So far, all the philosophical posts in this blog have had the same goal: to counteract philosophical ideas that are already in circulation. For example, the post on compatibilism was a counter to incompatibilists like Sam Harris:
You seem to be an agent acting of your own free will. The problem, however, is that this point of view cannot be reconciled with what we know about the human brain.
Harris is a neuroscientist, so I trust what he says about the human brain; but when he tells us what “cannot be reconciled” with what, then he is doing philosophy, just as much as we compatibilists are doing philosophy when we say the opposite.
Some people say they don’t want to get involved in philosophy, but it is surprisingly hard to avoid. You can stay away from the card-carrying philosophers, but then you might bump into Dostoyevsky’s novel The Brothers Karamazov:
‘But what will become of men then?’ I asked him, ‘without God and immortal life? All things are lawful then, they can do what they like?’
or the movie The Matrix:
You know, I know that this steak doesn’t exist. I know when I put it in my mouth, the Matrix is telling my brain that it is juicy and delicious. After nine years, do you know what I’ve realized? Ignorance is bliss.
or the physicist Lee Smolin:
… the Anthropic Principle (AP) cannot yield any falsifiable predictions, and therefore cannot be a part of science.
We’ve seen (here, here and here respectively) how philosophers have found fault with the opinions in bold type, and offered other (and I would say better) opinions in their place. We could describe that as remedial philosophy: philosophy as therapy. But is that all there is to the subject: correcting other people’s philosophical errors?
In this post I want to see whether philosophy can take the lead, on topics where we previously had no opinion. It’s one thing to justify philosophy as an alternative to worse philosophy, but I want to see if some part of it can be justified outright.
“Noooo,” a familiar voice bellows, “whatever you philosophers get up to in your studies and classrooms and libraries, it isn’t observation — and whatever isn’t observation must be guff!”
That would be the voice of crude empiricism. It blustered its way into one of my previous posts, and we saw then that it is unreasonable in its demands; not because it rules out philosophy, but because it rules out large amounts of hard science.
To draw the line between guff and science we must be empiricists, yes, but not crude ones. In that earlier post I considered several ways of drawing the line, and ended up with
the contribution criterion: a statement is guff if it makes no contribution to observational predictions. Or to spell that out: Ask what would happen if you dropped the statement. Would you lose the ability to predict some observation that you could have predicted when you had it? If so, then the statement is making a contribution. If not, then it’s guff.
While the motive for this criterion was to get hard sciences, such as physics, landing on the right side of the line, a pleasing side-effect was that logic and mathematics fell on the right side of the line also. Might some kinds of philosophy be just as fortunate? I’ll come to that question at the end, but first let’s look more closely at the mathematics case.
A mathematician proves a theorem, in some advanced branch of number theory, let us say. And let’s say he has no scientific application in mind. An application might turn up one day but we aren’t too hopeful. Nonetheless the theorem is justified, because it follows from some other mathematical statements that we already accept, via logical laws that we already accept. To put that another way: when we look at the proof, we can see that the price of not accepting the theorem would be doing without at least one of those other statements and logical laws. And we don’t want to pay that price, because all of those statements and logical laws have been proven from others; and we don’t want to do without those others because …; and eventually we get down to basic postulates: the bedrock of mathematics. And we are unwilling to do without those because … ?
Please don’t say that the basic postulates are intrinsically obvious. They really aren’t; they say things like this:
Given any set A, there is a set B such that, given any set x, x is a member of B if and only if x is a member of A and φ holds for x.
So no, obviousness is not the selling point here. Rather, the reason we won’t do without them is because the basic postulates produce all the theorems of mathematics, including the useful ones. To lose the postulates would be to lose a cornucopia of theorems, including theorems that we rely on in practical, empirical science.
If you follow that whole V-shaped rationale, from the new and apparently useless theorem, down to the postulates that implied it, and up to the useful theorems that the postulates imply, you can see how our brand of empiricism makes room for some arcane maths. We accept an unapplied theorem because the cost –the highly indirect cost– of not doing so would be a loss of observational predictions somewhere else.
Now I’d like you to notice something about this entire way of thinking: it depends on having logical laws that are spelled out explicitly. That is what allows us to track the long chains of “the price of doing without A is doing without B, and the price of doing without B is doing without C, and …”. If our theories had been held together with informal hunches and intuitions, there would have been no sense in asking whether the cost of dropping the mathematician’s “theorem” would or wouldn’t include a loss of observational predictions. Empiricism presupposes that logic is explicit.
The same point could be made by considering a new hypothesis in, say, particle physics. If it’s any good, it will add something to the set of observations that our theory as a whole predicts; but the path from the hypothesis to the predictions had better not go via hunches and intuitions, because they vary from one individual to another. In science, hypotheses are supposed to be testable equally by anyone.
