Fallibilisms in Fantl/McGrath

We’re doing Fantl/McGrath in my grad seminar, and it is really great stuff–I’ve had a very high opinion of the book since it came out, but it is interesting to see how blown away the students have been by it. Very neat!

Anyway, the first chapter is about fallibilism, and I’ve been working on the distinction between fallibilism and infallibilism for a bit, finding it perplexing. And there is something really interesting here that I noted.

First some quick background. My interest arises because I’d like to see a characterization of fallibilism and its denial that are both exclusive and exhaustive, making every epistemic theory one or the other and not both. It used to seem simple to do so: one talked about entailing evidence and the failure of such, and that was that. But then along came the Cheap Infallibilisms: Disjunctivism in the theory of perception, the Williamsonian identification of evidence with knowledge, etc. (I’ll add an addendum that shows my own cheap version as well, one that doesn’t endorse E=K, but is built off a deduction theorem in epistemic logic. It’s very cool (perhaps, or in part because, trivial), I think, but you’ll have endure to the end to see it (or skip if you prefer)).

So usual construals of fallibilism fail the exclusive and exhaustive test, settling for a sufficient condition for fallibilism only. That’s fine if all you want to do is make sure you embrace the true view(!), but I want more. And I found something perplexing and interesting in F/M on this score, which I’ll report below the fold.

So, here’s what F/M do. They identify 3 versions of (attempts at stating) fallibilism. The first, entailing conception noted above, they reject because, among other things, it doesn’t distinguish between cheap and real infallibilism. Good point, I say: one can embrace logical infallibilism and bear the same relation to real infallibism–the kind of which Descartes is an exemplar–that decoy ducks bear to ducks.

So, then they describe two other versions of fallibilism, strong and weak, which are:

WEAK: a belief can be adequate without being maximally justified;
STRONG: a belief can be adequate even though the epistemic chance of it being false is not zero.

To understand the difference, and ordering of strength, we need to know something about what maximal justification is and what epistemic chance is. And here’s where it gets interesting.

About maximal justification, they first endorse the idea that any non-entailing justification fails to be maximal, because an entailing one is better. Again, good point. But then they write something that also seems right, but causes a problem. They say (p. 10),

…[S]omething infallibly known in the logical sense can still be fallibly known in the weak epistemic sense. If you know Plato taught Aristotle on the basis of entaling evidence . . . this is still compatible with you justification being imperfect. Your justification might not be enough, for example, to make you reasonable in investing [as much confidence] as you would in other propositions, e.g., Plato is believed to have taught Aristotle, let alone Here is a hand.

This point seems right, and though I think F/M are thinking only about cheap infallibilisms here, the same point can be made about real infallibilisms. Take Cartesian certainty as the exemplar here: if you insist that one has to be metaphysically certain to know, or be justified in believing, you are a real infallibilist. But once you see what F/M say in the last quote, you should or at least might agree about the range of things a successful completion of the Cartesian project would generate. Thus, you might say,

Even though I’m metaphysically certain that I think, and metaphysically certain that I exist, and metaphysically certain that God exists, axiomatic systems work in such a way that one is not always in a position to be as confident about the theorems as about the axioms. So there are distinctions to be drawn between the claim that I exist and the claim that God exists, since the derivation of the latter involves a bit of complexity.

That is, once one makes the F/M point about cheap infallibilisms and entailing evidence, it looks like there is no good reason to insist that the same can’t be said of paradigm, real infallibilisms.

But if that is right, then one can be a weak fallibilist, in F/M terms, and a real, genuine article infallibilist.

The same might also happen with strong infallibilism, unless one adds the proviso that anytime one is metaphysically certain, the epistemic chance of error goes to zero. In the first chapter, they never explicitly endorse such a claim, though I expect they think it is true. I myself can’t tell if this claim is true, because I’m not yet sure what epistemic chances are (I think I have a better idea what objective chance is, or what objective or subjective probability is, but an epistemic chance isn’t any of these.)

