From Anti-Scepticism to the Contingent A Priori Brian Weatherson Cornell University

Section 1 A Russellian Argument for the Contingent A Priori

Russell’s Version of the Contingent A Priori Let e be our evidence Let e be our evidence Let p be something we know on the basis of e that isn’t entailed by e Let p be something we know on the basis of e that isn’t entailed by e I’ll call this evidence-transcendent knowledge I’ll call this evidence-transcendent knowledge Russell claims If e then p, or possibly something that entails this, is a priori Russell claims If e then p, or possibly something that entails this, is a priori

Russell’s Assumptions Evidence is propositional Evidence is propositional We acquire evidence-transcendent knowledge by inference We acquire evidence-transcendent knowledge by inference We know exactly what our total evidence is We know exactly what our total evidence is Evidence can’t teach us what evidence teaches us Evidence can’t teach us what evidence teaches us

The Familiar Argument for Scepticism P1. I don’t know I’m not a brain-in-a-vat P1. I don’t know I’m not a brain-in-a-vat P2. If I don’t know I’m not a brain-in-a-vat then I don’t know I have toes. P2. If I don’t know I’m not a brain-in-a-vat then I don’t know I have toes. C.I don’t know I have toes. C.I don’t know I have toes.

Why is P1 Plausible? Nozick’s Answer: Tracking Nozick’s Answer: Tracking Error-Theoretic Variant on Nozick Error-Theoretic Variant on Nozick Contextualist Answer Contextualist Answer Error-Theoretic Variant on Contextualism Error-Theoretic Variant on Contextualism Mixture of the Above Mixture of the Above

The ‘Challenge’ Whenever we claim to know p, we expose ourselves to a challenge Whenever we claim to know p, we expose ourselves to a challenge A Priori or A Posteriori ???? A Priori or A Posteriori ???? It’s hard to claim either in the case of (alleged) knowledge that we’re not BIVs It’s hard to claim either in the case of (alleged) knowledge that we’re not BIVs

A Posteriori Any evidence would be consistent with our being a BIV Any evidence would be consistent with our being a BIV But this argument shouldn’t convince a good fallibilist But this argument shouldn’t convince a good fallibilist Lack of BIV-type evidence is (fallible) evidence that we’re not BIVs Lack of BIV-type evidence is (fallible) evidence that we’re not BIVs But this point doesn’t show we can know that we aren’t BIV*s But this point doesn’t show we can know that we aren’t BIV*s

A Priori Since we could be BIV*s, we can’t know a priori that we aren’t Since we could be BIV*s, we can’t know a priori that we aren’t But this shouldn’t convince fallibilists either But this shouldn’t convince fallibilists either If a posteriori knowledge can go beyond evidence, why can’t a priori knowledge? If a posteriori knowledge can go beyond evidence, why can’t a priori knowledge?

First Argument Against Contingent A Priori P1.You can only know p on the basis of evidence e if it couldn’t have turned out that e is true and p is false. P1.You can only know p on the basis of evidence e if it couldn’t have turned out that e is true and p is false. P2.If you can only know p on the basis of evidence e if it couldn’t have turned out that e is true and p is false, then you can only know p a priori if p couldn’t have turned out to be false. P2.If you can only know p on the basis of evidence e if it couldn’t have turned out that e is true and p is false, then you can only know p a priori if p couldn’t have turned out to be false. C.You can’t know p a priori unless p couldn’t have turned out to be false. C.You can’t know p a priori unless p couldn’t have turned out to be false.

Second Argument Against Contingent A Priori P1.You can only know p if you have a reason to believe that p. P1.You can only know p if you have a reason to believe that p. P2.The only reason to believe that p a priori is that it couldn’t have turned out to be false. P2.The only reason to believe that p a priori is that it couldn’t have turned out to be false. C.You can’t know p a priori unless p couldn’t have turned out to be false. C.You can’t know p a priori unless p couldn’t have turned out to be false.

The BIV* hypothesis I’m not a brain-in-a-vat* = I’m not a brain-in-a-vat with evidence just like this = ~ (My evidence is just like this  I’m a brain-in-a-vat) = My evidence is not just like this  I’m not a brain-in-a-vat = My evidence is just like this → I’m not a brain-in-a-vat

Section 2 Restating Russell’s Argument

Two Different Assumptions Privileged access: We know what our total evidence is. Privileged access: We know what our total evidence is. A Priority: Whenever e justifies p, it is a priori that e justifies p. A Priority: Whenever e justifies p, it is a priori that e justifies p.

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 Restated

Section 3 Weakening the Assumptions

Reminder Of Assumptions Privileged access: We know what our total evidence is. Privileged access: We know what our total evidence is. A Priority: Whenever e justifies p, it is a priori that e justifies p. A Priority: Whenever e justifies p, it is a priori that e justifies p.

Introspective Properties A class of properties (intuitively, a determinable) is introspective iff any beliefs an agent has about which property in the class (which determinate) she instantiates are guaranteed to not be too badly mistaken. A class of properties (intuitively, a determinable) is introspective iff any beliefs an agent has about which property in the class (which determinate) she instantiates are guaranteed to not be too badly mistaken.

Weak Privileged Access What evidence we have, and hence which propositions we could justifiably believe, supervenes on what introspective properties we instantiate. What evidence we have, and hence which propositions we could justifiably believe, supervenes on what introspective properties we instantiate.

