In Defence of a Dogmatist Brian Weatherson May 2006

InIn Defence of a Defence of a DogmatistDogmatistBrian WeathersonBrian Weatherson

May 2006May 2006

What is Dogmatism?What is Dogmatism?

We’ll be primarily concerned here with We’ll be primarily concerned here with dogmatism about dogmatism about knowledgeknowledge, though , though we’ll also discuss dogmatism about we’ll also discuss dogmatism about justificationjustification

For some propositions For some propositions pp and evidence and evidence EE, , you can know you can know pp on the basis of on the basis of EE without without having independent or antecedent having independent or antecedent justification for justification for EE pp


I’m using evidence here in a very broad I’m using evidence here in a very broad sense, so it includes anything that justifies sense, so it includes anything that justifies beliefs, whether or not we are aware of it, beliefs, whether or not we are aware of it, or able to appeal to it in conscious or able to appeal to it in conscious reasoningreasoning

We’ll often be interested in more We’ll often be interested in more restricted, hence restricted, hence strongerstronger, dogmatist , dogmatist claims that say this is true for some claims that say this is true for some pp, , EE in a particular area (perception, induction)in a particular area (perception, induction)


I’m not going to say much about I’m not going to say much about independent or antecedent justificationindependent or antecedent justification

But I will insist that when But I will insist that when EE is all of our is all of our empirical evidence, a belief in empirical evidence, a belief in qq is is justified independently or antecdently of justified independently or antecdently of EE iff iff qq is justified, and knowable, a priori is justified, and knowable, a priori

So the dogmatist has an expansionary So the dogmatist has an expansionary view of actual justification, and a view of actual justification, and a restrictive view of a priori justificationrestrictive view of a priori justification

The Sceptical ArgumentThe Sceptical Argument

1.1. If I know I have hands, then I’m in a If I know I have hands, then I’m in a position to know that I’m not a handless position to know that I’m not a handless brain in a perfectly functioning vat brain in a perfectly functioning vat (BIPV)(BIPV)

2.2. I’m not in a position to know that I’m not I’m not in a position to know that I’m not a handless BIPVa handless BIPV

3.3. So I don’t know I have handsSo I don’t know I have hands


Not the strongest sceptical argumentNot the strongest sceptical argument Premise Two seems just wrong to mePremise Two seems just wrong to me I can deduce that it is wrong from the fact I can deduce that it is wrong from the fact

that I know lots of stuff that is that I know lots of stuff that is incompatible with my being a BIPVincompatible with my being a BIPV

A stronger sceptical challenge: is this A stronger sceptical challenge: is this knowledge a priori or a posteriori?knowledge a priori or a posteriori?


1.1. If I know I have hands, then I’m in a If I know I have hands, then I’m in a position to know that I’m not a BIPVposition to know that I’m not a BIPV

2.2. I’m not in a position to know a priori that I’m not in a position to know a priori that I’m not a handless BIPVI’m not a handless BIPV

3.3. I’m not in a position to know a posteriori I’m not in a position to know a posteriori that I’m not a handless BIPVthat I’m not a handless BIPV

4.4. So I don’t know I have handsSo I don’t know I have hands


I’m assuming here that any knowledge I’m assuming here that any knowledge which is not a priori is a posterioriwhich is not a priori is a posteriori

Both these technical terms are vague, Both these technical terms are vague, but I insist this is a penumbral connection but I insist this is a penumbral connection between thembetween them

So this argument is valid, and it is far So this argument is valid, and it is far from obvious which premise is wrongfrom obvious which premise is wrong

The sceptic has an argument for 2 and 3The sceptic has an argument for 2 and 3


To introduce it, we need one more To introduce it, we need one more technical termtechnical term

Say a HBIPVE is a handless brain in a Say a HBIPVE is a handless brain in a perfectly functioning vat with the perfectly functioning vat with the evidence I actually haveevidence I actually have

This seems to be the character that is This seems to be the character that is meant to worry me in normal sceptical meant to worry me in normal sceptical arguments: how do I know I’m not him?arguments: how do I know I’m not him?

