Show-Me the Argument

Review of John Hawthorne’s Knowledge and Lotteries (Oxford University Press, 2004)

by Kevin McCain

In this fascinating book, John Hawthorne describes lottery puzzles and sketches some of the more promising solutions to these puzzles. Although lottery puzzles are not a recent discovery, they have primarily been viewed as an interesting aside in epistemology instead of a major issue. Hawthorne convincingly argues that lottery puzzles have far-ranging implications for epistemology and that they may in fact motivate one of the more threatening versions of skepticism. Knowledge and Lotteries is divided into four chapters in which Hawthorne describes the basic form of lottery puzzles and examines the costs and benefits of four potential solutions.

In chapter one “Introducing the Puzzle” Hawthorne illustrates the basic structure of lottery puzzles and considers a possible solution to lottery puzzles based on the epistemic theories of Fred Dretske and Robert Nozick. Lottery puzzles have the following structure where ‘O’ is an ordinary proposition such as ‘I will not be able to go on Safari this year’ and ‘~L’ is a lottery proposition such as ‘I will not win the lottery’:

S knows O

S knows (O → ~L)

S knows ~L

Since S knows that she will not be able to afford to go on Safari and she knows that her not being able to afford to go on Safari entails that she will not win the lottery, she knows or is in a position to know that she will not win the lottery. This is a puzzle because intuitively we do not think that S is in a position to know that she will not win the lottery(in these lottery cases it is assumed that S has a ticket, the lottery is a fair drawing, and that S does not have any special way to access what the results of the drawing will be before they occur). Hawthorne makes it clear that lottery puzzles do not just affect our claims about conventional lotteries by presenting several examples of lottery puzzles which have lottery propositions that we do not normally associate with lotteries such as the proposition ‘I will have a heart attack’. After explaining how lottery puzzles can be generalized to cases that do not involve conventional lotteries, Hawthorne discusses a potential solution to these puzzles that is derived from the work of Dretske and Nozick, denying that knowledge is closed under known entailment. Although Hawthorne admits that denying closure would solve the lottery puzzles, he believes that the cost of denying closure is much too high.

In the second chapter, “Contextualism and the Puzzle,” Hawthorne briefly describes contextualism and how it can solve the lottery puzzles. Contextualists claim that the semantic value of ‘knows’ is dependent upon the context of the ascriber of a particular knowledge ascription. Contextualism offers a solution to lottery puzzles by allowing one to claim that it is correct to say of S that she knows the ordinary proposition and even that she knows she will not win the lottery in some contexts. If we as ascribers are in a low standards context where the possibility of S winning the lottery is not salient for us, then it is appropriate for us to say that S knows the ordinary proposition and she knows the lottery proposition. If we as ascribers are in a high standards context where the possibility of S winning the lottery is salient for us, then it is not appropriate for us to say that S knows either the ordinary proposition or the lottery proposition. Although contextualism does provide a solution to lottery puzzles, Hawthorne does not think the contextualist approach should be adopted because contextualism is at odds with the intuitive connection between knowledge, assertion, and practical reasoning.

Hawthorne discusses two other strategies for solving lottery puzzles in chapter three “Skeptical and Moderate Invariantism.” Both strategies that Hawthorne examines in this chapter are invariantist, which means, contra the contextualist, that the semantic value of ‘knows’ does not vary with context. Hawthorne begins by describing various skeptical invariantist solutions to lottery puzzles. The differing varieties of skeptical invariantism seek to solve the lottery puzzles by holding that in these lottery puzzles (and in large number of ordinary situations) the subject does not know ordinary proposition. Hawthorne points out that skeptical invariantism violates our assumption that we know many of the ordinary propositions that we take ourselves to know and it is difficult to reconcile with the intuitive connections between knowledge, assertion, and practical reasoning. After his treatment of skeptical invariantism, Hawthorne turns his attention to what he calls ‘simple moderate invariantism’. Simple moderate invariantism solves the lottery puzzles by claiming that we know the ordinary proposition and that we know the lottery proposition. According to Hawthorne, simple moderate invariantism has difficulties concerning multi-premise closure and with the intuitive connections between knowledge, assertion, and practical reasoning.

In the final chapter, “Sensitive Moderate Invariantism,” Hawthorne details sensitive moderate invariantism, which he thinks is the most promising solution to the lottery puzzles. Sensitive moderate invariantists maintain that the semantic value of ‘knows’ is sensitive to the subjects context (as opposed to the contextualists’ claim that ‘knows’ varies with the ascriber’s context). Hawthorne explains that whether or not someone knows a proposition depends upon the circumstances of her practical environment. If it is not permissible for someone to use P in her practical reasoning, then she does not know that P. Sensitive moderate invariantism solves the lottery puzzles by claiming that when someone goes through the reasoning involved in a lottery puzzle she realizes that she does not know the lottery proposition because of the possibility that she may win the lottery. Since this person is aware of the fact that she does not know the lottery proposition and that the lottery proposition is entailed by the ordinary proposition, she loses her knowledge of the lottery proposition because it is no longer permissible for her to use in practical reasoning. Although Hawthorne thinks that sensitive moderate invariantism is the most promising solution to lottery puzzles, he does point out that it cannot support both the Epistemic Possibility Constraint and the Objective Chance principle. Also, he mentions that sensitive moderate invariantism does lead to some counterintuitive results.

I think that Hawthorne offers a remarkable treatment of a fascinating topic; however, I have three minor complaints about this book. First, I agree with Hawthorne that lottery puzzles can have implications for general skepticism, but I believe that Hawthorne does not properly motivate this concern. Hawthorne attempts to demonstrate these implications with a somewhat obscure example utilizing quantum mechanics. His purpose would be better served if he illustrated more examples that demonstrate the connection between lottery puzzles and general skepticism. Second, Hawthorne’s discussion of the various skeptical invariantist solutions is rather cursory. Although this is a short book, it would have been nice if Hawthorne would have examined several of these solutions in a bit more detail. Third, Hawthorne leaves a bit to be desired in terms of clarity. In several places the structure of Hawthorne’s arguments is somewhat unclear. Also, he has a tendency to move from one subtopic to another without providing much explanation for the relevance of what is being discussed to his overall project. All of this being said, Hawthorne’s Knowledge and Lotteries is an excellent book and a significant contribution to epistemology. I recommend this book to anyone interested in lottery puzzles, the contextualism-invariantism debate, skepticism, or epistemology in general.