Maddy on logic

My blog postings on Maddy’s Second Philosophy came to an early halt, largely due to the pressure of other commitments. But our reading group is continuing to work through the book. I liked the partly historical, scene-setting, first part of the book a good deal. But I think we all found the second part of the book, on truth, unsatisfactory (not least because it was unclear what was distinctively second-philosophical about this part of the enterprise). We are now discussing her treatment of logic in the third part of the book.

She aims to give what she regards as a naturalized version of a Kantian account of the status of logic:

As a first approximation, then, the Second Philosopher hopes to develop an account of logical truth with two components: (1) logic is true of the world because of its underlying structural features, and (2) human beings believe logical truths because their most primitive cognitive mechanisms allow them to detect and represent the aforementioned features of the world. As soon as these two ideas are laid down, it’s natural to hope that they can be further reinforced by a connection between them: (3) human begins are so configured cognitively because they live in a world that is so structured physically.

But this way of putting things is surely going to ring alarm bells with well-brought-up logicians! Logic, we have learnt to say, is not about a special class of worldly truths, but is about what follows from what. Of course, regiment the rules about what follows from given assumptions in standard kinds of ways, and we’ll find ourselves saying that certain propositions follow from no assumptions at all: call those the logical truths. But note that this account of the logical truths emerges as, so to speak, a spin-off from something else, namely a prior account of logical inference. And it’s the account of logical inference which has to come first. So Maddy’s Second Philosopher is starting in the wrong place. Or so it will seem to many.

Maybe Maddy could retort that her way of putting things is recommends itself just for simplicity and to make connections with an earlier tradition. She could — couldn’t she? — have equally well started:

As a slightly better approximation, the Second Philosopher hopes to develop an account of logic with two components: (1′) logical inference is reliably truth-preserving because of features of the way the world is structured, and (2′) human beings accept certain inference rules because their most primitive cognitive mechanisms allow them to detect and represent the aforementioned features of the world.

But why is that supposed to be the obvious route for the hyper-naturalist Second Philosopher to take? After all there is a familiar enough alternative, much explored, which at a similarly broad-brush level runs:

However the worldly facts go, whatever structure the world has, our thoughts don’t always track those facts. We get things wrong. And thoughtful agents need a way of explicitly acknowledging they’ve got things wrong — we need a negation operator in our language.

Likewise, sometimes we can only narrow down the facts to some options. And thoughtful agents need a way of expressing the options without committing to any — so we need a disjunction operator as well. We need negation and disjunction, then, not because the world is full of negative and disjunctive facts which we have to track (whatever such facts might be), but because of our cognitive limitations. And so it goes, mutatis mutandis, for other logical operators too.

Now, what makes something a negation operator, a disjunction operator, etc.? Meaning is use! It’s what we do with the operator (in the jargon, the practice codified in the introduction and elimination rules) that fixes which operator is which, and shows it is apt for rejecting something as wrong, for narrowing down options, or whatever. Of course there are constraints — we can’t pair up introduction and elimination rules willy-nilly: that’s the lesson of tonk. But the constraints aren’t so to speak external, world-imposed, ones: in a naturalistically anodyne sense, they are a priori constraints of harmony imposed by sensible conservativeness requirements etc., needed to keep the enquiry game from falling apart.

The harmonious inferential rules, then, are meaning-fixing — we read off the content of complex sentences involving the operators from the rules in just such a way as to ensure that the rules are truth-preserving. So we don’t need to look at the way the world is structured to determine that they are truth-preserving. But there’s nothing naturalistically suspect about all this: we’ve indicated why limited cognitive agents have need of the likes of negation and disjunction working in the way they do.

Of course, I’m not saying that such an inferentialist story is utterly unproblematic. Far from it. But it is the obvious foil to Maddy’s sort of story. So good Second Philosophy methodology might suggest she should at least be taking the stories in parallel and devising some nice “crucial experiments” to decide between them.

But that isn’t how Maddy proceeds. In fact, she just doesn’t mention the well-trodden inferentialist path at all. Maybe she associates it with e.g. Dummett, who she would have marked down as a modern First Philosopher par excellence. But I don’t see that there is in fact anything especially first philosophical about inferentialism (in Tennant’s hands, his inferentialist treatment is bound up with what look to be rather Second Philosophical concerns — evolutionary considerations, thoughts about the inferential practices necessary for good science).

So I’m left rather puzzled about Maddy’s confidence that treating logical laws like particularly general laws of nature is evidently the way to go for the naturalist. It surely isn’t.

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