Trivializing Benacerraf and Monstrous Moonshine

[note: Sorry that this post is a little wordy. I'm trying to get back into blogging, and forcing myself to post stuff I'm not quite happy with is part of that. Also see this paper for a way more detailed and less aggro take on this issue.]

Remember that the access problem (aka the Benacerraf problem) for realists goes something like this: If moral/mathematical/etc realism is true, how can human accuracy and reliability about moral/mathematical facts be anything but a miracle or a mystery?

People like Justin Clarke-Doane and perhaps David Enoch, (call them The Trivializers) have been suggesting that we can answer all legitimate access worries besetting for realists about necessary domains like mathematics morals etc. just by “stapling together” two things to explain why we couldn't have easily been wrong (and providing a similarly trivial explanation for the sensitivity of our I won't discuss here):

• an  explanation (e.g.historical or evolutionary) for why we reliably believe certain moral/mathematical/etc claim,
• the fact that these claims are necessary truths

So, for example, a classic platonist might try answer access worries by explaining human reliability about mathematics like so:

TRIV: Mathematicians reliably believe truths because they reliably believe only those mathematical claims which can be proved in a certain formal system (e.g. ZFC) and this formal system is (necessarily) truth preserving w.r.t. the platonic mathematical objects.

Such an explanation is not likely to satisfy anyone who feels an intuitive access worry. For TRIV just explains one intuitively mysterious match between human psychology and objective which intuitively “cries out for explanation” (our acceptance of theorems that match whats going on in Plato's heaven) by positing another such mysterious match (our acceptance of axioms that match what's going on in Plato's heaven).

But it does (in some sense) suffice to explain the safety of human beliefs by deriving our reliability about realist facts concerning the relevant domain (i.e., that in all close possible worlds, our beliefs about these domains match up with the truth) from more general premises which the realist (if not their deflationary opponents) accepts.

And I take Trivializers to be suggesting that our intuitions that certain regularities involving necessary truths "cry out for" explanation in a deeper/more unified sense, which mere deductions of reliability/safety/sensitivity like TRIV need not provide, is an illusion.

There are two reasons why I don't buy this.

First, conceptually analyzing anything (from tablehood to justice) is infamously hard, but there are plenty of good paradigms for how to think about ”crying out for explanation” which seem to apply equally well to necessary and contingent regularities (e.g., norms that say we should preferring theories that have fewer degrees of freedom and or Kitcher’s idea of scientific explanation as unification).

Much more importantly though, embracing the Trivializers' position seems to have deeply implausible revisionary consequences for mathematical practice, since mathematicians sure seem to think that some regularities involving necessary truth truths can cry out for (non-trivial) explanation.

For example, consider this quote from a popularizing article about the history of John Conway's `Monstrous Moonshine' conjecture.

``Strangely enough, [the j- function]’s first important coefficient is 196,884, which McKay instantly recognized as the sum of the monster’s first two special dimensions.
Most mathematicians dismissed the finding as a fluke, since there was no reason to expect the monster and the j-function to be even remotely related. However, the connection caught the attention of John Thompson, a Fields medalist now at the University of Florida in Gainesville, who made an additional discovery. The j-function’s second coefficient, 21,493,760, is the sum of the first three special dimensions of the monster: 1 + 196,883 + 21,296,876. It seemed as if the j-function was somehow controlling the structure of the elusive monster group.'’’

Note that mathematicians already had separate proofs of facts about the j-function and monster group (and hence an `explanation' of for the match between these facts of the kind which TRIV provides, i.e., a deduction, from more general premises, of the fact that this relationship holds in all close possible worlds). But (once this match between apparently unrelated domains proved striking enough) they expected to find some further/deeper unifying explanation and this expectation guided choices for further research.

So I'm prima facie pretty suspicious of the idea that felt intuitive demands for unifying/satisfying/non-trivial explanations of regularities involving necessary truths are generally misguided. But maybe I'm not being charitable to Clarke Doane and/or he can find some way of separating the "this regularity cries out for further explanation" intuitions he wants to dismiss as unreliable from those which obviously do good work in mathematics.

Justifying Logic and the Normal Role of Proof in Justification

Some philosophers aim to show how we can be justified in accepting certain basic logical truths by giving "rule circular" proofs of the soundness of these basic logical truths. They admit that most people will never have considered the proofs in question, and they admit that these people still count as justified in using logic. But, they say that they showing that such proofs can in principle be given makes sense of how we can be justified in believing the basic logical claims established by the proofs right now.

That idea seems prima face implausible. In general the fact that someone 100 years later will prove P from premises that I accept (like the ZF axioms) doesn't suffice to show that I am justified in believing that P now. So why should the case be any different for the proofs of logical principles?

[I would rather say that we are prima facie justified in believing these logical principles in a way that has nothing to do with the possibility of giving further argument; coming up with more or less circular ways of proving the soundness of our logical principles is (at best) a way of improving our justification]

Three Arguments for A Priori Knowledge of (Very) Contingent Facts

Can we have a priori knowledge of contingent facts? For example, consider the proposition below. Can we know truths like the following a priori? NOT PEA SOUP: 'It is not the case that everything outside of a 5 foot radius around me is made of pea soup, which stealthily forms up into suitable objects as I walk by' Here are three positive arguments (in ascending order of strength IMO) for the conclusion that we can know NOT PEA SOUP a priori.