So perhaps strong fallibilism will turn out to be incompatible with real infallibilism, which would be a good thing. (It still won’t satisfy my other philosophical urge, because being a strong fallibilist isn’t obviously necessary for being a fallibilist, so I don’t yet get what I want, which is an exclusive and exhaustive taxonomy.) But what’s interesting is that F/M embrace a kind of argument that has a very reasonable extension that makes weak fallibilism compatible with real infallibilism.

So I recommend thinking of weak fallibilism in the way I think of cheap infallibilism: I throw them in the bin with decoy ducks and former senators and dead animals.


Suppose that E is (defeasibly adequate) evidence for p for S, where S is a person and both E and p, where we restrict everything to the domain of contingency. Then, in certain contexts, we’ll get a legitimate epistemic derivation of p from E. Suppose also that we find a deduction theorem attractive within this domain of contingency: if p is derivable from E, then the indicative conditional “if E then p” is derivable from nothing. And suppose one also thinks of all theorems within this domain as included in one’s body of evidence (this won’t work without the restriction to the domain of contingency, since one shouldn’t want all necessary truths to be in every body of evidence, but once restricted to the domain of contingency the view is much more plausible).

So, we then get a cheap infallibism, because in any circumstance in which p is justified for a person by E, that person’s evidence includes both E and the indicative conditional “If E then p”.

An interesting result to this extent: for those don’t appreciate the difference between cheap and real infallibilism, it is nice to find a very general form of the view that, by some attractive logic alone (rather than substantive epistemological commitments such as Disjunctivism or E=K), turns any fallibilist view about empirical knowledge into a cheap infallibilism.


Fallibilisms in Fantl/McGrath — 20 Comments

  1. Interesting argument for infallibilism!

    Here, maybe, is one way of responding to it…
    If evidence E defeasibly supports P then it seems plausible that the indicative conditional ‘If E then P’ should be defeasibly supported by an empty body of evidence. This would be a kind of ‘deduction theorem’ for defeasible evidential support. But the claim that ‘If E then P’ should always be a *part* of one’s evidence strikes me as a very significant further step – and I’m not sure that this extra step would be warranted.

    Suppose we think that one’s body of evidence must consist, at the very least, of truths (presumably, if we’re defining infallibilism in terms of evidence entailment then we will be thinking of evidence in this way). Since E only defeasibly supports P there will be possible situations in which E is true and P is false. In these situations the indicative conditional ‘If E then P’ will be false and, thus, could not count as a part of one’s evidence.

    One could still maintain, I suppose, that ‘If E then P’ is a part of one’s evidence in the ‘good’ cases in which E and P are both true – but this would seem to take us rather close to a kind of disjunctivist or Williamsonian account of evidence, or some fairly substantial commitments at any rate.

    This is my initial reaction to the argument anyway…I would like to think more about this!

  2. Martin, yes, that would stop the result, but at a burdensome cost. I think we should count as evidence anything we can use as a basis to extend our learning, i.e., anything we can properly base new beliefs on, where the new beliefs are doxastically justified. In extended defeasible reasoning chains of any sort, that would require counting as evidence some false claims.

    Another reason to allow false claims: we can come to know on the basis of false information. That’s the lesson of the Warfield/Klein counterexamples to the No False Lemma approach to the Gettier problem.

  3. Very interesting, Jon. You ask us to suppose “that…within this domain of contingency: if p is derivable from E, then the indicative conditional “if E then p” is derivable from nothing.” But I wonder why we should suppose that thing, as opposed to the following alternative: “that within this domain of contingency: if p is derivable from E, then ‘E justifies P’ is derivable from nothing.”

    On the latter alternative, we don’t (as far as I can see anyway) we end up with a cheap infallibilism just from the logic. Did you have any reasons in mind for going with your deduction theorem, as opposed to the foregoing alternative principle?

