1. Overview

Kripke had discovered the dogmatism paradox by 1972. After four decades of commentaries and secondary literature in the absence of the public availability of the maestro’s own work, it is fortunate that the original presentation of the paradox has been in print since 2011. Focusing on the relevant parts of Kripke’s paper, ‘On Two Paradoxes of Knowledge’,Footnote ¹ I aim at dissolving the paradox – and I aim at doing so without subscribing to any particular theory of knowledge.

My discussion is structured as follows. Section 1 – basically a set of quotations from Kripke (Reference Kripke2011) together with my brief comments – presents the paradox. Section 2 offers a definition of the very concept of being dogmatic with respect to a proposition. Section 3 makes a familiar distinction between two senses of ‘should’ in the statement ‘A should resolve not to be influenced by any evidence against p’. It is my hope that by appealing to this distinction we may see that perhaps not all forms of prescribing dogmatism have the same degree of weirdness; plus, I hope that making the distinction will shed some light on the role of the KK-principle in the paradox. Yet, being a digression in essence, the section may be skipped without significant loss insofar as one replaces steps (v) and (vi) in Kripke’s argument by corresponding steps (v*) and (vi*) presented towards the end of this section.

I offer my solution in Section 4, which is a defence of the idea that it is alright for us to be dogmatic with respect to what we know if, as is assumed by Kripke, what we wish above all else is to avoid losing true beliefs or gaining false ones. My concern in this article is Kripke’s original version of the paradox which, in a crucial premise to be discussed in detail, involves true belief, not knowledge; an appendix examines prospects of the possibility of a knowledge version of the paradox.

For the most part, this is a discussion in ‘traditional’ epistemology: save for a brief comment at the end of the paper, I sidestep the implications of the paradox for virtue epistemology.

2. The Paradox

The starting point is a closure principle:

The next premise does not involve knowledge as such:

Let p be a proposition,Footnote ² and suppose that A knows that p. It is not implausible to assume that our subject understands the general principle (ii) and has reasons for subscribing to it. So let us suppose that:

Assuming that A carefully carries out the relevant deduction, it follows that:

Kripke notes that this already looks rather strange, but let us continue. Here is the next premise, which is ‘very hard to state in a nice, rigorous way’ (p. 43):

Notice the parenthetical gloss: avoiding C is not merely the strongest among A’s desires – if that were the case, it would not follow that A should decide not to do anything of type T, for it could be the case that a cluster of A’s other wishes collectively trump his wish to avoid C. Rather, in the situation described by Kripke, A wishes to avoid C and nothing else matters for A. Kripke is considering cases where ‘A knows, at a certain time, that if he does anything of a certain kind in the future, it will lead to some consequence that he thinks bad, there being no other relevant consequences which would override it’ (p. 44).Footnote ³

With appropriate substitutions for C and T, premise (v) yields:

And what are the appropriate substitutions for C and T? Kripke’s explanation is crucial to my understanding of the paradox; so, let me quote it in full. Here is Kripke (p. 44):

Since (vi) is the very conclusion of the paradoxical argument, we may assume that (vi) itself is supposed to be unacceptable. But unacceptable in what way? It is fairly clear from the flavour of Kripke’s discussion that what he has in mind is that it is irrational for A to do what (vi) says he should do. Textual evidence for such a reading comes from what Kripke says just before presenting the (i)–(vi) argument: ‘… that if I know something now, I should, as a rational agent, adopt a resolution not to allow any future evidence to overthrow it. But this does not seem to be our attitude toward statements that we know – nor does it seem to be a rational attitude’ (p. 43).

So, I take this to be the real question concerning the dogmatism paradox: how could there be a sound argument which prescribes dogmatism?Footnote ⁵

3. Defining Dogmatism

Kripke does not offer an explicit definition of dogmatism – in fact, he uses ‘dogmatic’ and its cognates only once in his original discussion. In this section I shall try to define the concept. Here I am not concerned with dogmatism and open-mindedness as character traits; rather, I am dealing with them only with respect to a given proposition.Footnote ⁶

Kripke’s (vi) gives us a hint that dogmatism, as Kripke understands the concept, has something to do with the subject’s prior decision about what to do with the evidence against what he believes, should he encounter such evidence. Kripke elaborates on this when, in Appendix 3 to the paper, he comments on Harman’s well-known solution to the paradox. We need not disagree, says Kripke, with Harman’s view on how disregarding evidence would affect the subject’s knowledge; but ‘remember that I was talking about a resolution to be made in advance’ (p. 49).Footnote ⁷

So, I think it is fair to offer the following definition on behalf of Kripke: a subject S is dogmatic with respect to a proposition p iff S believes that p, and, moreover, S has resolved not to be influenced by any evidence against p. Thus, in particular, if S believes that p and he has resolved to ignore all evidence against p then S is dogmatic with respect to p.Footnote ⁸

Following Lasonen-Aarnio (Reference Lasonen-Aarnio2013, p. 3), one might cautiously add that the dogmatic subject is one who has resolved not to be influenced by any piece of evidence against p as it bears on p (not as it bears on other propositions). However, in the present enquiry we may bypass this nicety by assuming that we are talking about the subject’s attitude towards a single proposition p.Footnote ⁹ Also, in a more thorough investigation, it would be wise to define dogmatism with respect to a proposition relative to a mode of presentation, so that, for instance, the subject might be dogmatic with respect to the axiom of choice but not with respect to the principle of well-ordering even if they express the same proposition. But I think the definition that I just gave serves my purposes here.

