Is Knowledge True Justified Belief?

Yes, despite the counterexamples. It is fair to say that before Gettier’s paper the TJB analysis of knowledge was the accepted theory. The theory was not regarded as a work in progress, as somehow incomplete, or vulnerable to counterexample. If not self-evidently correct, it was taken to be clearly and incontrovertibly correct. It is true there were some doubts about the necessity of the three conditions for knowledge, but not the sufficiency: nothing meeting those conditions could fail to be knowledge. That is why Gettier’s counterexamples came as a surprise, a shock, and a blow. If TJB doesn’t define knowledge, then what does! Some tried to retain the old analysis by claiming that the examples all involve defective justifications (and there was something odd about those alleged justifications), but most accepted that the counterexamples refuted the analysis. How could we have been so wrong—so confident and yet so misguided? Thus the hunt was on for a better theory, one immune to counterexample. But surely there is something funny going on here: is it possible that the pre-Gettier confidence was actually well placed and yet his counterexamples do show the conditions not to be logically sufficient? In what follows I will defend this position, which may seem not to exist in logical space. The key will be to distinguish between being a good theory and being a theory that provides necessary and sufficient conditions in every possible world: the latter is not required for the former. Or, to put it differently, a theory of what knowledge is isn’t the same as a logically watertight analysis of the concept of knowledge, i.e. the provision of a (complex) concept identical to the concept of knowledge. We can have a good theory (a true theory) of knowledge without it being immune to conceivable counterexamples concerning possible cases; and TJB is such a theory.

            The TJB theory tells us that knowledge is not the same as belief, which can be both false and irrational or unjustified. It distinguishes knowledge from mere opinion, because knowledge requires truth and a rational basis. It identifies the main components of knowledge, as they distinguish knowledge from belief (this can be useful when fighting sophists, say). It connects knowledge to the normative concepts of truth and justification, revealing what attempts at knowledge aspire to. These are important insights, adequate for most practical purposes, and they are recognizable by any normal person. By these criteria the TJB theory is a good theory. The existence of Gettier-type counterexamples does not defeat these insights (which go back to Plato). So what do they tell us? They tell us that in conceivable cases the conditions are not logically sufficient—there could be cases in which they are satisfied but the believer doesn’t know. Not that such cases are common, or even actually occur, or that they show that knowledge is not different from belief after all, but just that they exist in logical space: we can imagine such cases and our intuition tells us that they don’t qualify as knowledge. The question is why this matters: so what if the theory doesn’t cover every imaginable case? Was it ever intended to? Can’t it be a good theory and not cover all of logical space?  What if we said it was only meant to cover actual or typical or central cases of knowledge? If we had said that knowledge is just belief, we would face the objection that this fails to cover even the most common and central cases; but Gettier cases are admittedly uncommon and not central, involving bizarre kinds of justification. A good theory needs to get the basic elements of knowledge right (truth and justification), but does it need to cover all conceivable cases, no matter how contrived or irrelevant to daily life? Can’t it be more like an empirical scientific theory, which doesn’t purport to cover all of logical space?

            Before pursuing this line of thought let’s remind ourselves of some analogous cases in which an illuminating philosophical theory runs into unexpected trouble with the logically conceivable. Take the causal theory of perception: in order for a sensory experience to count as a perception there must be a causal connection between the experience and the object; it isn’t enough to see a clock that a clock be there and you have an experience as of a clock. This theory rightly distinguishes perception from veridical hallucination and it points to the indispensible role of causation in constituting perceptual facts. (The same can be said about memory: the memory impression must be caused by an earlier event in order to count as remembering it.) But no sooner was this theory propounded than counterexamples to it were constructed (note the word): we had the problem of deviant causal chains. Does this show that the causal theory of perception is a bad theory? Not at all: it merely shows that the conditions it identifies don’t logically guarantee perception in every possible world—they are not logically sufficient. But in all actual cases there are no such deviant causal chains and the theory works just fine; more important, it identifies the main elements of the perception relation, illuminatingly so. We shouldn’t throw out the theory simply because counterexamples to it can be produced: it gives us important information about what perception consists in. Or consider Bernard Suits’s definition of a game: an activity in which inefficient means are adopted to achieve an end (I oversimplify). Suppose counterexamples could be contrived showing that logically possible cases could satisfy these conditions and not be games (not that I think this can be done). Does that imply that Suits failed to identify the central element in what distinguishes a game from what he calls a “technical activity”? Obviously not; and all actual games may well obey his theory (and no non-games). Thus we should distinguish theoretical adequacy from the provision of logically necessary and sufficient conditions. We detach the adequacy of a theory from any claim of complete modal coverage. We separate the project of providing a good theory of games (the things themselves) from the project of providing a (complex) concept identical to the concept of a game. These are quite different enterprises—one about the nature of things as they actually exist, the other about the content of a concept that we can extend to merely possible cases. Both enterprises may be worth pursuing, but they should not be confused—hence the failure to do the latter does not undermine the success of the former. A good theory of X need not be a good theory of the concept of X that covers every conceivable application.[1]