  4. Very interesting post, Jon. I don’t mean to interrupt the discussion of the clever argument in the appendix, but here’s some thoughts on the body of the post.
    I guess I think there are a number of notions of fallible knowledge and that there is no requirement that Descartes must be classified as an infallibilist on every such notion. If we understand fallible knowledge in the weak epistemic sense, then there will be no variations in degree of justification within the class of what’s infallibly known: if it’s known with maximal justification, it can’t be more or less justified than something else known with maximal justification. So, if you’re right that knowledge dependent on inference must lack maximal justification, then the only things known infallibly in this sense will be known noninferentially. This would show it’s hard *not* to be a weak epistemic fallibilist! However, one might hold out for some inferences transmitting maximal justification.

    As to the relation between metaphysical certainty and epistemic chance, I think we differ in that I feel I have a better grasp of the latter (by its role in rational choice and in determining the credences it is rational to have) than the former. However, I would hazard that moral certainty might be understood as having an epistemic chance of 1, and if metaphysical certainty required moral certainty, we could say that metaphysical certainty implies infallible knowing in the epistemic chance sense.

    It’s a fair point that our discussion of various fallibilisms doesn’t provide all that one would want in a taxonomy. Our main aim in the first chapter was to identify a plausible fallibilism with some important relevance to action, and then argue for conclusions about combining it with epistemological purism. (Well, that was one aim, and the other was to highlight the distinction, rarely noted, between logical/metaphysical conceptions of fallible knowing and epistemic conceptions.) However, one thing which we could have done, in the interest of developing a taxonomy, is to point out that someone (unlike Jeremy and myself) who thinks that epistemic chances can come apart from rational credences will regard the following definitions of fallibly knowing as non-equivalent:

    S fallibly knows that p iff S knows that p and the epistemic chance for S of p for S is less than 1.
    S fallibly knows that p iff S knows that p and S is not rational to invest credence 1 in p.

    I believe some philosophers who insist knowledge requires an epistemic chance of 1 grant that knowledge is compatible with its not being rational to invest credence 1 in what one knows. Some of these philosophers might also accept logical infallibilism (knowledge requires entailing evidence). They would then be able to call themselves fallibilists in the “rational credence” sense. If, as we suggest in the book, one might become more justified in p even after one’s rational credence in p is 1, fallibly knowing in the rational credence sense would not reduce to fallibly knowing in the sense of having less than maximal justification.

  5. Matt, this is where we part company, I think. If anyone is an infallibilist, Descartes is! If you guys had started the chapter by adopting an account of fallibilism and then noting that Descartes was one of them, that would be truly bizarre. So any account that leaves open having metaphysical certainty of the sort Descartes sought but being a fallibilist has to be mistaken. If one holds that once we get to entailing evidence, distinctions can’t be drawn anymore between quality of justification, metaphysical certainty would entail maximal justification. But once you allow distinctions even after entailing evidence, it looks like you’ll can have non-maximal justifications that still include metaphysical certainty.

    We agree, though, that the only important feature of the chapter for your project is how you characterize strong fallibilism, and for that I think all you need is something like what you note: at least by the time you get to metaphysical certainty, perhaps earlier at the point of moral certainty, the epistemic chances of error go to zero.

  6. Dennis, two things here. First, “derivable from nothing” is a bit misleading–it’s more like “derivable from whatever background system sustained the move from E to p in the circumstances in question.” Second, perhaps that E justifies p is also derivable here in addition to the indicative conditional. The reason for focusing on the conditional, though, is that it is the sort of thing one is likely to use when reasoning further, even if some epistemic sophisticates might use as premises things that include the language of justification.

  7. Jon, I think I missed something on my first reading of your post. Our thought about the cheap infallibilisms was this. Suppose you know P based solely on evidence E, where E is something else you know. Suppose also E itself comes short epistemically (e.g., by being imperfectly justified or by having an epistemic probability less than 1). Then even if E entails P, your knowledge that P will come short epistemically as well.

