## Knowledge, Decisions and Games

I was a little puzzled by Stephen Hetherington’s comments about my paper Knowledge, Belief and Interests in his review of Knowledge Ascriptions. Here’s the main thing he says about the paper.

Weatherson’s argument is centred upon the thesis that “knowledge plays an important role in decision theory” (p. 77). His central conditions are that “ (a) it is legitimate to write something onto a decision table iff the decision maker knows it to be true, and (b) it is legitimate to leave a possible state of affairs off a decision table iff the decision maker knows it not to obtain” (p. 77). (But does this entail that, when one does not know that p and one also does not know that not-p, one cannot legitimately write p onto a decision table yet one also cannot legitimately leave p off one’s decision table?)

Maybe that wasn’t the clearest way of putting the point I was trying to get at, but I hoped it would have come through clearly in the paper. Here’s another go.

In a decision table, there are rows for the decisions the agent can make, and columns for the possible states of the world, and values in the cells for what will happen if the relevant world-choice pair obtains. Now there are a lot of questions about how to interpret what is, and what is not, on these tables.

One set of questions I don’t take a stand on in this paper concerns what should be on the rows. There are two big questions here. When should we leave a row off, and when should we `collapse’ a class of possible agent actions into a single row? Brian Hedden had an interesting paper at Bellingham on some of these issues a couple of years back, and Heather Logue and Matthew Noah Smith had excellent comments on it, and I came away thinking that these were much harder questions than I’d realised. But they aren’t the questions KBI addresses.

I’m more interested in the columns, and to some extent the cells. Here are the (closely related!) questions I’m interested in.

First, when do we need to include a column in which p is true? Answer, I say, when the agent making the decision doesn’t know that p is not true.

Second, when is it legitimate to have a column for the possibilities in which p obtains? The answer here is less clear than to the previous question. Roughly, it’s when there’s no q such that the agent doesn’t know whether q obtains, and the relative success of different actions the agent might undertake is different depending on whether p and q are both true, or whether p is true and q is false.

Finally, there are some questions about what goes into the cells. These aren’t directly the focus of KBI either, but I have some views on them. I’m tempted by the view that one can write v into a cell as its value iff the agent knows that the relative, relevant payout of that cell is v. Why relative? Because all utilities are relative to some choice of baseline. Why relevant? Because how well one’s life goes after choosing an action is obviously unknowable in many important ways. Still, one can know how well things will go in a localised region around the decision, and if we’ve set the table up correctly, other outcomes will be independent enough of what we’ve done.

(Why can’t we just put expected values in the cells? Given an expected utility maximising decision theory, all that matters is that we put the right expected values in. The problem is that thinking about decision tables that way begs the question against those heterodox decision theorists, like say Lara Buchak, who reject expected utility maximisation. I’m a (reluctant) advocate of orthodox decision theory, but I don’t think we should conceptualise decision tables in a way that begs the question against our heterodox friends.)

So knowledge matters for decision theory. It also matters for game theory, though the relationship there might be a little less clear. (When we’re thinking about states of the world that are individuated by other actions another player might make, should we use our criteria for row addition/division, or our criteria for column addition/division? I think this question is close to the heart of the debate about the relationship between game theory and decision theory.)

As I said, I had hoped this was clear in the original paper. But maybe it wasn’t, so I’ve tried a different way of stating it here.

There’s another thing though which Hetherington says which I found more perplexing.

Brown’s “Words, Concepts, and Epistemology” confronts a concern many of us have felt. Is there a danger of some recent epistemology’s not really being epistemological? For instance, might even a book called Knowledge Ascriptions not really be so much about knowledge? The worry is whether we can understand epistemology as not being first and foremost about linguistic phenomena and “thought-experiment judgements” (p. 31), even as we encourage reflection upon thought and language — such as knowledge ascriptions — in order to understand whatever epistemology is about first and foremost. Brown’s carefully argued answer is optimistic. And the next three chapters, in effect, seize upon that licence. They defend impurist conceptions of knowledge: pragmatic encroachment (Jeremy Fantl and Matthew McGrath, in “Arguing for Shifty Epistemology”), interest-relative invariantism (often called IRI — Brian Weatherson in “Knowledge, Bets, and Interests”), and contextualism (Michael Blome-Tillmann in “Presuppositional Epistemic Contextualism and the Problem of Known Presuppositions”).

I don’t really know what the general category is supposed to be which sweeps up all the views described at the end of the paragraph. Contextualism is a theory, at least in the first instance, about ‘‘knows’‘. It isn’t really a theory about knowledge, and more than a theory of the context-sensitivity of ‘‘heavy’‘ is a theory of mass. But that’s not true of interest-relative invariantism. It is a theory of knowledge. It says that whether a person knows p depends, in part, on whether she is sufficiently confident to take p as given, give her interests. This implies something about ‘‘knows’‘, given the close relationship between ‘‘knows’‘ and knowledge, but it isn’t in the first instance a theory of ‘‘knows’‘, and more than Einstein’s theory of relativity is a theory of ‘‘heavy’‘.

I’m even more confused by the idea that linguistic phenomena and thought experiment judgments are in any way a natural kind when it comes to epistemological evidence. People who approach epistemology by looking at things like Stanley’s binding argument are not, I would say, taking the same approach people who start with Gettier cases or fake barn cases. And I’m not sure what is to be gained by lumping these methodologies together.

## Journal News

First, there’s a new issue of Thought out. Here are the articles:

• Infinite Lotteries, Perfectly Thin Darts and Infinitesimals (pages 81–89) by Alexander R. Pruss
• A Puzzle about Identity (pages 90–99) by Alexis Burgess
• Kripke’s Frege (pages 100–107) by Palle Yourgrau
• Not Just a Coincidence. Conditional Counter-examples to Locke’s Thesis (pages 108–115) by Giuseppe Spolaore
• Propositions and Multiple Indexing (pages 116–124) by Brian Rabern
• Burge on Representation and Biological Function (pages 125–133) by Agustín Vicente
• The Accidental Properties of Numbers and Properties (pages 134–140) by Harold Noonan and Mark Jago
• Strong Connexivity (pages 141–145) by Andreas Kapsner
• An Embarrassment for Double-Halfers (pages 146–151) by Michael G. Titelbaum
• Meaning, Expression, and Evidence (pages 152–157) by Ray Buchanan

And a call for papers: Philosophia Mathematica seeks to publish half a dozen survey articles on current and emerging areas of interest in philosophy of mathematics written by early-career philosophers. Please submit a 500-word sketch of the area that you propose to survey, along with a CV containing details of your publications, to the editor, Robert Thomas, by one of two deadlines, March 31 and September 30, 2013.

At March 31, submissions will be considered and some topics assigned.

Until Sept. 30, submissions will be considered as they arrive and may be assigned subject to not duplicating a previous assignment.

Inquiries are welcome. Publication will occur individually as articles are ready. Submissions of articles and shorter discussion notes on the subjects of special issues and any other topic in philosophy of mathematics are always welcome.