Kripke's standard meter

Back when there was a standard meter, Kripke claimed that it was contingent a priori that the standard meter is a meter in length.

This seems wrong. For anything narrowly logically entailed by something that’s a priori is also a priori. But that the standard meter is a meter in length entails that there is an extended object. And that there is an extended object is clearly a posteriori.

Kripke’s reasoning is that to know that the standard meter is a meter in length all you need to know is how “meter” is stipulated, namely as the actual length of the standard meterstick, and anything you can know From knowing how the terms are stipulated is known a priori.

There is something fishy here. We don’t know a priori that the stipulation was successful (it might have failed if, for instance, the “standard meter” never existed but with a conspiracy to pretend it exists). In fact, we don’t know a priori that any stipulations were ever made—that, too, is clearly a posteriori.

Maybe what we need here is some concept of “stipulational content”, and the idea is that something is a priori if you can derive it a priori from the stipulational content of the terms. But the stipulational content of a term needs to be defined in such a way that it’s neutral on whether the stipulation happened or succeeded. If so, then Kripke should have said that it’s a priori that if there is a standard meterstick, it is a meter long.

A posteriori necessities

The usual examples of a posteriori necessities are identities between kinds and objects under two descriptions, at least one of which involves a contingent mode of presentation, such as water (presented as “the stuff in this pond”, say) and H₂O.

Such a posteriori necessities are certainly interesting. But we should not assume that these exhaust the scope of all a posteriori necessities.

For instance, Thomas Aquinas was committed to the existence of God being an a posteriori necessity: he held that necessarily God existed, but that all a priori arguments for the existence of God failed, while some a posteriori ones, like the Five Ways, succeeded.

For another theistic example, let p be an unprovable mathematical truth. Then p is, presumably, not a priori knowable. But God could reveal the truth of p, in which case we would know it a posteriori, via observation of God’s revelation. And, plausibly, mathematical truths are necessary.

For a third example, we could imagine a world where there is an odd law of nature: if anyone asserts a false mathematical statement, they immediately acquire hideous warts. In that world, all mathematical truths, including the unprovable ones, would be knowable a posteriori.

An odd argument for an omniscient being

Here’s a funny logically valid argument:

1. The analytic/synthetic distinction between truths is the same as the a priori / a posteriori distinction.

2. The analytic/synthetic distinction between truths makes sense.

3. If 1 and 2, then every truth is knowable.

4. So, every truth is knowable. (1–3)

5. If every truth is knowable, then every truth is known.

6. So, every truth is known. (4–5)

7. If every truth is known, there is an omniscient being.

8. So, there is an omniscient being. (6–7)

I won’t argue for 1 and 2: those are big-picture substantive philosophical questions. I am sceptical of both claims.

The argument for 3 is this. If the analytic/synthetic distinction makes sense, then the two concepts are exclusive and exhaustive among truths: a truth is synthetic just in case it’s not analytic. So, every truth is analytic or synthetic. But if 1 is true and the analytic/synthetic distinction makes sense, then it follows that every truth is a priori or a posteriori. But these phrases are short for a priori knowable and a posteriori knowable. Thus, if 1 is true and the analytic/synthetic distinction makes sense, then every truth is knowable.

The argument for 5 is the famous knowability paradox: If p is an unknown truth, then that p is an unknown truth is a truth that cannot be known (for if someone know that p is an unknown truth, then they would thereby know that p is a truth, and then it wouldn’t be an unknown truth, and no one can’t know what isn’t so).

One argument for 7 is an Ockham’s Razor argument: it is more plausible to think there is one being that knows all things than that the knowledge is scattered among many. A sketch of a deductive argument for 5 that skirts over some important technical issues is this: if you know a conjunction, you know all the conjuncts; let p be the conjunction of all truths; if every truth is known, then p is known; and someone who knows p knows all.

Pain and water

One way for physicalists to handle the apparent differences between mental and physical properties is to liken the difference to that between water and H₂O. It is a surprising a posteriori fact that water is H₂O. Similarly, it is a surprising a posteriori fact that pain is physical state ϕ₁₃₅ (say).

Now, a posteriori facts are facts that are knowable by observation. But it is not clear that the proposition that pain is physical state ϕ₁₃₅ is knowable by observation.

Here is why. There are two main candidates for what kind of a state ϕ₁₃₅ could be: a brain state or a functional state. The choice between these two candidates depends on how strongly one feels about multiple realizability of mental states. If one is willing to say that only beings with brains like ours—say, complex vertebrates—feel pain, one might identify ϕ₁₃₅ with a brain state. If one has a strong intuition that beings with other computational systems anatomically different from those of complex vertebrates—cephalopods, aliens, and robots—could have consciousness, one will opt for identifying ϕ₁₃₅ as a functional state.

