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It's all about the deep questions.

So, if my goal is knowledge, I must first ask myself what it is to know. If a proposition had less than a probability of one, would I know that p? What I take to be knowledge is this: take all possible worlds in which the evidence for a proposition holds, if that proposition is true in all of these possible worlds, then, I take it, that evidence allows me to say that I have knowledge of that proposition. Now, what about someone who contests that this does not mesh well our intuitive grasping of the word knowledge? That person must then be committed to the claim that it is perfectly well for someone to say, “For all I know it could be the case that p is false, but I still know that p is true.” I take this to be a reductio ad absurdum. Therefore, knowledge requires absolute certainty.

One question to ask is: does this definition of knowledge perserve closure? So, say that by some reasons R, I am justified in knowing a proposition P. Furthermore, let it be true that P implies Q. Well, if P is true of all the possible worlds I can be in, so it is the case that Q is true of all the possible worlds I can be in. Therefore, knowledge must be closed under implication.

So, lets try to find out things that I know. Well, for starters, I know it is not the case that nothing exists. Since, any sensory evidence whatsoever would rule out the one possible world in which nothing does exist. I, obviously, know all the truths that are true by convention, but those are uninteresting (mathematical truths seem to be of this form). I know all truths of the form, “I am having sensory experience X”, since, by the definition of knowledge, I must take all possible worlds in which I have a sensory experience X and ask whether it is true that I am having sensory experience X. Obviously, the verdict comes down on the side of knowledge. Now, although this is somewhat substantial, it still hasn’t taken us anywhere useful. Going to have knowledge of things “outside” of my experience, however, cannot be done since I can imagine a possible world with nothing outside. (A caveat here: as an axiom prior to wherever my philosophizing takes me, I must assume that whatever is producing my thoughts does so in a rational matter. Not exactly that is perfectly rational in every sense of the word, but that it is capable of rationality. If it is the case that it isn’t, then there is nothing that I can do since my thoughts cannot be produced by anything other than what is creating my thoughts.) Clearly, this definition of knowledge cannot take us very far. This makes me a skeptic with regards to knowledge.

What I must therefore look to is probable beliefs, rather than beliefs that are absolutely true. What would make a belief probable? Ideally, we could apply the same definition: reasons R maks a belief B have probablility X iff the probability of being in a world where B is true, where the set of possible worlds in question is restricted to those in which R holds, is precisely X. The problem with this definition is that I am less than a perfectly imaginative being. I do not have a perfect grasping of the “probability space” of possible worlds. Since all beliefs hinge on this idea, the most worthwhile philosophical project is to flesh out as much as possible the space of possible worlds.

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