On Philosophy

September 9, 2007

Possibilities And Justification

Filed under: Epistemology — Peter @ 12:00 am

Previously I proposed that to say a claim is justified means that it is the most probable option out of a set of mutually exclusive and exhaustive possibilities. Which means that we could be justified in believing something to be the case that only has a 10% chance of being true, assuming all the other options were less likely. When I introduced this claim it was simply as part of a way of reasoning about situations involving probability, so now allow me to defend it.

One of the advantages of this understanding of justification is that it allows us to make definite judgments about it. Either we are justified in believing a possibility to be the case or we aren’t (assuming that all the facts about the relevant probabilities are known). This contrasts to understandings of justification based on probability where justification can come in different strengths. In many situations understanding justification as coming in different strengths may seem more intuitive. In the example given above, for instance, since the most likely outcome is still fairly unlikely, in absolute terms, it may seem reasonable to claim that our justification for believing it to be the case is weak. I admit that justification may come in different strengths, but I would also argue that when it comes to reasoning on the basis of justification that such strength should not be taken into consideration. Because once we start thinking of justification as coming in different strengths we lean towards the idea that we should assert the proposition that is most strongly justified (with an understanding that more probable means more strongly justified). The problem with this is that more “general” propositions (those that assert less) are almost always more likely than the more specific. For example, “a∨~a” is always more likely than “a” or “~a”. And so under this understanding of justification we should prefer “a∨~a” or either “a” or “~a”. Well, certainly we can’t go wrong with that claim, but that isn’t how we expect justification to work, we expect our reasoning about justification to encourage us to endorse specific claims, not non-claims such as “a∨~a”.

Given that such empty generalities are the most strongly justified we must revise what we want our theory of justification to yield. Obviously “statements most likely to be true” isn’t it. Well, one distinguishing feature of such general statements is that they can’t be acted upon. Even if you believe that “it will rain tomorrow ∨ it won’t rain tomorrow” is the case you can’t use that belief as a basis for action, while you can use “it will rain tomorrow” or “it won’t rain tomorrow” as a basis for action. Thus we might be inclined to claim that considerations regarding justification should endorse the claim that it is best to act on the basis of. This is an improvement, but it isn’t perfect either. The problem here is that what is useful to us and what is likely aren’t always the same thing. For example, even if the probability that “it will rain tomorrow” is significantly less than the probability of “it won’t rain tomorrow” we may still choose to act as if “it will rain tomorrow” is the case and bring an umbrella. This simply points out the fact that choosing how to act involves a costs-benefits analysis that really isn’t part of justification.

So then what is the point of justification? Intuitively it is to find the claims that are most likely to reflect what is the case. But then it seems that we are back to the problem where claims of sufficient generality are always the most justified. And, on the basis of this problem, I endorse my approach for its ability to deal with it. My approach essentially says that to say that a claim is justified must always be relative to a set of possibilities. “a∨~a” may be justified, but that doesn’t mean that we are to prefer it necessarily to “a” or “~a”, the latter two may also be justified; the first claim and the last two are justified relative to a different set of alternatives. Given that “a∨~a” is always true it can be the only possibility in its set, and so in my notation we would write {a∨~a} // {a∨~a}. This indicates both that we are justified in claiming “a∨~a”, and that the are in a state of complete ignorance even if we make that claim (because we have not ruled out any possibilities). If we are justified in claiming “a” then in my notation we write {a} // {a, ~a}. And here we see that our ignorance has in fact been diminished to some extent because an alternative has been ruled out. Even though the first and the second of these statements involve the same variables we cannot combine them, or reason on the basis of both of them. The statements are made with respect to different sets of possibilities, and so justification in the case of one of them doesn’t have any bearing, logically, on justification with respect to the other. Of course there is something to be said about the fact that having more possibilities involved usually diminishes the probability of even the most likely alternative, and thus the justification becomes less certain. And I should also mention that which set of possibilities we wish to consider is conditional upon what we want to know. But both of these are topics for another day.

Let me conclude with another example illustrating how justification is relative to the possibilities under consideration. Consider a four-sided die, numbered one through four, with the side numbered one colored red and the sides numbered two through four colored blue. And let us assume that side one has a 40% chance of being rolled, while the remaining sides have a 20% chance each. Now, of the four sides we are justified in thinking that side #1 will come up, or in my notation that {#1} // {#1, #2, #3, #4}. But we are also justified in thinking that a side colored blue will come up instead of a side colored red, in my notation {b} // {r, b} = {~#1} // {#1. ~#1} = {#2∨#3∨#4} // {#1, #2∨#3∨#4}. If we were considering justification as independent of the possibilities under consideration this would be a paradox, because claiming that both side number one will come up and that side number one won’t come up would be justified. But as my approach illustrates the two claims are not in fact directly comparable, and hence there is no paradox.

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