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Internalism

The following is a tutorial essay for Knowledge and Reality with Daniel Kodsi. In effect, it is a quick agenda for an hour-long discussion on a guiding question, which for this week was ‘Can cognition be factorized into internal and external components?’. A free-standing and much more readable version of some of the material may eventually go up on my Substack.

The key discovery takeaway here: true belief is prime, so what exactly is the primeness of knowledge supposed to demonstrate?

Following Williamson’s (2006) paper of the same title as this essay, I take cognition to be ‘something like the process of acquiring, retaining, and applying knowledge’. To be careful, we might distinguish between cognitive states (like seeing or believing) from cognitive processes (like deducing or forgetting); but for brevity, I’ll just talk about conditions obtaining, rather than states (or processes) obtaining (or occurring).

I’ll also take for granted that we can draw a clear distinction between the internal (roughly, conditions which depend only on things intrinsic to some cognitive agent) and the external (roughly, conditions which depend only on things extrinsic to some cognitive agent), so that we can get off the ground; the fine details should be relatively unimportant for present purposes. While it’s conceivable that no such distinction can be clearly drawn, and so cognition obviously cannot be factorized into such components, I won’t pursue that line here. Also, note that the trivial condition and impossible condition each count as both intrinsic and extrinsic.

Following Williamson (2000), call a condition ‘composite’ if it’s the combination of some internal component and some external component: that is, the cognitive condition obtains just when both the internal and external components obtain, such that the components are individually necessary and jointly sufficient. Call a non-cognitive condition ‘prime’. I take compositeness to be the operative notion of factorizability into internal and external components, but I return to this assumption later.

McGlynn (2014) remarks that ‘virtually everyone’ accepts ‘that knowing is prime’. Similarly, I expect virtually everyone to accept some other cognitive conditions are composite. If these claims are right, then there is a consensus that cognition cannot, in full generality, be factorized into internal and external components, but that some special cognitive conditions can be so factorized.

§I defends this consensus. §II explores a more deontic reading of the titular question, focusing (with the literature) on not whether one can but whether one may fruitfully factorize cognition where possible. I conclude that, although it would be premature to rule out fruitful factorizations of cognitive conditions, the prospects seem dim.

I. Primeness

Here, I rehearse the argument (Williamson 2000, 2006) that some important cognitive conditions are prime, and so cognition cannot always be factorized.

Suppose I have two informants, A and B, who each tell me that there are 50 cookies in the jar. If A actually counted but B just guessed, and I trust A’s testimony but not B’s, then I’d know that there are 50 cookies in the jar. So, A counting but B guessing satisfies any external condition necessary for knowledge. Alternatively, if B counted and A guessed, and I trust B but not A, then I’d also know that there are 50 cookies in the jar. So, trusting B but not A satisfies any internal condition necessary for knowledge. But then there cannot be an internal condition and an external condition individually necessary and jointly sufficient for knowledge, for then doubting A while she counted and trusting B while he guessed would satisfy both conditions and thus suffice for knowledge.

Slightly more generally, suppose we have n atomic internal conditions I1, I2, …, In, and n atomic external conditions E1, E2, …, En, with each Ij compossible with each Ek. Then each internal condition is the union of a family of Ij, and each external condition is the union of a family of Ej. Let harmony obtain just when, for some k, both Ik and Ek obtain. Then harmony is prime. If there were some internal condition I and external condition E individually necessary and jointly sufficient for harmony, then I1 with E2 would entail I (as I1 with E1 entails I) and E (as E2 with I2 entails E) and thus harmony. Although this is a bit weaker: take some impossible internal condition, or some impossible external condition, or just a jointly incompossible pair of conditions; then, vacuously, we have jointly sufficient conditions for any condition whatsoever. But something like harmony seems to be what happens when all goes well with cognition; some very natural aspects of cognition, then, cannot be factorized into internal and external components. In particular, it may be difficult to even state what the point of cognition is, without appealing to prime conditions of this sort.

