Reformed Philosophy

Do you know you are going to lose a lottery where you only have 1 out of 10¹⁰⁰ chance of winning? Given a Reformed view of epistemology, what is the right answer? I’m not sure yet, but it is a very interesting question. Below, I briefly elucidate the problem of the Lottery Example, and perhaps someone can offer some suggestions.  

The Epistemic Lottery of Life

“Hey, you never know!”

-New York State Lottery motto

We find in the standard Lottery Example an apparent dilemma between an arbitrary classification of knowledge and extreme scepticism. In light of the work of philosophers like John Hawthorne and Jonathan Vogel, I am arguing in this essay that it is plausible that this dilemma is a dilemma for most, if not all, knowledge claims; that is, the problem of the Lottery Example “generalizes”.[1] After elucidating the specifics of the Lottery Example predicament, I move down a series of steps toward my thesis, moving from abstract epistemic considerations to the more pragmatic. First, I argue that there is a close relationship between the Lottery Example dilemma and basic sceptical hypotheses. The next step is to look at the standard Gettier examples, which serve to question our initial epistemic intuitions. Finally, I move to apply the Lottery Example to some “everyday” knowledge claims.

The Lottery Example 

A standard Lottery Example:

You are playing a lottery where your odds of winning are 1 out of 10¹⁰⁰. Do you know that you will lose?[2]

The key features of the Lottery Example are twofold: 1) having an impressive amount of justification for p, which in this case is that you will lose the lottery (it might be conceded that in the more extreme versions of the lottery example, we have more justification for p than we do for almost any other proposition), and 2) the possibility of not-p. The Lottery Example is archetypal due to its clarity and simplicity. There are only two answers, namely “yes” and “no”, which at the outset establishes the fork for the dilemma. Let us first pursue the “yes” answer: If we say that “yes, you know you will lose in this lottery”, then if we slowly increase our odds, at what point do we no longer know we will lose the lottery? If our odds are 1 out of 10, say? At this point, what is classified as knowledge here seems arbitrary. Let us take the other route, saying that “no, you don’t know you will lose this lottery”, which someone might say due to the possibility of that one chance (indeed, this idea must play some roll in anyone’s rationalization for playing the lottery in the first place); however, this would be to say that knowledge requires certainty. If there is even the most remote conceivable possibility against any proposition, then I cannot be said to know that proposition. If I don’t know that I will lose a lottery where my chances of winning are 1 out of 10¹⁰⁰, then I won’t know any proposition I believe where the odds of my being mistaken are even greater than 1 out of 10¹⁰⁰ and thus develops the extreme scepticism.

Step One: The Lottery Dilemma and the Basic Sceptical Hypothesises

Let us look at two basic sceptical hypotheses, namely, Peter Unger’s certainty requirement and the Argument from Ignorance, as constructed by Keith DeRose. Both are formulations of a “no” answer to the Lottery Example question, that is, they both appeal to epistemic certainty. First, Unger’s certainty requirement, as found in “Skepticism and Nihilism”:

In respect of any suitable thing, say, that p, if someone knows for certain p then either he already knows for certain that any… argument to opposite effect fails of its purpose, or should he engage in suitable simple reasoning, he could come to know for certain that this is so.[3]

In Unger’s essay, this certainty requirement is foundational for his argument for radical scepticism, and from which he has two deductions: 1) no one can meet the certainty criterion and that 2) therefore, no one knows anything.^[4] As it turns out, since no one knows that all the opposing arguments against any given knowledge claim fail, no one can meet the certainty requirement placed on knowledge.

The other formulation of a “no” answer that I want to elucidate is Keith DeRose’s articulation of the Argument from Ignorance, which is found in his essay “Solving the Skeptical Problem”. DeRose is using the argument as a simplistic hypothesis that an external world sceptic might use. Where “H” is “a suitably chosen sceptical hypothesis (e.g., I am a bodiless brain in a vat…)” and “O” is “a proposition about the external world one would ordinarily think one knows (e.g. I have hands)”, the argument runs like this:

1) I don’t know that not-H

2) If I don’t know that not-H, then I don’t know that O, so,

C) I don’t know that O [5]

DeRose is using this basic argument as something like an entry point into what is “intriguing” about sceptical arguments and how best to solve their riddle. Consequently, I think the riddle of the sceptical arguments is the tied to riddle of the Lottery Example dilemma.

