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 p be something we know on the basis
of e that isn’t entailed by e
I’ll call this evidence-transcendent
knowledge
Russell claims If e then p, or possibly
something that entails this, is a priori
Russell’s Assumptions




Evidence is propositional
We acquire evidence-transcendent
knowledge by inference
We know exactly what our total evidence
is
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
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.
Why is P1 Plausible?

Nozick’s Answer: Tracking

Error-Theoretic Variant on Nozick

Contextualist Answer

Error-Theoretic Variant on Contextualism

Mixture of the Above
The ‘Challenge’



Whenever we claim to know p, we expose
ourselves to a challenge
A Priori or A Posteriori ????
It’s hard to claim either in the case of
(alleged) knowledge that we’re not BIVs
A Posteriori

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Any evidence would be consistent with our
being a BIV
But this argument shouldn’t convince a
good fallibilist
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
A Priori



Since we could be BIV*s, we can’t know a
priori that we aren’t
But this shouldn’t convince fallibilists
either
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.
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.
Second Argument Against
Contingent A Priori



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.
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.
A Priority: Whenever e justifies p, it is a
priori that e justifies p.
(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
(Assumption)
justified in believing If my total evidence is
that e then p.
(4) If my total evidence is e, then I am justified in From (2), (3)
believing If my total evidence is that e then p.
(5) If my total evidence is not e, I know my total
(Assumption)
evidence is not e.
(6) If I know my total evidence is not e, I am justified in
(Assumption)
believing it is not e.
(7) If I am justified in believing my evidence is not e, I
(Assumption)
am justified in believing If my total evidence is that e
then p.
(8) If my total evidence is not e, then I am justified in
believing If my total evidence is that e then p.
(9) I am justified in believing If my total evidence is that
e then p.
From (5), (6),
(7)
From (1), (4),
(8)
The Argument Restated
1. e  ~e
2. e  Jp
5. ~e  K~e
3. Jp  J(e  p)
6. K~e  J~e
4. e  J(e  p)
7. J~e  J(e  p)
8. ~e  J(e  p)
9. J(e  p)
Section 3
Weakening the Assumptions
Reminder Of Assumptions


Privileged access: We know what our
total evidence is.
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.
Weak Privileged Access

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
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
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Weak A Priori says that claims like this
are a priori
 J(e  Jp)
It does not say that claims like this are a
priori
 J(e  p)
So we’re not building contingent a priori
directly into Weak A Priori
The Main Proof
1. Fb  ~Fb
2. Fb  Jq
5. ~Fb  K~KKFb
3. Jq  J(KKFb  q)
6. K~KKFb  J~KKFb
4. Fb  J(KKFb  q)
7. J~KKFb  J(KKFb  q)
8. ~Fb  J(KKFb  q)
9. J(KKFb  q)
Section 4
Margins of Error and Privileged
Access
First Margin of Error Model
m
@
Kp is true at @ iff p is true
everywhere inside the margin.
First Margin of Error Model
m
@
If p is true at @, K~p is not true at w
Hence K~K~p is true at @
First Margin of Error Model
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The philosophical point is that if w is
within the margin of error at @, then @ is
within the margin of error at w.
It’s just like a Kripke model with a
symmetric accessibility relationship
And just like in those models, we have
p  □◊p
Second Margin of Error Model
m
@
m+
Kp is true at @ iff p is true everywhere inside
some sphere with radius >m
Second Margin of Error Model

m

@
m+

Assume that @ is the
only world inside the
circle.
Assume also that @ is
the only world where p
is true.
Assume also that there
is a world at every point
outside the circle.
Second Margin of Error Model


m
@
m+

Then K~p is true at all
points outside the circle.
So K~K~p is not true at
@ because there’s no
‘bigger’ circle
throughout which it is
true.
So p 
@
□◊p is false at
Second Margin of Error Model

m
@
m+

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In fact every schema
like p  □◊p is false at
@ in this model
E.g. p 
□◊◊p is false
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
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(You can probably ignore these details)
Delia suggested the following:
There is a world exactly half-way between any
two worlds.
This is much stronger than we need.
All that’s needed is:
r >1 w1w2 (d(w1,w2)<rm 
w3 d(w1,w3)<m & d(w2,w3)<m)
Why Believe the ‘No Island’
Constraint
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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
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 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.
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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.

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 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 antiscepticism implies.
Denying the 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.
Denying Weak Privileged Access

This is what some reliabilists deny

It clearly blocks the actual argument I offer

But it doesn’t obviously block the strategy
Denying Weak A Priori

This is what some naturalists deny

This move blocks every argument of the kind
I’ve offered

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

Vulnerable to BonJour style arguments about the
best explanation of inductive learning.