1.1. If I know I have hands, then I can know that I’m If I know I have hands, then I can know that I’m not a HBIPVE, and if I can know (a priori) that not a HBIPVE, and if I can know (a priori) that I have E I have E I’m not a HBIPVE, I can know (a priori) I’m not a HBIPVE, I can know (a priori) that I’m not a HBIPVEthat I’m not a HBIPVE

2.2. It could have turned out that I’m a HBIPVIt could have turned out that I’m a HBIPV

3.3. If it could have turned out that I’m a HBIPV, then it If it could have turned out that I’m a HBIPV, then it could have turned out that I’m a HBIPVEcould have turned out that I’m a HBIPVE

4.4. If it could have turned out that I’m a HBIPVE, then If it could have turned out that I’m a HBIPVE, then I can’t know a priori that I’m not a HBIPVEI can’t know a priori that I’m not a HBIPVE

5.5. If I can know a posteriori on the basis of my If I can know a posteriori on the basis of my evidence E that I’m not a HBIPVE, then I can evidence E that I’m not a HBIPVE, then I can know a priori that I have E know a priori that I have E I’m not a HBIPVE I’m not a HBIPVE

6.6. So I can’t know that I have handsSo I can’t know that I have hands


I think this is a fairly interesting argument I think this is a fairly interesting argument because epistemologists divide up so because epistemologists divide up so widely on what is wrong with itwidely on what is wrong with it

As we’ll see, versions of this argument to As we’ll see, versions of this argument to alternative sceptical conclusions are alternative sceptical conclusions are even more dramatic in this respecteven more dramatic in this respect

We could divide the premises even We could divide the premises even further, but we won’t further, but we won’t todaytoday

Premise One: ClosurePremise One: Closure

Our argument needs a conjunctive Our argument needs a conjunctive closure premise, but anyone who accepts closure premise, but anyone who accepts the original closure premise should like the original closure premise should like thisthis

I don’t have anything to add to the I don’t have anything to add to the debates over closure, so I’ll just note this debates over closure, so I’ll just note this argumentargument

Premise Two: PossibilityPremise Two: Possibility

This is denied by the so-called ‘semantic’ This is denied by the so-called ‘semantic’ response to scepticismresponse to scepticism

It has some plausibility in the case of It has some plausibility in the case of external world scepticismexternal world scepticism

As we’ll see, however, it doesn’t seem to As we’ll see, however, it doesn’t seem to generalise to other sceptical argumentsgeneralise to other sceptical arguments

Premise Three: EvidencePremise Three: Evidence

This is denied by externalists about This is denied by externalists about perceptionsperceptions

I can see that I have hands, so I have I can see that I have hands, so I have different evidence to a HBIPVEdifferent evidence to a HBIPVE

Williamson denies this premise in Williamson denies this premise in allall sceptical argumentssceptical arguments

This denial seems too strongThis denial seems too strong

Premise Four: EmpiricismPremise Four: Empiricism

In earlier work, I said that a In earlier work, I said that a rationalistrationalist response to scepticism is one that says response to scepticism is one that says we can know a priori something that we can know a priori something that could have turned out to be falsecould have turned out to be false

This is not the same as saying that we This is not the same as saying that we can know a priori some contingent thingscan know a priori some contingent things

Some necessary truths could have Some necessary truths could have turned out to be false, e.g. water is turned out to be false, e.g. water is molecularmolecular

Premise Four: EmpiricismPremise Four: Empiricism

More importantly, some contingent truths More importantly, some contingent truths could not have turned out to be falsecould not have turned out to be false

For example, that water is wateryFor example, that water is watery Things that could not have turned out Things that could not have turned out

false are ‘deeply necessary’ to use false are ‘deeply necessary’ to use Evans’s termEvans’s term

I borrow the phrasing ‘could have turned I borrow the phrasing ‘could have turned out’ from Stephen Yabloout’ from Stephen Yablo

By inclination, I’m a rationalistBy inclination, I’m a rationalist

On to DogmatismOn to Dogmatism

What is interesting about the dogmatist What is interesting about the dogmatist position, as I see it, is that the dogmatist position, as I see it, is that the dogmatist says that premise five is the false onesays that premise five is the false one

The dogmatist thinks that the sceptical The dogmatist thinks that the sceptical possibilities are possiblepossibilities are possible

And she thinks that sometimes And she thinks that sometimes knowledge outruns evidenceknowledge outruns evidence