DeRose’s rendition of the Argument from Ignorance fits nicely with Unger’s certainty requirement; if there is some H that I don’t know “fails of its purpose” then I am not certain of whatever proposition H is against. In addition, both are easily associated with our current topic of the lottery dilemma. Do you know you will lose the lottery? No, because you don’t know that the one small chance of winning the lottery will “fail of its purpose”, so to speak. There is one chance, H, that you will win the lottery, and you don’t know not-H. Indeed, Unger’s certainty requirement and the Argument from Ignorance are so connected with a “no” answer to the lottery question, that to deny them is to be faced with the problems associated with the “yes” fork of the dilemma. The Lottery Example dilemma is the dilemma of radical scepticism. The question of how good the odds of winning have to be before we no longer know that we will lose the lottery is translatable into the question of how much justification we need to acquire before we can be said to have knowledge. Piling up justification, waiting to call it knowledge, can quickly turn into a conceptual sorites argument. If choosing to deny a certainty requirement, choosing the “yes” answer to the lottery question, one must have some sort of story to combat the charge of arbitrariness, e.g. a story of “the right kind” of justification, or justification in “the right way”. But even so, such a story must take care to defend against the pertinent Gettier-styled counter-examples, which show that even “the right kind” of justification can lead to a circumstance that intuitively doesn’t seem like it should lead to knowledge. Importantly (as we will note in the next section), the Gettier examples are susceptible to the lottery dilemma as well.

Step Two: The Lottery Dilemma and the Gettier Cases

In this section I will be focusing on the traditional Gettier cases, opposed to the latter and more developed cases in the literature, because of the following two conjuncts: first of all, because the traditional cases are the most popular and familiar, indeed many philosophers probably have them memorized; second of all, the way the lottery dilemma affects the traditional Gettier cases would be paralleled in more advanced or complex Gettier-styled cases. With this in mind, let me now summarize the first of the two traditional cases found Gettier’s essay “Is Justified True Belief Knowledge?”:

Case 1: Smith and Jones are applying for the same job. Smith has very strong evidence for thinking that Jones will get the job (e.g. the employer tells Smith that he will hire Jones, etc.), and for thinking that Jones has 10 coins in his pocket (e.g. Jones emptied his pockets in front of Smith and then clearly, slowly, in good lighting, and perhaps even counting out loud placed 10 coins in his pocket). As such, Smith forms the general proposition p that the man who gets the job has 10 coins in his pocket. As it turns out however, Smith gets the job and he happens to also have 10 coins in his pocket. Thus, Smith’s belief in p was justified and true, but doesn’t seem like knowledge. [6]

The noticeable difference between the this Gettier case and the Lottery Example is what we might call the “Gettierization”, that is, the arriving at a general proposition p which turns out to be true for different reasons than originally suspected.[7] However, I propose that the basic dilemma for the Gettier cases is not the Gettierization, but rather a lottery dilemma.

This case, like the Lottery Example, has both 1) an impressive amount of evidence for p, that Jones will get the job, and 2) the possibility that not-p, the sceptical hypothesis. Since the Gettier case isn’t dealing with clear odds, it has to provide, as it were, a background story for the sceptical hypothesis: that Smith so happens to also have 10 coins in his pocket and it so happens that somehow Smith gets the job. The fact that the proposition in question, that the man with 10 coins in his pocket will get the job, happens to be true after the validation of the sceptical hypothesis (the Gettierization) is an interesting by-product of the basic lottery dilemma. Before the validation of the sceptical hypothesis, we could ask the question “Given all this evidence for p, does Smith know that p?”. Like the Lottery Example, how we answer that question decides which fork of the lottery dilemma we will take. If we say, “Yes, Smith does know”, the task becomes classifying knowledge in a non-arbitrary way; if Smith only heard the employer mumble who would get the job, would he still know p? If we say “no”, on the other hand, then we are heading down the path of requiring certainty for knowledge and consequently the path of radical scepticism. This is the foundation, the pre-conditions, of the consequent dilemma of Gettierization for the justified true belief model for knowledge. With the Lottery Example dilemma being at the root of both the radical sceptical hypothesis and the Gettier dilemma for justified true belief, I propose in the next section that the Lottery Example dilemma is a dilemma for most if not all knowledge claims.

Before moving on to the next step, I want to briefly note that the denial of closure or the elucidation of a sensitivity or safety principle for knowledge will not dodge the lottery dilemma. Closure, for example, is not necessary for the lottery-type problems I have described thus far (which I think is somewhat more basic or primitive than what Hawthorne describes).[8] Take any proposition p, and for p there will be a chance, a sceptical hypothesis, that not-p, be it a lottery ticket of sorts, a Brain in a Vat hypothesis, etc. (indeed, my intuitions are that the chances of my being a brain in a vat are greater than my chances of winning a lottery where I have 1 out of 10¹⁰⁰ odds!), and that is all we need for my basic lottery dilemma of either radical scepticism or the fight against arbitrariness. Though closure is important for the original Gettier cases, it is not necessary for the more recent Gettier-type cases in the literature. I don’t see how closure comes into play at the basic lottery dilemma.

Similarly, though issues of sensitivity and safety play a roll in many Gettier cases (though arguably not all), they do not, however, come into play at the foundational lottery dilemma. The general definitions of sensitivity and safety, as given by Ernest Sosa, are:

Sensitivity:  If it isn’t the case that p, then S would not believe p

Safety: If S believes p, then p is the case [9]

 As such, to use a sensitivity or safety principle to avoid the lottery dilemma would be to beg the question. For any highly justified p that I currently believe, there is a chance that not-p, and whether or not this chance makes the difference in attributing knowledge is the fork of the dilemma. To say that I wouldn’t believe p if it wasn’t the case or to say that since I believe p it is the case is to deny the possibility of not-p, perhaps a sceptical hypothesis, at the outset and, as far as I can tell, without justification.