    Our principle was: shortcomings in, shortcomings out. I think you were suggesting in your post that even if there are no shortcomings in, there can be shortcomings out if there is inference. It’s a different point. So, I don’t think our point alone will have the implication concerning Descartes. Your point would. Maybe your point is right. But I think perhaps with certain utterly simple inferences nothing is lost in the inference. Admittedly, the fancy argument in Meditation III is not an utterly simple inference! (However, one might think that the conclusion of that argument gains credibility by its fit with other knowledge.)

  8. If evidence can include false propositions then, as you suggest Jon, my objection will lose its bite. But if this is a presupposition of your argument for infallibilism, then it is at least close to a substantial epistemological one. If nothing else, it rules out certain theories of evidence (like E = K).

    One further thought… on the view that we should count as evidence anything that we can properly base new beliefs on. This sounds to me a *bit* as though whenever S justifiably believes that P, P should count as part of S’s evidence. It’s plausible that any justified belief should serve as a legitimate basis for the formation of further beliefs. But this view would lead directly to evidence-entailment-style infalliblism – we wouldn’t need to detour via the deduction theorem.

  9. Martin, I think we are in basic agreement here. My point wasn’t to defend this version of cheap infallibilism, but to show another route to the view.

    On the substantive point, you are right that there is a danger of every justified belief being part of one’s evidence. There are ways to resist that, but even if we granted it, the view I have in mind will leave open how the evidential connections go. So even if P is part of one’s evidence, one won’t be able to base anything on it legitimately until the evidential connections themselves get fixed. And that will be left open until something about the total informational state in question fixes it. In short, even if we get an epistemic argument from E to p, we won’t get an epistemic argument from p to anything else, no matter what the logical or probabilistic relations between p and other things are. So, I would say in such a case, that p isn’t yet part of one’s evidence. But one could just as easily say that p is part of your evidence, but that it doesn’t yet have any epistemic consequences.

    That’s so programmatic it’s almost useless! Sorry for being so cryptic–I’m in the middle of a book ms arguing for this. Hope to be done by summer, but I said that last year too!

  10. This is tangental to the discussion, but I am puzzled by the distinction between WEAK and STRONG versions of fallibilism, particularly if one invokes the machinery of probability to model what ‘less than maximal’ amounts to.

    There is a conjugacy relationship underpinning probabilified Lockean belief whereby WEAK iff STRONG, and the reëngineering needed to preserve coherence would seem to rely pretty deeply on this biconditional. I wouldn’t say it impossibile, but if this distinction is supposed to carry over into probabilistic models of WEAK and STRONG, that looks like a pretty heavy lift.

  11. Greg, we were thinking the following sort of view is coherent and maybe true. Even after p is so well justified that its epistemic chance for you is 1, still, your justification might be further enhanced. Think of Moore who reasonably is certain that he has hands, and so the epistemic chance for him is 1 that he has hands. Imagine, though, that he were to come upon a non-question-begging refutation of the skeptic. One might think this would enhance his justification but doesn’t make a difference to how certain he should be. The same might hold for Descartes when a simple mathematical truth is before his mind prior to and after he devises his argument for God.
    Of course, if one thought justification could increase while epistemic chance stayed put at 1, one wouldn’t want to model “less than maximal” by epistemic probability.

  12. Thanks for the clarification, Matt. I meant ‘coherent’ in the avoiding sure-loss sense of the term. If ‘less than maximal’ is not presumed to be probabilistic, this avoids this problem but then I am unsure how to understand ‘less than maximal’. What is maximal justification? Is it a limit point on some scale, or an optimized function? Then what scale, what function?

    I’m pressing here (or, gesturing that one should press here) because I read your case for pragmatic encroachment to be backed by classical decision theory, even though the exposition suggests that we are led there by independent reasons. Would you agree?

