I have been pondering about the following puzzle that I came across in Peacocke’s *Being Known*. Here is the puzzle.

The Cautious man accepts all the steps in a proof; grant that it is imaginatively obscure how he might come to revise that assessment; grant that there is every reason to believe that whenever the proof is reproduced in a satisfying way, it will lead to the same outcome; but dispute that there is anything in all that which justifies him in claiming to have apprehended any essential connection between basis, process and outcome—in claiming, indeed, of any statement in the vicinity that it ‘cannot but’ be true. (Wright’s formulation of the problem from Wittgenstein on the Foundations of Mathematics, p.455)

Is the Cautious man (henceforth CM) coherent in his attitudes?

The point of the story is that if the answer to the above stated question is ‘yes’, then modal discourse is not a fact stating discourse. For, if there were modal facts that determine CM’s attitudes then he would be incoherent in his attitudes.

Peacocke takes a route of showing that his account of metaphysics and epistemology of necessity can meet the challenge posed by the CM without postulating obscure faculties that have access to necessity or retreating to emprico-conventional epistemology of a priori truths.

I want to point to a different strategy that one could deploy in dealing with the CM problem. The idea is to point to an unexamined assumption upon which the CM example relies. If we can successfully challenge that assumption, we can say not that CM is incoherent but rather that the example is incoherent and rests on a false assumption.

In order to understand and evaluate whether CM is coherent in his attitudes it may be helpful to compare him with an ordinary cognizer who is cautious. Typically caution is called for when a thinker has a reason to think that she may be in error (for example, one may think that she doesn’t have enough evidence or that her evidence is potentially misleading). As a consequence of such suspicion, a thinker typically withholds the judgment though she may report that her psychological state is such that she feels pretty sure that what seems to her thus-and-so is thus-and-so.

For example, when seeing somebody from a distance who looks like a friend of mine, I am cautions to conclude that that is my friend. I am not really in the best position to make such an inference given my evidence. For, for all I know it could be somebody who just looks like the friend or it could be a robot disguised as my friend, or the circumstances are such that it may be very likely that I am in error because of some background information that I am aware of.

Now, CM, as described in the above stated puzzle, acts as if his intuition that the premises are true and that they entail the conclusion may be poor evidence. CM, as described, acts as if he has not enough evidence to believe that the conclusion of the argument must be true when based on the insight that the premises are true and that they entail the conclusion.

The only source of CM’s worries seems to be reliability of the process by which he gets to the conclusion, which is what we typically worry about in the case of perceptual seemings. But is it right to say that CM is like somebody who is seeing things from a distance, and that having an intellectual intuition is just like having a perceptual seeming? Further, is it right to say that intellectual insight resembles perceptual seemings in this way and that the epistemic role of intuitions is the same as the epistemic role of perceptual seemings—namely, that they are both evidence?

There are two important assumptions that the example relies on that one may have a reason do disagree with on the grounds that intuitions are unlike perceptual seemings for two crucial reasons: intuitions do not produce new knowledge and their epistemic role is not that of evidence for their contents or what can be inferred from them.

– Ivana Simic

on July 6, 2007 at 9:20 am |Rico VitzIvana,

Thanks for this (and your previous post) on the role of intuitions. I think these are terrific and interesting issues.

Bear with me for a moment. I’m unfamiliar with Wright’s formulation of this puzzle, so let me make sure I’m clear on two things. First, the essential question is whether CM’s attitude is coherent given that (i) he accepts that all the premises of an argument are true, (ii) he accepts that all the inferences of the argument are warranted, and yet (iii) he suspends judgment about the conclusion. Correct?

Second, you are taking issue with two of CM’s implicit assumptions: (i) “that having an intellectual intuition is just like having a perceptual seeming” and (ii) “that the epistemic role of intuitions is the same as the epistemic role of perceptual seemings—namely, that they are both evidence.” Is that correct?

on July 6, 2007 at 9:30 am |ivana simićYes, that is correct. I suspect that if we reject the two implicit assumptions that, I think, underwrite the puzzle then the puzzle dissolves–the scenario ceases to be coherently conceivable.

on July 6, 2007 at 10:09 am |Rico VitzExcellent. Thanks for the clarification.

Let me defend a CM-esque case to see what develops. Suppose I’m teaching a class in which we’re studying the ancients. We come to Zeno, and I present the following argument:

(1) Everything that appears to be in motion occupies a particular space at a particular time.

(2) Everything that occupies a particular space at a particular time is at rest.

Therefore,

(3) Everything that appears to be in motion is at rest.

