The Greg Restall Interview: For as long as I could remember, I liked asking the question “why?”

Greg Restall is Professor of Philosophy at the University of Melbourne and a Fellow of the Australian Academy of the Humanities. He received his Ph.D. from the University of Queensland in 1994, and has held positions at the Australian National University and Macquarie University, before moving to Melbourne in 2002. His research focuses on formal logic, philosophy of logic, metaphysics, and philosophy of language, and even some philosophy of religion. He has published over 80 papers in journals and collections, and is the author of three books, An Introduction to Substructural Logics (Routledge, 2000), Logic (Routledge, 2006), and Logical Pluralism (Oxford University Press, 2006; with Jc Beall). In this interview with Divanshu Sethi of Catharsis Magazine, he discusses his thoughts on logic, what we can learn from paradoxes, a possible solution to the liar paradox, relation between generics and stereotypes, and the aim of philosophy.

Divanshu Sethi: How did you get interested in Philosophy?

Greg Restall: For as long as I could remember, I liked asking the question “why?” and I was curious about many things—including philosophy—as a child. My academic interests started, however, with mathematics. As an undergraduate at the University of Queensland in the 1980s, I specialised in mathematics, and it was through that interest that I got interested in logic, and that was a gateway into academic philosophy. At that time, I was also trying to figure out what I believed about many things, so I was doing a lot of reading around issues in religion and philosophy, so when I discovered that at my university there was an excellent philosophy department, I transferred over to do work with them, and eventually to do a PhD in logic. I’ve been very fortunate to be working in Philosophy for the decades since then.

D.S: Being an expert in Logic, can you draw some of its basic ideas and important questions?

G.R: Logic has really flowered as an intellectual discipline since the late 19th Century. When I introduce logic to students, I try to introduce the wide range of tools and techiques that we use for examining the structures and features of information and our different representations of information. One way—that I think is insightful—to see the discipline that are two main lenses through which we examine logical questions and analyse logical concepts. By way of proofs and by way of models.

One notion that it important in logic is the concept of logical equivalence. We often have different ways of conveying the same information (in some sense of that phrase). If I one sign says “no smoking or drinking allowed” and another says “no smoking allowed and no drinking allowed”, most of us would agree that these two signs are conveying the same information: they ban the same behaviour. One way of making this idea precise is to enumerate all the different options (whether smoking is allowed: yes or no; whether drinking is allowed: yes or no) and show that the options ruled out by one statement are exactly the same options ruled out by the other. Listing the different “options” or “possibilities” and checking how each statement stands with respect to them is using the notion of different models or representations of how things could be. One way to analyse the the notion of equivalence is to say that two statements are logically equivalent if they are true all the same models.

Another way to analyse logical equivalence is by way of proofs. You’ll notice that the statements feature very important “logical structure words” like “no” (or negation) “and” (conjunction) and “or” (disjunction). There are basic rules of how we can reason with those words (from a disjunction A or B we split in to two cases and consider each option, for example) and another way to show that two statements are logically equivalent is to show how we can reason from one statement to conclude the other (and vice versa), using just these basic rules.

A great advance in the early 20th Century was clearly distinguishing these two different modes of analysis and showing how they are often (for different families of concepts and kinds of expressions) different ways of drawing the same distinction. For many different kinds of models and different rules for basic concepts, we can analyse the many logical relationships from these two different perspectives. Now the focus is on developing different kinds of models and analysing different kinds of systems of proofs to analyse the logical power of different kinds of concepts.

D.S: Paradoxes in logic is an interesting topic as it deals with language, contradiction, truth etc. What are some of the interesting ideas you have found over your time studying and teaching them? And what can the existence of paradoxes teach us?

G.R: One way to understand paradoxes is to think of them as arguments that really seem to be good, from premises that really seem to be true to conclusions that really seem to be false. Since a valid argument is one that never leads you from true premises to false conclusions, it looks like a paradox commits us to contradict ourselves—a painful position to be in. I’ve done some work over the years about paradoxes involving the concepts of truth, of properties, of sets and concerning vague concepts (concepts which admit of degree and have no sharp borderlines, like “red” or “large”, and so on).

Working with paradoxes is a really interesting task as a philosopher: it is very creative, in the sense that our usual understanding of how our concepts work needs to be in some sense modified or clarified to resolve the problem. What makes things paradoxical is that any resolution will be novel in some way. You have to try to see things from a different angle, or pick out some phenomenon that we haven’t focussed on before, to show that what we have taken to be true isn’t really true, or isn’t the whole picture. One of the things that seemed right, has to be wrong. But because in a paradoxical argument, different pieces all hang together to give the tension, options for resolving that tension come from many different places.