But in fact, assuming pain is a physical state, there is a broad spectrum of physical state candidates for identifying pain with, depending on how far we abstract from the actual physical realizers of our pains while keeping fixed the broad outlines of functionality (signaling damage and leading to aversive behavior). If we abstract very little, only brain states found in humans—and perhaps not all humans—will be pain. If we abstract a bit more, but still insist on anatomical correspondence, then brain states found in other complex vertebrates will be pain. If we drop the insistence on anatomical correspondence but do not depart too far, we may include amongst the subjects of pain other DNA-based organisms such as cephalopods. Further abstraction will let in living organisms with other chemical bases, and yet further abstraction will let in robots. And even when talking of the fairly pure functionalism applicable to robots, we will have serious questions about how far to abstract concepts such as “damage” and “aversive behavior”.

The question of where in this spectrum of more and more general physical states we find the state that is identical with pain does not appear to be a question to be settled by observation. By internal observation, we only see our own pain. By external observation, however, we cannot tell where in the spectrum of more and more general (perhaps along multiple dimensions) physical states pain is present, without begging the question (e.g., by assuming from the outset that certain behaviors show
the presence of pain, which basically forces our hand to a functionalism centered on those behavior).

Objection 1: An experimenter could replace the brain structures responsible for pain in her own brain by structures that are further from human ones, and observe whether she can still feel pain. Where the feeling of pain stops, there we have abstracted too far.

Response: There are serious problems with this experimental approach. First, mere replacement of brain pain centers will not allow one to test hypotheses on which what constitutes pain depends on the larger neural context. And replacement of the brain as a whole is unlikely to result in the experimenter surviving. Second, and perhaps more seriously, if replacements of the brain pain centers commit the same data to memory storage as brain pain centers do, after the experiment the agent will think that there was pain, even if there wasn’t any pain there, and if they have the same functional influence on vocal production as brain centers do, the agent will report pain, again even if there wasn’t any pain there.

Objection 2: We could know which physical state pain is identified with if God told us, and being told by God is a form of a posteriori knowledge.

Response: It seems likely that God’s knowledge of which physical states are pains, or of the fact that water is H₂O, would be a priori knowledge. God doesn’t have to do scientific research to know necessary truths.

Objection 3: We can weaken the analogy and say that just as the identity between water and H₂O is not a priori, so too the identity between pain and ϕ₁₃₅ is not a priori, without saying that both are a posteriori.

Response: This is probably the move I’d go for if I were a physicalist. But by weakening this analogy, one weakens the position that it defends. For it is now admitted that there is a disanalogy between water-H₂O and pain-ϕ₁₃₅. There is something rather different about the mental case.

Fundamental chaos

By fundamental chaos I mean a violation of the Principle of Sufficient Reason, a situation that occurs for no cause at all, something brute. What would we expect fundamental chaos to look like? Suppose that for no cause at all a world made of a variety of blocks came into existence. Intuitively, we'd expect it to look something like the first image.

But there is no reason why it wouldn't instead look like the second image. After all, by hypothesis, there is no reason for it to look one way than another.

One might think that because most world look messy, we would expect the brutish world to look messy. But there are two problems with this argument. The technical problem is that while in my two images, the worlds were created out of a finite variety of blocks within a finite universe, in reality there are infinitely many possible arrangements, and there are just as many neat-looking as messy-looking ones (after all, there are infinitely many worlds that look like the dragon world, differing in fine-scale details of what's inside the dragon).

But more seriously, even if there are more messy than neat worlds, it only follows that we should expect a messy world if the worlds are all equally probable. But when the worlds come about for no cause at all, in violation of the Principle of Sufficient Reason, there are no probabilities for the worlds, and so we cannot say that they are equally probable.

What this means is that the chaos hypothesis must be refuted a priori, not a posteriori. We need the Principle of Sufficient Reason.

The a priori and the a posteriori

I've been thinking about Chalmers' Constructing the World. It is absolutely crucial for Chalmers to have a distinction between what is a priori knowable and what is a posteriori knowable.

Now, imagine that we have evolved to believe that the number one has a successor (call this proposition "Two") as well as that many snakes are dangerous ("Snake"). In both cases, let us suppose, we evolved to believe the true claim because believing it conduced to our survival. (We may add that the reason belief in the claim conduced to our survival was explained by the truth of the claim, if we are worried about debunking arguments.) It now looks like Two and Snake are on par: either both beliefs are a priori or both beliefs are a posteriori. However, Chalmers cannot afford to say that Snake could be a priori—that will destroy much of his story.