1. Argument from Crude Reliablism

The belief-forming method of assuming that you aren't in a pea soup world is reliable. And even if we make things a little less crude by saying that good belief formation is belief formation that works via a chain of methods which are *individuated in a psychologically natural way* and are reliable, we will probably still get the same conclusion. For plausibly the most natural relevant psychological mechanism involved in generating that belief would be something like, 'believe not P when P is sufficiently gerrymandered'.

2. Argument from Probability and Conditionalization-Based Models of Good Inference

If you think that good reasoning is well modeled by the idea of assigning a certain probability measure to the space of possible worlds, and then ruling out worlds based on your observation, and asserting that P if and only if a sufficient fraction of the remaining probability is assigned to worlds in which P. There will be some propositions P that low enough prior probability to warrant asserting ~P before you have made any observations - and plausibly the pea soup hypothesis is one of them. Presumably in such cases your justification does not depend on experience. [I think Williamson has something like this in mind in one of his papers on skepticism, but his argument was more complicated]

3. Argument from Current Knowledge plus Inability to Cite Experiential Justification. The claim that NOT PEA SOUP is a priori follows from a claim about knowledge that only a skeptic would deny, plus a somewhat intuitive claim about the relationship between a priority and justification. The intuitive claim I have in mind is that if someone can count as knowing that P, without being able to point to any relevant experience (or memory of experience, or reason to believe that they had experience etc) as justification then they know that P a priori so P is a priori (i.e. a priori knowable). Everyone but the skeptic agrees that people know that they aren't in the pea-soup world. These people who know cannot point to any experience as justification. Hence, 'not-pea soup' must be knowable without appeal to experience for justification. You might try to defend the a posteriority of NOT PEA SOUP by saying that even if the man on the street can't make any argument from experience to NOT PEA SOUP, our intuition that people know that NOT PEA SOUP is based on the assumption that there exists some good argument from something about experience to NOT PEA SOUP, and philosophers just need to discover it. In this way, experience really is necessary to justify the belief that NOT PEA SOUP so the proposition is a posteriori.

However, this response threatens to generate the unattractive conclusion that people today do not know NOT PEA SOUP. For, in general, the mere existence of a good argument for some proposition that I believe does not suffice to make me justified in believing that proposition now, if I cannot (now) give that argument. If I believe some mathematical theorem T on a hunch or on the basis of tea leaf reading, the mere fact that there is a good argument for T on the basis of things that I accept, doesn't suffice to allow me to count as knowing that T. So even if there is some cunning philosophical argument yet to be discovered which justifies NOT PEA SOUP on the basis of experience, it would seem that this argument cannot suffice to justifies people now accepting that NOT PEA SOUP. If people now are justified that NOT PEA SOUP, and can give no argument from experience for this claim, it must be that the claim can be justifiably believed without appeal to experience.

Reliablism and the Value of Justification: The Angel's Offer

A major objection to reliablism about justification is that it doesn't explain why we value having knowledge of a given proposition more than mere dogmatic true belief. For, believing a true proposition via a method that's reliable is just more likely to lead you to believe other true propositions; there's no obvious sense in which your relationship to true beliefs formed by reliable methods is thereby intrinsically any better or more valuable than you relation to mere true beliefs. If we don't like a particular cup of good expresso any better for it being the product of a machine that reliably makes good expresso, why should we like a particular state of believing a truth any better from the fact that it was produced by processes that reliably lead to believing the truth?

But maybe we DON'T value having the special relation we do to justified true beliefs over and above it's tendency to promote having stable true beliefs. Consider this thought experiment:

An angel convinces you that he knows the true laws of physics and maybe also that it can do super-tasks and thereby knows certain statements of number theory which cannot be proved from axioms which you currently accept. The angel offers to make it the case that you find these true principles feel obvious to you - the way that you now feel about 'I exist' or '2+2=4'. He will wipe your memory of this conversation so that you will not be able justify these feelings to yourself by appeal to the reliable way you got them - but of course you won't feel the need to justify them to yourself since they will just feel obvious and you will be inclined to immediately accept them. [Suppose also, if it matters, the angel will do the same to everyone in your community, that community members prefer to go along with whatever choice you make, that the angel is already going to blur your memories of not finding these claims obvious in the past etc.]
Would you accept the offer?

I personally would definitely take the offer. And I think many people would share this preference. If there were something intrinsically valuable about knowing verses merely dogmatically assuming a necessary truth, then this would be a strong reason not to take the angels offer. But if Plato is right (as thinking about the example tempts me to think that he is) to say that the only bad thing about dogmatically assuming truths rather than knowing them is that dogmatic assumptions don't stay tied down, then the angel's offer to make you and everyone else in your community find these truths indubitable fixes that problem - and you should take him up on his offer.

Old Evidence and Apologies

If the problem of old evidence for Bayesian epistemology is just the following, then I don't think it's a problem:

Sometimes it seems like we should change our probabilities based on discovering logical consequences of a theory, but Bayesian updating only involves changing probabilities when you make a new observation.

For (it seems to me) this objection has the same ultimate structure as the following, surely bad, objection:

Sometimes it seems like we should apologize, but obeying so-and-so's moral theory involves never wronging anyone - and hence never apologizing.

If old evidence E is logically incompatible with hypothesis H, then Bayesianism says that you should *already* have ruled out all the worlds where H is true, and changed your probabilities accordingly, whenever you observed that E. So, I see no problem for the Bayesian epistemologist in saying that when you discover that you have failed to update in the way required by the theory (by not noticing a logical incompatibility), you should fix the mistake and change your probabilities accordingly.