  13. Greg, I wish I had something more useful to say than just this: “a limit point on the scale of justification.” You’re right that we were aiming to propose epistemic principles that are consistent with classical decision theory. In the first chapter, though, we explore a number of conceptions of fallible knowledge only one of which employs the notion of epistemic chance, that one being the strong epistemic conception. It’s the strong conception that is the one we use in the rest of the book.

  14. Thanks, Matt. Your book is on my stack to read!

    I have a thread I’d like to pull on, which I’ll sketch here. I don’t know the consequences for your specific view; it may in the end be something that you endorse. I’d like to sketch the point as a possible source of trouble, however.

    Teddy Seidenfeld has a recent paper (w/ Jay Kadane and Mark Schervish) discussing de Finetti’s two notions of coherence, both of which are based on some notion of an ‘undominated’ choice, and his (deF’s) famous representation theorem linking the two. The mathematics are fine, but each conception gives a very different operational definition of probability (i.e., procedures for eliciting credences). The one notion, most familiar, is the two-person game between ‘Bookie’ and ‘Bettor’ which has as a special case the familiar Dutch Book argument. The other, less familiar but no less important, is the one-person ‘Forecaster’ game which turns on a proper scoring rule that incentivizes the agent to minimize Brier score. De Finetti thought the latter conception was a better operationalized definition of probability, as it avoids strategic confounds that the two-person game introduces. Proper scoring rules build in ‘more directly’ the incentive for the Forecaster to give his honest opinion about the outcome. To cut a long story short, through this path you get a nice way to yoke partial belief more closely to the ‘true’ estimation of the outcome of the event in question. It is a rope to tie down the decision model to something that appears to be epistemologically invariant.

    Teddy’s paper cuts this rope by showing that the story hinges on the currency that beliefs are scored and bets taken be the same; the ‘units’ of the utilities have to be held constant. If you price one set of bets in euros and another in dollars, for example, you are at sea, which means that in the background there must be *some* designation of units for the machinery to go. To put the point in your terms, pragmatic encroachment infects belief and not merely justified belief.

    Teddy takes this to be an unhappy consequence of de Finetti’s program. As an aside, Wlodek Rabinowicz gave a talk in Vienna in December which embraced (in effect) this consequence.

    This is a long set up. But, the question I’m curious to explore is whether the idea of pragmatic encroachment on *epistemic justification* is a stable position. What I mean by that is whether in fact the position collapses to pragmatic encroachment on *belief* simpliciter.

  15. Hi Jon (and Martin),

    I had a quick question about something you said to Martin about evidence and falsehoods. You mentioned two reasons that one might like the idea that falsehoods constitute evidence.

    You said that we should count as evidence anything we can use as a basis to extend our learning, serve as the basis for justified beliefs, etc. I worry about this rationale because I cannot see any good reason to reject the following possibility (unless you come to believe some of the strange things that I do): you get arbitrarily strong misleading evidence for believing that p is a genuine bit of evidence that can justify further beliefs. Intuitively, if you justifiably believe that p is a justifying reason, you can justifiably infer the obvious consequences of p but I don’t think p ‘becomes’ a real reason.

    You also mentioned the Warfield/Klein cases. Here’s a worry I have about those cases. It seems that the intuitions we have about such cases are pretty robust. Too robust, you might say. Suppose Virginia believes she’ll have presents and her belief is based on her further belief that Santa will deliver them. I think many of us have the intuition that she knows that she’ll have presents and that we’ll still have this intuition when we fill in an important further fact–most children like Virginia have a cluster of beliefs about presents, Santa, their parents, etc. that form an inconsistent set of propositions (e.g., that her parents don’t know Santa personally, that Santa enters the home without asking, that Santa is a good person, that good people don’t enter the homes of strangers without asking). Now, I think that the elements of this set are the sorts of things that Virginia might justifiably treat as reasons for her beliefs, but if each element is part of her evidence, there’s the worry that her body of evidence is a set of inconsistent propositions. If we assume that evidence is evidence because it raises the probability of what it’s evidence for, we get a problem (i.e., the probability of a hypothesis on a body of evidence is undefined when P(e) = 0 and it seems that P(e) = 0 if e includes the propositions listed above). I wonder what’s to be gained by insisting that your evidence includes what you justifiably believe rather than saying that you can justifiably treat something as if it is evidence if it is justifiably believed? I think Fantl and McGrath retreat to this weaker principle and it’s a good idea for them to do so because they don’t want to deny that falsehoods can constitute reasons/evidence, etc.