Why isn’t it coherent to suppose that my students could accept both that the premises are true and that the inference is warranted, and yet, suspend judgment (or even deny) that the conclusion is true? Is it that in this case there is

not“every reason to believe that whenever the proof is reproduced in a satisfying way, it will lead to the same outcome”?on July 6, 2007 at 5:53 pm |Aidan McGlynnI’m not sure that Rico Vitz’s ‘essential question’ above is the problem Wright is pointing to. That just makes the Cautious man into Carroll’s Tortoise, as far as I can tell. So what’s at issue isn’t the coherence of accepting the premises of an argument one accepts as valid, yet suspending judgment concerning the conclusion. It’s a somewhat less familiar issue.

Forget the issue over the truth of the premises; that the Cautious man grants the premises used in the proof isn’t a premise here. Take a proof of T from P, R & S. The Cautious man accepts all of the steps of the proof, yet crucially refrains from accepting that the following condition is necessarily true: P, R & S -> T. The issue concerns the relationship between the epistemology of proof and modality. Must someone who recognizes that a proof is a proof also recognize a necessary connection between premises and conclusion? If the Cautious man is genuinely conceivable, that suggests not.

I’m not seeing how the proposed remedy engages the issue, once it’s in focus.

on July 6, 2007 at 6:31 pm |Ivana SimicThanks for the comments to both Rico and Aidan(if I may). What Rico suggested does not appear to be a good defense of CM-esque case because, as Aidan puts, it “The issue concerns the relationship between the epistemology of proof and modality”, while Rico’s case seems to have something to do with the soundness of the argument he put forward.

The Cautious man case is different. The Cautious man refuses to move from a proof for X (where X is a sentential letter for a non-modal statement) to necessarily X.

on July 6, 2007 at 8:52 pm |Rico VitzThanks, Aidan and Ivana. I think we’re making some progress, but I’m still unclear on the nature of the puzzle. Specifically, I’m unclear about the scope of the necessity operator on the proposition about which CM is hesitant. Sticking with Aidan’s example, is CM hesitant to affirm (1) necessarily: if P, R, and S, then T, or (2) necessarily T?

on July 6, 2007 at 10:53 pm |ivana simić“Sticking with Aidan’s example, is CM hesitant to affirm (1) necessarily: if P, R, and S, then T, or (2) necessarily T?”

It is (2)–the box operator is supposed to “go through” implication.

on July 7, 2007 at 2:31 pm |Joseph LongThis is an interesting issue. I wonder if I, too, may ask for a clarification. Mr McGlynn states that CM “refrains from accepting that the following condition is necessarily true: P, R & S -> T. ” This sounds like the box operator is ranging over the arrow, in which case the question–as I understand it–is this: Given that CM accepts the proof is sound, must he accept that it is sound in all possible worlds, as it were, or otherwise fail to be coherent?

Ms Simić, on the other hand, indicates that “box operator is supposed to ‘go through’ implication.” From this, it sounds like the question is this: Given that CM accepts the proof is sound, must he accept that the conclusion is true in all possible worlds or otherwise fail to be coherent?

If the latter question is the issue, then I don’t understand why incoherency threatens. For, one can pretty easily accept P & (P -> Q), and yet deny that Q is true in all possible worlds (e.g., if P = “Pat is a bachelor” and Q = “Pat is unmarried”).

If the former question is what’s at issue, then it seems, to my mind, that CM is being incoherent or he simply fails to understand that deductive derivations hold in all possible worlds. Perhaps he fails to understand the difference between deductive and inductive inference. But once the difference is explained, if CM still withholds his consent, the it seems he is in fact being incoherent. So, I guess I would ask, why think CM is being coherent? Is there some independent motivation for wanting to say CM is coherent? Or, perhaps a more aptly, am I just failing to understand the puzzle?

on July 7, 2007 at 2:43 pm |Aidan McGlynn“If the former question is what’s at issue, then it seems, to my mind, that CM is being incoherent or he simply fails to understand that deductive derivations hold in all possible worlds.”

It’s not that he fails to understand this. It’s that he’s so cautious that he doesn’t think we’ve got good enough grounds to believe it – hence his agnosticism about this claim. So the issues are: is this a coherent attitude, given the other things the Cautious man accepts, and if it is, what can we do to convince him that this thought is not simply presumptuous?

on July 7, 2007 at 3:08 pm |Joseph LongThanks for the clarification. At first glance, it sounds like CM is essentially a “radical” skeptic about modality. Perhaps he’s a little different in that he might accept that some statements are necessarily true, while denying deductive arguments are necessarily valid. But even with this distinction, it seems like, as in the case of other radical skeptics (I have in mind skeptics about sense perception), there’s probably not much to say to CM, other than attempt a Moorean move: Announce (with a bit of table pounding, if you’re interested in theatrics) that CM’s position is pretty much a conversation stopper, and, well, so much the worse for CM. That’s at first glance, but perhaps there is more to be lost in that move than what I see.

on July 8, 2007 at 12:29 pm |Ivana Simic“Given that CM accepts the proof is sound, must he accept that it is sound in all possible worlds, as it were, or otherwise fail to be coherent?”