At this stage, one might question the identification of compositeness with being factorizable into internal and external components. For true belief is certainly factorizable into an internal component (belief) and an external component (truth). But take Ii as my believing that there are j students in the college, and Ek as there actually being k students in the college. The condition that my belief is true, i.e., that harmony obtains, is prime. Surely, the objection goes, this shows that primeness comes too cheap.

The issue here is the conflation of having a true belief in some particular proposition, and having a true belief about the answer to some question. In the former case, we can certainly factorize true belief as believing that p internally and it being the case that p externally. Indeed, this case turns out composite. But in the latter case, there is generally no particular answer which must be believed for one to have a true belief, and no particular answer which must be true for one to have a true belief. Having true belief about the number of students in college may not be obviously factorizable after all. (Of course, having a true belief may still be some function or other of internal and external components, especially if fixing the internal and external conditions fixes all of the conditions; but factorizability does seem to be a bit stronger than analyzability.)

At first blush, our result that some cognitive conditions are prime seems somewhat surprising: as just noted, determining the internal and external conditions might fully determine all conditions. This sounds a lot like the claim that all conditions are composite. The trouble is that the former claim just implies that each condition has some pair of internal and external conditions jointly sufficient for it. The latter claim requires that these conditions are also individually necessary. This suggests that we can replace prime conditions by composite ones, but perhaps at some loss of generality (a thread we’ll pick up on later).

On second thought, though, the result that some important cognitive conditions are prime is totally unsurprising: if a condition requires some dependence between the internal and the external, then we can’t capture the condition by specifying an internal component and an external component independently.

One should not take the above lesson too far, though: not all cognitive conditions are prime. One’s belief in some proposition might be purely internal, and so trivially composite. Self-knowledge might be considered purely internal, and so also composite. The cognitive process of inferring from what one already knows may likewise be purely internal. Some mathematical knowledge (or knowledge of necessary truths in general) may depend only trivially on external conditions, and so be factorizable. With itself as the internal component and a trivial external component. Of course, any of these examples might be disputed. For instance, one’s belief in a proposition might count as partly external, if two internal duplicates can have beliefs with different contents—perhaps ‘I’m in Oxford’ picks out a different proposition in the head of each duplicate. But we can also give a more general scheme, such that however one draws the boundary between internal and external, we may find an internal cognitive component: one may extract an internal component of any condition by finding the strongest internal condition necessary for that condition. Thus, for instance, we might take something like (rational) belief as a purely internal component of knowledge.

So, some but not all components of cognition are composite; in other words, some but not all can be factorized into internal and external components. What about cognition in general? One way to interpret the question is as whether the condition of some cognition occurring is factorizable. Plausibly, internal conditions wholly determine whether cognition occurs (without internal thinking, there’s no cognition; with internal thinking, there’s cognition), and so the occurence of cognition comes out as a trivially composite condition: cognition can be factorized into internal and external components, because whether or not it occurs is already a wholly internal matter. Another, perhaps better, way to interpret the question is as whether every cognitive condition can be so factorized. But as the argument above shows, some very natural components of cognition (perhaps what cognition aims towards in the first place) cannot be specified merely by specifying internal and external components independently. Cognition cannot be factorized into internal and external components, because knowledge (a general cognitive state) cannot be.

II. Factorization

Most of the debate is not over to what extent one can factorize cognition into internal and external components, but over whether or not one should do so.

One initial reason for thinking so is that, in some sense, cognition occurs in the head: the way that cognition proceeds depend only indirectly on external conditions, through their influence on internal conditions. So, cognitive conditions that depend in some extra way on external conditions are thereby inferior for explaining the way that cognition proceeds.

A first defense is to argue that some of these external conditions may become more relevant over time. The way cognition proceeds over time depends in some part on how much the internal conditions get changed independently; and this depends in some part on the external conditions. See Williamson 2000, 2006.

