Knowledge, Discovery and Stuff

I was thinking of writing up some kind of reply to Scott Soames’s reply to my reply to his book. But the threat of an infinite regress was looming, and I thought it would be more fun to ruminate on his title: “What we Know Now That We Didn’t Know Then”. Because there are some fun puzzles about philosophical knowledge that the end of Soames’s book brings up.

Let’s start first with a puzzle about discovery. Consider the following situation.

  • p is a true philosophical claim.
  • S1 is the first to believe that p, but on the basis of a bad argument, so she doesn’t know that p.
  • S2, knowing that S1 believed that p, comes up with the first good argument that p, and so is the first one to know that p.

Question: Who, if anyone, discovered that p?

To make things more concrete, let p be the proposition that there are necessary a posteriori truths. Kripke wasn’t the first philosopher to believe that p is true. He wasn’t even the most prominent, I think. If I’m reading him aright, Aquinas holds that God’s existence is necessary a posteriori. I imagine Aquinas wasn’t the first to believe this about God, or more generally about propositions to do with the divine, but for the sake of the example let’s say that he was so he can fit S1 in the schema. I don’t know if Aquinas bothered to do the simple inference to the claim that some true proposition is necessary a posteriori, but I think we can credit him with tacitly believing this, as I’ll do for the sake of the example1.

Now many of us, probably most of us who aren’t Thomists, think that Aquinas’s reasoning did not grant him knowledge that there are necessary a posteriori truths. But does his true belief suffice to block Kripke’s claim to have discovered that there are necessary a posteriori truths? Whatever intuitions I have say yes. (At least assuming Kripke knew of Aquinas’s views. But I suspect he did as a tolerably well read philosopher. And assuming of course that my reading of Aquinas on this point is right, which is always dubious.)

Of course, Kripke discovered plenty of necessary a posteriori truths. But that’s different from discovering that there are any. (One can discover lots of spiders without discovering that spiders exist.) And he discovered the first good argument that there are necessary a posteriori truths (I assume, though Thomists might beg to differ). But I don’t think it’s right to make the propositional discovery claim.

It doesn’t seem like I can discover philosophical truths by going back through old philosophical works, finding plausible claims that are badly argued for, and finding arguments for them. That might be a good way to discover interesting philosophical arguments, but I don’t think by doing this I’d get credit as the discoverer that various philosophical claims are true. Not that I’d mind – I’m more interested in discovering arguments than anything else.

This does raise an awkward question: who (in our example) did discover that there are necessary a posteriori truths? I think the answer is no one. Aquinas didn’t discover this. Discovering that something is true requires having a good argument that it is true, and Aquinas didn’t have such an argument. Discovering that p might even require knowing that p. But we don’t need such a strong claim to deny that Aquinas discovered that there are necessary a posteriori truths. And I argued above that Kripke didn’t discover this either.

My position here has the unfortunate consequence that a truth came to be known without anyone discovering it. I think that’s a consequence that we can live with, indeed that we have to live with in some circumstances. Consider the following kind of case, which I imagine happens all the time in mathematics. A hypothesis q is widely believed, perhaps because there is a purported proof of it, and is used in the proof of many theorems. It turns out, however, that q is false, and something close, q* is true. (Imagine that q* is a version of q with slightly restricted quantifiers.) The difference between q and q* is not relevant for the proofs in which q was used, and in many cases it’s too trivial to even publish a note showing this. Now consider the theorem at the end of one such proof. We know now that it’s true. But who discovered it? The person who proved it on the basis of q? Arguably they didn’t know it was true, because q is false, and hence didn’t discover it. The person who proved q*? That will lead them to getting an enormous amount more credit than we feel they intuitively deserve. I think nothing to be said here other than that we came to know the theorem without anyone actually discovering it.

Well, this is all assuming that Kripke did know that there are necessary a posteriori truths. And we might question that. Rather than get the details right, I’ll work through an imaginary example to illustrate why I’m worried here. Expand the story above in the following way.

  • S2 provided a good argument for p, but also a bad argument that p, and she insisted that each argument is sound.

Does the bad argument defeat S2’s claim to knowledge? It’s somewhat plausible that it does. It certainly suggests that S2’s judgment around here is fallible, perhaps so fallible that judgment is not a ground for knowledge. If we put things in reliabilist terms, S2 is 1 for 2 in detecting good arguments for p. And whatever the threshold for reliability is, I imagine it’s normally meant to be above 50%. Well perhaps that’s the wrong reference class. But I hope you see why there’s a plausible threat to knowledge here.

