On Philosophy

August 11, 2006

More On Knowledge

Filed under: Epistemology — Peter @ 12:33 am

Last time I discussed a few objections that have been raised against the standard account of knowledge. Previously I had argued that the standard account was flawed (for other reasons), and that knowledge should be defined simply as sufficiently justified statements. Now I will examine how a treatment of knowledge as simply justified statements can deal with the objections to the standard account mentioned last time, as well as a few others.

The Job

The situation is as follows: “Smith and Jones are both applying for the same job. Smith has good evidence that Jones will get the job, and he knows that Jones has 10 cents in his pocket. From this he concludes that the man who will get the job has 10 cents in his pocket. However in a surprising turn of events Jones gets the job, and more surprisingly he has 10 cents in his pocket (unbeknownst to Jones).” Is the proposition that “the man who gets the job has 10 cents in his pocket” knowledge? No, not under the definition of knowledge as justified statements. Before Smith got the job he may have considered it knowledge, and rightly so if he had justification for believing that Jones would get the job with a high degree of probability. However, after Smith got the job he can no longer consider the statement to be knowledge, since it is no longer founded on beliefs about Jones (as the probability that Jones gets the job is now 0).

Brown’s Location

“Smith has strong evidence that Jones owns a Ford. He also has no idea where Brown is at the moment. From this he constructs three propositions: ‘Jones owns a Ford or Brown is in Boston’, ‘Jones owns a Ford or Brown is in Barcelona’, and ‘Jones owns a Ford or Brown is in Brest-Litovsk’. Then, again by coincidence, it turns out that Jones has sold his Ford, unbeknownst to Smith, but that Brown is in Barcelona.” Is the proposition “Jones owns a Ford or Brown is in Barcelona” knowledge? This case is actually a bit tricky, because we don’t have all the information about what Smith knows. If Smith doesn’t know that Jones has sold his car then all three statements that he has generated are equally knowledge, albeit not very useful knowledge since we can’t deduce any new facts from them. Of course if Smith knows that Jones has sold the car then, once again, none of the statements should be considered knowledge, because there is no longer justification for any of them.

Fake Barns

Consider then this situation: You are driving through the countryside when you see a barn. Normally your perceptions are accurate enough that in this case you could be sure that it was a barn with a high degree of certainty, and in fact it is a barn. However earlier you have been informed by a reliable source that there are many fake barns in this area. Is the statement that “this is a barn” knowledge? Well normally it would be, but given that you know that many barns in this area are fake you don’t have justification for this belief, where you normally would, and thus it isn’t knowledge. Does this seem contradictory, that the addition of new information can deprive you of knowledge when you would normally have it? Well there are two ways of looking at this. One is that now you can look at what seems to be a barn and conclude “this is a fake barn” with more certainty than you could have otherwise. The other reaction is that we shouldn’t be too surprised if a false connection between evidence and the facts leaves us “knowing” less when its error is pointed out to us. For example you “know” less when someone points out that the correlation between height and intelligence you have been depending on is false, but in return you have increased accuracy when determining people’s intelligence.

This brings us to a more interesting problem, specifically how we should deal with the possibility of “defeaters” statements such as “the barns are fake” that invalidate our normal connections between evidence and the facts. Even if we judge that the probability of a given defeater is low there are an infinite number of possible defeaters, and thus taken as a whole perhaps we should feel that it is likely that there is some defeater, and hence that we can’t know anything. My response to this is that even if there are an infinite number of possible defeaters it doesn’t mean that there is a high probability of some defeater being true. In theory we could estimate the probability that there is some defeater by making many observations and seeing how often they were wrong. But already perform this calculation, when we attempt to judge how accurate some instrument or sense is in a situation. For example if I judge that my vision is 99.9% accurate that means that the probability of one or more defeaters is 0.1%. So not only are defeaters of negligible consequence in most cases, but we have already appropriately compensated for them when accounting for observational accuracy.

Justification and Probability

This brings me to my final objection to knowledge as justified statements. So far we have been assuming that a statement that justification reveals as sufficiently probable is knowledge. But consider the following case: we have a statement such as “particle X decays into Y after 5 seconds.” Now assume that this isn’t actually true, but that the X to Y decay happens only in a fixed percentage of cases, say 60%. Then as we conduct more trials evidence will result in a judgment that the probability of the statement is 60%. This is fine, but consider that the probability of the X to Y decay could be arbitrarily high, even 99% or 99.9%. It seems then that we can’t set a cut off number which will allow us to say that a highly probable statement is sufficiently justified to be knowledge without admitting some of these “false positives”. It is true that such a cut off point can’t be picked, but that doesn’t mean we have to give up on probability. First I must point out that there is a maximum probability that can be assigned to any statement due to observational error, and that this upper limit will vary depending on the situation. What I propose then is that the statements we should consider true are those whose probability is trending upwards as we conduct more observations or those that have reached the maximum possible probability given how we are gathering evidence. Probabilities that are stable at some value less than 100%, even 99.9%, will not reach the upper limit, and will stabilize at some lower value. And if we do find stable probabilities that aren’t at the limit we can test new statements such as “X will happen Y% of the time”, where Y was the stable probability from our previous observations, and the probability of these statements will trend towards the upper limit if they are true.

Of course I haven’t gone through all the objections to standard theory of knowledge, for example situations dealing with clairvoyants and such, but I trust that the reader will see how they can be resolved in a manner similar to the ones presented.


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