On Philosophy

November 30, 2007

Two Kinds Of Claims

Filed under: Epistemology — Peter @ 12:00 am

Yesterday I briefly introduced a distinction between two kinds of claims. On one hand, I said, we have claims about the structure of a model of the world, and on the other we have claims about the world arising from the model. For example, the claim that there are forces is a claim about the Newtonian model, but the claim that things fall at 9.8 m/s2 is a claim about the world that might be deduced from the model. Previously I was specifically interested in identity, and asserted that identity claims are about the model and not the world. This solves a number of problems associated with them, because, taken about the world, identity claims seem trivial and uninformative. But, at the level of the model, claims about identity can be genuinely interesting because they affect which objects our model contains. That is simply one application of the distinction, but it illustrates that what we take a claim to be about, in this sense, may affect how we handle it, one of those differences being, as I will elaborate on, epistemological, with claims on one side of this divide being handled differently than those on the other.

Let’s begin with claims that are essentially about the world, but which follow from our model, meaning that, according to the model, the claim can be the case if and only if some particular fact holds in the model. For example, going back to Newton, something can only be under acceleration if there are forces acting on it, and for any particular acceleration and object there can only be a single vector sum for the forces acting on it. Thus we might justifiably treat the truth of such claims as being essentially tied up with deduction. Either we can deduce them from our model and the state that we think it is in, or we can deduce facts about what state the model must be in from them. (Given that we are working with some particular model.) Another feature of such claims is that they are verifiable, at least in principle. If we believe something to be accelerating then we can check that hypothesis with careful measurement. In fact this is the easiest way to distinguish what counts as claims about the world and about the model: if we can check them with uncertainty arising only from the nature of our measurements then they are claims about the world, but if they are always, even in principle, some distance from being able to be completely confirmed then they are claims about the model.

(Complicated digression: it follows from this that what may be claims about a model may change into claims about the world depending on our instruments, at least in some sense. I think this is essentially correct; consider, for instance, a model of the world that is atomic. And eventually instruments will be developed that allow people to look at these hypothetical atoms directly. Obviously when they make the observations they will take what they see to be the hypothetical atoms. But what has really happened is that they have discovered a new domain of phenomena and extended the old atomic model in a one to one correspondence to account for it. However, what is called “atoms” has changed from a part of the model to a part of the world simply because what is now called atoms are the things observed with the instruments, not primarily the hypothetical entities of the theory, and if they act in ways that disagree with the entities previously called atoms we will revise the atomic theory in response. Which proves that they are no longer part of a model, because when your model doesn’t correspond to reality you conclude that the entities defined by your model don’t exist, given that they were defined completely by the model, and you introduce new entities, possibly similar to the old ones, with different definitions. But when you have turned claims about atoms into claims about the world it is no longer possible to conclude that the atoms of the theory don’t exist, you can only revise the theory to make them act differently.)

In contrast, claims about the model are never deductive. We don’t deduce which model is correct, rather we infer it by determining which model best matches up to reality. And, obviously, we can never be completely sure that we have found a model that perfectly matches reality because there are always more particular facts about the world to examine which it may very well be inconsistent with. And, as mentioned above, claims about the model are also never directly verifiable; we can never find the entities that exist in our model themselves, we can only find the phenomena that we think correlate with them. None of this makes models, so described, undesirable. Obviously we would prefer perfect certainty, but when dealing with the world perfect certainty is impossible, and working with models in this way is simply the best we can do. Of course certain examples may seem to imply that deduction does play a role in models. For example, from an atomic theory of liquids and Newtonian mechanics we can “deduce” laws about water pressure. Thus we may think that a new model about water pressure has been arrived at by deduction from our previous ones. But this is not what has happened at all, all that we have done is simply apply the models we had already developed, the facts about water pressure were already contained within them in a latent form, just waiting to come out. Of course by extending the model we may arrive at more claims about the world, and thus more ways of testing it, but that doesn’t mean that there is anything new in the model. Furthermore it should also be clear that there is necessarily some core part of the model that cannot be arrived at by deduction and extension in this way, which must be confirmed by tests, and thus which must always be necessarily less than completely certain.

Another difference between claims about the world and the models we use to understand it is in the level of ambiguity that can exist. When it comes to claims about the world ambiguity is, in principle, impossible. Assuming we have made a well-formed claim we could go out and either confirm it or disprove it. Thus, again in principle, it is never an open question whether some claim about the world is true or not. In contrast it is quite possible for there to be systematic ambiguity when it comes to our models of the world. There might be two different models of the world that give rise to the same claims about the world (in fact there will necessarily always be such alternate models). And we cannot, even in principle, decide which of these two models is “right”, because there really is no fact of the matter at all about one of them being right, as they are both equally good models of the world. Still, in such situations we are generally going to prefer one of the models to the other, for reasons that have nothing to do with one of them being right and the other wrong. First we will always prefer the stronger model, the one that makes more claims about the world, both because stronger models are more useful, and because, by making more predictions, they are easier to confirm or refute, and thus we can be more certain of them. If two models are equally strong then we will tend to prefer the simpler and easier to conceptualize one, for the practical reason that they are easier to work with, and such practical reasons factor heavily into why we develop such models in the first place.

Thinking about things in this way has a number of implications, one of which is that we should never attempt to devise models though deduction from other principles, nor should we defend them in that way. A simple glance at science will show you that the best models there are usually justified by their results, and not by any simpler principles that they follow them. Indeed many successful models contain idea that may seem intuitively absurd, although that doesn’t stop them from being good models. And thus if we were committed to deducing our models from simpler principles we might be moved to reject them, illegitimately, because of the absurdity of the principles that would be required to arrive at them. The problem, as I see it, is that in philosophy part of our task seems to be to come up with such models and use them to explain various parts of the world. Indeed in this very post I am working with a particular model of theories and knowledge. Thus we shouldn’t be looking to prove our philosophical theories, as so many try to do, rather we should be constantly checking them against reality to see if they line up with it. A second consequence of this way of thinking about claims is that it illustrates that not all questions we might direct at the model need answering. Remember the model is not itself justified, and thus that we need never answer questions about why the model is the way it is, why a single object models two phenomena that may have seem distinct, or why a particular law holds. Rather the model has to submit to inquiries about its testability and whether it actually leads to claims about the world. It is only in the context of claims about the world that we can legitimately ask why they are the case, why an object is particular shade of red, or why two phenomena are correlated. And if our model purports to explain those things it must answer such questions or be revealed as falling short.

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