Now that is arguably just what happened with Kripke. Here, for instance, is the abstract of a paper by Soames on Kripke’s work.

Kripke’s discovery of the necessary aposteriori is placed in historical and philosophical perspective. I argue that his first, essentialist, route to the necessary aposteriori has led to a distinction between metaphysical and epistemic possibility that is an important advance, while his second route to the necessary aposteriori has led to an attempted revival of pre-Kripkean orthodoxy which both threatens that advance, and leads to suspect philosophical results – including his own flawed argument against mind-body identity theories.

Sounds to me like Kripke fits the description of S2, and there’s reason to deny that in general S2 knows the philosophical claim in question.

Note that if we think discovery that p requires knowledge that p, as I think is at least plausible, we have a pretty clear case here of knowledge without discovery. The first critic who reads S2’s work and realises that the first argument is good but the second is lousy is the first person to know that p. But surely they don’t discover that p. So we can accrue philosophical knowledge without anyone making a philosophical discovery. So the initially attractive analysis of S discovered that p as S is the first to know that p is sadly mistaken.

1 I’m relying here on a fairly literal reading of the Third Way, and I’m sure there are reasons not to read it this way. One such reason might be that if read literally, it contains many modal fallacies. But as far as I can tell, any way of reading it will contain many modal fallacies, so charity doesn’t point against the literal reading here. Still, I’m no Aquinas scholar so perhaps there are better reasons to otherread him here. Admittedly the Third Way doesn’t look particularly a posteriori either, but I’m sure Aquinas intended it to be an a posteriori argument.

18 Replies to “Knowledge, Discovery and Stuff”

  1. I couldn’t help but to notice the similarity between your example and Fermat’s Last Theorem. I mean, the discovery of the result should be credited to Fermat or to Andrew Wiles? Or, to make matters worse, to no one? I am no specialist in mathematics, but I understand that the theorem is connected with fundamental properties of the space, so it seems a rather big achievement that we now know it (well, at least those of us who understand Wiles’s proof…). If my analogy is correct, your verdict bears upon scientific discovery as well, and perhaps all knowledge: to put it in your own words, we can accrue knowledge without anyone making a discovery. Of course it is not important who makes the discovery, but that the discovery occurs; this is what we call progress. Yet it seems to me that your picture greatly diminishes the role of individual efforts; it is as if there are various items of knowledge that are actualized by humans at various times, and somewhat at random, since we cannot establish that the production of a specific knowledge is the result or the effect of some action. Doesn’t this make the idea of scientific progress somewhat passive, something that just happens to the human race? Just a thought.

  2. “So the initially attractive analysis of S discovered that p as S is the first to know that p is sadly mistaken.”

    I agree, but aren’t there simpler examples that illustrate that this is mistaken? This morning, Alice snuck into Betty’s room and absconded with Carl, Betty’s cat. When Betty came back from the store, she discovered that Carl wasn’t in her room. But Alice already knew that.

  3. Hi Brian,

    Just a quick question that probably is trivial. You say thta “kripke discovered many necessary a posteriori truths”. But that can’t be right, can it? It should be that, if anything, he discovered that certain necessary a posteriori truths were such, not the truths themselves. If I understand his view at all, necessary a posteriori truths are discovered by people like scientists, and what the philosopher does, if anything, is discover that this necessary a posteriori truth discovered by a scientist is such. (Even that might not be right- Maybe what we ought to say about Kripke is that he gave the right account of what necessary a posteriori truths are. But surely he didn’t discover any of the things he discusses, even if you accept they are necessary a posteriori truths.)

  4. Brian,

    You make an interesting point, and I think I agree with the main thrust of your post. I do think your example is flawed in a number of ways. But I think it would be easy enough to find a more fitting example. (Here’s a try. I am shamefully ignorant of the history of science, but my comic-book level understanding of the turn to heliocentrism has it that Galileo and Copernicus came to the truth that the earth goes around the sun, but did so on the basis of inadequate science. When some later scientist came up with better scientific evidence for the truth of the claim that the earth goes around the sun, then that claim became knowledge. But, of course, that later scientist didn’t discover that the earth goes around the sun, and, arguably, neither did anyone else.)

    Anyway, on the Aquinas example, I have one quibble and one more serious concern. Here’s the quibble. Obviously, one needn’t be a Thomist to think that St. Thomas’s argument in support of the claim that “God exists” is necessary a posteriori works.

    More importantly, the relevant discussion in the Summa Theologiae happens not in the 3rd Way, but, rather, in a preceding article. (Prima Pars, Question One, Article Two. See ) And I don’t see anything at all dubious about that discussion.

