personal and doxastic justification

In their “The Basic Notion of Justification” (Phil. Studies, 1989), Kvanvig and Menzel incredibly attempt to defend the equivalence (J) by appeal to the lambda calculus:

(P) S is justified in believing p

(D) S’s belief that p is justified

(J) (P) ≡ (D)

Kent Bach and my friend Clayton hold that (P) involves the notion of personal justification — roughly, the kind of justification that is a property of responsible cognitive agents — while (D) involves the notion of doxastic justification — the kind of justification that is a property of justified beliefs. According to them, these are distinct notions and so (J) is a false equivalence; there are cases where an instance of (D) is true of some person, but the relevant instance of (P) is not, and vice versa.

Kvanvig and Menzel give a counterargument which I think is wrong. They begin by assuming that the logical form of (D) is as follows:

(DL) J1[λ(Bsp)]

(DL) gets the following reading: J1 (some kind of justification) is a property of the proposition that S believes that p. (In K&M’s logic, any instance of the formula λ(ψ) — i.e., any formula with a non-binding abstraction operator — denotes the proposition that ψ.)

I can’t really make heads or tails of this, because I don’t know what it is for justification to be a property of a proposition in this way. (DL) does not seem to be a correct rendering of (D)’s logical form, since (D) does not appear to be claiming that the state of affairs expressed by ‘S believes that p‘ is justified, but that S’s belief that p is justified. If (DL) is supposed to be a rendering of (D)’s logical form (and it seems that it is), then it is a bad rendering, since it makes a hash of both the syntax and semantics of the original sentence. (DL’) seems to me a more defensible rendering of (D)’s syntax:

(DL’) [NP S’s belief that p][VP is justified]

The process of computing a meaning for (DL’) will go roughly as follows (understand I as a function from pieces of syntax to their interpretations).

I[(DL’)] = (S’s belief that p’)(λx[J1(x)])
= J1(S’s belief that p’)

Now there are two ways of establishing the equivalence (J). One can argue either (i) that the move from (P) to (D) and from (D) to (P) is licensed by the syntax of the sentence, or (ii) that it is licensed by their semantics. I’m not entirely sure which way K&M opt for. Here is their argument (emphasis mine):

Personal justification involves the attribution of a property, being justified in believing p, to a person S. This property, however, is complex and should be represented as such … [T]he complex property in question can be understood as involving the attribution of some form of justification to [S’s believing p, i.e. to] the proposition that S believes p

(2) [λx J2[λ(Bxp)]]s

(2) reads as follows: S has the property of being an x such that x’s believing p … is justified … Given [(2)], we are in a position to see that personal justification is easily explainable in terms of [doxastic justification]. For by λ-conversion, (2) [is] equivalent to:

(2*) J2[λ(Bsp)]

Let us take the argument here to be that it is trivial to represent the syntax of (P) using, let us assume for sake of minimal correctness, (DL’). This is false (as I’ll argue below), but note that even if it were true it would not be adequate to establish K&M’s conclusion. Doing so requires that they establish that deploying I on the relevant instances of (DL’) will yield identical meanings. But this is of course precisely what is at issue. In other words, assume (what is false) that it is trivial to represent the syntax of (P) with (DL’). The computation of (P)’s meaning proceeds as follows (we use a new subscript ‘2’ on the justification property in order to avoid prejudging the question of whether or not the relevant notions of justification are identical):

I[(DL’)] = (S’s belief that p’)(λx[J2(x)])
= J2(S’s belief that p’)

Compare the meaning we computed for (D): J1(S’s belief that p’). We cannot identify these meanings without hearing an argument that the properties J1 and J2 are identical, and K&M have nothing of this sort to offer us.

K&M argue that this isn’t the case, for the following reason:

What we have shown is that the properties distinctive of personal justification attach to the very same object in the very same way as those properties distinctive of doxastic justification. Hence, there remains no reason to deny that the predicates which ascribe justification to a person are the same predicates which ascribe justification to a belief.

Even if they had shown this (and they haven’t), the claim here would be incorrect. What would need to be argued is that the interpretation function I assigns the same values to the relevant pieces of syntax. Whether or not they take the same arguments in the same way (whatever this is supposed to mean) is neither here nor there. Showing that two expressions share some basic formal properties is in general not even a prima facie argument for assigning them the same interpretation in a model.