And, most importantly, she’s empiricistAnd, most importantly, she’s empiricist


The primary argument for dogmatism, as The primary argument for dogmatism, as I see it, is that for some sceptical I see it, is that for some sceptical arguments, the other premises are truearguments, the other premises are true

But the sceptical conclusion is crazyBut the sceptical conclusion is crazy Hence dogmatism!Hence dogmatism! This requires rejecting a priori knowledge This requires rejecting a priori knowledge

(and justification) of things that could (and justification) of things that could have turned out falsehave turned out false


There is a long tradition, especially in There is a long tradition, especially in Anglophone philosophy, of being very Anglophone philosophy, of being very sceptical of the a priorisceptical of the a priori

That would include being sceptical of That would include being sceptical of claims to know we’re not HBIPVE a prioriclaims to know we’re not HBIPVE a priori

I think any good I think any good argumentargument against against dogmatism should respect this attitudedogmatism should respect this attitude

Personally, I reject dogmatism because I Personally, I reject dogmatism because I simply lack the attitudesimply lack the attitude


If we are to argue for dogmatism this If we are to argue for dogmatism this way, we need a sceptical argument way, we need a sceptical argument whose other premises are plausiblewhose other premises are plausible

External world scepticism doesn’t helpExternal world scepticism doesn’t help The premise about The premise about evidenceevidence is rather is rather

implausible I thinkimplausible I think The inductive sceptic argument is betterThe inductive sceptic argument is better Roger White is, I think, first to explicitly Roger White is, I think, first to explicitly

discuss dogmatism about inductiondiscuss dogmatism about induction

Inductive ScepticismInductive Scepticism

pp is some proposition that I can know is some proposition that I can know inductively, e.g. that it will be hotter in inductively, e.g. that it will be hotter in Austin than Anchorage next yearAustin than Anchorage next year

E is my evidence, and E* is the E is my evidence, and E* is the proposition that my evidence is Eproposition that my evidence is E

hhTT is the history of the world to date is the history of the world to date

So ~So ~pp & & hhTT & E* is a sceptical possibility, & E* is a sceptical possibility,

where the history of the world and my where the history of the world and my evidence is the same, but evidence is the same, but pp is false is false

1.1. If I know If I know pp, then I can know ~(~, then I can know ~(~pp & & hhTT & E*), and if & E*), and if

I can know a priori that E* I can know a priori that E* ~(~ ~(~pp & & hhTT & E*), then & E*), then

I can know a priori that ~(~I can know a priori that ~(~pp & & hhTT & E*). & E*).

2.2. It could have turned out that ~It could have turned out that ~pp & & hhTT

3.3. If it could have turned out that ~If it could have turned out that ~pp & & hhTT, then it , then it

could have turned out that ~could have turned out that ~pp & & hhTT & E* & E*

4.4. If it could have turned out that ~If it could have turned out that ~pp & & hhTT & E*, then I & E*, then I

can’t know a priori that ~(~can’t know a priori that ~(~pp & & hhTT & E*) & E*)

5.5. If I can know a posteriori on the basis of my If I can know a posteriori on the basis of my evidence E that ~(~evidence E that ~(~pp & & hhTT & E*), then I can know a & E*), then I can know a

priori that E* priori that E* ~(~ ~(~pp & & hhTT & E*) & E*)

6.6. So I can’t know that So I can’t know that pp


The first two premises seem very The first two premises seem very plausible to me, but I don’t have anything plausible to me, but I don’t have anything new to say about themnew to say about them

What makes the inductive sceptic What makes the inductive sceptic interesting is that premise 3 is plausibleinteresting is that premise 3 is plausible

Williamson denies it because of E=KWilliamson denies it because of E=K But it follows from the (very plausible) But it follows from the (very plausible)

principle that evidence supervenes on principle that evidence supervenes on causal history, so I’ll accept itcausal history, so I’ll accept it