[Compare this with the following popular intuition in ethics: you should promise to visit your grandmother and then visit her, but given that you aren't going to visit you shouldn't promise to visit her.]

Obvious vs. embarassing mistakes

As you've probably noticed, this blog has been on a bit of a hiatus. I'm going on the jobmarket this year so things have been very busy. I do have a little time now though, to note something about the relationship between two phenomena that are ubiquitous in my life :)

Not all obvious mistakes are embarrassing mistakes. Any mistake you make while adding two numbers will be an obvious mistake, but nearly everyone doing calculations makes such mistakes some fair fraction of the time, and these errors are not (intuitively) embarrassing mistakes.

further questions:
-Is being obvious once pointed out a necessary condition for being an embarrassing mistake? [edit: appropriately enough, i had originally put "sufficient" :)]
-Is the mere fact that a mistake is made with high frequency in some community sufficient to prevent it from being an embarrassing mistake? (maybe inferring the consequent is made with high frequency yet also embarrassing).
-Will trying and failing to give principled necessary and sufficient conditions for a mistake being embarrassing make one feel less embarrassed by embarrassing mistakes?

[hat tip to E.M. for suggesting this would make a cute post]

Why Math and Morals Aren't Companions in Guilt

Intuitively, many people feel that epistemic worries about moral facts (if there are moral facts, how to explain why our moral intuitions should be even even remotely correct about them?) are WAY more serious than epistemic worries about mathematical facts (if there are mathematical facts, how to explain why our mathematical intuitions should be even even remotely correct about them?). But is there really a difference here?

Well, here's one thing that I think does make a difference: mathematical claims about number theory have direct and specific consequences for stuff that we can check by logic and/or scientific observation.

-what will happens whenever a person or a computer to successfully applies a certain syntactic alogorithm
-how many apples-or-oranges do you have when you have n apples and m oranges (cf Frege for why this is a logical fact)

This matters because, plausibly, the need to get these concrete applications right likely prevents our beliefs about number theory from getting too off the wall - whereas, our moral intuitions have no such multitude of consequences which are directly checkable by logic and observation.

Epistemology verses Foundations in Philosophy of Math

The epistemology of math task: Get a true theory of what under what circumstances a person counts as knowing something. Or, at least, square our beliefs about what people have or lack knowledge of what particular mathematical beliefs, with general beliefs about what’s required for knowledge (e.g. causal contact.

The foundations of math task: extend our mathematical knowledge.

I claim that making this distinction matters a lot, because:

Arguments that are helpful for foundations of math are (in themselves) useless for the epistemology task. Suppose we have a working derivation D of certain facts of arithmetic from logic. And suppose we have a perfectly adequate, intuition-matching story about what it takes to count as knowing the relevant logical facts.
This still does not allow us to account for current knowledge of arithmetic (i.e. reconcile our theory of knowledge with the intuition that people now know things about arithmetic). This is because - in general - it is not enough for S to know that P, for P to be true, S to believe that P, and P to be derive*able* from things which S knows. In general, the subject S needs to have some kind of access to the derivation. The mere fact that I believe that P, and P can be proved from other things that I know, hardly suffices to establish that what I have counts as knowledge. If a lawyer is asked to show that some contractor knew that a bridge was safe, it doesn’t suffice to show that one *could* derive from laws of physics and facts about the blueprint which the contractor knew that the bridge was safe - we also need to suppose that the contractor did derive it, or get testimony from someone who derived it or the like.

Hence, a foundational argument which derives (say) one body of mathematics from premises that are more certain is not directly relevant to the general epistemological project.

Conversely, an accurate epistemology of mathematics can be almost perfectly useless to the task of setting some shaky region of mathematical theory on firmer foundations. For example, one classic account of knowledge is reliablism. If we modify reliablism so as to apply non-trivially to mathematics (following suggestions by Linnebo and Field) we get the idea that someone has knowledge if they have a true belief which is reliable in the sense that: they accept a sentence which expresses p, and if that sentence had not expressed a truth, they would not have accepted it. This is a perfectly decent candidate for a general account of mathematical knowledge. But note that, even supposing that it is right, it does nothing to help satisfy foundational desires for, say, more secure foundation for the axiom of choice. If someone has foundational worries about the axiom of choice, they have worries about whether it is true. They might express these worries by saying ‘how do you know that the axiom of choice holds?’ but the emphasis here is on truth, not on knowledge. It would be silly to respond by saying that we know AC because AC is true, and we have reliable beliefs (as defined above) to that effect. What the foundation-seeker really wants is to know whether AC. They want to acquire knowledge about whether AC, not get a general theory of what it would take to count as knowing AC.

So, I have been trying to argue that it’s important to make a distinction between the epistemological project of trying to come up with a general theory of when someone knows something about math, and the foundational project of trying to make it the case that we know more things about math, by supplementing inadequate arguments with additional arguments that appeal to premises which are already known. The one focuses on the most bland an uncontroversial cases of mathematical knowledge, and tries to reconcile our other beliefs about the nature of knowledge with our particular judgments about this case. The other seeks out the most controversial regions of mathematical claims, and seeks to secure knowledge for us about these claims, by connecting them to claims that are more securely known. Enticing answers to one project can easily seem to frustratingly miss the point for someone who is interested in the other, as shown in the examples above. Hence it’s important to make the distinction.