            Let me illustrate the distinction by reference to a well-known paradigm—scientific natural kinds. Suppose a chemist announces that water consists of H2O. That is a very good theory: it connects water to molecular theory and it distinguishes water from other substances, among other things. Then a philosopher comes along and objects as follows: couldn’t there be some other chemical combination that also qualifies intuitively as water, as it might be H3O, so that the H2O theory doesn’t provide a logically necessary condition? Moreover, couldn’t hydrogen and oxygen molecules be distributed in a ratio of two to one but be so spread out as not to form what we would intuitively call water, so that the condition isn’t sufficient? The point is not so much that these are genuine counterexamples to a claim of logical necessity and sufficiency—though they do appear to be—but that they are irrelevant to the chemist’s claim. For the chemist was not asserting that, as a conceptual truth, water is H2O in all possible worlds; his claim was more limited than that (no matter what a philosopher may expect). His claim was more like this: the theory identifies the main elements of water, distinguishing it from other substances, and connecting it with molecular theory. It’s about actual water and what it’s made of not about how things are in possible worlds. He might go as far as to say that his claim is a nomological necessity—a lawlike truth about the actual world—but he has no interest in venturing claims about how things might be out there in logical space. His attitude towards the counterexamples cited will be one of sublime indifference, given that they do nothing to undermine his claim to winning a Nobel Prize in due course. Or consider heat and the theory that heat is molecular motion. Someone might object that there are conceivable cases in which we have heat without molecular motion and molecular motion without heat: some possible things that we would intuitively count as heat are correlated with some other physical phenomenon, and in some conceivable circumstances there could be molecular motion but no heat. Again, it doesn’t matter whether the counterexamples are persuasive; the point is that they don’t matter so far as the physical theory is concerned. That theory is not intended as a theory of how the concept of heat applies in imaginary possible worlds; it’s about heat as it actually exists and acts here and now.

