September 12, 2017

Some of my phrasing in the last two posts about what I love about philosophical logic have emphasised capacities, or abilities. I’ve described the pleasure of the “aha!” moment in terms of the kinds of mastery you acquire in handling the concepts you have, and I described the joys of conceptual expansion in terms of abilities gained. This is to take a pragmatic perspective on logic, to consider the connection to practices and actions.

Thinking of things “pragmatically” can be understood in a very crude way, fixing in advance what how you want to measure costs and benefits, and then doing some naïve cost/benefit calculation and then choosing option that somehow maximises benefits and minimises the costs (if that is even possible). This is not what I mean when I consider the connection between logic and pragmatics. I don’t think that the best way to select some logical system or logical theory is on the basis of that kind of cost/benefit analysis. Rather, it’s that there are connections between features of logical systems and the practices of asserting, denying, inferring, questioning, etc. What kind of connections are there? It’s not that the laws of logic are descriptively correct as a theory about how assertion and denial and inference actually work in practice. Rather, they can be understood as norms governing how those acts can be evaluated. (In particular, I think that if the argument from the premise \(A\) to the conclusion \(B\) is valid, then taking a position in which \(A\) is asserted and \(B\) is denied is out of bounds. If you’ve asserted \(A\) and \(B\) follows from \(A\) then in some sense, \(B\) is undeniable, in that any positions where you rule \(A\) in and \(B\) out are out of bounds. For more on this, take a look at my “Multiple Conclusions”, the critical literature it’s spawned, and the manuscript I’m working on right now.) There’s much more to say about this, but I think that it’s a clarifying perspective on the connection between core concepts in logic and the different kinds of acts we can actually engage in, like asserting, or believing, like denying or rejecting. It is a normative pragmatic position concerning logic, that the concepts provide norms or standards by which acts can be evaluated.

You might worry that thinking of logic in terms of rules for a contingent human practice makes those rules themselves contingent too. Now, there’s nothing wrong with laws and rules being contingent. However, it’s a radical view of logic that takes the rules of logic to be contingent on human practices. If it’s a law of logic that either \(p\) or not \(p\) for all propositions \(p\), then it would seem to follow that either all non-avian dinosaurs were extinct by 65 million years ago, or not all non-avian dinosaurs were extinct by 65 million years ago, and that this still would have been the case even if there weren’t any people (or sentient creatures) around to reason about it. Contingently existing human reasoners like us can reason about all sorts of things, including what went on before contingently existing human reasoners existed.

Here’s an analogy I find compelling and clarifying when it comes to understanding how we can have a contingent practice with non-contingent rules. It’s the example of arithmetic and our counting practices. It’s contingently useful to creatures like us to engage in counting practices, introducing vocabulary for things we call “numbers”, which codify various practices of enumerating and pairing things up. Given that we want to engage in such a contingent practice (we have reason to keep track of the number of sheep we have in our flock, to make sure trades are fair, etc., but there was a time before any humans were doing these things), we have (again, contingent) reasons to use counting practices like those we actually have. At the very least, our counting practices give us ways to attend to patterns among practices of pairing things up. (It’s easy enough to figure out that if you have five sheep and I promised to give you three bags of grain for each of your sheep that I’ll owe you 15 bags of grain, than to laboriously pair up three bags with each sheep.) But the (contingently existing) practice of using number vocabulary in this way gets its power by having results that apply invariantly and necessarily. It’s not necessary that we have the concepts of 3 and 5 and multiplication, but it is necessary that if we do have concepts like these, governed in this way, then no matter what they’re counting, 3 times 5 is 15, and it is, necessarily. (Why do we want such necessity? I’d say that this is tied up with interaction between counting and planning: it is also true if I’ve promised three bags of grain for every sheep, then if I want 2 sheep, I owe you 6 bags; 3 sheep, then 9, etc. It’s not that the rules of counting apply differently in different hypothetical scenarios. They are applied the same way in all hypothetical scenarios.) A practice can be contingently useful while having norms that apply non-contingently.

The same holds, I think, for so-called logical laws, and the account I prefer puts this down to norms governing assertion and denial. The laws of logic can be understood as arising out of fundamental norms governing the practices of assertion and denial, and their interrelationship. The generality of certain laws of logic can be explained in terms of norms applying to assertion and denial as such, independently of any specific subject matter of those assertions and denials. The behaviour of the regular propositional connectives can be explained as ways to make explicit what is already implicit in the practice of assertion and denial. The behaviour of modal operators can be understood in terms of making explicit norms governing different kinds of supposition, while those for quantifiers make explicit relations of substitution and generality, once the practice of assertion and denial is rich enough to involve singular terms. The story, I think, is rich in connections.

I love how philosophical logic is—when rightly understood—tied up with practices and activities. Through these connections, we see that understanding the grounds of our conceptual capacities brings logicians into the realm of practical action, in a way rather different to the picture that logicians are calculators solving predefined problems. Instead, logic is a normative discipline which describes some of the norms governing practices of assertion, denial, description, theorising, conjecture, and the like.

You don’t often find human concerns, our own contingent and local interests, preferences and desires — let alone the social and political concerns of life in a community — playing an explicit role inside a philosophical logician’s proof. These would be as alien there as they would inside a mathematical demonstration. However, this does not mean that these considerations are divorced from philosophical logic. After all, our interest in matters of logic have grown up with our interest in the communicative practices of asserting, denying, arguing and reasoning, and those are nothing if not social practices. Our own contingent and local circumstances and interests help explain why concepts like those from logic are worth using. It is a loss to the discipline if we don’t heed that connection.

The connection with pragmatics is the seventh of twelve things that I love about philosophical logic.

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I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews.



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