A closely related concept is that of open-mindedness. Surely, we would not say of a subject that he is open-minded with respect to p simply by virtue of his not believing that p (or by virtue of his not having entertained p at all); hence we cannot define open-mindedness by simply negating the conjunction given in the above definition. It seems to me that S’s open-mindedness with respect to a proposition p consists in, first, his readiness to consider all the available evidence for p, as well as all the available evidence against it, if S has not yet come to believe either p or not-p and p is of some importance for S, and, second, S’s readiness to consider all the available evidence against p if he does believe that p.

Note that, insofar as the definition of dogmatism is concerned and in the absence of further argument, S’s dogmatism with respect to p seems to be independent of his knowledge that p – though at the end of the day our preferred theory of knowledge might tell us that dogmatism with respect to p may lead to the destruction of the subject’s knowledge that p.

The subject’s dogmatism with respect to a proposition need not be a result of his psychological certainty about that proposition. Thus consider the case of Bill James, who has to jump out of the third floor of a burning building to save his own life. He has somehow managed to form the not-so-firm belief that he has the nerve to jump off. As he also thinks that a necessary condition for his success is to sustain this belief, he tries not to lose it. Specifically, he decides not to consider any evidence against the belief – not estimating the height of the building, not reminding himself of his acute acrophobia, etc. Bill is thus dogmatic with respect to a proposition, but he is not absolutely certain about it.Footnote ¹⁰

Concerning dogmatism with respect to a given proposition, as I understand Kripke’s conception of it, the defining feature is that the subject has made a resolution not to be influenced by any counterevidence; carrying out the resolution is not of major importance for the paradox. Besides, S is not dogmatic if it just happens that he ignores all the counterevidence. To make this point more emphatically, we may use the term de jure dogmatic for what I have simply called dogmatic, and call S de facto dogmatic with respect to p iff S believes that p and, without any prior resolution, no evidence against p will ever influence S.Footnote ¹¹ Now it seems to me that it is only de jure dogmatism which might be considered a sin against rationality, and it is only habitual de jure dogmatism (with respect to a significantly large class of propositions) which is, or may be, a vice in the sphere of rationality. A de facto dogmatic agent may be careless or irresponsible; but he is not thereby guilty. To be considered as a crime, disregarding the evidence should be premeditated.

4. Quibbling with Kripke: What the Subject May Not Know

Note one thing the conclusion of the (i)–(vi) argument does not say: (vi) does not say that A knows or even believes that he should resolve to disregard all evidence against p; it just says that A should so resolve. There is no contradiction in asserting (vi) and adding immediately, ‘but A does not believe that he should resolve not to be influenced by any evidence against p’. It is as if someone located at an Archimedean point judges that A should be dogmatic with respect to p. To wit, it is only in an objective, not subjective, sense of ‘should’ that (vi) says that A should be dogmatic with respect to p.

Although the terminology is transparent and the distinction intuitive enough, let me give two examples of different senses of ‘should’.Footnote ¹² Suppose that Bernadette is gravely ill, that she knows this fact, and that she wishes above all else to be healed. Suppose that there is a cup of panacea in front of her. It seems quite obvious that there is a sense of ‘should’ – the objective sense – that Bernadette should take the cup. Equally obviously, however, there need not be a subjective sense in which she should take the cup: she might not have the slightest idea about the curative effect of taking it.

To give an example which goes in the opposite direction, consider Thelma who is driving in a highway. She believes, perhaps with warrant, that she should keep her seat belt fastened, and this is a subjective ‘should’: for all she knows, there could be a collision or a sudden stop, and she knows that in a typical accident a fastened seat belt reduces the risk of injury. But now suppose that, as a matter of fact, there will be no accident today. Then it is not the case that, objectively, Thelma should fasten her seat belt. (Allow me to set aside issues like Thelma’s peace of mind when the belt is fastened, and the likelihood of her being fined by the police for not having her seat belt fastened; let us assume that the only relevant issue for Thelma is to avoid accident-caused injury.) Of course, it is safe to say that a typical driver on a typical day does not know that she will not have an accident – hence the practical uselessness of talking about the objective sense of ‘should’ in cases like this.