One internalist response is that one may add in these external conditions ‘by hand’ if necessary: one should give more local explanations for more local phenomena, and less local explanations for less local phenomena. If the reliability of one’s belief-forming mechanisms becomes explanatorily relevant, simply add it to the explanation! So, the internalist’s explanations can always be made to perform as well as the explanations involving prime conditions.

They may also perform even better: just as the internalist may complain that the externalist’s prime explanations depends on too much, the externalist may complain that the internalist’s factorized explanations depend on too little. To be as sufficient as the prime explanation, the factorized explanation must hold either the external or the internal conditions fixed. In the first case, one may appeal to the most general internal condition compatible with the fixed external conditions; in the second case, one may appeal to the most general external condition compatible with the fixed internal conditions. Of course, breadth might be traded off for simplicity, but the increase in breadth might even make the internalist explanation more general in certain places than the externalist explanation. For instance, a factorized explanation might appeal to an internally-rational belief that p along with the fact that p, instead of one’s knowledge that p. The former captures all cases where all goes well internally and one gets a good outcome (which might include, for instance, traditional Gettier cases). In the analogy with counterfeit money, these are cases like those where one successfully buys something using counterfeit money. In an analogy with poker, these are cases like those where one plays optimally and wins, but only due to luck. From the internalist perspective, the focus on knowledge seems to lack the generality to cover these cases.

An externalist reply (and a second defense against the initial line of thought) is that the one-size-fits-all explanations involving prime conditions do better on other theoretical virtues, such as simplicity. Impressionistically, the real power of a theory is not just getting a lot out of it, but getting much more out of it than you put in. There is some trade-off between having a tighter explanation (which depends less on not-immediately-relevant factors) and having a simpler explanation. In general, building fake generality with disjunctions looks like cheating: to use an example from Williamson (2000), ‘if someone was crying because she was bereaved, it does not improve the explanation to say that she was crying because she was bereaved or chopping onions.’ In particular, the only reason why a constructed knowledge-like condition (made of, e.g., infinite disjuncts) seems to have some plausibility is that knowledge itself is a very simple and natural kind, with real generality. The knowledge-like condition is parasitic on knowledge. Further, human (and perhaps other animal) theory of mind has been optimized by evolutionary processes to be relatively cheap to compute and relatively predictive of behavior. Our natural theory of mind seems to be built around explanations which make use of prime conditions such as knowledge. This is a decent indication that such explanations work well in some sense.

However, it seems too strong to conclude that factorization can never be fruitful. A second reason for thinking that one should factorize cognition is normative. A core concern of epistemology is how to reason. Factorizing cognition into internal and external components clarifies which pieces one has control over, and so can be subject to praise or blame for. Conditions that aren’t wholly internal will build too much luck into the evaluation. By (loose) analogy: when studying how to play, say, poker, we want to distinguish between the contributions of luck (external) and skill (internal) to one’s winning. If knowledge is something like an earned win, in some hand-wavy sense, it seems like we might fruitfully discuss skillfully played wins instead (something like rational true belief), even though this may involve some loss and some gain in generality.

Further, suppose we’re interested in some more specific type of cognition. Let a subtype of some condition be some condition sufficient for it (that is, a subtype of a condition obtains in a subset of the cases the condition obtains in). Subtypes of prime conditions can be composite. (In fact, since the impossible condition is a subtype of every condition, and the impossible condition is composite, every condition has a composite subtype.) It’s the intersection of the impossible internal condition and the impossible external condition, for instance. Disjunctions of composite conditions, of course, have those conditions as subtypes. It’s thus at least conceivable that, although knowledge is prime, some interesting subtype of knowledge is composite: for instance, some knowledge via competent ampliative inference, with the internal component being belief by competent ampliative inference, and the external component being truth. However, nothing specific seems very promising. More promising are the examples of knowledge which is at most trivially dependent on external conditions, mentioned earlier; but in these cases, factorization is trivial, and so unfruitful.

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