So three premises look goodSo three premises look good But the conclusion is untenableBut the conclusion is untenable So it’s down to rationalism or dogmatismSo it’s down to rationalism or dogmatism That’s an interesting conclusion already!That’s an interesting conclusion already! If I had to pick, I’d pick rationalismIf I had to pick, I’d pick rationalism But I don’t think the existing But I don’t think the existing argumentsarguments

against dogmatism are that goodagainst dogmatism are that good

DogmatismDogmatism

I’m going to discuss three argumentsI’m going to discuss three arguments Some of these are primarily arguments Some of these are primarily arguments

against dogmatism about justificationagainst dogmatism about justification But they also seem to tell against But they also seem to tell against

dogmatism about knowledgedogmatism about knowledge One, the bootstrapping argument, is One, the bootstrapping argument, is

primarily an argument against perceptual primarily an argument against perceptual dogmatismdogmatism

DominanceDominance

Roger White discusses the following kind Roger White discusses the following kind of objection (slightly modified)of objection (slightly modified)

The dogmatist says I can’t know, or even The dogmatist says I can’t know, or even justifiably believe, a priori thatjustifiably believe, a priori that~(~~(~pp & & hhTT & E*) & E*)

But a priori I can run a dominance But a priori I can run a dominance argument that has as its conclusionargument that has as its conclusion ~(~ ~(~pp & & hhTT & E*) & E*)

DominanceDominance

Either I will get evidence E or I won’tEither I will get evidence E or I won’t If I do, then I’ll be justified in believing If I do, then I’ll be justified in believing pp I’ll then be able to infer ~(~I’ll then be able to infer ~(~pp & & hhTT & E*) & E*)

If I don’t, then I won’t even have E so I’ll be If I don’t, then I won’t even have E so I’ll be able to infer ~(~able to infer ~(~pp & & hhTT & E*) & E*)

So I can know a priori that either way I’ll So I can know a priori that either way I’ll be justified in believing ~(~be justified in believing ~(~pp & & hhTT & E*) & E*)

So I’m justified a priori in believing thisSo I’m justified a priori in believing this

DominanceDominance

The problem with this argument is that it The problem with this argument is that it slides between facts about evidence I slides between facts about evidence I have, and facts about what I’m justified in have, and facts about what I’m justified in believing about my evidencebelieving about my evidence

It is possible that I’ll not have evidence E, It is possible that I’ll not have evidence E, but not be justified in believing that I don’t but not be justified in believing that I don’t have evidence E, let alone knowing thishave evidence E, let alone knowing this

So the second half of the disjunctive So the second half of the disjunctive argument seems to failargument seems to fail

BootstrappingBootstrapping

This is primarily an argument against a This is primarily an argument against a certain kind of perceptual dogmatismcertain kind of perceptual dogmatism

In Pryor’s version, the dogmatist In Pryor’s version, the dogmatist endorses the following principleendorses the following principle

If it appears to the agent that If it appears to the agent that pp, then in , then in the absence of defeaters, she is justified the absence of defeaters, she is justified in believing that in believing that pp, even if she isn’t , even if she isn’t justified in advance in believing that justified in advance in believing that appearances are reliableappearances are reliable


This seems to run into a version of This seems to run into a version of Stewart Cohen’s easy knowledge Stewart Cohen’s easy knowledge argumentargument

Cohen is primarily concerned with Cohen is primarily concerned with attacking reliabilismattacking reliabilism

But the objection, if sound, seems to tell But the objection, if sound, seems to tell against the dogmatist as wellagainst the dogmatist as well

Imagine my 7 year old son asking me if my Imagine my 7 year old son asking me if my color-vision is reliable. I say, “Let’s check it color-vision is reliable. I say, “Let’s check it out.” I set up a slide show in which the screen out.” I set up a slide show in which the screen will change colors every few seconds. I will change colors every few seconds. I observe, “That screen is red and I believe that observe, “That screen is red and I believe that it is red. Got it right that time. Now it’s blue it is red. Got it right that time. Now it’s blue and, and, look at thatlook at that, I believe it’s blue. Two for two , I believe it’s blue. Two for two …” I trust that no one thinks that whereas I …” I trust that no one thinks that whereas I previously did not have any evidence for the previously did not have any evidence for the reliability of my color vision, I am now actually reliability of my color vision, I am now actually acquiring evidence for the reliability of my color acquiring evidence for the reliability of my color vision. But if Reliabilism were true, that’s vision. But if Reliabilism were true, that’s exactly what my situation would be.exactly what my situation would be.


