# Knowledge, concept of

DOI
10.4324/9780415249126-P031-1
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DOI: 10.4324/9780415249126-P031-1
Version: v1,  Published online: 1998
Retrieved June 21, 2021, from https://www.rep.routledge.com/articles/thematic/knowledge-concept-of/v-1

## 9. The epistemic principles and some paradoxes

There are many epistemic paradoxes (see Paradoxes, epistemic). I here consider two in order to show how they depend upon some of the epistemic principles considered earlier.

• The Lottery Paradox: Suppose that enough tickets (say n tickets) have been sold in a fair lottery for you to be justified in believing that the one ticket you bought will not win. In fact, you are justified in believing about each ticket that it will not win. Thus, you are justified in believing the following individual propositions: t 1 will not win. t 2 will not win. t 3 will not win.… t n will not win.

Now if the conjunction principle is correct, you can conjoin them, ending up with the obviously false but apparently justified proposition that no ticket will win. So, it seems that you are in the awkward position of being justified in believing each of a series of propositions individually, but not being justified in believing that they are all true. Some philosophers have thought that this seemingly awkward position is not so bad after all, since there is no outright contradiction among any of our beliefs as long as the conjunction principle is rejected. But others have thought that making it rational to hold, knowingly, a set of inconsistent beliefs is too high a price to pay.

Others have suggested that we are not actually justified in believing of any ticket that it will lose; rather what we are justified in believing is only that it is highly likely that it will lose. But the lottery can be made as large as one wants, so that any level of probability (below 1) is reached. Thus, this suggestion seems to rule out our being justified in believing any proposition with a probability of less than 1. That is a very high price to pay! There is no generally agreed-upon solution for handling the Lottery Paradox (see Probability theory and epistemology; Confirmation theory).

1. The Grue Paradox: The so-called ‘Grue Paradox’ was developed by Nelson Goodman and has been recast in many ways (see Goodman, N.). Here is a way that emphasizes the role of ET-P:

1. All of the very many emeralds examined up to the present moment, t now, have been green. In fact, one would think that since we have examined so many of them, we are justified in believing that (G): all emeralds are green. But consider another proposition, namely that all emeralds examined up to t now are green, but otherwise they are blue. Let us use ‘grue’ to stand for the property of being examined and green up to t now but otherwise blue. It appears that the evidence which justifies us in believing that all emeralds are green does not justify us in believing that (N): no emerald is grue.

What are we to make of this version of the paradox? First, note that it depends upon ET-P. Although (1) our inductive evidence (the many examined green emeralds) justifies (G), and although (2) (G) does entail (N), the inductive evidence does not justify (N). In other words, this version of the paradox arises because the evidence does not transfer as the principle would require. Second, note that CLO-P is not threatened by this paradox since it is the evidence for (G) that is inadequate for (N). (The issue is not whether we are justified in believing (N) whenever we are justified in believing that (G).)

But if ET-P were not valid, then the sting of this version of the paradox can be pulled. Recall the original Grabit case. In that case, I had adequate evidence for being justified in believing that Tom stole the book, that is, the person stealing the book looked just like Tom. It seems clear that this evidence is not adequate to justify the proposition that it was not Tom’s identical twin who stole the book. If it were the twin, things would appear to be just as they did appear to be. But this tends to show that we do not typically impose ET-P on our evidence.

There are other versions of the Grue Paradox that do not make explicit use of ET-P. For example, since ‘all emeralds are green’ and ‘all emeralds are grue’ are alternative hypotheses, it seems paradoxical that the very same evidence that justifies believing the first alternative also seems to support the second. But perhaps, like the version considered above, this apparent paradox rests on a mistaken intuition. Consider the Grabit Case once again. Here, the evidence which justifies the belief that Tom is the thief would also support the claim that Tom’s identical twin stole the book. To generalize further, consider any hypothesis, say h, that is justified by some evidence that does not entail h. It is always possible to formulate an alternative hypothesis that is supported by that very evidence, namely (not-h, but it appears just as though h because of…). Thus, an intuitively plausible epistemic principle similar to ET-P might be invalid. That principle is: if there is some evidence, e, that justifies S in believing that x, and x is an alternative hypothesis to y, then e does not support y.

To sum up, if ET-P and similar epistemic principles do not accurately capture our normative epistemic practices and if the argument for scepticism that depends upon CLO-P begs the question, then the sting of Cartesian scepticism (considered in the previous section) is numbed and the Grue Paradox can be addressed. But those are big ‘ifs’, and the issue remains open (see Induction, epistemic issues in).