In reality, it is not at all trivial to represent to syntax of (P) with (DL’). Here is a first pass at rendering the syntax of (P):

(PL) [NP S][VP is justified [VP\VP in believing p]]

(PL) and (DL’) are obviously not identical, and there is, I’m going to argue, no sense in which they are equivalent. (DL’) and (PL) instantiate the following syntactic forms respectively:

(f1) S is X in A-ing
(strictly: [NP S] [VP is X [VP\VP in A-ing]])

(f2) S‘s A-ing is X
(strictly: [NP S‘s A-ing] [VP is X])

If there were a sense in which (P) and (D) were syntactic equivalents (i.e., logically equivalent in virtue of their syntax), it would have to be because it is generally ok to move back and forth between sentences that instantiate (f1) and (f2) in the same way. But it isn’t, as the following two sentences illustrate.

(s1) My cat Rori is content in rolling in the dirt
(s2) #Rori’s rolling in the dirt is content

(s2) is borderline nonsense, since events don’t have psychologies. (You might object that we predicate apparently psychological properties of behaviors all the time, which I suppose is true. In that case, take note of the fact that someone can have a certain psychological state in doing an action that is not necessarily reflected in the behavior; I can be angry in doing you a favor, but there needn’t be anything angry about my actual doing of the favor.) This seems to decisively establish that the move from (P) to (D), if legitimate, is not legitimate in virtue of the syntax. I do however think the move from sentences that instantiate (f1) and (f3) in the same way is generally good, so long as X ranges over adjectives and not noun phrases.

(f3) S A-s X-ly
(strictly: [NP S] [VP A-s [VP\VP X-ly]])

So the move from (P) to (s3) is good.

(s3) S believes that p justifiably/justifiedly.

The move from (s4) to (s5) is, however, no good, so it cannot generally be true that sentences that instantiate (f3) and (f2) in the same way are mutually entailing.

(s4) Rori rolls in the dirt happily
(s5) #Rori’s rolling in the dirt is happy

In short, there seems to be no way to establish that (P) and (D) are mutually entailing by virtue of their syntax alone.

Perhaps there are semantic reasons for holding that (P) and (D) are mutually entailing. To show this, it would need to be shown that the result of removing the S arguments from (PL) and (DL’) and abstracting over the empty argument-slot yields identical functions from individuals to propositions. Doing this to (DL’) and (PL) would yield the following functions, respectively:

(PL*) λx[x is justified in believing p’]

(DL*) λx[x’s belief that p is justified]

In lieu of a syntactic argument, however, identifying (PL*) and (DL*) will require a substantive argument for identifying these properties. K&M appear to gesture in this direction in the bolded part of the quoted passage, which I’ll repeat here for convenience:

Personal justification involves the attribution of a property, being justified in believing p, to a person S. This property, however, is complex and should be represented as such … [T]he complex property in question can be understood as involving the attribution of some form of justification to [S’s believing p, i.e. to] the proposition that S believes p

This is, however, nothing more than a gesture — and a grossly question-begging one at that.

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13 Responses to personal and doxastic justification

  1. […] Friday, August 3rd, 2007 in Epistemology, Language, Philosophy I’ve cleaned up and added to the argument from my earlier post on personal and doxastic justification. The results are posted over at Go Grue. […]

  2. jon kvanvig says:

    Nate, thanks for taking the time to think about our piece. Though I’m tempted to respond as Jason did at Pea Soup recently, I’ll just talk about your argument. A couple of points here. First, the argument beginning at (f1) and (f2) is a classic philosophical blunder: you generalize a point in an argument and attack the generalization, instead of the argument you are considering (I posted about this general form of mistake here at Certain Doubts a while back). It is simply false that the general claim has to be true for the specific one to be correct. Second, you shouldn’t stop at DL’ with so much ordinary language still in place, since the point about syntax is that once we get the logical form down for each kind of justification, certain results follow. DL’ contains reference to S’s believing that p. What is that thing? Presumably, a state of affairs, either a type or token. In order to simplify our ontology, Chris and I assumed that states of affairs could be identified with propositions. If we remove this assumption, then can talk about a property of justification being attributed to a state of affairs. The same point holds about representing PL, except there you don’t even try to represent beyond the initial sorting in NP’s and VP’s, but go straight to the generalization point. In either case, we’d have to add to the language we assumed to disambiguate predications of propositions from predications of states of affairs, but I’m not sure what the additional complexity accomplishes. If you can’t make sense of justification being attributed to a proposition, I’m not sure why things should get clearer when it is attributed to a type of state of affairs.