The argument is directly targeted at the The argument is directly targeted at the dogmatist about perceptiondogmatist about perception

But we can imagine a similar argument But we can imagine a similar argument against the inductive dogmatistagainst the inductive dogmatist

I sit down and make a number of I sit down and make a number of inductive inferencesinductive inferences

I then conclude, from the truth of those I then conclude, from the truth of those conclusions, that I’m a reliable inductorconclusions, that I’m a reliable inductor


This reasoning is badThis reasoning is bad Some say dogmatists must endorse itSome say dogmatists must endorse it But in fact there are a number of reasons But in fact there are a number of reasons

to reject it even given dogmatismto reject it even given dogmatism Worries about projectionWorries about projection Worries about randomness of sampleWorries about randomness of sample Worries about ‘radiance’Worries about ‘radiance’ Radiance and randomnessRadiance and randomness

ProjectionProjection

The bad inference has the form, all Fs so The bad inference has the form, all Fs so far have been Gs, so generally Fs are Gsfar have been Gs, so generally Fs are Gs

But perhaps being an F isn’t a natural But perhaps being an F isn’t a natural kindkind

I shouldn’t, for instance, conclude from I shouldn’t, for instance, conclude from the reliability of my visual perception that I the reliability of my visual perception that I have an accurate sense of smellhave an accurate sense of smell

So the argument only works if I’m So the argument only works if I’m concluding that a single method is reliableconcluding that a single method is reliable

ProjectionProjection

Arguably, I need to know that I’m Arguably, I need to know that I’m evaluating a single methodevaluating a single method

If for all I know, I use many perceptual, If for all I know, I use many perceptual, even visual perceptual, and inductive even visual perceptual, and inductive methods, this is a bad inferencemethods, this is a bad inference

Since I can’t tell from the armchair what is Since I can’t tell from the armchair what is a single method, I can’t learn about my a single method, I can’t learn about my own reliability from the armchairown reliability from the armchair

RandomnessRandomness

The dogmatist only says that we can The dogmatist only says that we can conclude that things are as they appear conclude that things are as they appear in cases where there aren’t defeatersin cases where there aren’t defeaters

That suggests that the cases where we That suggests that the cases where we can infer from appearances to reality can infer from appearances to reality won’t be a random sample of all caseswon’t be a random sample of all cases

But we need a random sample to do the But we need a random sample to do the enumerative inductive inference being enumerative inductive inference being consideredconsidered

RadianceRadiance

Those two responses are far from tellingThose two responses are far from telling I think the big worry with the argument is I think the big worry with the argument is

that it makes a that it makes a radianceradiance assumption assumption The idea of radiance is based on The idea of radiance is based on

Williamson’s discussion of luminosityWilliamson’s discussion of luminosity A property is luminous iff whenever it is A property is luminous iff whenever it is

instantiated, we are in a position to know instantiated, we are in a position to know that it is instantiatedthat it is instantiated

RadianceRadiance

A property is A property is radiantradiant iff whenever it is iff whenever it is instantiated, we can justifiably believe instantiated, we can justifiably believe that it is instantiatedthat it is instantiated

Williamson argues against luminosityWilliamson argues against luminosity His arguments don’t carry over to His arguments don’t carry over to

arguments against radiancearguments against radiance That’s because the arguments centrally That’s because the arguments centrally

appeal to the factivity of knowledgeappeal to the factivity of knowledge

RadianceRadiance

Still, there is good reason to doubt in Still, there is good reason to doubt in many cases that properties are radiantmany cases that properties are radiant

In particular, it is possible that we could In particular, it is possible that we could have evidence, or appearances, or have evidence, or appearances, or beliefs, without so much as being justified beliefs, without so much as being justified in believing we have themin believing we have them

Perhaps ideally our evidence, beliefs or Perhaps ideally our evidence, beliefs or appearances would be radiant, but we appearances would be radiant, but we can’t assume things are idealcan’t assume things are ideal

RadianceRadiance

If appearances aren’t radiant, then If appearances aren’t radiant, then Cohen’s version of the argument failsCohen’s version of the argument fails

When I get a red appearance, I’m justified When I get a red appearance, I’m justified in believing I’m looking at something redin believing I’m looking at something red

