What the Indispensibility Argument Isn't

When I first heard of Quine's indispensibility argument (We are committed to the existence of abstact objects, since we must quantify over them in order to state our best physical theory), years ago, I misunderstood it.

I thought Quine was trying to draw an analogy between nominalists and, say, people who deny that there are planets, but will admit all the usual observations through telescopes. We find the planet denier's position implausible. We want to say "If there aren't planets, how come -as you admit- everything we see through telescopes behaves just as it would if there were planets? If there are planets, this explains the order and regularity of what we see through telescopes. But if there aren't planets, how come - out of all the mindbogglingly many possible patterns of optical illusions - we happen to have ones that are just like ones that could be produced by seeing persisting objects in space?"

But, even aside from being not what Quine meant (as I was soon told), this is really not a good argument, as I shall now argue for the benefit of anyone else who is tempted by it.

The explanatory inadequacy argument above, crucially turns on our having a notion of the observations we would have if there were planets vs. various other patterns of observation which would *not* be consistent with there being planets. The planet denier's position is unattractive, because on their theory it looks like a miracle that we happened to get a coherent pattern of optical illusions that could have been produced by normal vision of real objects.

But, in the mathematical case, there is no such contrast. There is no pattern in the behavior of physical objects which suggests the existence of numbers. For what would the contrast class to exhibiting this pattern be? It's not like we think: actually cannonballs accelerate towards the earth at 9.8 m/s^2, but if there weren't numbers, they would probably just fly around crazily. On the platonist's own view the objects (numbers and functions) in calculus don't come down and beat on cannonballs to make them behave in ways that are describable by short differential equations. Nor do they prevent cars from going two meters per second for two seconds, in a given direction, but only traveling 1 meter in total (cars don't need to be prevented from doing the metaphysically impossible). So it's not the case that he would expect different behavior if there weren't any numbers (the way we would expect different behavior of telescopes if there weren't any planets). Thus, there's no argument to be made against the nominalist, along the lines of "If there aren't numbers, how can you explain the fact that things happen to look just like they would if there were numbers?"

Instead, the point of the Indispensibility Argument (or the only plausible version of it) is that the Nominalist cannot even *state* his theory of the physical objects he accepts, and how they behave, without quantifying over abstract objects, and hence contradicting himself. To summarize: Quine isn't saying we need numbers to explain observed patterns in the behavior of physical objects. He's saying we need numbers to even state the relevant patterns in the behavior of physical objects.

Against Kim's argument against naturalized epistemology

In Epistemology Naturalized, Quine suggests that we stop worrying about epistemic normativity, and just study the engineering problem of how to get into situations where we reliably form true beliefs. So, for example, we might do scientific studies on the reliability of witnesses of various kinds of events, under various conditions. Or, we might use informal mathematical arguments to show that all reasoning of a certain formal kind are truth-preserving.

Jaeguon Kim objects to this, by making the following claim: the notion of justification and epistemic normativity is necessary to make sense of the very idea of beliefs. Someone believes that P iff an ideal interpreter would assign them the belief that P. And such an ideal interpreter assigns them beliefs, by interpreting their utterances in such a way as to jointly maximize a) the simplicity of the interpreter's theory and b) the degree to which (on the whole) the subject comes out to have beliefs that are justified. Thus, it doesn't make sense to study the reliability with which someone forms true beliefs, while rejecting the notion of epistemic normativity.

However, I don't buy that in order to understand the notion of belief we must accept some kind of analysis of it into other terms. You might think: we are just trained in the practice of interpretation, like we are trained to recognize certain things as games. We don't do this by consciously reasoning about justification, and Davidson's maxims or any other thing that one might use to try to define the notion of belief. Maybe there aren't any informative necessary and sufficient conditions for having a belief that P, or the only conditions are extremely complicated and will only be discovered after years of work by linguists.

If this is right, the argument `Unless the notion of justification is coherent, there will be no informative analysis of what it takes to count as having a given belief! Therefore, the notion of justification is coherent.' looks pretty unconvincing. Maybe the notion of belief is primitive.

Note, that saying there need not be necessary and suffcient conditions does not mean that there cannot be interesting cognitive science done, breaking down our capacity to recognize when a subject S counts as standing in the belief relation to a proposition P into various components.

Consider the following little fish. It has (among other things) four sensors a, b, c and d. Whenever a and b are touched it says "I feel xish", whenever c and d are touched it says "I feel y ish" and whenever a and c are touched it says "I feel z ish". There are no informative necessary and sufficient conditions to be given within the fishes' language (assuming this is all his vocabulary that relates to these four sensors). And yet there is nice simple relationship between these three claims at the level of sub-personal cognitive processing.

Thus, if the naturalized epsitemologist prefers to take "believes that" as a primitive (by not attempting to define it in any other terms) this doesn't suggest any kind of defeatism about the power of cognitive science to explain our complex linguistic capacities by appeal to simple systems.

But maybe, I didn't need to say any of the stuff in the last three paragraphs, because, (usually?), the proponents of epistemic normativity think its irreducible. So, I should think, it's no worse to take there to be primitive facts about the believing relation, than about epistemic normativity.