    I think it is important to recognize that, at the point in the article you are focusing on, we’ve already put aside the idea that the language of justification is ambiguous, so if we get justification predicates attributed to the same items by the logical operations in the lambda-calculus, we get at least logical equivalence between personal and doxastic justification. If one wants still to insist that the distinction is hyperintensional, that is a position we have no compelling argument against (though it won’t help those who embrace the distinction for purposes of finding one kind of justication in cases where the other is absent). If the distinction is an intensional one, then what needs to be argued is what the logical form of personal justification is that prevents the argument for logical equivalence from working.

  3. nate charlow says:

    Jon,

    Thanks for your comment. A few points in reply. (I’m writing this on the run, so apologies in advance for any careless mistakes.)

    It seems to be that the argument relying on (f1) and (f2) does establish that the move from (P) to (D) is not a matter of the syntax. Since that’s all I was attempting at that point to establish (and since the point is not insignificant), I don’t think I’m making that blunder. I think it is true that the general claim about sentences instantiating (f1) and (f2) needs to be true in order for the move from (P) to (D) to be licensed in virtue of the syntax alone (though not for it to be licensed simpliciter, but I never suggest otherwise!).

    I can’t tell exactly what your argument is — i.e., whether you’re claiming that the move is licensed in virtue of the syntax alone (which seems to be false), or whether you’re claiming that the move is licensed in virtue of the semantics (which might be true). In the article you write: “Personal justification involves the attribution of a property, being justified in believing p, to a person S. This property, however, is complex and should be represented as such … [T]he complex property in question can be understood as involving the attribution of some form of justification to [S’s believing p, i.e. to] the proposition that S believes p…” This passage is ambiguous — I think you might be making either of the following claims:

    (SYNTAX) The syntactic features of (P) warrant the move from (P) to (D).

    (SEMANTICS) The complex properties (PL*) and (DL*) are identical.

    (PL*) λx[x is justified in believing p’]

    (DL*) λx[x’s belief that p is justified’]

    (SYNTAX) is false (or so I argued), and (SEMANTICS) can’t, I think it’s fair to say, be assumed without argument — it might be true, but it’s definitely not trivially true, as the argument from (f1) and (f2) also demonstrates. So we should probably look at some cases to decide. (Incidentally, Clayton Littlejohn has a few of these that appear to favor his view.)

    You’re certainly entitled to put aside the question of ambiguity (though I think doing so dramatically decreases the reach of your argument). Here’s an interesting side-issue. You can use one and the same lexical entry for “justified” for both (P) and (D) — i.e., you can deny that there’s any kind of lexical ambiguity in play — and still deny that they are mutually entailing. Presumably we’re using the same lexical entry for “content” in both (s1) and (s2), but (s1) and (s2) still aren’t mutually entailing. (Incidentally, how does your argument avoid establishing that (s1) and (s2) are mutually entailing?)

    I don’t want to argue about the metaphysics (over my head), except to note that the relevant NPs don’t seem to me to be referring to states of affairs at all, but rather to much more mundane things like beliefs (still over my head!). My point about (DL) vs. (DL’) isn’t really important. As long as you’re not committed to saying that the strictly correct LF — (DL’) — and interpreted LF — I[(DL’)] — are incorrect, I don’t have a problem.

  4. jon kvanvig says:

    Let me try it this way. We have some sentences in English with variants of ‘justified’ in them. We first ascertain the logical form of such sentences by representing them in our favored formal language. Then, for the formal language, there is both a syntax (including its proof theory) and a semantics. I think when you read us saying that the argument is syntactic, you are thinking about the syntax of the natural language, not the formal language. We are talking about the latter.