But it doesn’t follow that I’m justified in But it doesn’t follow that I’m justified in believing things are as they appearbelieving things are as they appear

Because I might not be justified in Because I might not be justified in believing that the thing believing that the thing appearsappears red red

Radiance & RandomnessRadiance & Randomness

It might be objected that usually It might be objected that usually appearances and beliefs are radiantappearances and beliefs are radiant

But unless they are But unless they are alwaysalways radiant, we radiant, we won’t know the cases we know about won’t know the cases we know about form a random sampleform a random sample

Further, unless the property of not being Further, unless the property of not being appeared to redly is radiant, for all we appeared to redly is radiant, for all we know there may be many cases where know there may be many cases where we have an inaccurate appearance of redwe have an inaccurate appearance of red

Radiance & RandomnessRadiance & Randomness

We also get randomness problems if we We also get randomness problems if we aren’t always aware of our appearancesaren’t always aware of our appearances

If sometimes I have a red appearance, If sometimes I have a red appearance, but don’t believe I have one, then it might but don’t believe I have one, then it might be that the cases where I believe I have a be that the cases where I believe I have a red appearance are a non-random part of red appearance are a non-random part of the samplethe sample

So the argument needs a self-awareness So the argument needs a self-awareness assumptionassumption

Radiance & Radiance & BootstrappingBootstrapping

But the big problem isn’t that the few But the big problem isn’t that the few actual failures of radiance threaten the actual failures of radiance threaten the randomness of the samplerandomness of the sample

Rather, it is that the assumptions needed Rather, it is that the assumptions needed to get the anti-dogmatist argument going to get the anti-dogmatist argument going are inconsistentare inconsistent

These are that appearances are radiant, These are that appearances are radiant, that we are aware of appearances and that we are aware of appearances and that bootstrapping arguments are badthat bootstrapping arguments are bad


Assume that appearances are radiantAssume that appearances are radiant So if I’m appeared to redly, I believe that So if I’m appeared to redly, I believe that

I’m appeared to redly, and this belief is I’m appeared to redly, and this belief is justified justified

So I can reason as follows:So I can reason as follows:I believe that’s a red appearanceI believe that’s a red appearanceAnd it is a red appearanceAnd it is a red appearanceIntrospection works again!Introspection works again!


Given radiance and self-awareness, I can Given radiance and self-awareness, I can do this over and over againdo this over and over again

Eventually, I’ll have a large sample of Eventually, I’ll have a large sample of cases where my introspective beliefs are cases where my introspective beliefs are accurateaccurate

So I can conclude on the basis of this So I can conclude on the basis of this little reflection that my introspective little reflection that my introspective beliefs are generally accuratebeliefs are generally accurate


But this is crazyBut this is crazy It takes serious psychology to know that It takes serious psychology to know that

my introspective beliefs are accuratemy introspective beliefs are accurate A little armchair reasoning like this won’t A little armchair reasoning like this won’t

cut itcut it This reasoning is as bad as the reasoning This reasoning is as bad as the reasoning

that Cohen parodiesthat Cohen parodies Indeed, it Indeed, it isis just that reasoning, with a just that reasoning, with a

different targetdifferent target


If we really want to block all bootstrapping If we really want to block all bootstrapping arguments, we have to reject not just arguments, we have to reject not just dogmatism, but also the radiance and dogmatism, but also the radiance and self-awareness assumptionsself-awareness assumptions

Otherwise an introspective bootstrapping Otherwise an introspective bootstrapping argument will be licensedargument will be licensed

But dogmatism without radiance and self-But dogmatism without radiance and self-awareness doesn’t allow bootstrapping, awareness doesn’t allow bootstrapping, so dogmatism can’t be faulted hereso dogmatism can’t be faulted here

Bayesian ObjectionBayesian Objection

Our final argument comes from principles Our final argument comes from principles of Bayesian epistemologyof Bayesian epistemology

The dogmatist thinks that when we get E, The dogmatist thinks that when we get E, our credence in E our credence in E pp can go up can go up

Or at least, she thinks that we can go Or at least, she thinks that we can go from not being justified in believing E from not being justified in believing E pp to being justified in believing itto being justified in believing it

But this can’t happen in Bayesian modelsBut this can’t happen in Bayesian models


We’ll work through a simple version of We’ll work through a simple version of this argumentthis argument

