From Anti-Scepticism to From Anti-Scepticism to the Contingent A Priorithe Contingent A Priori

Brian WeathersonBrian Weatherson

Cornell UniversityCornell University

Section 1Section 1

A Russellian Argument for A Russellian Argument for the Contingent A Priorithe Contingent A Priori

Russell’s Version of the Russell’s Version of the Contingent A PrioriContingent A Priori

Let Let ee be our evidence be our evidence Let Let pp be something we know on the be something we know on the

basis of basis of ee that isn’t entailed by that isn’t entailed by ee I’ll call this evidence-transcendent I’ll call this evidence-transcendent

knowledgeknowledge Russell claims Russell claims If e then pIf e then p, or possibly , or possibly

something that entails this, is a priorisomething that entails this, is a priori

Russell’s AssumptionsRussell’s Assumptions

Evidence is propositionalEvidence is propositional We acquire evidence-transcendent We acquire evidence-transcendent

knowledge by inferenceknowledge by inference We know exactly what our total We know exactly what our total

evidence isevidence is Evidence can’t teach us what Evidence can’t teach us what

evidence teaches usevidence teaches us

The Familiar Argument for The Familiar Argument for ScepticismScepticism

P1.P1. I don’t know I’m not a brain-in- I don’t know I’m not a brain-in-a-vata-vat

P2.P2. If I don’t know I’m not a brain- If I don’t know I’m not a brain-in-a-vat then I don’t know I have in-a-vat then I don’t know I have toes.toes.

C.C. I don’t know I have toes.I don’t know I have toes.

Why is P1 Plausible?Why is P1 Plausible?

Nozick’s Answer: TrackingNozick’s Answer: Tracking

Error-Theoretic Variant on NozickError-Theoretic Variant on Nozick

Contextualist AnswerContextualist Answer

Error-Theoretic Variant on Error-Theoretic Variant on ContextualismContextualism

Mixture of the AboveMixture of the Above

The ‘Challenge’The ‘Challenge’

Whenever we claim to know Whenever we claim to know pp, we , we expose ourselves to a challengeexpose ourselves to a challenge

A PrioriA Priori or or A Posteriori A Posteriori ???????? It’s hard to claim either in the case of It’s hard to claim either in the case of

(alleged) knowledge that we’re not (alleged) knowledge that we’re not BIVsBIVs

A PosterioriA Posteriori

Any evidence would be consistent Any evidence would be consistent with our being a BIVwith our being a BIV

But this argument shouldn’t convince But this argument shouldn’t convince a good fallibilista good fallibilist

Lack of BIV-type evidence Lack of BIV-type evidence isis (fallible) (fallible) evidence that we’re not BIVsevidence that we’re not BIVs

But this point doesn’t show we can But this point doesn’t show we can know that we aren’t BIV*sknow that we aren’t BIV*s

A PrioriA Priori

Since we could be BIV*s, we can’t Since we could be BIV*s, we can’t know a priori that we aren’tknow a priori that we aren’t

But this shouldn’t convince fallibilists But this shouldn’t convince fallibilists eithereither

If a posteriori knowledge can go If a posteriori knowledge can go beyond evidence, why can’t a priori beyond evidence, why can’t a priori knowledge?knowledge?

First Argument Against First Argument Against Contingent A PrioriContingent A Priori

P1.P1. You can only know You can only know pp on the basis of on the basis of evidence evidence ee if it couldn’t have turned out that if it couldn’t have turned out that ee is true and is true and pp is false. is false.

P2.P2. If you can only know If you can only know pp on the basis of on the basis of evidence evidence ee if it couldn’t have turned out that if it couldn’t have turned out that ee is true and is true and pp is false, then you can only know is false, then you can only know pp a priori if a priori if pp couldn’t have turned out to be couldn’t have turned out to be false.false.

C.C. You can’t know You can’t know pp a priori unless a priori unless pp couldn’t have turned out to be false.couldn’t have turned out to be false.

Second Argument Against Second Argument Against Contingent A PrioriContingent A Priori

P1.P1. You can only know You can only know pp if you have if you have a reason to believe that a reason to believe that pp..

P2.P2. The only reason to believe that The only reason to believe that pp a priori is that it couldn’t have turned a priori is that it couldn’t have turned out to be false.out to be false.

C.C. You can’t know You can’t know pp a priori unless a priori unless pp couldn’t have turned out to be couldn’t have turned out to be false.false.

The BIV* hypothesisThe BIV* hypothesis

I’m not a brain-in-a-vat* =I’m not a brain-in-a-vat* =

I’m not a brain-in-a-vat with evidence just like I’m not a brain-in-a-vat with evidence just like thisthis = =

~ (My evidence is just like ~ (My evidence is just like thisthis I’m a brain-in-a-vat) I’m a brain-in-a-vat) = =

My evidence is not just like My evidence is not just like thisthis I’m not a brain-in-a- I’m not a brain-in-a-vat =vat =

My evidence is just like My evidence is just like thisthis → I’m not a brain-in-a-vat → I’m not a brain-in-a-vat

Section 2Section 2

Restating Russell’s ArgumentRestating Russell’s Argument

Two Different AssumptionsTwo Different Assumptions

Privileged accessPrivileged access: We know what : We know what our total evidence is.our total evidence is.