    Now, if your point is simply that it is not simply a matter of the syntax of natural language that our argument relies on, of course that’s right. And it is also correct to point out that an awful lot of the work of the argument is done by generating the logical forms that we do and by the assumption that the language of justification isn’t ambiguous.

    One way to interpret Clayton’s reservations about the argument is that the success of the argument doesn’t show that Kent and others are mistaken to identify some valuable property relevant to epistemology that they label “personal justification.” He’s right about that, but the argument wasn’t intended to show that. What the argument is intended to show only is that there is no grounds on the basis of ordinary linguistic usage to treat “S is justified in believing p” as the distinctive way to express the notion of personal justification that Bach and others are after. When people distinguish propositional justification from doxastic justification, there are distinctive ways in ordinary usage for differentiating the two, since the sentence “S’s belief that p is justified” implies, in one of the ordinary senses of the phrase, that a certain belief exists (and the sentence “p is justified for S” has no such implication).

    You say you don’t want to argue about metaphysics, but that is unavoidable here: to get the right logical form in the formal language with the appropriate model requires getting the metaphysics right. In any case, we first need the logical form, which neither PL* nor DL* give us, since they are neither sentences in English or in any formal language. Our claim is that once the form is represented correctly, each is a lambda-conversion of the other. To block that claim, we either have to get lambda-conversion wrong or we have to get the logical form of the sentences wrong (perhaps by encoding in a language that is not fine-grained enough to capture important features of natural language). It’s pretty clear that you agree on the logical form for doxastic justification, and though we were pretty explicit about how we generated the logical form for “S is justified in believing p,” perhaps that’s where you think the error is?

  5. nate charlow says:

    Jon,

    The syntax of the metalanguage won’t license the move from (PL) to (DL’), either.

    (PL) [NP S][VP is justified [VP\VP in believing p]]
    (DL’) [NP S’s belief that p][VP is justified]

    It will of course license the move from (2) to (DL), on a no-lexical-ambiguity assumption.

    (2) [λx J2[λ(Bxp)]]s
    (DL) J1[λ(Bsp)]

    But, as you recognize, in this case the burden shifts to arguing that (2) is the correct LF representation of (P). (The syntax of the metalanguage is of course orthogonal to this question.) And your argument on this score (which I have quoted nearly in its entirety in my prior comment) seems to rely on either (SYNTAX) or (SEMANTICS), both of which are problematic for reasons already given. Others and myself just don’t accept your suggested paraphase of the complex property attributed to S in (P), and, given the falsity of (SYNTAX), I don’t see how it is possible to argue us into doing so. And I see nothing in your argument that would stop us from changing it into an argument for mutual entailment between (s1) and (s2).

    The cases of Clayton’s I’m thinking of are actually ordinary language cases — cases which induce, in me at least, substantial resistance to accepting your suggested paraphrase of the property attributed to S in (P) — so I don’t think it’s correct to interpret his reservations in that way.

    Anyway, I’m glad that we’re at least in agreement about the source of the disagreement.

  6. jon kvanvig says:

    The argument we give doesn’t rely on the syntax of the metalanguage. It also doesn’t use your claims SYNTAX or SEMANTICS. If (2) isn’t the correct representation of “S is justified in believing p”, that would be interesting and important. So why do think it isn’t? The argument for representing it as (2) is this:
    “personal justification involves the attribution of a property, being justified in believing p, to a person S. This property, however, is complex and should be represented as such. One way to understand its complexity is as follows: it involves the attribution of some form of justification to S’s (token or type) believing of p. Since we are here assuming the identity of abstract states of affairs and propositions, the abstract state of affairs S’s believing p is just the proposition that S believes p. Further, the representation of the same claim read as an attribution of justification to a token state of affairs should have the same logical form as that of an attribution to the correlative abstract state of affairs, with the exception that the abstract state is replaced by a corresponding token state. So, in the abstract case, the complex property in question can be understood as involving the attribution of some form of justification to the proposition that S believes p. ”
    It wouldn’t make much sense to object to the step that (P) involves the attribution of of some complex property to S, and the second step is that this complex property involves the state of affairs of S’s believing p. Which of these steps don’t you like?