    But, then, I am a Thomist, or at least something relevantly similar to a Thomist.

    Oh, and a different kind of point. I think one certainly ought to read the 3rd Way literally. St. Thomas was a very careful and very precise thinker. He said what he meant (and he meant what he said). The problem that you point out (i.e. the alleged modal fallacies) doesn’t arise from a literal reading, but, rather, from a reading the imports contemporary concepts regarding modality, etc., into the argument. The common supposition that the Summa was written “for beginners” and that therefore anyone (or even any philosopher) can just pick it up and figure out what’s going on is, I think, a bad mistake. Fr. Jenkins has argued, compellingly (to me) that the beginners St. Thomas had in mind were beginning graduate students in theology, who had already gone through the entire philosophy program in the faculty of arts. These are folks to whom the Aristotelian notions that St. Thomas employs in the Summa would have been perfectly familiar. Most of us, however, aren’t so lucky to have studied at the University of Paris in the 13th century. So we tend to have a harder time understanding what’s going on in the Summa than the original readers did.

  5. two worrisome steps are:

    1. that which might not have been at some time is not.

    2. it follows from (1) that if everything might not have been, then at some time there would be nothing.

    certainly Thomas gets (1) from Aristotle (the de Caelo and elsewhere) and so perhaps shouldn’t be blamed for the bad arguments there. But I think he does bear responsibility for (2).

  6. David,

    I don’t see any “bad arguments” for 1, as much as I see a quite distinct notion of necessity and possibility. Given the notion of possibility in play here, it is actually a conceptual truth that “that which is possible not to be at some time is not.” So no argument, bad or otherwise, is needed to establish 1. All that’s needed to see why someone would assert 1 is a grip of the concepts involved. Contingency (or possibility) here is simply the correlate of temporal necessity—which is the kind of necessity had by those things that exist at all times. And thus, all and only those things that fail to exist at some time are contingent. You may think that’s a silly notion of necessity and contingency. But the terms are clearly defined, and I don’t see why St. Thomas can’t use them as he sees fit.

    As to 2, if you read it as an instance of the quantifier shift fallacy, then it does make sense to say Aquinas should “bear responsibility” for it. Again, though, given an appreciation of the modal notions St. Thomas is working with, it is not at all clear that St. Thomas commits that fallacy. This one is tougher to try to explain, so I’m going to cop out, and say that I don’t want to fill up the comments box with this discussion, since it is peripheral at best to the point Brian was making in his post.

  7. I guess I fail to see how this kind of attention to the word ‘discover’ is really interesting. That Aquinas believed in the necessary a posteriori doesn’t seem to me very relevant to assessing progress in the areas of philosophy that interest Soames. There is surely some sense in which Kripke’s discussion of the necessary a posteriori is very relevant to progress in these areas and this not just because philosophers working in these areas read Kripke and not Aquinas, but because what Kripke said was more conducive to these areas than was what Aquinas said. In other words, if this is supposed to be an argument against Soames, it seems to me more of a terminological correction than a substantive argument against his placement of Kripke in the history of philosophy.

  8. Lots of interesting comments here. A few random replies.

    The Soames link is definitely working, but it’s a Word doc and some computers may not handle that.

    I agree entirely that being the first to know is not necessary for discovery. What I was really surprised to discover was that it’s not sufficient either. But I should have made this clear.

    As David says, the big fallacy in the Third Way is going from “Everything might not exist” to “It might be that everything doesn’t exist”. Even if you read Aquinas as talking about temporal necessity or some such, so the ‘Aristotelian’ step isn’t a fallacy, there’s still that fallacy.

    I agree too that there are plenty of ways other than being a Thomist to believe that God’s existence is necessary a posteriori. Presumably those who believe the argument from religous experience to be sound (and believe in God’s necessity) believe that God’s existence is necessary a posteriori. So I was wrong to suggest that it’s only Thomists who should be moved here.

    Matt’s right of course that Kripke didn’t discover the necessary a posteriori truths – the scientists did. What he discovered was that they are necessary a posteriori. My bad.

    Finally, as to why I’m interested in this. Soames in his reply lists three characteristics of the ordinary language philosophers. I happen to think Ryle, Strawson and Austin satisfied at most one of them (the same number that Quine and Williamson satisfy) so the list of characteristics probably isn’t right. But I think he left out one crucial and quite positive feature of the ordinary language crew. They thought it was important to look at lots of examples, not just the same old same old that we always look at (the bent stick, Macbeth’s dagger) and they thought it was important to learn about lots of relevant concepts, not just the ones we ordinarily consider (e.g. knowledge, belief, etc.) Rather than spending 26 weeks on KNOWLEDGE and none on DISCOVERY or LEARNING or the like, we should have a more even distribution. So I wanted to do some cheap conceptual analysis of ‘discovered that’, partially for fun, partially for the sake of the workout (this of this like the philosophy gym) and partially because it might reflect something back about knowledge.

