allzermalmer

Truth suffers from too much analysis

Gettier Problem of Knowledge

Posted by allzermalmer on July 17, 2011

This blog is based on the Gettier problem of knowledge. This is a blog based on the paper by  Edmund L. Gettier called  “Is Justified True Belief Knowledge?”, and appeared in the philosophy journal  Analysis  Vol. 23, pp. 121–23 (1963)

There is, or was, this common idea of what constituted Knowledge. It was said to be based on three things. If these three things were met, then it was said for you to have knowledge. Thus, if I made a claim that I had knowledge, then I would have knowledge if I met these three criteria.

Plato presents us with an idea of what knowledge is, which is called “Justified True Belief”. This carries three things within it. They are, respectively, as follows:

S knows P if and only if…
[1.] P is true
[2.] S believes P
[3.] S is justified in believing P

In another way, in plain english, it would be as follows: “Allzermalmer knows ‘the sun is yellow’ if and only if it is true that ‘the sun is yellow’, and Allzermalmer believes that ‘the sun is yellow’, and Allermalmer is justified in believing that ‘the sun is yellow'”.

Now, there is a problem with [1.], and there is a problem with [3.]. Anyone and their mother could meet [2.]. However, Gettier goes on to say a couple of things, which would follow along these lines.

He states, “First, in the sense of ‘justified’ in which S’s being justified in believing P is a necessary condition of S’s knowing that P, it is possible for a person to be justified in believing a proposition that is in fact false.”

So, I must be justified in believing ‘the sun is yellow’ in order to have knowledge that ‘the sun is yellow’. This is a necessary condition. So, we could wonder, “what is a necessary condition?” A necessary condition is, “a condition without which a specified event cannot occur.” (Logic: An Introduction 2nd edition). Here is an example of what it takes for a necessary condition:Having gasoline in my car (I have a gasoline engine) is a necessary condition for my car to start. Without gasoline (x) my car (y) will not start. Of course, having gasoline in the car does not guarantee that my car will start. There are many other conditions needed for my car to start.”

He states, “Secondly, for any proposition P, if Allermalmer is justified in believing P, and P entails Q, and Allzermalmer deduces Q from P and accepts Q as a result of this deduction, then Allzermalmer is justified in believing Q.”

Now, Gettier presents two cases in which someone meets condition [1.] as true, though it is false that the person knows that proposition. Here are some examples.

Case 1

Smith and Jones applied for a certain job. Smith has strong evidence for the conjunctive proposition: “Jones is the man who will get the job, and Jones has ten coins in his pocket.” (Proposition in question)

Now, in order to support his proposition, Smith has evidence for the proposition listed, since the president of the company assured Jones that he would end up being selected. Also, Smith has counted the coins in Jone’s pocket ten minutes ago.

The proposition listed entails that “the man who will get the job has ten coins in his pocket.” So, we find that Smith sees the entailment of “Jones is the man who will get the job, and Jones has ten coins in his pocket.” to“the man who will get the job has ten coins in his pocket.”. The second proposition follows from the first, which means that the second proposition is entailed by the first proposition, and Smith sees that the second proposition follows from the first. Smith also has strong evidence for the first proposition. Thus, Smith is clearly justified in believing that “the man who will get the job has ten coins in his pocket.”

Now let us assume that, unknown to Smith, that he will get the job and Jones will not get the job. Also, unknown to Smith, he has ten coins in his pocket. Thus, we find that it is still true that “the man who will get the job has ten coins in his pocket.” However, the proposition “Jones is the man who will get the job, and Jones has ten coins in his pocket.”, which Smith inferred “the man who will get the job has ten coins in his pocket.” from, is false.

So, from all of the above, we find certain things: (1.) “the man who will get the job has ten coins in his pocket.” is true. (2.) Smith believes that “the man who will get the job has ten coins in his pocket.” is true. (3.) Smith is justified in believing that “the man who will get the job has ten coins in his pocket.” is true.

However, it is clear that Smith does not know that “the man who will get the job has ten coins in his pocket.” ; For“the man who will get the job has ten coins in his pocket.” is true by the virtue of the number of coins in Smith’s pocket, yet Smith does not know how many coins are in his pocket, and the base of his belief in “the man who will get the job has ten coins in his pocket.” on account of the coins in Jone’s pocket, which Smith falsely believes to be the man who will get the job.

Case 2

Suppose that Smith has strong evidence for the proposition “Jones owns a Ford”.

Smith’s evidence follows as such: Jones has, at all times in the past within Smith’s memory, owned a Ford. Jones just offered Smith a ride while driving a Ford.

Imagine that Smith has another friend, which is called Brown, and Smith does not know where Brown is. Smith selects three place-names quite at random, and he constructs three propositions. They go as follows:
Either Jones owns a Ford, or Brown is in Boston.
Either Jones owns a Ford, or Brown is in Barcelona.
Either Jones owns a Ford, or Brown is in Brest-Litovsk.

All three of the propositions just listed are logical entailments of the proposition “Jones owns a Ford”. So, Smith realizes that all three of the propositions of where Brown is is entailed by “Jones owns a Ford”, and he accepts all three of those propositions on the basis of “Jones owns a Ford”.Thus, Smith is completely justified in believing all three propositions of where Brown is, and yet Smith has no idea where Brown actually is.

Let us now imagine two further conditions: The first is that Jones does not own a Ford, yet he is driving a rented car at present. Second, by pure coincidence, Brown is in Barcelona. If these two conditions are held, then Smith does not know that Either Jones owns a Ford, or Brown is in Barcelona is true, even though it is true since Brown is in Barcelona. Smith does not believe that Either Jones owns a Ford, or Brown is in Barcelona. And Smith is justified in believing that Either Jones owns a Ford, or Brown is in Barcelona is true.

Case 3

The farmer Smith has a prize cow named Milky. Smith  is very concerned  when the dairyman tells him that Milky is in the field, and  grazing in the field, that Smith says that he needs to know.

Smith goes out to the field and stands by the gate to look at a distance. At a distance, behind some trees, Smith sees some white and black shape, which he goes on to recognize as his prize cow Milky.

The dairyman goes on to check on the cow as well. He goes out into the field, and sees Milky having a nap in a hollow, which is behind a bush, which is well out of sight of the gate from which Smith looked from. The dairyman also sees a large piece of black and white paper caught in a tree.

So we find this:
[1.] Milky is safe
[2.] Smith believed that Milky was safe
[3.] Smith is justified in believing that Milky was safe

However, Smith was wrong, since he never saw that Milky was safe, yet thought he saw what he thought was Milky.

So, the conclusion that Gettier makes is this: “These (three) examples show that definition ( of Knowledge) does not state sufficent condition for someone’s knowing a given proposition.”

As a side note, which shall be dealt with at some future date, the condition of “P is true” is based on our theory of truth. There are around three common forms, and these have their own problems, which can undermine “P is true”. The condition of “S is justified in believing P” also has its problem. In fact, “P is true” and “S is justified in believing P” are met with in Agrippa’s Trilemma.

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