  7. nate charlow says:

    I think it will be instructive to actually look at (s1) and (s2). Adapting your argument seems to establish that they are mutually entailing.

    (s1) involves the attribution of a property, being content in rolling in the dirt, to Rori. This property, however, is complex and should be represented as such. One way to understand its complexity is as follows: it involves the attribution of some form of contentness to Rori’s rolling in the dirt.

    This is, I hope you’ll agree, objectionable. (Do you have an argument against the adaptability of your argument to (s1)?) Intuitively, the argument is bad because for many X you can truly predicate X of a person S who is A-ing without truly predicating X of S’s A-ing. There’s nothing mysterious or formally strange about this — for any such X, S, and A, the lexical entry for “X” will be a function F s.t. F takes I(S’s A-ing) to false and F combines with I(in A-ing) to yield a function that takes S to true. Roughly, this is why it is incorrect to say that the complex property (s1) attributes to Rori may be understood as attributing some form of contentness to Rori’s rolling in the dirt.

    Mutatis mutandis, this is roughly the diagnosis I would give to your argument about “justified”. It might be that the complex property (P) attributes to S may be understood as attributing some form of justification to S’s believing that p, but as (s1) and (s2) show this is not a trivial matter (in fact, it seems clearly substantive/lexical). Lexical disputes such as this are settled with case data, not by formal arguments.

  8. jon kvanvig says:

    No, s1 and s2 are sentences in english. As I see it, you keep wanting to raise objections to things that we don’t say and have no commitments to. Good work in philosophy has to start with exegesis, and your discussions here don’t succeed at that. So to repeat one more time, and then I’m gone:
    Take the sentence “Joe is justified in believing that it will rain tomorrow.” This sentence predicates a complex property of Joe. This complex property can itself be represented as such, and if we do, it involves some notion of justification and the state of affairs of Joe’s believing that it will rain tomorrow. That’s all that’s needed to get to (2) from a couple comments back. Nothing in this explanation commits us to the view that s1 and S2 are anything but nonsense.

  9. nate charlow says:

    Justification-ascriptions are sentences in English too, Jon.

    (s1) is not nonsense. It’s perfectly good English. Adapting your argument (as I did in the prior comment) appears to let us get an absurd LF for (s1). Why are you not committed to this adaptation?

    The fundamental problem here, I think, is you fail to realize that the order in which meanings combine can affect the meanings of complex constituents. See, e.g., your comment that “This complex property can itself be represented as such, and if we do, it involves some notion of justification and the state of affairs of Joe’s believing that it will rain tomorrow. That’s all that’s needed to get to (2) from a couple comments back.”

    ADDENDUM: Here’s a less controversial way of framing the objection. (s1) and (s2) show that the following argument form is invalid:

    (1) A sentence P involves the attribution of a property, being X in A-ing, to S.

    (2) P involves the attribution of some form of X-ness to S’s A-ing.

    Jon’s argument instantiates this argument form and seems to add no further relevant premises (and it seems that having this form is all that it has going for it). Jon’s argument is accidentally valid, at best (and at this point, we have no reason to believe that it is).

    (comment edited at 10:01 AM, 10:30 AM)

  10. nate charlow says:

    Incidentally, it is unfair of Jon to accuse me of failing to respond to his arguments. Nothing I’ve written here adds much of anything to the comment I made yesterday: “Others and myself just don’t accept your suggested paraphase of the complex property attributed to S in (P), and, given the falsity of (SYNTAX), I don’t see how it is possible to argue us into doing so.”

  11. Clayton says:

    I’ll largely repeat what I said in a previous thread, but I thought I’d pitch in.

    To me, it seems that the formalization Kvanvig and Menzel are offering don’t capture the spirit of Bach’s proposal. What I’m proposing (inspired, obviously by Bach), is supposed to capture the idea that there are two kinds of epistemic evaluations you might engage in, one that concerns the agent, one that concerns the attitude. As we use different criteria for evaluating these two very different kinds of things, it is not surprising that if we used some single term ‘justified’, ‘defensible’, etc… to state that one kind of evaluation turned out well, we should be able to use the term to say that S is justified in believing p without having to concede that the belief is justified, too.

