Numbers can be anything
Chapter 1: Introduction

Objections to Naturalized Epistemology

The second point that I need to make about my naturalized approach is that it does not allow me to say what actually is and what is not mathematics, which seems to lead to a major problem. For example, consider Sid who every Saturday afternoon spins around until he loses his footing, and calls this doing mathematics. When Sid is talking about doing mathematics he is talking about his Saturday spin, hence I would owe some account of this activity in my account of mathematics. My approach is to give a description of what people think is doing mathematics, so it lacks the normative element which would say that eccentric behaviour such as Sid's is not really doing mathematics.

Many philosophers would reject my approach because it is not normative: Peter Kosso, for one, claims in "Empirical epistemology and philosophy of science" that

The task of epistemology of science is two-fold: A valuable epistemology should provide an accurate description of the acquisition and justification of scientific knowledge. It should also provide a prescription for validation of scientific claims. This normative step could be described as the determination of appropriate level of justification of scientific claims. [Kosso,1991, p.350]

Three paragraphs on he rejects out of hand Quine's approach of abandoning the normative role of epistemology of science, saying that "this gives up exactly what is most worth doing in epistemology" [Kosso,1991, p.350].

Steven Stich objects to what he calls "Strong Naturalism" in his paper "Naturalizing epistemology: Quine, Simon and the prospects for pragmatism", using the example of Capgras syndrome sufferers. He writes

Consider, for example, those "physical human subjects" who suffer from Capgras syndrome. These people typically believe that some person close to them has been kidnapped and replaced by a duplicate who looks and behaves almost exactly the same as the original. Some people afflicted with Capgras come to believe that the replacement is not human at all; rather it is a robot with electrical and mechanical components inside. There have even been a few cases reported in which the Capgras sufferer attempted to prove that the "duplicate" was a robot by attacking it with an axe or a knife to expose the wires and transistors concealed beneath the "skin". Unfortunately, not even the sight of quite real wounds and severed limbs that result from these attacks suffice to persuade Capgras patients. [Stich,1993, p. 4]

Stich argues that a purely descriptive epistemology will be able to describe how the Capgras sufferers come to their beliefs, but traditional epistemologists do not want to know this. Rather, as he puts it, "they want to know how evidence relates to theory in subjects who do a good job of relating them. Among the many actual and possible ways in which evidence might relate to theories, which are the good ways and which are the bad ones?" [Stich,1993, p. 4]. According to this view an epistemology of the beliefs of Capgras suffers should not only tell how they come to the beliefs that they do, it should also tell us that this is a bad way of deriving knowledge. Summing up his objection Stich says

The Quinean naturalized epistemologist can explore in detail the various ways in which different people construct their "picture of the world" on the basis of the evidence available to them. But he has no way of ranking these quite different strategies for building world descriptions; he has no way of determining which are better and which are worse. And since the Quinean naturalized epistemology can provide no normative advice whatever, it is more than a little implausible to claim that his questions and projects can replace those of traditional epistemology. [Stich,1993, pp. 4-5]

Both Kosso and Stich reject the purely descriptive flavours of naturalized epistemology on the grounds that they cannot perform the basic function of ranking the possible methods of arriving at knowledge. My current work is an example of the offending naturalized epistemologies, so this is a criticism that I need to defend it from.

I will start my defence on the offensive, by questioning the ability of normative philosophy to rank the possible methods of arriving at knowledge. Consider a Capgras sufferer, Charlie, and a non-sufferer, Natalie, who agree that epistemology needs to be normative; they then work together on an epistemology. Are they really going to able to determine which of them has the better and which has the worse way of constructing their pictures of the world? Presumably, Charlie will accept the ways that lead him to believe that Whoever is a duplicate (otherwise he would be cured), while Natalie will reject them. This exercise in normative epistemology would leave us with two rankings of methods of arriving at knowledge, and no way of deciding between them.

This would not be a particularly surprising revelation for Stich; he says that his own version of naturalism, pragmatism, is relativistic. He writes

on the pragmatist view, the good cognitive strategies for a person to use are those that are likely to lead to the states of affairs that he or she finds intrinsically valuable. This is, of course, a thoroughly relativistic account of good reasoning. For if two people have significantly different intrinsic values, then it may well turn out that a strategy of reasoning that is good for one may be quite poor for the other. [Stich,1993, p. 9]

His pragmatic naturalism would seem to have been set up in such a way that the problem of multiple values being generated does not arise. He says

As I envision it, the pragmatist project for assessing reasoning strategies proceeds as follows. First, we must determine which goal or goals are of interest for the assessment at hand. We must decide what it is that we want our reasoning to achieve. This step, of course, is fundamentally normative. Empirical inquiry may be of help in making the decision, but science alone will not tell you what your goals are... The second step is to locate people who have done a good job at achieving the goal or goals selected. The third step - and typically it is here that most of the hard work comes in - is to discover the strategies of reasoning and inquiry that these successful subjects have used in achieving the specified goal. [Stich,1993, pp. 9-10]

A project of pragmatist epistemology of our knowledge of others might go something like this. First we decide that one of the things we want our reasoning to achieve is the recognition of those close to us. Next we find people who are good at recognising their close family and friends, which means most non-Capgras sufferers. Finally we investigate the mechanisms by which we achieve recognition of those close to us. Once this project is completed, we could go back to the Capgras sufferers and use our knowledge of how to recognise people well to find out where it is that they go wrong. However, this project will only work if the people referred to as "we" does not include Capgras sufferers. If it does then we will not be able to agree on who are the people who are good at recognising others; Capgras sufferers will think that they are good at recognising others, but non-sufferers will disagree. Charlie and Natalie would not be able to use Stich's project to decide between themselves which of them is better at recognising Whoever, because their joint project would not be able to get past step two.

This can be contrasted with a purely descriptive account, in which we (including Capgras sufferers) can go straight on to discovering strategies of inquiry without prejudging them. It would be possible for Charlie and Natalie to agree on a purely descriptive epistemology, in which it was stated as a mater of fact how they differed in their ways of arriving at knowledge of the identity of others. Each would still think that the other's method was wrong, but this would not be an issue within the epistemological account. Once the project had been completed they would have their joint description which make the details of their disagreements explicit, and so make it easier to find possible agreements. The descriptive epistemology would need to include an account of how Natalie comes to believe that Charlie is mistaken, and how Charlie comes to believe that Natalie is mistaken. In general it can say that non-Capgras sufferers have, according to their standards, good reasons for disregarding the strategies of reasoning that bring Capgras sufferers to come to their, so called, deluded beliefs about the identity of those close to them.

Going back to my example of Sid, it is true that I cannot say that what Sid is doing is not mathematics, but what I can say is that according to my own understanding of mathematics, and the understanding of everyone who I know, Sid is definitely not doing mathematics. If I were to meet Sid I could use a naturalistic account of mathematics to explain why most people think that he is not doing mathematics, but it would be up to him whether or not he let the information influence his practice; a normative account of mathematics could be used to tell Sid that he is wrong to think of his Saturday spin as doing mathematics, but he would still be at liberty to reject the conclusions of the normative account. If Sid accepts my understanding of mathematics then the information provided by a naturalistic account would be enough for him to decide that he is wrong; if he does not accept my understanding of mathematics then not only will a naturalistic account not give him reason to decide he is wrong, but he will have no reason to accept any normative claims I might make about him being wrong either. My naturalistic approach can still fulfil the normative requirements of telling me what are good ways of practising mathematics, given my understanding of what mathematics is; what it cannot do is provide me with any reassurance that there is anything special about my understanding of mathematics.

© Patrick Killeen 1995