Let A be the proposition Let A be the proposition it appears to me it appears to me that there is a handthat there is a hand

H is the proposition H is the proposition there is a handthere is a hand F is the proposition F is the proposition it falsely appears to it falsely appears to

me that there is a handme that there is a hand, i.e. A , i.e. A H. H. And Pr is our And Pr is our priorprior probability probability

1.1. Pr(A) < 1Pr(A) < 1 premisepremise

2.2. Pr(F) > 0Pr(F) > 0 premisepremise

3.3. Pr(F | A) ∙ Pr(A) = Pr(F Pr(F | A) ∙ Pr(A) = Pr(F A) A) probability def’nprobability def’n

4.4. Pr(F Pr(F A) = Pr(F) A) = Pr(F) from definition of from definition of FF

5.5. Pr(F |A) ∙ Pr(A) = Pr(F)Pr(F |A) ∙ Pr(A) = Pr(F) from 3, 4from 3, 4

6.6. Pr(F | A) > Pr(F)Pr(F | A) > Pr(F) from 1, 2, 5from 1, 2, 5

7.7. Pr(~F | A) = 1 - Pr(F | A)Pr(~F | A) = 1 - Pr(F | A) probability probability theoremtheorem

8.8. Pr(~F) = 1 - Pr(F)Pr(~F) = 1 - Pr(F) probability probability theoremtheorem

9.9. Pr(~F | A) < Pr(~F)Pr(~F | A) < Pr(~F) from 6, 7, 8from 6, 7, 8


All that is mathematically soundAll that is mathematically sound But it usually gets a philosophical glossBut it usually gets a philosophical gloss The last line is read as saying that the The last line is read as saying that the

probability of ~F goes down when we get probability of ~F goes down when we get evidence Aevidence A

This relies on an undefended claim, This relies on an undefended claim, namely that we should update credences namely that we should update credences by conditionalisationby conditionalisation


If we grant conditionalisation, things look If we grant conditionalisation, things look bad for the dogmatistbad for the dogmatist

The dogmatist says that we can know, The dogmatist says that we can know, and justifiably believe ~F when our and justifiably believe ~F when our evidence is A, but not beforeevidence is A, but not before

But it seems plausible that evidence that But it seems plausible that evidence that justifies a belief shouldn’t make its justifies a belief shouldn’t make its credence go credence go downdown


Can the use of conditionalisation here be Can the use of conditionalisation here be defended?defended?

I think it can’tI think it can’t Conditionalisation usually is the right Conditionalisation usually is the right

approach to updatingapproach to updating But it isn’t always the right approach in But it isn’t always the right approach in

cases where cases where uncertaintyuncertainty is relevant is relevant


Can the use of conditionalisation here be Can the use of conditionalisation here be defended?defended?

I think it can’tI think it can’t Conditionalisation usually is the right Conditionalisation usually is the right

approach to updatingapproach to updating But it isn’t always the right approach in But it isn’t always the right approach in

cases where cases where uncertaintyuncertainty is relevant is relevant


Game plan for the last few slidesGame plan for the last few slides Distinguish risk from uncertaintyDistinguish risk from uncertainty Describe a model for representing Describe a model for representing

uncertaintyuncertainty Describe a new approach to updating in Describe a new approach to updating in

that model, one that blocks this argumentthat model, one that blocks this argument Give a dogmatist defence of that Give a dogmatist defence of that

approachapproach

By ‘uncertain’ knowledge, let me explain, I do not mean merely By ‘uncertain’ knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to probable. The game of roulette is not subject, in this sense, to uncertainty; nor is the prospect of a Victory bond being drawn. uncertainty; nor is the prospect of a Victory bond being drawn. Or, again, the expectation of life is only slightly uncertain. Even Or, again, the expectation of life is only slightly uncertain. Even the weather is only moderately uncertain. The sense in which I the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or twenty years hence, or the obsolescence of a new invention, or the position of private wealth owners in the social system in the position of private wealth owners in the social system in 1970. About these matters there is no scientific basis on which 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and decision know. Nevertheless, the necessity for action and decision compels us as practical men to do our best to overlook this compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed.its appropriate probability, waiting to be summed. (Keynes (Keynes 1937: 114-5)1937: 114-5)