However, this is not to say that there’s no relationship between the epistemological and foundational projects. Thinking about big picture issues about justification in general, can influence your judgments about particular cases. A kind of trivial example of this is intuitions about what you can take for granted, while still counting as being justified. Just off the top of one’s head, it can seem attractive to say that someone doesn’t count as knowing that P if all they can give is a circular justification for P, an infinite regress of justifications, or a justification that comes to a halt at a certain point. But when you consider these three options together and notice that they exhaust all the possibilities, you will likely be inclined to give up the principle that someone who can only give a justification of one of these kinds must thereby not count as having knowledge. So, if two realists about AC are attempting to provide and evaluate firmer foundations for AC, it may be helpful for them to general questions about what’s required for knowledge and justification – to make sure that their evaluation of the evidence in this case, doesn’t depend on assumptions about justification which turn out to be incoherent or conflict with what they take to be sufficient evidence more generally.

Knowledge and Cannonical Mechanisms

In my first epistemology class in college, the prof encouraged us to look for adequate necessary and sufficient conditions for knowledge by making the following (imo appealing) argument. We expect that there's SOME nice relationship between facts about knowledge and descriptive facts not containing the word knowledge, since our brains seem to be able to go, somehow, from descriptions of a scenario (like the Gettier cases) to claims about whether the person in that scenario has knowledge. However, philosophical attempts to find a nice definition of knowledge in other terms seem to have systematically failed. This suggests that there may be a correct and informative definition of knowledge to be found, but this definition is just too long to be an elegant philosophical hypothesis, but not too long to correspond to what the brain actually does when judging these claims.

So here's what I propose that the true definition of knowledge might look like:

We describe messy physical processes by talking about symple mechanisms, and a notion of what these mechanisms tend to do "ceterus paribus". People agree surprizingly much on which mechanisms approximate what (e.g. how to go from facts about swans to claims about the swan lifestyle, how to divide up actual dispositions to behavior into "behaving normally" vs, "something special happening whereby the ceterus aren't paribus"). One thing that can be so approximated is human belief forming. We think about actual human belief formation by saying that it "ceterus paribus" it approximates combination of various belief forming mechanisms (e.g. logical deduction, looking etc). A reliable beleif forming mechanism is one whose ceterus paribus behavior yields true beliefs.

Certain belief forming mechanisms are popular, and remain popular with people even when they undergo lots of reflection. Some of these are cannonical, in the sense that we count them as potential conduits for knowledge. But, if we ever come to believe that some such mechanism is not reliable (jn the sense defined above) we will stop saying that beleifs formed via it count as knowledge. So here's what I think a correct definition of knowledge might look like.

We have, say, 300 cannonical reliable mechanisms for producing knowledge, 200 cannonical reliable mechanisms for raising doubt (100 optional and 100 obligitory), and 200 cannonical reliable mechanisms for assuaging doubt. Call these CRMs. Our definition starts by giving a finite list of all these CRMs.

You know P, if and only if your belief in P was generated by some combination of CRMs for producing knowledge, and you went through CRMs from assuaging doubt corresponding to a) all optional CRMS for doubt raising that you did engage in b) all non-optional CRMs for doubt assuaging that apply to your situation.

Even though this is just a claim about what the form of a correct definition of knowledge would look like, it already has some reasonably testable consequences:
1. That situations where it seems unclear of vague what mechanism best describes a person's behavior (should I think of the student as correctly applying this specific valid inference rule, or fallatiously applying a more general but invalid inference rule?) will also make us feel that it's unclear or vague whether the person in question has knowledge.
2. That we should seem unclear whether to attribute knowledge about when reliable but science fictiony and hence non-cannonized mechanisms are described. For example, most people would say it's OK to take delivarances of the normal 5 senses at face value, without checking them against something else. But what about creatures with a 6th sense that allowed them to reliably read minds, or form true beliefs about arbitrary pi 01 statements of arithmetic (imagine creatures living in a world with the weird physics that allows supertasks, and suppose that they have some gland that has no effect on conscious experience, but whose deliverances reliably check each case). Would they count as knowing if they form beliefs by using these?

Fallacious but psychologically attractive inferences

I like to start with really simple theories and see where they go wrong. Recently this lead to an interesting combination of experiences

When I say:

People are justified in making those a priori inferences which are both necessarily truth preserving and psychologically compelling for normal humans.

People say: But reasoners do have initial justification for accepting certain attractive but ultimately fallacious arguments e.g. tricky arguments for the existence of God.

But when I take out the requirement of being genuinely truth-preserving and say...

People are justified in making those a priori inferences which are psychologically compelling for normal humans.

People say: But what about those bad but psychologically compelling inferences like inferring the consequent?

So which is it (do you think)?

When someone makes a psychologically compelling but invalid inference like the gambler's fallacy or inferences about naive set theory are they:
a) justified, (though presumably thinking about the right questions may later give them justification for changing their mind) or
b) unjustified
c) somehow there's a difference between the gambler's fallacy and naive set theory in this regard

I don't have a dog in this race, or think anything deep is going on here, but I'd really like to know which way normal language intuitions go.

Doubting Conceptual Truths

Some things, some Kantians say about the justification for logic suggest the following superficially attractive idea:

a) Certain sentences have the property that anyone who can think about them must thereby be inclined to accept them (e.g. you can't even think thoughts involving `and' if you aren't willing to accept 'If it's raining and it's snowing then its raining')

b) We are justified in accepting such sentences, because we have no other option.