            Old hands will no doubt be clamoring to explain about the necessity of identity: if the scientist is making a claim of identity, then he is committed to rejecting the counterexamples, so that they do count against his theory if they are genuinely possible cases. But why should we foist any such interpretation on his words (or thoughts)? This identity business is philosophy talk not chemistry talk. He said that water consists of H2O and heat is a manifestation of molecular motion; and these don’t force any modal claims on him—he might readily allow that water and heat could be different in other possible worlds.[2] Similarly, the epistemologist need not claim that knowledge is identical to true justified belief, which would land him in trouble with the Gettier counterexamples, given the necessity of identity; his claim could rather be that these are the main elements of knowledge, or that nearly all knowledge fits this analysis, or that it is a matter of natural law that knowledge is TJB, or that the central cases of knowledge conform to the theory, etc. He might cheerfully allow that the theory does not cover all conceivable cases, even acknowledging that the concept of knowledge is not identical with the concept of true justified belief. After all, philosophers only recently started fretting about necessary and sufficient conditions for concepts to apply: before that they were content to offer theories of things. In fact, this practice started around the middle of the twentieth century, possibly as a result of the logicist program in philosophy of mathematics—the attempt to rigorously define mathematical notions in terms of logic. Here the idea of a priori necessary and sufficient conditions had some purchase (see Russell’s theory of descriptions as an offshoot), and it was natural to hope for something similar in other areas of philosophy. But this was not the project of philosophy in earlier times, or independently of certain trends in analytical philosophy (Frege could be said to be the originator); instead people were trying to produce adequate theories, as judged by the usual criteria. The demands on conceptual analysis in terms of logically necessary and sufficient conditions are very stringent, but the philosopher need not be wedded to that methodology; and this means that there is room for a type of theory that doesn’t have such lofty goals. We can thus accept that TJB provides a good theory of knowledge without insisting that it captures all conceivable cases, either through lack of necessity or lack of sufficiency. This is what knowledge basically, centrally, paradigmatically, is—even if there are odd cases that don’t quite conform to it. It can be argued that not all knowledge requires belief (uncertain knowledge, animal knowledge), that not all knowledge requires justification (direct knowledge of one’s own mental states), and that not all knowledge even requires truth (can’t someone know that the golden mountain is golden, though this proposition is neither true nor false?): but these are not central cases, so they don’t undermine the general goodness of the TJB theory. Similarly, Gettier-type cases involve strange kinds of defective justification (e.g. Russell’s example of the accidentally accurate stopped clock); they are by no means common or central. This explains why no one thought that the TJB theory was vulnerable till Gettier came along—it wasn’t vulnerable, given its aims. What Gettier in effect did was force us to distinguish between two projects: giving a sound theory of knowledge (the thing) and providing necessary and sufficient conditions for the application of the concept of knowledge in all conceivable cases. We can engage in both projects but we shouldn’t let one be hostage to the fortunes of the other. We certainly shouldn’t give up on providing a theory of knowledge just because we can’t find necessary and sufficient conditions for the application of the concept. The TJB theory is a fine theory by any standards, a solid philosophical achievement, despite the counterexamples.[3] Indeed, we might applaud it for being precise enough to allow the construction of counterexamples to it (a simple true belief theory will not lead to the kind of ingenious cases invented by Gettier and others). The same is true for the causal theory of perception and memory and Suits’s theory of games (also Grice’s original analysis of speaker meaning). These are all great theories, exhibiting the power of a priori philosophical analysis, despite the possibility of clever counterexamples. One might be tempted to conclude that there will always be counterexamples in philosophy, but that doesn’t prevent us from coming up with excellent theories. There are counterexamples to the claim that tigers are striped and have four legs, but that doesn’t mean that this “theory” is defective in any way when properly understood.

[1] Compare the case of sentences: we could define a sentence as a meaningful combination of words expressing a complete thought. Is this definition sufficient? Isn’t Shakespeare’s “But me no buts” a meaningful combination of words expressing a complete thought, but it’s not a sentence (it isn’t grammatical)? It’s like “On me no ons” or “It me no its”. So a meaningful combination of words expressing a complete thought need not be a sentence. Fair enough, one might say, but that hardly undermines the general correctness of the definition in question. It only fails to apply in the oddest of cases.  

[2] A different kind of example: it might be a good theory of life to say that life is the operation of selfish genes, i.e. DNA molecules, while allowing that on other planets, or in other possible worlds, reproduction works differently with no DNA involved. It’s a good theory because of its explanatory power and unification of macro biology and microbiology, but it need not aspire to metaphysical necessity. In philosophy too a good theory might have many such “counterexamples”, just as a bad theory may have none (e.g. “knowledge is a very special kind of belief”).

[3] As Kripke would say, something can be a good “picture” without being a watertight “theory”; or as I prefer, something can be a good theory without being a watertight conceptual analysis. And it isn’t that such a theory aspires to being conceptually leak-proof.