So it seems that if Chalmers' story is to work, we will have to say that Snake and Two are a posteriori. However, it is also important for Chalmers to say that fundamental principles like Two are knowable a priori. The story doesn't destroy this: after all, something can be both a posteriori known and a priori knowable (say, a result of a calculation done with a calculator). Nonetheless, there is a problem here. It may well be that all fundamental principles like Two are known by us through something like this evolutionary mechanism (and "something like" includes the theistic variant where God instills this belief in us on account of its truth). And if so, then what reason do we have to think that they are a priori knowable, given that we don't know them a priori? One might have some conviction that some hypothetical or actual non-human reasoner knows them a priori, but it is difficult to see that conviction as justified.

However, I think there is a speculative non-naturalist story one could give that would help make the distinction. Suppose that all our knowledge is at base perceptual. However, sometimes what we perceive are abstracta and sometimes what we perceive are concreta. Knowledge that is grounded only in perception of abstracta is a priori, while knowledge that is grounded at least in part in perception of concreta is a posteriori. It may be that we can just see the number two as the successor of the number one. There is some phenomenological plausibility to this.

This would be really nice for Chalmers. For it is plausible that if any abstracta and their abstract relations are observable, they all are. If so, then all facts about the realm of abstracta are a priori knowable.

Granted, on this story knowledge of abstracta is observational and hence empirical. But while this does mean that the above use of "a priori" and "a posteriori" is idiosyncratic, the above use nonetheless may help recover at least some of Chalmers' story.

Some, but perhaps not the two-dimensionalism? For the account above is apt to make it a priori that wateriness is H₂O-ness, since that seems to just be a fact about abstracta.

The authority of science and the A-theory of time

The A-theory of time holds that there is an objective distinction between past, present and future (or past and future, or past and non-past, or non-future and future, or present and past, vel caetera). A standard argument against the A-theory of time is that scientific theories do not make this distinction, and hence the distinction is bogus. This is a bad argument (for a true conclusion!). Here are some reasons why.

First, as has been noted before, it is simply false that scientific theories do in fact fail to make this distinction. It seems like a perfectly fine scientific theory to say that birds "arose nearly 200 million years ago". But of course this claim presupposes a distinction between past, present and future, since otherwise the "ago" makes no sense.

Maybe this objection is uncharitable. Perhaps the correct claim is that no fundamental scientific theory presupposes a distinction between past, present and future. A worry I have about this version of the argument is the question of the criteria for fundamentality—there may be a circularity in that we reject the fundamentality of a theory that does make a distinction between past, present and future.

Perhaps, then, we should say:

1. The laws of nature, as we know them, make no reference to the objective distinction between past, present and future, but treat all times on par.

But it is now rather hard to fill in the details in the argument. Is there a suppressed premise like the following?

2. If the laws of nature make no reference to some distinction, then that distinction is probably not objective

But surely here is a counterexample to (2): the laws of nature make no reference to the distinction between right and wrong, but the distinction is nonetheless objective. This counterexample won't convince the hard-nosed irrealist about ethics, and perhaps one might modify the suppressed premise by saying:

3. If the laws of nature make no reference to some distinction, and the distinction concerns a topic amenable to scientific examination, then the distinction is likely not objective.

Here we need the additional premise that the nature of time is amenable to scientific examination. I think (3) is dubious, in part due to the vagueness of the concept of amenability. But I now want to pursue a different criticism of the argument against the A-theory.

If we can know a priori that science must come to a particular conclusion, then our argument for the conclusion is no longer a scientific one. For the peculiar epistemic authority of science is based on scientific methods' responsiveness to empirical data, and in such a case we have no responsiveness. Given an a priori argument that science must come to a particular conclusion, we might accept the conclusion, but if we do so, we do so on the basis of a meta-scientific argument, not a scientific one.

Now, I think we can know a priori that the laws of nature that science arrives at will not have an objective distinction between past, present and future. For the laws of nature that science formulates are timeless. Consider what a law that makes such a distinction would be like. It might, for instance, say that some property is had by an entity now but not in the future. But then the sentence will shortly no longer be true. And that is not the sort of sentence that formulates anything we recognize as a scientific law.

But if we know a priori that the laws of nature that science arrives at will not make a distinction between past, present and future, then we cannot use the lack of such a distinction as a scientific argument against the A-theory.

Of course there may be other and maybe even scientific arguments against the A-theory.