But actually, its plausible that we can reasonably doubt many sentences with this property. This is because sometimes you can turn out to have been working with an 'incoherent concept' like tonk, or bosh, the naive concept of set or perhaps various philosophical concepts. In such a case, you don't count as thinking with the concept unless you are willing to make certain (bad) inferences.

Now, you might argue that someone who was taken in by this kind of incoherent concept doesn't count as thinking anyway (e.g. there's no proposition which ``it's raining tonk its snowing" expresses). So maybe you only count as *thinking* in the good case, where it turns out that your concepts are coherent. But, given that we know that very smart and conscientious people can wind up with bad concepts, it intuitively seems reasonable to not completely dismiss the possibility that various new concepts you are learning are among the bad ones.

Hence*, it would seem that, we can rationally doubt claims which it would not be possible to deny. (what we're concerned about here is not the possibility that the claim is false - which we can't entertain- but that one of the concepts figuring in it is incoherent, so the claim is nonsense)

*if a) is true

Bookclub: Pedersen on Wright's Entitlement

This latest installment is about Nikloj Pedersen's recent Synthese article on Crispin Wright. Pedersen criticizes (correctly in my opinion) certain possible motivation for Wright's idea that we are entitled to assume certain "cornerstone" propositions (like 'I'm not a brain in a vat') just because assuming these is requisite for getting any substantative theory of a given area off the ground. (You can't just point out that accepting ~BIV leads you to have many and no fewer true beliefs than the skeptic if BIV is true, and no fewer true beliefs if BIV is false. For, avoiding false beliefs is presumably also epistemically important, and assuming ~BIV imposes a risk of having many more false beliefs)

Instead he proposes that such cornerstone assumptions have "teleological value" insofar as they are aimed at something of value (namely, true belief), whether or not they actually succeed in producing such true beliefs. But this seems to immediately generalize to all beliefs - not just cornerstone ones.

For, what beliefs aren't aimed at the truth? It's just as true of the person who assumes the existence of a massive conspiracy as of the person who assumes the existence of the external world that they aim at having many true beliefs. Indeed, many people would say that it's a necessary truth, part of what it means for something to be a belief, that in believing that P one is trying to believe the truth.

With the possible exception of cases like the millionaire who bribes you to believe some proposition, all beliefs would seem to aim at truth. Hence it seems that all beliefs inherit teleological justification in Pedersen's sense.

One might be able to make this into an interesting view - all beliefs (not just cornerstone ones) are warranted until one gets active reason to doubt them. Such a position is remeniscent of conservitivism and coherentism. But, from the article Pedersen shows no sign of intending to say that all beliefs are default justified.

Analyticity: No Free Lunch

Consider the following pardigmatic examples of analytic and synthetic sentences:

(1) "Dogs once existed."
(2) "Prime numbers have two distinct divisors: themselves and one."

Both of these statements feel extremely obvious to us. And, if anything we're more likely to stop asserting (2) than (1) - if some perverse person wants to count 1 as a "prime" number, that's fine with me, so (if he's insistent enough) I'll adopt his usage and hence stop saying sentence 2 (and e.g. change how I state the fundamental theorem of algebra accordingly). So - we wonder, after reading Quine, what does the further claim that (2) is analytic amount to?

Here's an idea: If someone asked me to back up my assertion of (1), I'd be surprised, but there are things I would do to support this e.g. give an example of a dog. If (bizzarely) I couldn't state any other claims in support of (1), I'd be troubled. In contrast, if asked to justify (2) I wouldn't be able to give any kind of argument for it AND I wouldn't be troubled by this, or inclined to revise. (Note: this is exactly when claims about analyticity and meaning come up in ordinary contexts - people say 'that's just what I mean by the term' when faced with skepticism about certain things.)

S is basic analytic in P's idiolect iff: either P is happy to accept S without being able to provide any further justification

S is analytic in P's idiolect iff: S is basic analytic S is derivable via some combination of premises and inferences, each of which is basic analytic.

This seems to pick out a relatively sharp class of sentences, and accord with our intuitive judgments of analyticity (at least if we assume that experience can somehow be cited as a justification [or something more sophisticated], so that direct observations don't count as analytic for the observer).

Does this refute Quine? No. For, let's think about what epistemological siginificance (this notion) analyticity has. Do we have some kind of special access to analytic truths?

Making a bunch of new sentences analytic in your idiolect is just a matter of developing the inclined to say "that's just what I mean by the word" when pressed for a justification of these sentences. And this refusal to provide extra justification doesn't somehow ensure that the sentences you assert so boldly come to express truths.

For, what bucking up your insouciance like this does, is change the facts about your use of words so that (now), if the certain of your words are meaningful at all, these sentences will express truths. Thus, it makes these sentences/inferences function as a kind of implicit definition of your terms. But, as the famous case of Tonk shows, not all implicit definitions are coherent. Also, in changing the meanings of your words in this way, you run the risk of making other non-analytic sentences that you currently accept now express falsehoods.

Thus, saying that some sentence S is analytic isn't some kind of epistemic free pass for you to accept that sentence. All it does is semantically push all your chips into the center of the table with regard to S. Whereas before you ran the risk that S would express a falsehood, now there's a better chance that S will express a truth, but if it doesn't both S and a bunch of other sentences in your language will be totally meaningless.