Intentionality and Psychologism

Brentano’s thesis is that every mental phenomenon is directed to an Object distinct from itself.[1] It has an extra-mental correlate—the thing thought about or perceived or desired or loved or hated, etc. This entity may or may not exist (but I will ignore the latter case from now on). On the one hand, we have the mental phenomenon itself, on the other, the Object of the phenomenon. What this Object is can be quite various; it is certainly not to be identified with an existent material thing. It can be viewed as a theoretical entity whose existence (sic) follows from the nature of the mental: objects, properties, and states of affairs will be included, but also anything else called for by the mental phenomenon in question. There is nothing in Brentano’s formulation that requires the Object to be part of common sense, or even cognitively available to the subject. One question we can ask is what counts as a mental phenomenon for Brentano: does he mean a whole mental state like a judgment or desire, or does he mean to include constituents of such a state? That is, do concepts also have intentionality? I mean “concept” in the broadest sense that corresponds to meaning or Frege’s Sinn not just mental representations of properties—thus including quantifier concepts, connective concepts, modal concepts, ethical concepts, logical concepts, and so on. Do all of these have an extra-mental correlate as their Object? I propose that we take Brentano’s thesis literally and apply it to these mental phenomena too; indeed, we might take the Object of a whole mental state to be a function of the Objects corresponding to the constituents of that state. If so, we are going to need a specification of which Object such a mental primitive is directed towards (compare Frege’s generalized theory of reference).

            I said that each mental phenomenon must have an extra-mental correlate, but of course this is wrong construed completely generally, since some mental states take other mental states as Objects, either in oneself or in others. I can believe that I’m in pain[2] and I can deplore your political beliefs, for example. But these mental states must themselves be about something other than themselves, so that my mental states directed towards them will inherit their Objects. In fact, a potential regress lurks here: if the mental state that my mental state is about itself has a mental state as its Object, then we will need a further Object to be the Object of this mental state. According to the intentionality thesis, then, such chains of mental states will bottom about in a non-mental Object. So we may as well say that every mental state ultimately has a non-mental Object as correlate. But we have still not said what these Objects are—what is it that every mental phenomenon must bring with it as a distinct entity? Here our options are wide open; so far we have only a schema not an articulated theory. We might favor existing material objects and their properties, or we might prefer some sort of peculiar “intentional object”; and when it comes to quantifiers and connectives we can wax more abstruse—maybe the Objects here are Fregean functions, taken either in extension or intension. We might even suggest that the Object of the concept and is the truth table corresponding to conjunction. Nothing in Brentano’s formulation stipulates that the subject should be conscious of the Object, let alone be in a position to define or articulate it: Brentano doesn’t say the required Object must be known by the subject—it merely has to be. So the Object of and could be a set of introduction and elimination rules, or a functional role, or even a brain state—as long as it is distinct from the concept and itself (it could even be an idea in the mind of God). The essence of the thesis is just that every mental phenomenon is directed to an Object of some sort as part of its very nature. In principle it could be abstract, fictional, or recondite.