The issue is not about soundness, it is abut validity.

Approximately, CM thinks that in order to infer form p, and p–>q that q, and form that necessarily q, he needs another premise, namely that the modus ponens is a valid form of inference and that necessarily when the proof is reproduced in such a manner the outcome will be the same. CM thinks that he doesn’t have a reason to believe that modus ponens preserves truth and withholds the judgment that necessarily q.

“Thanks for the clarification. At first glance, it sounds like CM is essentially a “radical” skeptic about modality.”

CM is not supposed to be skeptic about modality (in Quinean sense–namely that there is no intelligible concept of necessity). The issue is really about the epistemology of modality.

If CM were the skeptic about modality the puzzle would not really be a challenge to the view that modal discourse is a fact stating discourse–it would simply beg the question.

on July 8, 2007 at 2:38 pm |Aidan McGlynn“Approximately, CM thinks that in order to infer form p, and p–>q that q, and form that necessarily q, he needs another premise, namely that the modus ponens is a valid form of inference and that necessarily when the proof is reproduced in such a manner the outcome will be the same.”

How would these additional premises allow him to reach necessarily-q from these premises? One doesn’t need to be cautious in order to think that p and p->q don’t in general allow you to infer necessarily-q. That’s a given, surely. So in answer to Rico Vitz’s question above, the answer surely has to be (1), not (2). It isn’t in dispute whether the modality ‘goes through’ implication in the manner suggested – we know that it doesn’t.

(The relevant question is this:

“Specifically, I’m unclear about the scope of the necessity operator on the proposition about which CM is hesitant. Sticking with Aidan’s example, is CM hesitant to affirm (1) necessarily: if P, R, and S, then T, or (2) necessarily T?”)

on July 8, 2007 at 3:08 pm |Joseph LongSorry about my use of ‘soundness’; I see clearly the issue has to do with validity (as per my last comment).

on July 8, 2007 at 4:21 pm |ivana simić“How would these additional premises allow him to reach necessarily-q from these premises? One doesn’t need to be cautious in order to think that p and p->q don’t in general allow you to infer necessarily-q. That’s a given, surely. So in answer to Rico Vitz’s question above, the answer surely has to be (1), not (2). It isn’t in dispute whether the modality ‘goes through’ implication in the manner suggested – we know that it doesn’t.”

All I wanted to say is that the CM refuses to make a transition from an outright proof in a propositional calculus of the non-modal statement T to the conclusion that it is necessary that T.

To do so CM thinks he needs an additional premise, namely that it is necessary that when a proof is constructed in a certain way (in accordance with the rules of valid reasoning) the last line (the outcome will always be the same) and hence necessarily true. Falling short of a reason for such a premise CM withholds judgment that it is necessary that T.

Maybe my example with modus ponens was not the felicitous though I did prefix it with “approximately”.

So, strictly speaking CM is hesitant about neither (1) or (2) from Rico’s list. He is hesitant about the transition from T –> necessarily T, given that he has proven T.

To hesitate about (1), as Aidan suggested, would amount to CM’s hesitating about whether what he is looking at is a proof. But the description of the case is such that CM clearly accepts that what he is looking at is a proof. He just denies that the proof is good enough ground for thinking that the outcome ‘cannot but’ be true.

on July 8, 2007 at 5:52 pm |Aidan McGlynn“To hesitate about (1), as Aidan suggested, would amount to CM’s hesitating about whether what he is looking at is a proof. But the description of the case is such that CM clearly accepts that what he is looking at is a proof.”

No, this is just what’s in dispute. Wright’s question, as I understand it, is precisely whether agnosticism concerning the necessity of the conditional is already to hesitate about whether he’s got a proof on his hands. So the fact that it’s a stipulated feature of the case that he agrees what he’s looking at is a proof doesn’t yet show he accepts the necessity of the conditional. As I’m reading things, that’s the whole issue. My (1) interpretation is still in the running, as far as I can tell.

Once we start to focus on ‘outright’ proofs, things change. Examples of proofs discussed above, where the Cautious man was considering a derivation of T from P, Q and R, or of q from p and p->q, presumably aren’t outright proofs of their conclusions in any reasonable sense, since they aren’t proofs depending only on the empty set of premises. So let’s ignore these cases. Let’s suppose instead that CM agrees that it can be shown by steps he accepts that T is a theorem. Then is the issue just whether he must now accept that T is necessarily true?

Well, yes, I think so. But notice that this question is just a special case of what I’ve suggested the real issue is. It’s just the case where the premise set is empty. And I can think of no reason to hold that CM can entertain these kinds of doubts for proofs of the form |- T, but he can’t entertain doubts for proofs of the form R, S |- T.