One thing that the paradoxes teach us in philosophy is the subtle relationship between formal technical tools in logic and their application to our understanding. It’s one thing to use a technical trick or to develop a model to show how a particular problem could be avoided. (Building models is very easy once you get the hang of it.) What is much more difficult is the task of using those models to gain real insight. Does the model help us understand how our concepts actually do (or could) work? Is this the best way of understanding our language and our world? This is the dance between designing using formal tools and attempting to gain philosophical insight. Both are important and inform each other, in the best work in this area.

D.S: An interesting paradox for many years is the Liar Paradox —  an argument that arrives at a contradiction by reasoning about a Liar Sentence. Many logicians and philosophers have given their solution to the paradox, but there is little consensus. Some have called for acceptance of such contradictions and limitations. What is your take on the subject?

G.R: Oh, this is such a hard question! I have danced back and forth in many different ways on this question! The liar paradox arises out of a very simple sentence. A sentence that says of itself that it is not true. Here is one of them:

(1) The sentence labelled with (1) is not true.

It gives rise to a paradox because of what looks like our basic rules of the concept of truth: Let’s suppose first that the sentence labelled (1) is true. If it is, then what is says goes, and the sentence labelled (1) is not true. So it is not true. But then, it seems that what the sentence (1) says is true. Since either it is true or it isn’t, we have just argued that it is true, and that it isn’t. A contradiction.

When I was a PhD student first working with my supervisor Professor Graham Priest, I was convinced that his analysis is correct. The sentence is both true and untrue, and we have to accept this contradiction at the limits of our concepts of truth. Some concepts are self-contradictory and these contradictions are unavoidable.

Then when I developed my thesis, I saw that while that analysis could work for some concepts (like arguments using negation, and the liar paradox), the answer given for other contradictory sentences like this

(2) If this sentence is true then you have $1,000,000,000.

(from which exactly the same sort of reasoning leads you to conclude that you have a billion dollars) must be very different. Graham Priest’s answer to this is not to accept the surprising conclusion (we aren’t all billionaires!) but to understand the concepts of conditionality (the “if…then…”) in ways which block the reasoning. When I compared that to his analysis of the liar paradox, it seemed that these supplied two very different answers where only one was needed. A uniform solution to these problems would block the reasoning in the same way and so, I then concluded that the liar sentence was neither true nor false.

Since then I’ve changed my mind again and again, and I have no settled view on how the concept of truth actually works in every detail. But it is such an interesting field with many different applications and insights to be gained.

D.S: The generalisation of ideas and thought often exist in our language which could have implications on the truth. You gave a talk on a similar topic recently. What do you think are the consequences of using stereotypes as a tool in our language? And how can philosophy help in able to better think and understand about these generalisations?

G.R: I have been doing some work recently on generics and the way they often express stereotypes. In logic we often focus on precise concepts like “all” or “at least one”. We say things like “Not all birds fly”, or “at least one bird does not fly”. These statements are clearly true. But before we learn precise statements like these, we learn generic statements like “birds fly”, which don’t mean that all birds fly. They don’t even mean that most birds fly, but they say something about birds and flying, and what to expect or how to explain things. We use these generic judgements all the time in our thinking and our speaking, and I’ve been interested in the connections between generics and our stereotypes and our modes of explanation. These generics allow us to express things in a very fast and loose way, and they help us coordinate on our modes of explanation and our habits and expectations, but their unclarity can make disagreement hard to uncover. Consider the reaction when someone (justifiably!) says “men are dangerous” when hearing of another case of sexual violence, and the reaction “not all men!”, as if the generic judgement was expressing an exceptionless universal generalisation. The generic judgement is expressing something important, but we don’t have good habits or understanding to allow us to work with these fruitfully in cases where we have significant disagreement.

The tools of logic, and the habits of asking questions like “what would it take for this to be true?” or “what would it take for this to be false?” can help us gain some different perspectives on what we are actually saying—especially in cases where that is unclear, like in our use of these generic judgements.

D.S: What do you think is the aim of philosophy? And for our readers, could you recommend some papers or books to better understand the nature of your work?

G.R: I love Wilfrid Sellars’ way of putting this:

The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term.

The aim is understanding our world and our place in it, in the broadest possible senses of these terms. If I were to add one thing, it would be to say that this understanding aims not only at appreciating how things are, but help us clarify of how things could be and to inform our actions. I agree, with Marx, that the point is not to leave things as they are, but to take part in our world and to make it a better place.

As to what I could recommend, my book Logical Pluralism which I co-wrote with my colleague and friend JC Beall is a good place to start: it has a nice balance of philosophical reflection and formal logic. Beyond that, keep an eye on the writing section of my website — I link to all my papers and books there.

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