  9. Three points:

    1. First off, it does seem right to point out that philosophers prior to Hume (say) did believe that there could be necessary a posteriori truths, if by this we mean that there are necessary truths that we can come to know only by experience.

    2. But it’s also not clear that these necessary a posteriori truths are of the sort whose possibility Kant dismisses in the first Critique and elsewhere; i.e. they require experience for us to come to know them, but we don’t justify them by way of the experience itself in the same way that we justify, e.g., the claim that there’s a computer on the desk. (I’m not sure if this is right, but it seems plausible to me.)

    3. This, though, raises the question of whether Kripkean identities are a posteriori in Kant’s sense as opposed to (say) Aquinas’s or Aristotle’s. This is a tricky point. But one reason to suspect that they’re not is that merely pointing to the fact that the clear stuff in this glass is composed of H20 won’t show us that all water is necessarily composed of H20; something extra is needed. (I think Fodor makes a similar point in his LRB article “Water’s Water Everywhere”.) In any case, the way we justify “this particular stuff is made of H20” is quite different from the way we justify “this kind of stuff is made of H20”. Whether this shows that Kripke and Kant are on entirely different wavelengths, I don’t know. But again, it seems worth considering.

    The upshot, I take it, is that it is (once again) important to get the history right on its own terms.

  10. John, I agree that the distinction you draw in 2 is very important to keep in mind here, but I think there’s a decent case to be made for saying Aquinas really held that God’s existence is a posteriori in the stronger sense. After all, he explicitly rejects the Anselmian claim that we can know the proposition God exists is true merely by understanding it. Now admittedly the bits of ‘empirical’ evidence he marshalls in favour of God’s existence are not always things we’d count as clearly a posteriori (e.g. everything has a cause). But I think he thinks at least that this is on a par (or at least on a continuum) with regular empirical investigation.

    Having said all that, I’m basing this on a fairly flat footed reading of the relevant passages, and someone who knows more of the context might be able to easily correct me.

  11. Brian, according to one plausible construal of the 3rd Way, the modal notion that’s relevant to explaining why St. Thomas doesn’t commit a quantifier shift fallacy is the “Principle of Plenitude,” according to which, given an infinite amount of time, all real possibilities are realized.

    If everything is contingent in the Aristotelian sense ironed out above, then it’s a real possibility that nothing exist. So if the Principle of Plenitude is true (and if the world is “eternal,” which this argument’s first advocate, Avicenna, would certainly have built into it) then at some time, there would be nothing real. There is no fallacy to be found in this line of reasoning.

    That’s not to say there’s nothing objectionable about it. You might think the Principle of Plenitude is obviously false. Or you might think it’s obviously false that the world is eternal. But to say that an argument has an (arguably) false premise (or two) is quite different from saying that it commits a fairly elementary logical fallacy.

    There’s the further concern, in interpreting the argument this way, that St. Thomas himself rejects the Principle of Plenitude, as well as the thesis that the world is eternal. So one might wonder why St. Thomas is advancing an argument that has premises he deems false. But, again, that’s a very different kind of worry.

  12. Brian, you make a good point in response, but I take it that the reason St. Thomas rejects Anselm’s argument is that he thinks the existence of God is ANALYTIC in Kant’s sense, not that it is a posteriori. I.e., it can’t be known merely from the meanings of words, but requires more than that. This doesn’t show, though, that it’s a posteriori in the relevant sense. I will try to get someone who knows more about Aquinas than I do to confirm whether this is right, on which more anon.

  13. I don’t think the problem is that “God exists” is supposed to be analytic in Kant’s sense. I think the problem is rather that we don’t have access to God’s essence. (This is true, even for those who have come to believe in God on the basis of a posteriori argument. Our knowledge of God is always, in this life, based on excess and remotion.) And since we don’t have access to God’s essence, we can’t claim to know that essence well enough to judge in advance that God’s essence is existence. And in the absence of that knowledge, we can’t judge that God exists on an a priori basis.