A final point on this:

“To do so CM thinks he needs an additional premise, namely that it is necessary that when a proof is constructed in a certain way (in accordance with the rules of valid reasoning) the last line (the outcome will always be the same) and hence necessarily true.”

Notice that this seriously departs from Wright’s description of the case. His CM remains unconvinced about the modal connection between the premises and conclusion even when he grants that every time the proof is constructed in a certain way the outcome will be the same. Look again at the quote from the start of the post (the crucial bit has been placed in stars):

“The Cautious man accepts all the steps in a proof; grants that it is imaginatively obscure how he might come to revise that assessment; **grants that there is every reason to believe that whenever the proof is reproduced in a satisfying way, it will lead to the same outcome**; but disputes that there is anything in all that which justifies him in claiming to have apprehended any essential connection between basis, process and outcome—in claiming, indeed, of any statement in the vicinity that it ‘cannot but’ be true.”

So Wright’s CM doesn’t dispute that the outcome will be the same every time, but rather whether there’s is any grounds for holding that there’s an ‘essential connection between basis, process and outcome’. So the Wright’s problem isn’t that CM doesn’t think we have sufficient grounds for thinking the outcome will be the same every time, and so questions the necessity of the conclusion on that basis. His CM may explicitly grant that the outcome will be the same in every suitable instance, and yet he still can’t see what grounds he has to affirm the existence of a necessary connection between premises and conclusion (basis and outcome).

on July 8, 2007 at 6:17 pm |Joseph Long“But the description of the case is such that CM clearly accepts that what he is looking at is a proof. He just denies that the proof is good enough ground for thinking that the outcome ‘cannot but’ be true.”

It occurred to me that ‘proof’ might be best understood as a proof for a theorem, which seems indicated by the quoted statement. If so, then it seems that the Necessitation Rule (NR) is what is at issue:

(NR) If Q is a theorem, then Q is necessarily true.

Here’s another rule, the Distribution Rule:

(DR) [Necessarily (P->Q)] entails [necessarily P implies necessarily Q].

Like I said, I take it CM is agnostic about the former,

viz.,NR. (Is this right?) If I’m right, then one might then ask in virtue of what is he agnostic about the necessity of Q?Take for example the following:

(S) For any

x, ifxis a triangle, then the sum of the interior angles ofxequals 180 degrees.Suppose (S) is proved to be a theorem, then CM is shown the proof, agrees that it’s a proof, and yet remains agnostic about whether (S) is necessarily true. We might ask, Why? It seems there are two possible reasons: Either

(a)he is unsure that the axioms whence (S) was derived are necessarily true, or(b)he is unsure that the rules for deriving (S) from the axioms are truth-conducive in all possible worlds. It seems to me that being unsure about the necessary truth of a set of axioms is not being overly cautious. If agnosticism about axioms’ necessary truth is not being overly cautious, then CM must be agnostic in virtue of the derivation rules’ being truth-conducive in all possible worlds (otherwise, he fails to live up to his name). But being agnostic about the derivation rules’ being truth-conducive in all possible worlds just is being agnostic about the necessity of deductive validity, not the necessity of (S).So, in short, (NR) reduces to (DR) when we take into account the axioms whence Q is derived. If that is right, then I fail to see why it is overly cautious to be agnostic about the necessary truth of (S).

on July 17, 2007 at 9:23 am |Richard BrownHi guys,

This is an interesting discussion of a difficult problem. For what its worth, I think that Aiden is right in the way that he interprets the problem. The question is whether CM can consitently accept all of the things he does and yet still deny []((R & P & S) –>T)…and Joseph, as Aiden also pointed out, in the case where T is shown to be a theorem then the issue is the necessitation rule NR…but that is just a special instance of the problem as described because the left side of the conditional is empty so CM will just be faced with accepting []T instead of []((P & R & S) –> T) (since theorems follow from no premises). Of course one might dispute this way of characterizing a proof and insist that the axioms used in the proof count as premises ( I think this is what you had in mind) but then the issue would return to being whether CM accepts []((P & R & S) –> T) where P and R and S are axioms…I also think that you are right that being overly cautous about the necessity of a group of axioms is not an unreasonable thing to do…I mean there are, after all, about 1 gazillion different candidates for axioms that people doubt are necessary and I also think you are right that it is not unreasonable to doubt that a certain rule is necessary…so I do think that CM is consistent in his attitudes, he represents most of the people who work in modal logic! But I don’t think that this means that they are agnostic about deductive validity…they are rather skeptical about a certain formalization…so for instance one might be skeptical about (S) because one is skeptical of the assumption that space is flat and so skeptical of some of the axioms of Euclidean geometry or therefore skeptical of the proof procedure (using two dimensional plane figures and reasoning about them) but it doesn’t seem plausable to think that this person, ineither case, is agnostic about deductive validity, that would make him the tortise, as I think someone also pointed out…