So, here's my current position: the analytic-synthetic distinction is real, but it doesn't give the epistemological free lunch* which the logical positivists hoped it would.

*i.e. just saying that facts about something (like math) is analytic doesn't banish mysteries about how we came to know these facts.

Freedom and Resentment in Epistemology

Everyone likes to talk about Neurath's boat, but I think common discussion leaves out something critical. Not only do we all start with some beliefs, but we also start out accepting certain methods of revising those beliefs, in response to new experience or in the course of further reflection. This is crucial because it brings out a deep symmetry between all believers:

At a certain level of description, there's no difference between the atheist philosopher who finds it immediately plausible that bread won't nourish us for a while and then suddenly poison us, and the religious person who finds it immediately plausible that god exists, or the madman who finds it immediately plausible that he's the victim of a massive conspiracy. Everyone involved is (just) starting with whatever they feel is initially plausible, and revising this in whatever ways they find immediately compelling.

Thinking about things this way, can make one feel uncomfortable in deploying normative notions of justification. Being justified is supposed to be a matter of (something like) doing the best you can, epistemically, whether or not you are lucky enough to be right. But there's no difference in effort (or even, perhaps, in care) between the philosopher and the madman. It's just that the philosopher is lucky enough to find immediately compelling principles *that happen to be mostly true*, and inference methods *that happen to be mostly truth-preserving/reliable*. So how can we say that one of them is justified?

One reaction to this is to deny that there is such a thing as epistemic normativity. There are facts about which people have true beliefs, and which of them are on course to form more true beliefs, which belief forming mechanisms are reliable (in various senses) etc. But there are no epistemically normative facts e.g. facts about which reliably true propositions are OK to to assume, or which reliable inference methods are OK to employ without any external testing.

Another possible reaction is to say that even though "ultimately" there's no difference between believing finding it obvious that bread will nourish you if it always has in the past vs. believing you are the center of a conspiracy, there still are facts about justification. We can pick out certain broad methods of reasoning (logical, empirical, analytic(??), initially trusting the results of putative senses) which are both popular and generally truth preserving, and what it means to be justified is just to have arrived at a belief via one of those.

In either case, the result will give an answer to philosophical skepticism. The skeptic asks: "how can you be justified in believing that you have a hand, given that it depends on your just assuming without proof that you aren't a BIV?" Someone who has the first reaction can simply deny the contentious facts about justification. Someone who has the second reaction will be unimpressed by the point that they are "just assuming" that ~BIV. All possible belief is a matter of starting out "just assuming" some propositions and inference methods, and then applying the one to the other.

Explaining vs. justifying beliefs

Suppose I say that there's a fire in my room, and then you ask me why I believe there's a fire in my room. I could give a causal explanation for my belief (e.g. 'Some light bounced off a fire and this hit my eyes causing such-and-such brain changes in me) or I could try to justify the claim (e.g.'I seem to see a fire, and I don't tend to hallucinate').

These are two very different things! Thus, I think it's totally wrong to assume that the (potentially infinite series of) other beliefs I might express if asked to justify my claim that there's a fire in my room, somehow figured in causing the belief. If anything, these extra beliefs are probably simultanious results of a common cause, namely the fire.

Fire
-causes->
Light hits my retina
-simultaniously-causes->
I believe there's a fire.
I believe that I seem to see a fire.
I believe that I seem to seem to see a fire.
...

This is not to deny that beliefs CAN cause beliefs though, as in the case of conscious, Sherlock-Holmes-style chains of inference. Also the absence of certain beliefs might be necessary for the production of other beliefs (e.g. the absence of the belief that I have taken fire-hallucination causing drugs, might be required for causal stimulation by light from a fire to cause me to form the belief that there's a fire)

Skepticism and Normativity

Thinking you have figured out how to solve age old philosophical problems, very quickly, is generally a bad sign.

Nonetheless, ever since TFing Intro Epistemology last semester, I find myself feeling more and more that worries about external world/other minds/memory skepticism involve an incoherent melange of a sharp proof theoretic question, together with a fuzzy normative question.

The proof theoretic question is something like:
- Can you prove the external worlds exist, starting from premises that contain only necessary truths?
- Can you prove memory is reliable starting from premises containing only necessary truths and true statements about current experience?
[Where "prove" can be cashed out in various formal ways - e.g. first order logic, or modal logic, or intuitionistic logic - to yield different variants of the question.]

And the normative question is:
When is it empistemically OK to assume premises in a given set X, given that I cannot prove them (in logic L) from premises in set Y?

Once we've made this distinction, and noted that some premises which one might assume are true, and others false, the normative question looses much of its interest (at least for me).

Furthermore, we can point out to the skeptic who e.g. believes in the reality of past experiences but not in the external world, that his position appears exactly analogous to our own. We can challenge the skeptic to provide any kind of distinction between what's OK to assume vs. not OK to assume that looks remotely principled enough to motivate our revising our judgments on the subject.

"In what sense," we can say to the skeptic, "do you know that e.g. there are infinitely many primes, or that it's impossible to know things about the external world, such that I don't also (by those very same standards) count as knowing that I have a hand?. In both cases, there are more radical skeptics whom we cannot persuade. Thus, in saying that you know, but I do not, you seem to be just stomping your foot and making the unmotivated value judgment that it's OK to assume what you assume and not OK to assume what I assume.

Why should I be more confident that you have correct moral beliefs about what it's OK to assume, than that I have correct descriptive beliefs about whether I have a hand?"

