we met while looking at the predestination debate, went so far as to say that any proposition signifies everything that it implies because as soon as you accept that the proposition is true, all its consequences may be validly inferred. In some cases, you can validly draw conclusions that seem entirely irrelevant to the stated premises. Occam and others accept inferences like, some human is immortal, therefore Groucho doesn't smoke cigars, because it's impossible that some human is immortal and once you assume that something impossible is true, anything will follow. Conversely, this argument also works, Groucho smokes cigars, therefore humans are mortal, because humans are necessarily mortal and a necessary truth may validly be affirmed from any premises. Other logical writings explored the so-called insolubilia and sophismata, meaning, respectively, paradoxical arguments and arguments that look valid but in fact are not. Bradwardine's name comes up again here, because he offered an influential solution to the famous paradox of the liar in his work on insolubles. The paradox arises with sentences like, what I am saying right now is false. As a moment's reflection shows, this sentence would seem to be true, if it is false, and vice versa. Bradwardine's solution is worthy of Dunne's scotus in its subtlety. He carefully defines the notions of true and false so as to prevent the problem from arising. For him, a proposition is true if it signifies only as is the case. A false proposition, by contrast, signifies otherwise than is the case. The key here is the word only in his definition of true. A true sentence must signify only as is the case, whereas a false sentence is under no such constraint. Thus, the liar statement cannot be true on Bradwardine's definitions, for suppose that it were true, then the statement would signify that it is true, which would be the case, but also that it is not true, which would not be the case. Conversely, there is no such problem with its being false, since false statements are allowed to signify both otherwise than is the case and as is the case. All these logical methods and distinctions come together in a fascinating and somewhat mysterious activity that was pursued by the scholastics at their universities, a game called Obligations. Several of the authors we have discussed wrote about Obligations, including notably Walter Burley. So did a couple of authors not yet mentioned, Richard Kelvington and Roger Swineshead, both active in the 1330s. The game was already played in the 13th century, as we know from numerous treatises on the topic, including some by unnamed authors, yet another example where anonymous works are among the most important ones to survive today. A game of Obligations goes as follows. There are two players, called Opponent and Respondent. In the most common version of the game, the opponent proposes something, which the respondent is to assume is true until the round is over, unless it is something impossible, in which case he should deny it. Then, the opponent keeps offering more propositions, trying to get the respondent to make a mistake by contradicting himself, admitting something he should deny, or vice versa. So, to take a simple case, if the respondent is sitting down, the opponent might start by getting him to admit he is standing, then ask him whether or not he admits, either you are standing or the King of France is in the room. The respondent should admit this on his former assumption, even though he is sitting down and there is no royal presence. Though it would be an exaggeration to say that all of 14th century logic was just intended to help Scholastics win at this game, sometimes you do almost get that impression. The terminology of Obligations is pervasive in discussion of other questions, including theological debates. Being able to distinguish between different sorts of supposition and to disambiguate between the possible interpretations of a given sentence was crucial for the respondent, as was recognizing when the opponent might be leading him into a paradoxical or sophistical trap. But surely, being good at obligations was not an end in itself. Why were these scholars spending so much time on this logical game? Appropriately, this is a question much debated by modern day scholars. One idea is that it was just a way of exploring the topic of inferences. One anonymous author of the 13th century suggests as much. But, in the 14th century, there was that whole other genre of logical work devoted especially to inferences, the aforementioned works on consequences. So this seems an inadequate explanation. Another possibility is that the Scholastics wanted to explore what is nowadays called counterfactual reasoning. In other words, the opponent gets the respondent to assume something false in the first move, and thereafter the conversation simply discovers what would lead from this false assumption. This is another reason the respondent shouldn't agree to suppose anything impossible in the first move, since as we've already seen, you can infer anything you like from an impossible proposition. But a close look at the work on obligations by Kelvington shows him making the point that we would actually have to change the rules of the game if we want to think about counterfactual reasoning. He gives the following example. Let's say I am the opponent and you are the respondent. As my opening move, I get you to assume, falsely, that you are in Rome. You should agree, since this is not impossible. Next I ask you to agree to the proposition, either you are not in Rome or you are a bishop. In fact, this is true because in real life you are not in Rome, and by normal, obligational rules, you should admit anything that is true, if it doesn't contradict what you have already agreed to. Next I point out that these two premises prove that you are a bishop. So the whole argument would go like this. You are in Rome. Either you are not in Rome or you are a bishop. Therefore, you are a bishop. And this doesn't look like a good example of counterfactual reasoning. No one would think that it follows from my being in Rome that I am a bishop. Kelvington thus says that if we want to restrict ourselves to the counterfactual implications, the respondent should be allowed to refuse the second premise, even though it is true. Effectively, the respondent would pretend to inhabit a counterfactual situation where he is in Rome and should give all his answers supposing that he lives in that alternative world rather than in the real world. This is only to scratch the surface of the game of obligations and its philosophical implications. It's such an intriguing feature of later medieval logic that I have tracked down a respondent of my own for the sake of learning more. You're not obligated to join me for the next episode, but if you miss it there will be consequences, notably that you won't get to hear me speaking to Sarah Uckleman and even playing a few rounds of obligations with her here on The History of Philosophy Without Any Gaps.