            Suppose I am thinking about physics and contemplating the law of gravity: I am deploying the concept the law of gravity. What is the Object of my mental act? Surely it is the law of gravity, construed as a non-mental thing. So natural laws can be Objects of mental states too. I could be wrong about such laws, but they would still be the Objects of my thought (compare perception and material objects). Or suppose I am thinking about morality and contemplating the Golden Rule: isn’t the Object of my thought precisely the Golden Rule? But then it must be distinct from my contemplation of it, by Brentano’s thesis; and the same for any moral thought—the value that is thought about must be distinct from the thinking about it. The concept good must have an Object that is not identical to that concept, which we might think of as the property of being good (or the Form of the Good if we follow Plato). Not that we are constrained to such entities by Brentano’s thesis alone, but they would be examples of the kind of thing that is required by the thesis. What matters is that they are not mental. For the thesis is that the mental is always inextricably bound up with the non-mental. Now let’s consider logical reasoning: I am thinking logically about a problem and I engage in a bit of logical inference, say by modus ponens. What is the Object of my mental process? The answer is modus ponens (or something else if we want to get eccentric about it, say the Andromeda galaxy, but let’s stick to modus ponens). But this logical law must be non-mental in order to be the Object of my mental act of employing it. Therefore psychologism is false. The law can’t be identical to the mental process I am engaging in, since that process needs an extra-mental correlate to be its Object. Thus Brentano’s thesis refutes psychologism about logic. The mental process of logical reasoning must be about something, but this something can’t be itself, so logical laws can’t be identical to logical reasoning. Of course, we might have come to this conclusion on other grounds (see Frege), but it is striking that the relatively anodyne claim of universal intentionality should yield such a powerful result. There seems to be a strong tendency to psychologize logic, but this is incompatible with the principle that all mental phenomena need a non-mental Object. We simply need to extend Brentano’s thesis from the obvious cases to take in such mental phenomena as logical reasoning: because inference too has intentionality, like thinking about natural laws and ethical precepts. The mental process of inferring must itself be about something, and that something is logic. If we were to try to reduce logic to logical reasoning (i.e. adopt psychologism), then we would face the question: “But what is logical reasoning about?” It can’t be about itself, so it must be about something else, and that something is surely logical reality (whatever exactly that is). A sensory perception must be about something, but that something can’t be itself, so there has to be something non-mental involved (e.g. a material object); logical reasoning obeys the same rule, so that psychologism is excluded. Psychologism with respect to logic is really a species of idealism, and Brentano’s thesis cuts against idealism, since mental states must be directed towards extra-mental entities of some sort (not even Berkeley thinks that ideas of sense are representations of themselves). At the least we need something like intentional objects, which are not mental (what they are is hard to say). So Brentano’s thesis has metaphysical teeth precisely because it connects the mental with the non-mental. His insight was that the mind is essentially a representing thing, but that it doesn’t represent itself qua mind: it opens out onto a wider world (though this world might not exist). In contrast, the body is a non-representing thing, making no reference to anything beyond itself (it makes no referenceat all). Idealists (including proponents of psychologism) make the mistake of assimilating the mind to the body, ironically enough, ignoring the way the mind reaches out beyond itself; but once we take the measure of intentionality we see that there cannot be only the mind (there could be only the body). If there is mind, there must be something other than mind, such as objects, properties, states of affairs, truth functions, natural laws, ethical values, and laws of logic. It isn’t that the existence of mind entails the existence of the commonsense world (we haven’t refuted skepticism), but there has to be a level of reality (there is no other term) beyond the mental as such. There has to be something non-mental for the mind to latch onto even if it is just those elusive intentional objects (or possibly Platonic forms).[3]  

[1] I write “Object” to indicate that I am using the word in the sense it has in “object of thought” where anything thought about qualifies as an Object (including properties and functions).

[2] It is sometimes thought that pain is a counterexample to Brentano’s thesis, since it has no Object beyond itself. There are two cases to consider: emotional pain and physical pain. In emotional pain the extra Object will be whatever is the cause or occasion of the pain—the rejection, loss, treachery, or perfidy, as the case may be. In physical pain it will be the part of the body where the pain is felt to occur (which may not actually exist). No pain is ever completely dissociated from accompanying allusions to distinct Objects.  

[3] The question of why the mind is intentional is left open and is difficult to answer. Could there be a type of mind, not necessarily conceivable by us, that is not intentional? What function does intentionality serve, if any? Does it have anything to do with information processing? What is its physical basis in the brain? Does it derive from any more basic feature of the cosmos? What is its connection to consciousness? How did it evolve? It is certainly something remarkable and not present in non-mental reality, but we know little about it beyond its evident existence.  

Quantifiers and Mass Terms

The usual approach to quantification focuses on quantifier words combined with count nouns, as in “All men are mortal” and “Some sheep are black”. We are told that such sentences require a paraphrase by means of variables ranging over objects (the “domain of quantification”)—“for some object x etc.”. But there are quantified sentences that employ mass terms not count nouns, as in “All coal is black” or “There is some milk in the fridge”. No objectseems to be meant—no x such that… It makes sense to ask how many objects are thus and so in response to a quantification using a count noun, but we can’t ask how many coal are black or what the number of milk is. We can ask how much coal or milk there is in a certain location, but not how many coal or milk is there. Mass term quantifications don’t “range over” a class of countable objects that can be assigned to bound variables. That is not how their semantics works. Yet the logic of such sentences follows the logic of count noun quantifications: from “All coal is black” and “This is coal” we can infer “This is black”. So it looks as if the standard semantics doesn’t capture the logical implications that are involved. This means that predicate logic is inadequate to capture quantifier entailments. Not good!