  16. Clayton, here’s the part that I don’t buy from the first paragraph: ” Intuitively, if you justifiably believe that p is a justifying reason, you can justifiably infer the obvious consequences of p but I don’t think p ‘becomes’ a real reason.” That’s just false, I’d say. In any case, it’s a clear extension from the point I was making to Martin, since it didn’t endorse the JJ implies J principle you use here.

    Note also that I didn’t claim that everything a person justifiably believes is part of their evidence, though that remains an option, I suppose. And I don’t see any more reason to think our evidence has to be consistent than to think that all of our justified beliefs have to be consistent. That entails, quite straightforwardly, that you can’t model this with probabilities, but we knew that on independent grounds. I also doubt that Virginia in fact has inconsistent beliefs about presents. To get it in your example, you have to attribute to her the belief that nobody ever enters the home of a stranger without asking. I doubt there’s any good reason to think Virginia thinks this, or to think that she thinks that Santa is a stranger to either her or her parents. I do expect, however, that if you started to interrogate her, you could get her to respond inconsistently at some point, but that doesn’t get the inconsistency you posit here.

  17. Hi Jon,

    I agree that the JJ principle wasn’t something you committed yourself to. Just to clarify, which bit is false? Is it that if you have sufficient evidence to justifiably believe _p is a piece of evidence_ and you justifiably believe that _p is a piece of evidence_ you can justifiably infer the obvious consequences of p? Or, is it that you thought that when you have sufficient evidence to justifiably believe _p is a piece of evidence_ and you believe on this evidence that _p is a piece of evidence_, p just is a piece of evidence?

    Maybe the following doesn’t strike you as intuitive, but it strikes me as intuitive: if you justifiably believe _p is a piece of evidence_, you can rationally infer p v q and rationally believe p v q on the basis of your rationally held belief _p is a piece of evidence_. I don’t think, however, that it follows that p is indeed a piece of evidence. Don’t know if you agree with the rationality intuitions or if you think that what’s rationally believed and what’s justifiably believed aren’t always the same thing.

    As for the Virginia case, I think most kids like Virginia do believe that good people don’t enter the homes of strangers without permission, that Santa never asked their parents permission, that Santa is a good person, etc. (I might not have fleshed out the details with sufficient care, but who can find a quiet place to blog these days? Not me. I blog next to a very loud dryer with a dog pulling on my sweatshirt.) What I think is implausible is the idea that whether Virginia’s belief about presents constitutes knowledge depends upon whether her total outlook on Santa is consistent. (I think we agree there.) You might be right that we cannot model the notion of evidential support with probabilities, but I guess I don’t want to reject out of hand the idea that evidence supports by means of probability raising. I get that people think factive accounts of evidence conflict with their intuitions, but often the conflict is brought out by appeal to principles about the role of evidence where I don’t have any idea where these principles come from. I guess I don’t see what’s gained by saying that whatever a justified belief is based on is a bit of evidence rather than saying that whatever justifies belief justifies treating something as if its evidence and leaving it at that. (Not that you defend the view that Jp entails Ep, mind you.)

  18. Clayton, I reject the relevance of -p is a piece of evidence-. You can get to q when -p implies q- is part of your evidence, provided p itself is part of your evidence as well (in which case the conditional isn’t really needed, except as an epiphenomenon of p being evidence for q). In short, what matter is that p is evidence for q, not something that requires the discharge of an operator or relation, such as the evidence operator or relation.

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