Step Three: Applying the Lottery Dilemma to “Everyday” Knowledge Claims

Given the Lottery Example’s ties to sceptical hypotheses like Unger’s certainty requirement and the Argument from Ignorance, I imagine it is somewhat intuitive that the dilemma affects our common knowledge claims as well. This final step will be rather straightforward, simply applying the lottery dilemma to some of our basic, “everyday”, knowledge claims, namely memory beliefs and current experiences.

With the basic framework of the Lottery Example and the first Gettier case, I think it is quite clear that knowledge claims about future events (like losing the lottery, or Jones getting the job) are susceptible to the lottery dilemma, but what about knowledge claims about past events, that is, memory beliefs? I think I have a lot of justification in my belief that I ate Frosties (“Frosted Flakes” if you are from the United States) mixed with strawberry yogurt for breakfast yesterday (not a usual meal for me, but I was running late for class and I was out of milk); however, I am willing to concede that there are some sceptical hypotheses that I do not know that they fail, e.g. perhaps my Frosties box was filled with an off brand of cereal such that I didn’t recognize the difference, perhaps I have my days mixed up as I am writing this essay and yesterday wasn’t really Monday (sadly that happens all too often), or perhaps, simply, yesterday morning I was the victim of an evil demon or an Alpha Centurion prank. Though it is impossible to tell, again I imagine the odds of some, if not all, of these sceptical hypotheses occurring is greater than my chances of winning a lottery where my odds are 1 out of 10¹⁰⁰. As such, to deny me knowledge concerning my memory of yesterday’s breakfast because of these sceptical hypotheses is to acquiesce to radical scepticism. To grant me knowledge concerning this memory despite sceptical hypotheses, is to begin the fight against arbitrary classifications of knowledge claims. What if I had a little less justification for my memory belief? Is there a non-arbitrary amount of justification I need to have in order to know my previous dietary experiences? Even given a story to guard against arbitrariness in the amount or kind of justification required, are there Gettier-styled cases to be concerned about, which themselves carry the seed of the lottery dilemma? Thus runs the dilemma for memory beliefs

What about beliefs about my current experiences? How are they susceptible to the lottery dilemma? Clearly if the lottery dilemma is tied to Unger’s certainty requirement and the Argument from Ignorance, my beliefs about my current experiences are susceptible to the dilemma if for no other reason than the possibility of standard sceptical hypotheses, e.g. brain in a vat scenarios, evil demon scenarios, etc. However, I don’t think we need to appeal to such extreme science fiction or supernatural hypotheses to feel the force of the dilemma. As an example, I am currently looking at a red chair in the corner of my flat, and I form the belief that the chair is indeed red. I would like to say that I know the chair is red. Nevertheless, while I was at the library this morning my wife, being an artist, could have decided to start a series of pieces on the limitations of our finite epistemic faculties; as such, she replaced the red chair with a practically identical white chair with red lights shining on it (presumably from hidden locations; she could have pulled this off, she is indeed a very talented artist!). Conceding that this is a sceptical hypothesis, my current experiential belief about the chair in the corner is at the fork of the Lottery Example dilemma. Do I know that the chair is red? If we say “no” because of the sceptical hypothesis, then we are at the brink of radical scepticism. If we say “yes”, again, it is not clear how to determine how much justification one needs for a belief before it counts as knowledge that is not arbitrary. Since sceptical hypotheses, the proverbial chances that I win the lottery, can be provided for any of my current experiences, then all of my current experiences are susceptible to the lottery dilemma.

Conclusion

By elucidating the Lottery Example dilemma and then walking through a series of steps starting with radical sceptical hypotheses, moving through Gettier examples, and then finishing with “everyday” knowledge claims, showing them all to be susceptible to the dilemma, I have argued for the plausibility of the view that the lottery dilemma is a dilemma for nearly all knowledge claims. As such, related research has and should proceed down two lines: 1) What exactly is the extent of the applicability of the Lottery Example dilemma; are mathematical beliefs or beliefs of personal consciousness susceptible to the dilemma? 2) How do we deal with the dilemma, be it by finding a way around it or by taking one of the forks of the dilemma and defending a particular position as still feasible?

Works Cited:

Ebert, Philip. Course Lecture. “The Gettier Problem.” Stirling University, Scotland.

November 17, 2007.

Hawthorne, John. Knowledge and Lotteries. Oxford: Oxford University Press, 2004.

Sosa, Ernest. “How to Defeat Opposition to Moore.” Noûs. 13 (1999): 141-153

Sosa, Ernest and Jaegwon Kim, eds. Epistemology: An Anthology. Oxford: Blackwell

Publishers, 2000.

Unger, Peter. “Skepticism and Nihilism.” Noûs. 14 (1980): 517-545.