KNOWLEDGE

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?

Gettier Counterexamples

DESCARTES' SOLUTION

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:

Contextualism

Pojman's "

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.