Weak A Priori For some Moorean fact q, there is some property F of evidence such that For some Moorean fact q, there is some property F of evidence such that a)it is a priori that anyone whose evidence is F could justifiably believe q; but b)the conditional If I know that I know my evidence is F, then q is deeply contingent

Weak A Priori Weak A Priori says that claims like this are a priori Weak A Priori says that claims like this are a priori J(e  Jp) J(e  Jp) It does not say that claims like this are a priori It does not say that claims like this are a priori J(e  p) J(e  p) So we’re not building contingent a priori directly into Weak A Priori So we’re not building contingent a priori directly into Weak 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 Proof

Section 4 Margins of Error and Privileged Access

First Margin of Error Model Kp is true iff p is true everywhere inside the margin.

First Margin of Error Model If p is true K~p is not true at w m w Hence K~K~p is true

First Margin of Error Model The philosophical point is that if w is within the margin of error is within the margin of error at w. The philosophical point is that if w is within the margin of error is within the margin of error at w. It’s just like a Kripke model with a symmetric accessibility relationship It’s just like a Kripke model with a symmetric accessibility relationship And just like in those models, we have And just like in those models, we have p  □◊pp  □◊pp  □◊pp  □◊p

Second Margin of Error Model m+ Kp is true iff p is true everywhere inside some sphere with radius >m

Second Margin of Error Model m+ Assume is the only world inside the circle. Assume is the only world inside the circle. Assume also is the only world where p is true. Assume also is the only world where p is true. Assume also that there is a world at every point outside the circle. Assume also that there is a world at every point outside the circle.

Second Margin of Error Model m+ Then K~p is true at all points outside the circle. Then K~p is true at all points outside the circle. So K~K~p is not true because there’s no ‘bigger’ circle throughout which it is true. So K~K~p is not true because there’s no ‘bigger’ circle throughout which it is true. So p  □ ◊p is false So p  □ ◊p is false

Second Margin of Error Model m+ In fact every schema like p  □ ◊p is false in this model In fact every schema like p  □ ◊p is false in this model E.g. p  □ ◊◊p is false E.g. p  □ ◊◊p is false But this really relies on the odd features of the model. But this really relies on the odd features of the model. If we put a ‘no islands’ constraint on models then p  □ ◊◊p is always true.

Details of the ‘No Island’ Constraint (You can probably ignore these details) Delia suggested the following: There is a world exactly half-way between any two worlds. Delia suggested the following: There is a world exactly half-way between any two worlds. This is much stronger than we need. This is much stronger than we need. All that’s needed is:  r >1  w 1 w 2 (d(w 1,w 2 ) 1  w 1 w 2 (d(w 1,w 2 )<rm   w 3 d(w 1,w 3 )<m & d(w 2,w 3 )<m)

Why Believe the ‘No Island’ Constraint Possibly because it follows from something much stronger – that the epistemic possibilities are densely packed Possibly because it follows from something much stronger – that the epistemic possibilities are densely packed Possibly because it is really hard, if not impossible to come up with concrete examples Possibly because it is really hard, if not impossible to come up with concrete examples The two points are related: you can’t just stipulate what is and isn’t possible. The two points are related: you can’t just stipulate what is and isn’t possible.

Summing up this section If the margin of error model plus the ‘no islands’ constraint is appropriate for a domain of discourse, then p  □ ◊◊p is true when p is in that domain. If the margin of error model plus the ‘no islands’ constraint is appropriate for a domain of discourse, then p  □ ◊◊p is true when p is in that domain. If weak privileged access is true then the margin of error model is appropriate when talking about evidence. If weak privileged access is true then the margin of error model is appropriate when talking about evidence. And the ‘no islands’ constraint seems right in general. And the ‘no islands’ constraint seems right in general. So p  □ ◊◊p is true when p is about my evidence. So p  □ ◊◊p is true when p is about my evidence.

Section 5 Summing Up

Contingent A Priori Given a privileged access principle, and an a priority of epistemology principle, we can draw a dominance argument for the existence of the contingent a priori. Given a privileged access principle, and an a priority of epistemology principle, we can draw a dominance argument for the existence of the contingent a priori. Russell (tacitly) used implausible versions of these principles. I showed how to rebuild the argument with more plausible premises. Russell (tacitly) used implausible versions of these principles. I showed how to rebuild the argument with more plausible premises.

Connection to Scepticism I claim that these contingent a priori principles are crucial to arguments for scepticism. I claim that these contingent a priori principles are crucial to arguments for scepticism. I think the idea that there’s no contingent a priori is tacitly crucial in many sceptical arguments. I think the idea that there’s no contingent a priori is tacitly crucial in many sceptical arguments. Also there may seem to be a modus tollens looming here if I’m right about what anti- scepticism implies. Also there may seem to be a modus tollens looming here if I’m right about what anti- scepticism implies.

Denying the Assumptions That modus tollens will be blocked if we deny either of my main two assumptions. That modus tollens will be blocked if we deny either of my main two assumptions. But the two denials lead to fairly different positions. But the two denials lead to fairly different positions.

Denying Weak Privileged Access This is what some reliabilists deny This is what some reliabilists deny It clearly blocks the actual argument I offer It clearly blocks the actual argument I offer But it doesn’t obviously block the strategy But it doesn’t obviously block the strategy

Denying Weak A Priori This is what some naturalists deny This is what some naturalists deny This move blocks every argument of the kind I’ve offered This move blocks every argument of the kind I’ve offered It has one very quirky feature It has one very quirky feature Can come to know a disjunction when all of your evidence is that one of its disjuncts is false Can come to know a disjunction when all of your evidence is that one of its disjuncts is false Vulnerable to BonJour style arguments about the best explanation of inductive learning. Vulnerable to BonJour style arguments about the best explanation of inductive learning.