The analysis of knowledge

Question 1

The JTB analysis

Answer 1

S knows that P if and only if
- It is true that P
- S believes that P
- And S is justified in believing that P
- holds that knowledge is equivalent to justified true belief; if all three conditions (justification, truth, and belief) are met of a given claim, then we have knowledge of that claim

Question 1

Gettier’s argument

Answer 1

• Assumption 1
  In whatever case of “justified” that is relevant to clause iii above, it is possible for someone to be justified in believing something false
• Assumption 2
  “For any proposition P, if S is justified in believing P and P entails Q and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q”.

Question 2

The case of Smith and Jones

Answer 2

Smith has strong evidence for, and is thus justified in, believing:
(D) Jones is the man who will get the job, and Jones has ten coins in his pocket.
But (D) entails this:
(E) The man who will get the job has ten coins in his pocket.
Suppose that Smith appreciates the entailment and comes to believe (E) on this belief. Given Assumption 2, Smith is justified for this.
But now suppose that, unknown to Smith, Smith himself, not Jones, will get the job and that he has ten coins in his pocket. Thus, Smith has a justified true belief in (E).
But surely Smith doesn’t know that (E) is true.

Thus, conditions from the JTB analysis do not offer an analysis of knowledge.

Question 3

K = JTB + infallible evidence

Answer 3

• The idea here is that justification is necessary for knowledge but one is only ever justified in believing that P when one’s evidence for believing that P guarantees that P is true.
• This succeeds in avoiding Gettier cases. But it’s almost certainly a non-starter. It is at odds with Gettier’s assumption 1, which seemed very plausible. It also makes it too difficult to know anything.

Question 4

JTB + no false lemmas

Answer 4

• Notice that the reasoning which leads Smith to believe (E) passes through a false step aka “lemma” (D). Perhaps it is a condition on knowledge that it not be the result of reasoning through any false steps.
  ○ This doesn’t avoid Gettier cases.
  ○ For example, the fake barn country.
  In Fake Barn Country, there are dozens and dozens of fake barn facades around. As you drive through, you happen to see the one real barn and come to believe that there is a barn. This belief is true and justified and not the result of any false lemmas. But you don’t know that there is a barn.

Question 5

KTB + no defeaters

Answer 5

• In the fake barn country example, there is some information that you are in fake barn country, where fake barns are rife, which is such that if you learned of it your justification for believing that there is a barn would be “defeated”.
  ○ A “defeater” is information which, if learned, would undermine the justification for a belief.
  ○ In Gettier’s example, the information that Jones won’t get the job is the defeater.
  This won’t work (see the robber case)

Question 6

Other proposals

Answer 6

• It is true that P
• S believes that P
• If it weren’t true that P, then S wouldn’t believe that and
• If it were true that P, then S would believe that P
  This new analysis is supposed to help capture the idea that knowledge requires a tighter connection to the truth than mere luck

Question 7

Williamson proposal

Answer 7

Factual knowledge cannot be analyzed, that it is, for purposes of doing epistemology, a primitive or basic notion.

Question 8

Epistemic vs practical grounds for belief

Answer 8

• A belief is epistemically rational if it is likely to be true given the evidence
• A belief is practically rational if holding it is likely to have good consequences

Question 9

Pascal’s reasoning

Answer 9

• Can be modeled using decision theory, a mathematical theory of rational choice. According to standard decision theory, a practically rational agent always acts so as to maximize expected utility.
• If this is correct, the action you have pragmatic grounds for performing is the action with the highest expected utility, where the expected utility of an action is the sum of the utilities of the action’s possible outcomes weighted by their probability.

Question 10

Example of decision theory

Answer 10

• We can measure these probabilities with numbers 0-1.
• Suppose that chicken and beef are equally likely. Then the probability of each is 0.5.
  ○ Expected utility of bringing white = (10x0.5)+(2x0.5)=6
  ○ Expected utility of bringing red = (7x0.5)+(10x0.5)=8.5
  ○ Expected utility of bringing red > Expected utility of bringing white

Question 11

God exists w/ decisioun theory

Answer 11

• Assume that the probability that God exists is 0.5.
• Assume that the utility of the afterlife of a believer is infinite. We can represent this value as a number (infinity). Some assumptions about doing arithmetic with (infinity)
  ○ Expected utility of believe (infinity x 0.5)+(17x0.5)= infinity + 8.5 = infinity
  ○ Expected utility of don’t believe (17x0.5)+(17x0.5)=17
  ○ Expected utility of believe > Expected utility of don’t believe

Question 12

Objections to Pascal

Answer 12

• Even if one is convinced by Pascal’s reasoning, how can one just decide to believe? Does deciding to believe even make sense?
• Pascal’s response:
  Even if deciding to believe is impossible, it doesn’t matter, since there is another way of causing oneself to believe: simply behave as if you do and belief will come.
• Pascal assumes that the choice is between believing or not believing in the divine being posited by the standard monotheistic conception. But what about other gods? What about the gods of other, nonstandard monotheistic traditions? Etc?