    Consider two rooms, A and B. In Room A, you could overhear the following exchange:
    Audrey: Coop believes that Laura’s killer is going to be found soon.
    Ben: Agent Cooper is a fool. There’s no defending a guy like that. He has no good leads, and he should know better than to think he’s getting any closer to figuring out what really happened.
    Audrey: You have no right to criticize Coop, Ben. If you were in his shoes and didn’t know how things worked around here, you’d think you were getting closer to figuring out who killed Laura.

    In Room B, you could overhear the following exchange:
    Bobby: Coop believes that Laura’s killer is going to be found soon.
    Donna: Is there any justification for thinking that?
    Bobby: No, not really. He thinks there is, but he hasn’t figured out that this town is full of secrets. He’ll be chasing blind leads for a while now. Not that he’s a fool, mind you.

    Now, it seems that Bobby has asserted something that negates the claim that Coop’s belief is justified. It seems that Audrey has asserted something that establishes that Coop can be justified in spite of what he believes. It doesn’t seem they disagree. And this suggests that if we say that x is justified when x can be defended from criticism, what it is for x to be justified if x is a person is for criticism that implies fault to be negated. What it is for x to be justified if x is an action or attitude is for criticism that implies that x contravenes some norm can be negated. And while you _can_ come up with a way of stating the logical form of justification ascriptions in such a way that this intuitive distinction cannot be captured, that’s consistent with the further claim that you can come up with a way of stating the logical form of these ascriptions on which Audrey disagrees with Ben, not Bobby. Audrey and Bobby agree that Coop can be defended even though his belief isn’t one that they think can be defended.

    In short, to say that S is justified in believing p is to say that there’s something about S in virtue of which S can be defended from criticism even though S believes p. To say that S’s belief is justified is to say that there’s something about S’s belief in virtue of which that belief can be defended from criticism.

    If I say S is justified in believing p, I cannot see much going for this report:
    Clayton is saying that S has the property of being the x such that x’s believing of p is justified. In saying that S is justified in believing p, I’m trying to report something about S and not the deontic status of S’s beliefs (that someone’s attitudes or actions have some deontic status tell us little if anything about S).

  12. simon says:

    i’m curious as to how mssr kvanvig thinks comments like these advance his argument:

    Though I’m tempted to respond as Jason did at Pea Soup recently, I’ll just talk about your argument. (in fact, a passive aggressive stab at the former)

    Good work in philosophy has to start with exegesis, and your discussions here don’t succeed at that.

  13. Jon S. says:

    Hi Nate,

    Two thoughts of indeterminate worth.

    What happens if you translate your S1 and S2 into lambda calculus? Do they then have the same logical form as the analogous sentences in Kvanvig’s argument? If so, he should have an answer about why they aren’t analogous. But he seems to think that they won’t translate into the preferred formal language the same way, or at least, his thinking that would make sense of his complaints that S1 and S2 are natural language sentences. (Perhaps analogous translation into lambda calculus of S1 and S2 is obviously absurd, whereas it’s arguably correct with Kvanvig’s sentences?) Since I’m as comfortable with lambda calculus as I am with cats, I’ll leave the translation to you.

    A second thought, that might make Kvanvig’s initial response more palatable. S2 commits an obvious category error, whereas Kvanvig’s sentence D obviously doesn’t. Kvanvig doesn’t need that a move from a syntactically S1-like sentence to a syntactically S2-like sentence to work when S2 commits a category error, but only when it doesn’t. I think that category errors happen at a semantic level rather than a syntactic one, but he doesn’t need your SEMANTICS in any case if he claims the equivalence is to be justified syntactically (modulo category errors). Rather, he just needs:

    (SYNTAX+) The syntactic features of (P) warrant the move from (P) to (D), when (D) does not commit a category error.

    That’s obviously an ad hoc formulation, but there could be some less ham-fisted way of getting the restriction so he can use SYNTAX without being committed to an S1 to S2 move. You’ll surely know more than I do about how category errors are handled in formal semantics, but it seems to me that Kvanvig has some more wiggle room than you’re giving him here. Let me know what you think, here or around the department.

    Best,
    Jon

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