Representing UncertaintyRepresenting Uncertainty

Traditional Bayesian models didn’t have Traditional Bayesian models didn’t have an easy way to represent uncertaintyan easy way to represent uncertainty

There is a common way this is doneThere is a common way this is done Instead of representing credal states by a Instead of representing credal states by a

single probability function, we represent single probability function, we represent them by sets of probability functionsthem by sets of probability functions

Say S is the agent’s Say S is the agent’s representorrepresentor iff it is iff it is the set of functions representing herthe set of functions representing her

Representing UncertaintyRepresenting Uncertainty

The idea is that more uncertain The idea is that more uncertain pp is, the is, the larger this set islarger this set is

{x: For some Pr in S, Pr(p) = x}{x: For some Pr in S, Pr(p) = x}

Now we can represent uncertainty in a Now we can represent uncertainty in a distinct way from riskdistinct way from risk

Updating UncertaintyUpdating Uncertainty

This kind of model is widely used in the This kind of model is widely used in the literatureliterature

It is usually assumed, without much It is usually assumed, without much argument, that we should update S on argument, that we should update S on evidence E by conditionalisationevidence E by conditionalisation

That is, the new representor is derived That is, the new representor is derived from the old one by conditionalising each from the old one by conditionalising each elementelement


That is what I want to rejectThat is what I want to reject I think the agent might sometimes use I think the agent might sometimes use

her new evidence to realise that she need her new evidence to realise that she need not have been as uncertain as she wasnot have been as uncertain as she was

So we’ll get from the old representor to So we’ll get from the old representor to the new one by first cutting some the new one by first cutting some functions from the set, and second functions from the set, and second conditionalising the remaining membersconditionalising the remaining members


The benefit of this approach is that it lets The benefit of this approach is that it lets us say something quite attractive about us say something quite attractive about the a priori rational credal statethe a priori rational credal state

It is somewhat intuitively that a priori we It is somewhat intuitively that a priori we should treat all possibilities symmetricallyshould treat all possibilities symmetrically

It is notoriously hard to implement this It is notoriously hard to implement this intuition consistently in a traditional intuition consistently in a traditional Bayesian theoryBayesian theory

But we can if we allow for uncertaintyBut we can if we allow for uncertainty


The a priori rational credal state is The a priori rational credal state is represented by the set of represented by the set of allall analytically analytically coherent probability functionscoherent probability functions

A probability function is analytically A probability function is analytically coherent iff it assigns probability 0 to coherent iff it assigns probability 0 to anything that could not turn out to be true anything that could not turn out to be true and conforms to the Principal Principleand conforms to the Principal Principle


If we accept the usual conditionalisation If we accept the usual conditionalisation approach to updating, we cannot accept approach to updating, we cannot accept that this is a rational a priori statethat this is a rational a priori state

That’s because updating this state by That’s because updating this state by conditionalisation does not allow for conditionalisation does not allow for ampliative learningampliative learning

But if updating involves culling the set, But if updating involves culling the set, then we can learn things that go beyond then we can learn things that go beyond our evidenceour evidence


And dogmatists should be very pleased And dogmatists should be very pleased with this idea for representing the a prioriwith this idea for representing the a priori

Our discussion of dogmatism started with Our discussion of dogmatism started with the idea that we shouldn’t allow for a the idea that we shouldn’t allow for a priori justification of substantive beliefspriori justification of substantive beliefs

Any initial credal state other than this one Any initial credal state other than this one seems to adopt some substantive claims, seems to adopt some substantive claims, at least about relative probabilityat least about relative probability


If when the agent sees that she appears If when the agent sees that she appears to have hands, she culls as well as to have hands, she culls as well as conditionalises her representor, it won’t conditionalises her representor, it won’t follow that her credence in ~F will lowerfollow that her credence in ~F will lower

So that evidence might ground her belief So that evidence might ground her belief that ~Fthat ~F

In short: the Bayesian objection to In short: the Bayesian objection to dogmatism seems to show up a problem dogmatism seems to show up a problem for the Bayesian, not the dogmatistfor the Bayesian, not the dogmatist

Documents

In Defence of a Dogmatist Brian Weatherson May 2006