Justification Puzzle #3: Indubitably, my dear Dr. Leary

What does it mean to say that a proposition is self-evident, or indubitable? Is our intuitive notion even coherent?

Here are three ways you might try to clarify what it is for a proposition p to be indubitable, and why they don't work. The puzzle is to do better.

1. It's metaphysically impossible to doubt whether p.

The idea behind this approach is that there are some things, like logic, which are so fundamental that if you tried to doubt them, you wouldn't count as thinking at all - and hence you wouldn't count as doubting.

But, the problem is, there don't seem to be any single propositions with this feature. If we think about someone rejecting "logical reasoning" as a block, arguably they wouldn't count as a thinker. But, as Williamson has recently emphasized, this property doesn't seem to hold for any single propositions.He takes the example 'All vixens are vixens', and describes two apparently intelligible philosophers whose theories (e.g. that a statements about all Xs is only true if there's some instance, and that the apparent existence of vixens is a hoax) would lead them to reject this claim.

Here are two more examples (of my own devising), of putatively indubitable propositions which it's metaphysically possible to doubt.


"I am thinking" Alice is a dualist in her philosophy of mind, and a hardcore externalist in her philosophy of language. Thus she thinks that, what it takes for the experience of having some strong of words pass through your mind, depends on the role that your dispositions to use these words in your further thoughts and actions plays in your life. e.g. The same phenomonology "I would like a glass of water" corresponds to one thought in the mind of someone from earth, and another in the mind of someone from twin earth.

What about a brain+phenomenology that randomly pops into existence in the middle of the sun and is burned up the next second? Since it doesn't have a body, or any meaningful dispositions to use words a certain way, Alice would say that the brain doesn't count as thinking.

Now, when reading Descartes' meditations, Alice thinks: how do I know that I am not such a brain, popped randomly into existence for one second, and about to be consumed by fire the next? Such a brain would have exactly the phenomenology that I am having, yet it would not count as thinking.

"I am having an experience as if of a red patch" Bob thinks, I'm certainly inclined to characterize the experience i'm having as one as if of a red object. But yesterday Alice asked me if I had ever seen fucia and green together, and I said yes, that rug over there is fucia and green. But then everyone else at the party pointed out that fucia is a kind of pink, not purple like the rug. So I was wrong when I judged 'I seem to see something fucia' before answering Alice's question. How do I know the same thing isn't happening now?

Admittedly, people certainly talk about whether things are red much more than about whether they are fucia, so if i was similarly wrong about how to identify (experiences as if of) red things, its likely it would have gotten caught by now. But I might just be really unlucky, like those brains in vats Alice keeps telling me about.

2. It is impossible to conceive of a scenario in which one is wrong in judging that p.

This analysis fails because, by this definition, any necessary truth would be indubitable. Suppose (unknown to me) there are infact infinitely many twin primes, and then I hear someone say 'Hasty Harry claims to have proved that there are infinitely many twin primes'.

Intuitively, it seems reasonable for me to doubt whether Harry is right, and whether there are, in fact, infinitely many primes. On its own, the latter claim is not indubitable - e.g. we want a proof partly because this will establish this apparent fact, on the basis of claims that are indubitable.

However, I cannot conceive of a scenario in which I am wrong in judging that there in infinitely many twin primes, for to do this would require conceiving of a scenario in which there are not infinitely many twin primes. But (on the assumption that there really are infinitely many twin primes) what would count as conceiving of a scenario in which there are not? Surely I don't need to do this to be justified in doubting that there are infinitely many twin primes, suspending judgment until I find firmer proof etc.


3. Psychologically, people are unable to feel doubt about whether p.

As Hume pointed out, we can doubt different things in the philosopher's closet vs. at the billiard table. Adding mind altering drugs that inspire confidence (alcohol) or paranoia (caffeine) or decrease the length of arguments you can hold in your head at once only extends the range.

Perhaps we should say something is indubitable if there is no possible psychological condition under which someone could doubt it. But, given the current state of psychology, do we have any evidence that any proposition has this feature?

Do we even have reason to think that there is such a limit? Absent a priori arguments that there are propositions about which doubt is unintelligible (see the argument against 1) it might be that for any thinkable proposition, there's some possible psychological state of entertaining doubt as to whether p?

Justification Puzzle #2: The TF's Dilemma

Suppose someone makes the following inference, and you have to decide whether they count as being justified in accepting the conclusion.

3 is odd
3 is prime

Intuitively, one wants to say: if they are making the inference "x is odd ---> x is prime" then the answer is no, but if they are making the inference "3 is F ---> 3 is prime" then they are. So how do we tell/what determines what inference they are making?

a. phenomenology: Is the answer to this question a matter of how the subject feels when making the transition above? But, let me stipulate that this is a psychologically basic inference for them in the sense that they don't consciously think of any rule before making it (on pain of regress there have to be some inferences which have this status for us, if we make any inferences at all). So all they experience is saying to themselves with confidence and conviction "3 is odd" and then, a moment later "3 is prime".

b.what other inferences they would make: Or maybe what matters is, whether they tend to accept other things, that are instances of the bad inference procedure, but not the good one (e.g. would they say "15 is odd" and then, a moment later, "15 is prime")?

But it will always be the case that a person is disposed to accept some bad, and some good, particular inferences. So, how do we carve up the space of different inferences they are willing to make into different "kinds" of inference?

