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Sunday, January 6, 2013

Gettier Intuition

One common criterion used to determine whether or not something is knowledge is the "justified true belief" criterion (JTB). It has many forms but the basic idea is this:

S knows that P means:
  1. S believes that P.
  2. S has justification for believing P.
  3. S is true.
In 1963 Edmund Gettier proposed counterexamples to the above relationship. The idea is pretty simple. Construct a scenario in which (1), (2) and (3) are satisfied, but it fails to be knowledge. We'll look at an example from his original paper: Is Justified True Belief Knowledge? In particular, we'll look at Case I.

The basic idea is that Smith has evidence for two propositions:
  1. Jones is the man who will get the job.
  2. Jones has ten coins in his pocket.
From this, Smith infers that "The man who will get the job has ten coins in his pocket".

Looked at this with quantification we'll let G(x) denote "x is the man who will get the job" and H(x) denote "x has 10 coins", then the argument looks something like:
  1. Smith is justified in believing G(j)
  2. Smith is justified in believing H(j)
  3. Therefore, Smith is justified in believing:
    ∃x G(x) & H(x)
The rule that gets one from 1 and 2 to 3 is known as existential generalization. But there's actually more going on here. "Smith is justified in believing" is a modal operator. So minimally this requires some rules of "epistemic logic" with some sort of justification operator. And there needs to be spelled out rules of inference for that.

Gettier then claims (without argument) that Smith does not know that "The man who will get the job has ten coins in his pocket." This is what I shall refer to as a "Gettier intuition".

So there are a few questions at issue:
  1. Is this a Justified True Belief (JTB)?
  2. Is this an example of knowledge? 
  3. Does epistemic closure apply?
I'm less interested in offering an answer to these questions but rather am more interested in what role "intuition" plays in all of this. I've already expressed my critical views on intuition here.  As a result I'm mostly interested in what intuitions  motivate the particular conclusions that are drawn and why we might have such intuitions. (And for that matter, do we have such intuitions?)

The answer to the first question (or rather the "intuitions" which imply an answer to the first question) will partly depend upon one's intuitions on epistemic closure which relates to the third question.

Regarding the second question, one interesting aspect to all of this is that it is presumed this is not knowledge. The appeal is to some intuition. Experimental research into this has not indicated that everyone has the same intuition. So must everyone have the same intuition in this respect?

Regarding the third question, I plan to look at closure in more detail in another post but a few quick comments will suffice for now.

At first glance, the above argument doesn't seem too problematic. But consider the following scenario. Suppose that 1 million people are all in a raffle and have an equal chance of winning. One might claim that:

I am justified in believing that John (who is in the contest) will not win the prize. 

Likewise, the same statement might be made for each contestant. From that one can infer that:
 I am justified in believing that no one will win the prize.
Of course we know that one of the individuals will win the prize. As a result, I don't have any "intuitions" on whether or not epistemic closure applies to fallible justification.

In particular, we might ask the following question:

Suppose that I am (1) justified in believing that P, (2) P implies Q, and (3) P happens to be false. Am I therefore justified in believing that Q?

If my justification for P were infallible, (3) wouldn't apply. But as the case may be, it could turn out that I have adequate justification for believing P, and yet P turns out false. One might suppose the following requirement:

S is justified in believing Q provided that:
  1. S is justified in believing P.
  2. P implies Q
  3. P is true.
My guess is that the third requirement may play a role in the above Gettier intuition. 

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