“Empiricism presupposes that logic is explicit” is a maxim that I’ll lean on heavily, so I want to make sure that it isn’t misunderstood. So let me put on the record, first, that I still see a place for hunches and intuitions. I’m sure that all kinds of wonderful, strange things take place inside the mind of a scientist creating a hypothesis, or a mathematician creating a proof. Those processes can be as opaque and idiosyncratic as you like. Explicit logic only becomes a requirement when a finished product emerges, and we try to assess it. And second, even in the finished product, corners may be cut. Instead of spelling out every detail in a formal language, as logic strictly requires, it’s okay to use colloquial English (or colloquial Russian, Hindi etc.), so long as all parties are satisfied that what is said could be replaced by statements in the logical language, without any special difficulty or controversy.
As far as I know, all the branches of mathematics and all the hard sciences meet this standard. It’s not a trivial claim, but I’m confident that the necessary work has been done to support it. (And in any case it’s not the issue I want to take up today.)
Sadly, though, we do not live on mathematics and hard sciences alone. Sometimes we want to predict who will win a council election, or when the next bus will come, and then we don’t work it out from the laws of physics and set theory. Maybe a future supercomputer will do it that way, but for us humans, living in the present, the only option is to use common sense. That is to say, we must use a lot of what “everyone knows”, about medium-sized objects, the weather, people’s motivations, and so on, all expressed in colloquial language.
Common sense: can’t live without it — but can we live with it? That theory (if that is the right word) was designed (if that is the right word) over thousands of years, mostly by people who shared none of our scruples about logic and empiricism, so you shouldn’t be too surprised when I tell you that it is both wild and woolly. Here are just a few of its eccentricities:
- The word “if”. Think about the difference between “If Oswald didn’t shoot Kennedy, then someone else did” and “If Oswald hadn’t shot Kennedy, then someone else would have.” And then you’ve got “There are biscuits on the sideboard, if you want them.” By contrast, the sort of formal logic that does for maths and science has only one kind of “if”.
- Causation. Have you noticed that the citizenry of the United States has not yet reached consensus on whether it is guns or people that kill people? Is that due to a lack of empirical data? No; it’s because speakers of English don’t fully understand their own concept of causation.
- Possibility and necessity. Common sense isn’t satisfied with distinguishing what happened from what didn’t happen; it goes on to say that some of what happened had to happen, and some of what didn’t happen could have happened. These are distinctions you don’t find in, say, chemistry; at least not in the parts of chemistry that you use when you predict an observable outcome. Nor do you find them in maths.
- Fifty shades of existence. In conventional formal logic, existence is black or white. Its symbolic language lets you say the equivalent of “There are cows”, or the equivalent of “There aren’t any unicorns”, and you don’t get to say anything in between. So what are we to do with English sentences like “There is something we have in common”, “There is a good chance I’ll sell my house this week”, and “There are nine characters in the play, four of whom really exist”?
- Attributing thoughts to people. “Jane knows that Fido eats fish” is one sentence with two verbs, “knows” and “eats”, put together in a grammatical structure that you’ll never find in maths or the physical sciences.
There is nothing wrong with speaking colloquial language per se, but as empiricists we would like to know that we could, if challenged, replace what we say with statements in a logical language; i.e. a language for which the rules of logical inference have been spelled out. How can we get to that point?
One way to approach it is by analysing ordinary language. For each troublesome idiom of English (or Russian, etc.), we could look for schemes to translate statements that use the idiom into equivalent statements in the logical language. In some cases we might need to add features to the logical language (special symbols for possibility and necessity are a popular choice), and spell out new logical laws that apply to them.
A problem with this approach is that it’s hard to tell when it has succeeded. If the ordinary concept of causation, for example, is hopelessly unclear, then how can we decide whether a given analysis has captured it accurately?
Another problem is that it takes on needless work. Take “There are biscuits on the sideboard, if you want them.” We could go to great pains to analyse this special use of “if”, and translate the statement (and others like it) into formalized statements that faithfully reproduce the nuance of the original. Then, after all that work is done, we could remember that we’re empiricists, and that the reason we did it was to get a statement that would formally submit to the question “What does it add to our ability to predict observations?” So at long last we ask the question, and as the sun sets we find the answer: “There are biscuits on the sideboard, if you want them” contributes nothing that we couldn’t have had from “There are biscuits on the sideboard”. All the careful analytical work was like building a sandcastle only to have it knocked down.
I suspect that something like this has been going on, for almost a hundred years now, over possibility and necessity. Enormous effort has gone into analysing them, and incorporating them into formal logic in highly ingenious ways; but when it’s done, we’ll be left with the question of what they’re worth, empirically speaking. I fear that it will end in another sandcastle tragedy.
A more efficient approach, I would suggest, is to remember that we’re empiricists at the beginning. When we consider any troublesome part of ordinary language, start by asking what it contributes to observational predictions right now, using the informal methods of unreconstructed common sense. If the answer is “nothing”, then stop; it’s a part of common sense that we can live without. If, on the other hand, it does contribute informally to observational predictions, then study those predictions, and try to engineer something into the logical language that will bear the same fruit.