KNOWLEDGE à TRUTH?
What is truth?
(1) Correspondence Theory
(2) Coherence Theory
(3) Pragmatic Theory
(4) Redundancy Theory
What is the "God's eye" objection? Why is it similar to the Permanent Picture Gallery objection to Lockean representationalism?
What does it mean to "conflate truth with justification" Pojman, p. 10)?
KNOWLEDGE à TRUE BELIEF?
What is belief? Occurrent or dispositional?
THE TRADITIONAL "TRIPARTITE" ANALYSIS OF KNOWLEDGE
KNOWLEDGE ó JUSTIFIED TRUE BELIEF
What is justification? Epistemic vs. practical reason.
Strong vs. weak justification.
(1) Knowledge à Justified True Belief?
(2) Justified True Belief à Knowledge?
Strong Knowledge: Justification must be infallible.
How much Strong Knowledge is there?
What is the alternative?
Weak knowledge does not require infallible justification.
Weak knowledge seems to require a fourth condition on knowledge.
THE SEARCH FOR THE MISSING FOURTH CONDITION FOR A COMPLETE LOGICAL ANALYSIS OF KNOWLEDGE
Pojman's Four Alternatives. These are examples. Typically there is more than one variation on each category of alternative.
(1) No False Belief Basis Condition
If R is part of the subject's reasons for believing that p, then R must be true.
(2) Conclusive Reasons Condition (A Subjunctive Condition)
If R is part of the subject's reasons for believing that p, then it must be the case that if p were not true, R would not be true.
(3) The Causal Condition
The belief that p is caused by the fact that p.
(4) Indefeasibility Condition
There is no other truth q, such that believing that q would have defeated the subject's justification for believing that p.
Other Less Precise Alternatives:
BonJour's "No Accident" Condition
THE LOTTERY AND PREFACE PARADOXES:
Two Versions of the Conjunction Paradox.
The Lottery Paradox: How probable must a belief be to qualify as knowledge? Call it P. Design a fair lottery in which one winning number will be picked and each ticket has exactly the same chance of winning. Let n be the number of tickets. If n > 1/p, then each ticket's probability of losing is higher than P. Let t be a ticket in the lottery. Can you know that t will lose even before the lottery is held?
If so, you would be able to know that each ticket will lose. The conjunction of each of those beliefs implies that all the tickets will be losers. But you could not know that all the tickets will be losers, because you know that one ticket will win. How can we resolve the paradox?
The Preface Paradox: Suppose I write a book in which I assert 1,000 independent beliefs. Suppose I think of each of them as having a probability of .99. Let the conjunction of all 1000 of them be C. C is implied by my beliefs. Should I believe that C is true?
–C = at least one of the conjuncts of C is false. What is the probability of –C on the above assumptions? [.99995]. So I should be even more certain that –C is true than I am that any one of the conjuncts of C is true. If I believe –C (i.e., that one of my 1000 beliefs is false), my beliefs are inconsistent. What should I believe?
The Conjunction Paradox for Weak Knowledge
It is natural to think that knowledge is closed by known logical implication. But when two beliefs are probabilistically independent and each have probability less then one, the conjunction will have lower probability than either conjunct. As a result, the process of adding probabilistically independent beliefs with probability less than one to a conjunction will inevitably decrease the probability of the conjunction below any positive threshold (i.e., will eventually make it arbitrarily close to zero). So if weak knowledge is closed by known logical implication, then it is possible to be justified in believing a conjunction with probability arbitrarily close to zero.