How do we decide that e.g. being willing to infer `15 is odd'...`15 is prime', counts against being justified in inferring `3 is odd'...`3 is prime', but being willing to infer `3 is greater than 2'...`the number of gods is greater than 2', does not?

c. neuroscience: Well, maybe the workings of the brain will be best described by carving it up into different mechanisms which produce different classes of inferences. So, maybe we need to look at the class of inferences which are made via the workings of the *same brain mechanism* that lead the person to say "3 is odd...3 is prime"? But we know almost nothing about how brain-functioning is best individuated into different `processes'. So, if this were right, it would seem that we aren't yet in a position to evaluate claims about justification, even in normal cases.

d. just saying there's a brute primitive division of inferences into natural kinds: Ok, this is the best I can come up with, but it's certainly not very attractive.

p.s. I realize this is kindof like the generality problem for reliablism. But this problem seems to apply to everyone who accepts that we can be justified in making some logical/mathematical inferences.

Against Kim's argument against naturalized epistemology

In Epistemology Naturalized, Quine suggests that we stop worrying about epistemic normativity, and just study the engineering problem of how to get into situations where we reliably form true beliefs. So, for example, we might do scientific studies on the reliability of witnesses of various kinds of events, under various conditions. Or, we might use informal mathematical arguments to show that all reasoning of a certain formal kind are truth-preserving.

Jaeguon Kim objects to this, by making the following claim: the notion of justification and epistemic normativity is necessary to make sense of the very idea of beliefs. Someone believes that P iff an ideal interpreter would assign them the belief that P. And such an ideal interpreter assigns them beliefs, by interpreting their utterances in such a way as to jointly maximize a) the simplicity of the interpreter's theory and b) the degree to which (on the whole) the subject comes out to have beliefs that are justified. Thus, it doesn't make sense to study the reliability with which someone forms true beliefs, while rejecting the notion of epistemic normativity.

However, I don't buy that in order to understand the notion of belief we must accept some kind of analysis of it into other terms. You might think: we are just trained in the practice of interpretation, like we are trained to recognize certain things as games. We don't do this by consciously reasoning about justification, and Davidson's maxims or any other thing that one might use to try to define the notion of belief. Maybe there aren't any informative necessary and sufficient conditions for having a belief that P, or the only conditions are extremely complicated and will only be discovered after years of work by linguists.

If this is right, the argument `Unless the notion of justification is coherent, there will be no informative analysis of what it takes to count as having a given belief! Therefore, the notion of justification is coherent.' looks pretty unconvincing. Maybe the notion of belief is primitive.

Note, that saying there need not be necessary and suffcient conditions does not mean that there cannot be interesting cognitive science done, breaking down our capacity to recognize when a subject S counts as standing in the belief relation to a proposition P into various components.

Consider the following little fish. It has (among other things) four sensors a, b, c and d. Whenever a and b are touched it says "I feel xish", whenever c and d are touched it says "I feel y ish" and whenever a and c are touched it says "I feel z ish". There are no informative necessary and sufficient conditions to be given within the fishes' language (assuming this is all his vocabulary that relates to these four sensors). And yet there is nice simple relationship between these three claims at the level of sub-personal cognitive processing.

Thus, if the naturalized epsitemologist prefers to take "believes that" as a primitive (by not attempting to define it in any other terms) this doesn't suggest any kind of defeatism about the power of cognitive science to explain our complex linguistic capacities by appeal to simple systems.

But maybe, I didn't need to say any of the stuff in the last three paragraphs, because, (usually?), the proponents of epistemic normativity think its irreducible. So, I should think, it's no worse to take there to be primitive facts about the believing relation, than about epistemic normativity.

Can one intelligibly deny that one ought to form true beliefs?

It's sometimes said that you can't intelligibly deny that it's ceterus paribus valuable to have true beliefs (i.e. no one who doesn't accept this claim counts as having thoughts at all). The idea is, that in order to count as a thinker at all, you have to tend to have mostly true beliefs (or ones that are mostly reliable, truth preserving or justified). For Davidsonain reasons, we can't interpret people at all, unless we make them out to be mostly true/reliable/justified etc.

But I claim that actually, even if this Davidsonain idea is right (I think it probably is) it doesn't entail that someone can't coherently deny that having true beliefs is valuable.

For, all the Davidsonain considerations mentioned above would seem to require is that a person DOES modify their belief in a way that tends towards truths/matches up with what they would be justified in believing etc. They don't have to BELIEVE it would be GOOD to so modify their beliefs. Thus, I claim, a philosopher who denied that there was such a thing as epistemic normativity, would count denying that it is ceterus paribus valuable to have true beliefs (they don't think anything is valuable). (On the other hand, it is probably not possible for someone to deny that its ceterus paribus good to have true beliefs, but think something else would be ceterus paribus good).

What makes a crucial difference here, is the difference between thinking about whether Obama is a good president and thinking about whether one has reason to think that Obama is a good president. Colloquially we often use the expressions interchangably. But, in fact, in normal deliberation I don't entertain any propositions about what I should believe. I don't think about reasons, or beliefs. I just think about Obama, and then to form beliefs mostly in cases where (in fact) it is reasonable to form such a belief.

All we need to translate someone as having beliefs, is for them to tend revise these beliefs in cases where they should revise them, NOT for them to have any beliefs to the effect that they should revise them. The philosopher who denies epistemic normativity is an example of how you can have one without the other.