A PriorityA Priority: Whenever : Whenever ee justifies justifies pp, it , it is a priori that is a priori that ee justifies justifies pp..

(1) Either my total evidence will be e or it will not. (Assumption)

(2) If it is e, then I am justified in believing that p. (Assumption)

(3) If I am justified in believing that p, then I am

justified in believing If my total evidence is

that e then p.

(Assumption)

(4) If my total evidence is e, then I am justified in

believing If my total evidence is that e then p.

From (2), (3)

(5) If my total evidence is not e, I know my total

evidence is not e.

(Assumption)

(6) If I know my total evidence is not e, I am justified in

believing it is not e.

(Assumption)

(7) If I am justified in believing my evidence is not e, I

am justified in believing If my total evidence is that e

then p.

(Assumption)

(8) If my total evidence is not e, then I am justified in

believing If my total evidence is that e then p.

From (5), (6),

(7)

(9) I am justified in believing If my total evidence is that

e then p.

From (1), (4),

(8)

1. e ~e

2. e Jp

3. Jp J(e p)

4. e J(e p)

5. ~e K~e

6. K~e J~e

7. J~e J(e p)

8. ~e J(e p)

9. J(e p)

The Argument RestatedThe Argument Restated

Section 3Section 3

Weakening the AssumptionsWeakening the Assumptions

Reminder Of AssumptionsReminder Of Assumptions

Privileged accessPrivileged access: We know what : We know what our total evidence is.our total evidence is.

A PriorityA Priority: Whenever : Whenever ee justifies justifies pp, it , it is a priori that is a priori that ee justifies justifies pp..

Introspective PropertiesIntrospective Properties

A class of properties (intuitively, a A class of properties (intuitively, a

determinable) is determinable) is introspectiveintrospective iff any iff any

beliefs an agent has about which beliefs an agent has about which

property in the class (which property in the class (which

determinate) she instantiates are determinate) she instantiates are

guaranteed to not be too badly guaranteed to not be too badly

mistaken.mistaken.

Weak Privileged AccessWeak Privileged Access

What evidence we have, and hence What evidence we have, and hence

which propositions we could justifiably which propositions we could justifiably

believe, supervenes on what believe, supervenes on what

introspective properties we instantiate.introspective properties we instantiate.

Weak A PrioriWeak A Priori

For some Moorean fact For some Moorean fact qq, there is some , there is some property property FF of evidence such that of evidence such that

a)a) it is a priori that anyone whose it is a priori that anyone whose evidence is evidence is FF could justifiably believe could justifiably believe qq; ; butbut

b)b) the conditional the conditional If I know that I know my If I know that I know my evidence is F, then qevidence is F, then q is deeply is deeply contingentcontingent

Weak A PrioriWeak A Priori

Weak A PrioriWeak A Priori says that claims like says that claims like this are a priorithis are a priori

J(e J(e Jp) Jp) It does not say that claims like this It does not say that claims like this

are a prioriare a priori J(e J(e p) p)

So we’re not building contingent a So we’re not building contingent a priori directly into priori directly into Weak A PrioriWeak A Priori

1. Fb ~Fb

2. Fb Jq

3. Jq J(KKFb q)

4. Fb J(KKFb q)

5. ~Fb K~KKFb

6. K~KKFb J~KKFb

7. J~KKFb J(KKFb q)

8. ~Fb J(KKFb q)9. J(KKFb q)

The Main ProofThe Main Proof

Section 4Section 4

Margins of Error and Margins of Error and Privileged AccessPrivileged Access

m@

First Margin of Error ModelFirst Margin of Error Model

Kp is true at @ iff p is true everywhere inside the margin.

m@

First Margin of Error ModelFirst Margin of Error Model

If p is true at @, K~p is not true at w

mw

Hence K~K~p is true at @

First Margin of Error ModelFirst Margin of Error Model

The philosophical point is that if The philosophical point is that if ww is is within the margin of error at @, then within the margin of error at @, then @ is within the margin of error at @ is within the margin of error at ww..

It’s just like a Kripke model with a It’s just like a Kripke model with a symmetric accessibility relationshipsymmetric accessibility relationship

And just like in those models, we haveAnd just like in those models, we have

pp □□◊◊pp

Second Margin of Error Second Margin of Error ModelModel

m@

m+

Kp is true at @ iff p is true everywhere inside some sphere with radius >m

Second Margin of Error Second Margin of Error ModelModel

m@

m+

Assume that @ is the Assume that @ is the onlyonly world inside the world inside the circle.circle.

Assume also that @ is Assume also that @ is the the onlyonly world where world where pp is true.is true.

