philosophy discussion

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iii) Skepticism also conflicts with the principle about practical

reasoning: ”In deliberating about what to do, you should

only use known propositions as premises“

From the principle about rational reasoning plus skepticism it

follows that almost all of our practical reasoning is flawed.

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Acceptance of Conclusion

Proposal: We do know lottery propositions

Problems:

i. Inconsistent beliefs: If you know that ticket T1 will not win the lottery,

then it seems plausible, by parity of reasoning, to say the same thing

about ticket T2, ticket T3, etc. But then it seems that you can know of

an arbitrarily large percentage of tickets that they will not win. So you

are inconsistent if you also believe that the lottery is fair.

ii. Practical inconsistency: If you know that the ticket you are about to

purchase is a loser why do you purchase it?

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Denial of Closure Principle

• Counterexample: You're at the zoo, and in the pen in front of you is a striped

horse-like animal. You seem to know that the animal is a zebra. But what

about the possibility that it's a mule painted to look like a zebra? You may

have some reason to believe that it's not a cleverly-disguised mule. But your

evidence isn’t good enough to know that it's not a cleverly-disguised mule. So

you don't know it. However, the latter proposition denying the disguised-mule

hypothesis can be easily known by you to be entailed by the former

proposition asserting that the animal is a zebra. Hence, closure under known

implications fails.

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Closure under known implication: If S knows that p and if S knows

that p implies q, then S knows that q.

The Cost of Closure Denial

• 1. Given that knowledge is the norm of assertion, denial of closure under

known implications sanctions inconsistent assertions.

• Example:

I ask S whether she agrees that p. She asserts that she does. I then ask

S whether she realizes that q follows from p. “Yes,” she says. I then ask

her whether she agrees that q. “I’m not agreeing to that,” she says. I ask

her whether she now wishes to retract her earlier claims. “Oh no,” she

says. “I’m sticking by my claim that p and my claim that p entails q. I’m

just not willing to claim that q.” S is clearly inconsistent.

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• 2. Denying closure under known implications amounts to denying

either of these three principles:

Addition Closure: If S knows p and competently deduces (p or q)

from p, thereby coming to believe (p or q), while retaining

knowledge of p throughout, then S knows (p or q).

Equivalence Principle: If S knows a priori that p is equivalent to q

and knows p, then S is in a position to know q. (see lecture 13.1,

slide #13)

Distribution Principle: If S knows that p and q, S knows p and S

knows q.

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Suppose you know the ordinary proposition:

That is a zebra

Given Addition Closure you can deduce:

That is a zebra or that is a thing that is not a cleverly

disguised mule

And this statement is equivalent to the lottery proposition:

That is not a cleverly disguised mule

So denying closure under known implications implies denying either

addition closure or the equivalence principle.

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Suppose I know the ordinary proposition:

That is a zebra

By equivalence I can know:

That is a zebra and that is not a cleverly disguised mule

By distribution I can know the lottery proposition:

That is not a cleverly disguised mule

• So denying closure under known implications implies denying either

the equivalence principle or the distribution principle.

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Restricting Closure

Proposal:

Problems:

• Ad hoc solution

• Vague definition of lottery propositions

• Logical principles are supposed to hold for all propositions,

regardless of their content

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Restricted closure under known implications: If S knows that p and if S

knows that p implies q, then S knows that q, unless q is a lottery proposition.

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Relevant Alternative Closure

• The crucial question in assessing a knowledge attribution is whether S

would believe that p even if some not-p alternative, q, were in fact the

case.

• But not all of the not-p alternatives are relevant, for otherwise skepticism

would follow. If knowing that p would require the elimination of every

known alternative to p, as suggested by the closure principle, we could

never know anything about the world around us.

• A more plausible view might be that knowledge requires the elimination

of only relevant not-p alternatives and that skeptical alternatives are

normally not relevant. Which not-p alternatives are relevant depends on

the context.

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What is Relevance?

• In the objective reading, the relevance of an alternative has to do

with the objective probability of its realization.

• In the subjective reading, an alternative is relevant if the believer

takes it to be probable. Here relevance depends on the salience the

alternative.

• The subjective reading comes in two flavors. The relevance of an

alternative can be dependent on the conversational context of the

epistemic subject (knower) or on the conversational context of the

person describing the epistemic subject as a knower or a non-

knower (knowledge attributor).

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