            It might be thought (hoped) that mass term quantification can be analyzed by means of count noun quantification; we just need to bring in an ontology of chunks, lumps, pieces, volumes, morsels, and smidgens. Thus we have “All chunks of coal are black” and “There is a volume of milk in the fridge”. This already sounds stilted, but it also trades on a correspondence that doesn’t amount to a paraphrase. It is true that we can manufacture a truth about objects by employing such dummy sortals, but that doesn’t mean that the two mean the same thing. Likewise we can contrive a mass term quantification for any count noun quantification, but it would be wrong to claim semantic equivalence. Consider “There are many cod fish in the North Sea” and “There is a large amount of codfish in the North Sea”, where “codfish” functions as a mass term like “salmon” or “halibut”. Where there are fishy objects there is fishy stuff, and where there is fishy stuff there are fishy objects. But does anyone think we can analyze “All men are mortal” as “All man stuff is mortal”? One type of sentence speaks of objects of a certain kind; the other type speaks of stuff of a certain kind. Objects and stuff go together, but talking of one is not talking of the other. Also, the paraphrase in terms of dummy sortals doesn’t always get the truth conditions right: it may be true that all coal is black but not that all pieces of coal are black, because some pieces might be too small to have color; and the milk in the fridge might be scattered about not collected into a discrete volume. And isn’t it consistent to reject an ontology of objects while accepting that the world contains stuffs? There is coal and milk and gold and blood but there are no objects corresponding to these stuffs (“stuff metaphysics”). Stuffs are manifested at locations, according to this view, but there are no real objects that fall under mass terms. You can be an eliminativist about objects but a realist about stuffs. There is certainly no obligation to accept the count noun paraphrase, clunky as it is. It looks like an ad hoc attempt to save a theory not a natural semantic analysis.

            Note that this point also destroys Russell’s theory of descriptions: for we also have “The milk in the fridge is off”, and this can’t be paraphrased by quantifying over milky objects (“There is a unique volume v such that v is milk and v is in the fridge and v is off”). Mass term definite descriptions don’t mean the same as corresponding count noun definite descriptions. Russell’s theory works smoothly enough for descriptions that speak of objects but not for descriptions that speak of stuffs—kings of France but not amounts of butter (“The butter on the table is rancid”). True, we can still use quantifier expressions to paraphrase such descriptions, but these expressions can’t be analyzed by using the standard apparatus of variables and domains of quantification. This is no more plausible than supposing that object quantification can be analyzed using an ontology of stuffs—as with “cod fish” and “codfish”. Objects are made of a certain kind of stuff, but talking about objects is not talking about the stuff they are made of. So it turns out that Russell’s theory, as normally formulated, is too wedded to the standard analysis of quantification; we need to broaden that analysis so as to take in descriptions that employ mass terms.

            So what is the correct analysis of such quantification? I don’t know: it seems to defy the usual type of semantic construction built out of words for objects and properties. What does “some milk” mean? Part of the problem is not knowing what “milk” means: does it refer to the aggregate of all volumes of milk (whatever exactly that means), or is it an abstract singular term denoting the Platonic form MILK, or is it not referential at all? And is some milk a part of the reference of “milk”, or an instance of it, or not a relation to it at all? The semantics of quantifier phrases like this (“most milk”, “a lot of milk”, “nearly all milk”, etc.) is obscure. So we really don’t have a decent semantics for quantifier words as they occur in natural language; and predicate logic (“quantification theory”) is a poor representation of the logic of quantifiers. At best it deals with a restricted class of quantificational inferences. People like to proclaim the great success of modern logical symbolism in capturing the logic of quantifiers, but it turns out that this is only half the story; a lot of quantifier logic is not captured by this symbolism. It works nicely for mathematical quantification because arithmetic isn’t about numerical stuff, but for stuff-related quantification it doesn’t even get off the ground. We already knew that mass terms make trouble for the semantic categories recognized in formal logic (are they predicates or individual constants?); well, it turns out that they also upset the usual theory of quantifiers, both standard and non-standard. Logicians might want to drink some warm milk.[1]

[1] I wouldn’t be surprised if linguists have noted the linguistic phenomena here recorded, but my knowledge of linguistics doesn’t extend far enough to be sure. There was a flurry of work about mass terms a couple of decades ago in philosophy, but I don’t recall any mention of the difficulties posed by mass term quantification.