    Here’s the text: A thing can be self-evident in either of two ways: on the one hand, self-evident in itself, though not to us; on the other, self-evident in itself, and to us. A proposition is self-evident because the predicate is included in the essence of the subject, as “Man is an animal,” for animal is contained in the essence of man. If, therefore the essence of the predicate and subject be known to all, the proposition will be self-evident to all; as is clear with regard to the first principles of demonstration, the terms of which are common things that no one is ignorant of, such as being and non-being, whole and part, and such like. If, however, there are some to whom the essence of the predicate and subject is unknown, the proposition will be self-evident in itself, but not to those who do not know the meaning of the predicate and subject of the proposition. Therefore, it happens, as Boethius says (Hebdom., the title of which is: “Whether all that is, is good”), “that there are some mental concepts self-evident only to the learned, as that incorporeal substances are not in space.” Therefore I say that this proposition, “God exists,” of itself is self-evident, for the predicate is the same as the subject, because God is His own existence as will be hereafter shown (3, 4). Now because we do not know the essence of God, the proposition is not self-evident to us; but needs to be demonstrated by things that are more known to us, though less known in their nature—namely, by effects.

  14. I take it that those considerations about not knowing God’s essence are exactly the reason why we can’t know his existence analytically: it is because we don’t know God’s essence that we don’t know that the meaning of ‘God’ is ‘That than which nothing greater can be conceived’ (or whatever). So I stand by my point so far.

    The basic ideas I have in mind are that while [a] St. Thomas thinks it is necessary to experience certain very particular things in order to know that God exists, [b] his conception of a posteriority (“from what is prior relatively only to us”) is nevertheless importantly different from Kant’s (“borrowed solely from experience”), and so© I’m not sure that he thinks the existence of God is known a posteriori in Kant’s sense.

    But this still leaves open the question of where Kripke fits on the map. I haven’t yet memorized Naming and Necessity, so I’ll leave this one up to others. In any case, though, while it does seem clear to me that Aquinas would regard “Water is H20” as a posteriori and necessary, I’m not sure that Kant would need to allow the former (cf. again Fodor).

  15. I don’t think the Principle of Plenitude really helps Aquinas all that much in this context. Two reasons for this.

    First, even with the Principle the argument doesn’t work. We still need a step that takes us from “Everything is such that it might not exist” to “It might have been that everything didn’t exist”. That’s not a logically valid argument, and indeed on some nominalist theories it will even have a true premise and a false conclusion.

    Second, I don’t think that it’s much of a defence to a claim that X committed a logical fallacy by saying that with an extra premise the argument works. Every fallacious argument can be fixed up with an extra premise. To be fair, there could be good reason to think that Aquinas was taking this premise for granted, but I don’t think there’s much of a distinction between tacitly making dubious assumptions and committing logical fallacies.

  16. Brian,

    If everything is contingent in the relevant sense—i.e. if, for every particular thing, there is some time at which that thing fails to exist—then it surely is possible that, at some time, nothing exists. There doesn’t seem to be any argument or extra step needed here (why would one think it’s impossible that these things all fail to exist at the same time?). And once you have this possibility established, the Principle of Plenitude will get you its actuality. So again, I think the charge of the quantifier shift fallacy is off target. Perhaps I’m just misunderstanding your objection?

    As to your second point, I think one really has to keep the Summa’s intended audience in mind. There are lots of things that St. Thomas can reasonably take for granted when he’s writing a textbook for Dominican seminarians. The Avicennian context of the 3rd Way is one of those things, I think.

    Imagine a contemporary philosopher who pledges allegiance to the Credo of the Canberra Planners writing a paper on ontology, and framing arguments that take four-dimensionalism for granted. If the paper is a contribution to an ongoing debate among people who all take four-dimensionalism for granted, then—even if the person didn’t bother to flag that presupposition in a footnote—it might be fine to just take for granted what everyone else is taking for granted. Or imagine a paper on reducing modality that never bothers to try to convince us that reducing modality is a sensible project before giving its attempt to reduce modality. I myself am an antireductionist about modality and a presentist. So I would say that in both cases, dubious assumptions are being tacitly made. But I wouldn’t suggest that the arguments are thereby fallacious, or just as bad as fallacious. I would say, perhaps, that they are uncompelling (to me), because they rely on dubious assumptions. But, of course, the people making the assumptions won’t see them as dubious at all. Nor, perhaps will many of their readers.

    Whether something is dubious is, at least in many cases, a person-relative question. Whether something is fallacious isn’t. And whether it’s legitimate to make certain assumptions is a context-relative question. Whether something is fallacious isn’t. So I’m strongly inclined to think that “The 3rd Way is uncompelling because it assumes the Principle of Plenitude” is a perfectly appropriate objection. And I’m strongly inclined to think “The 3rd Way is fallacious because it commits modal fallacies (or something very much like modal fallacies)” is not.

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