Assume also that there Assume also that there is a world at is a world at everyevery point outside the point outside the circle.circle.

Second Margin of Error Second Margin of Error ModelModel

m@

m+

Then K~Then K~pp is true at all is true at all points outside the points outside the circle. circle.

So K~K~So K~K~pp is not true at is not true at @ because there’s no @ because there’s no ‘bigger’ circle ‘bigger’ circle throughout which it is throughout which it is true.true.

So So pp □□◊◊pp is false at is false at @@

Second Margin of Error Second Margin of Error ModelModel

m@

m+

In fact every schema In fact every schema

like like pp □□◊◊pp is false is false at @ in this modelat @ in this model

E.g. E.g. pp □□◊◊◊◊pp is false is false

But this really relies But this really relies on the odd features on the odd features of the model.of the model.

If we put a ‘no islands’ constraint on If we put a ‘no islands’ constraint on models thenmodels then

pp □□◊◊◊◊pp is always true. is always true.

Details of the ‘No Island’ Details of the ‘No Island’ ConstraintConstraint

(You can probably ignore these details)(You can probably ignore these details) Delia suggested the following:Delia suggested the following:

There is a world exactly half-way between There is a world exactly half-way between any two worlds.any two worlds.

This is much stronger than we need.This is much stronger than we need. All that’s needed is:All that’s needed is:

r r >1 >1 ww11ww2 2 (d((d(ww11,,ww22)<)<rmrm ww33 d( d(ww11,,ww33)<)<m m && d(d(ww22,,ww33)<)<mm))

Why Believe the ‘No Island’ Why Believe the ‘No Island’ ConstraintConstraint

Possibly because it follows from Possibly because it follows from something much stronger – that the something much stronger – that the epistemic possibilities are densely epistemic possibilities are densely packedpacked

Possibly because it is really hard, if not Possibly because it is really hard, if not impossible to come up with concrete impossible to come up with concrete examplesexamples

The two points are related: you can’t The two points are related: you can’t just stipulate what is and isn’t possible.just stipulate what is and isn’t possible.

Summing up this sectionSumming up this section

If the margin of error model plus the ‘no islands’ If the margin of error model plus the ‘no islands’

constraint is appropriate for a domain of discourse, constraint is appropriate for a domain of discourse,

then then pp □□◊◊◊◊pp is true when is true when pp is in that domain. is in that domain.

If If weak privileged accessweak privileged access is true then the margin of is true then the margin of

error model is appropriate when talking about error model is appropriate when talking about

evidence.evidence.

And the ‘no islands’ constraint seems right in general.And the ‘no islands’ constraint seems right in general.

So So pp □□◊◊◊◊pp is true when is true when pp is about my evidence. is about my evidence.

Section 5Section 5

Summing UpSumming Up

Contingent A PrioriContingent A Priori

Given a privileged access principle, and an a Given a privileged access principle, and an a

priority of epistemology principle, we can priority of epistemology principle, we can

draw a dominance argument for the draw a dominance argument for the

existence of the contingent a priori.existence of the contingent a priori.

Russell (tacitly) used implausible versions of Russell (tacitly) used implausible versions of

these principles. I showed how to rebuild the these principles. I showed how to rebuild the

argument with more plausible premises.argument with more plausible premises.

Connection to ScepticismConnection to Scepticism

I claim that these contingent a priori I claim that these contingent a priori

principles are crucial to arguments for principles are crucial to arguments for

scepticism.scepticism.

I think the idea that there’s no contingent a I think the idea that there’s no contingent a

priori is tacitly crucial in many sceptical priori is tacitly crucial in many sceptical

arguments.arguments.

Also there may seem to be a modus tollens Also there may seem to be a modus tollens

looming here if I’m right about what anti-looming here if I’m right about what anti-

scepticism implies.scepticism implies.

Denying the AssumptionsDenying the Assumptions

That modus tollens will be blocked if we That modus tollens will be blocked if we

deny either of my main two assumptions.deny either of my main two assumptions.

But the two denials lead to fairly different But the two denials lead to fairly different

positions.positions.

Denying Weak Privileged Denying Weak Privileged AccessAccess

This is what some reliabilists denyThis is what some reliabilists deny

It clearly blocks the actual argument I offerIt clearly blocks the actual argument I offer

But it doesn’t But it doesn’t obviouslyobviously block the strategy block the strategy

Denying Weak A PrioriDenying Weak A Priori

This is what some naturalists denyThis is what some naturalists deny

This move blocks This move blocks everyevery argument of the kind argument of the kind

I’ve offeredI’ve offered

It has one very quirky featureIt has one very quirky feature

Can come to know a disjunction when all of Can come to know a disjunction when all of

your evidence is that one of its disjuncts is your evidence is that one of its disjuncts is

falsefalse

Vulnerable to BonJour style arguments about Vulnerable to BonJour style arguments about

the best explanation of inductive learning. the best explanation of inductive learning.