Back to the (i)–(vi) argument, suppose A knows that p. Hence p is true. It follows from (ii) that any evidence against p is misleading. Let us assume, like Kripke (p. 44), that gaining a false belief or losing a true one is what A wishes above all else to avoid. It follows from (v) that, as a matter of fact, A should resolve not to be influenced by any evidence against p. For all we are told by (i)–(vi), this is like Bernadette’s case and panacea: objectively speaking, A should be dogmatic with respect to p. However, A may not be aware of the obtaining of this objective ‘should’-situation: A himself may not be able to reach the conclusion I should resolve now to disregard all the evidence against p.

As presented by Kripke, therefore, the (i)–(vi) argument does not endorse a subjective dogmatism. Now there are some ‘should’-statements that while they sound shocking or outrageous if construed in the subjective way, are less so when construed objectively – ‘Hitler’s mother should have drowned him at birth’ might be an example in the realm of (utilitarian) morality, while ‘Pharaoh should have killed baby Moses’ might be considered an objectively true prudential ‘should’-statement. Perhaps the prescription of dogmatism provides another group of examples?

However that may be, even if we think that prescribing dogmatism in the objective sense is unproblematic, this would be cold comfort since the paradox can be easily strengthened. Although (vi) is not the statement of a subjective requirement of dogmatism, such a requirement, viz.,

would follow from a straightforward readjustment of (v):

so that, with truly little ado, Kripke’s argument could be transformed into an argument for the conclusion that A should be dogmatic with respect to p, in the subjective sense of ‘should’.

Now a number of philosophers have argued that (iv), which is needed to derive (vi*) from (v*), does not follow from (iii) unless the KK-principle holds,Footnote ¹³ a principle according to which, for every proposition p, whenever a subject knows that p, he also knows that he knows that p. However, interesting as the question of indispensability of KK to the dogmatism paradox may be, we need not take a stance on it here. True, the KK-principle is not warmly embraced by everyone;Footnote ¹⁴ yet this does not solve the dogmatism paradox even if we think that KK is needed for the validity of the paradoxical argument, for, as noted by Sorensen (Reference Sorensen1988, p. 437), the critics of KK do not have to deny that there are some cases where the subject has second-order knowledge, and we can run the asterisked version of the (i)–(vi) argument at least for such cases. Thus, questioning the KK-principle as the (alleged) hidden premise of the dogmatism paradox would not help us solving the paradox, if we think that dogmatism is never a rational attitude.

So, while I think the subjective/objective distinction helps us seeing the issue more clearly and illuminates the role of the controversial KK-principle in the paradox, it does not solve the paradox. Let us ask a more fundamental question concerning the very notion of dogmatism.

5. Dogmatism: Is It Invariably Irrational?

In (i)–(vi) we have an argument with seemingly plausible premises whose conclusion says that the subject should be dogmatic with respect to what he knows. (My preferred version of the argument, described in the previous section, has it that this is a subjective ‘should’-statement, in the strong sense that the subjects also knows that he should be dogmatic.) Naturally enough, the literature on the paradox includes numerous works which try to either question the truth of one of the premises or else attack the validity of the argument. My plan, however, is to bite the bullet and argue that there need not be anything wrong with a person’s dogmatic attitude towards what he knows.Footnote ¹⁵

Is dogmatism always an irrational attitude? Arguably, if the highest epistemic duty of a rational agent is not to lose knowledge and if, moreover, one loses knowledge by not properly investigating all the members of the relevant class of counterevidence, then one must avoid dogmatism; besides, dogmatism may harm our understanding of the things we truly believe. Be it as it may, and independently of the real effect of dogmatism on knowledge and understanding, we recall that Kripke’s subject wishes above all else to avoid ‘gaining a false belief – or at least losing a true one’ (p. 44), wherein there is no mention of knowledge. But if what one wishes above all else is to avoid gaining a false belief or losing a true one, then of course one should be dogmatic if one’s belief has already hit the target. If to be influenced by a piece of evidence against a true proposition p makes it more probable that the subject will give up the belief that p, then he should be dogmatic with respect to p, given that his ruling wish is not to lose this true belief.Footnote ¹⁶

While discussing dogmatism, philosophers – if they are not working in virtue epistemology – typically take it for granted that dogmatism is irrational or even overtly absurd, and do not pause to explain why: the irrationality of dogmatism is perhaps something of a dogma by itself.Footnote ¹⁷ However, a distinction has to be made here. If we are looking for a strategy to deal with our beliefs, then dogmatism is not always a wise choice, for it ignores the fact that a good number of our beliefs are false.Footnote ¹⁸ But what about a particular true proposition p believed by the subject? Would it be rationally obligatory for him to stick to the strategy of open-mindedness and go through all the evidence against p? If the rationale for examining all the available and relevant counterevidence is to avoid falsehood, then it is hard to see what would be the point of adhering to the strategy in a case where the goal is already achieved. In the setting of the dogmatism paradox, the subject is assumed to know that p, hence having a true belief that p; to insist that he should nonetheless keep an open mind with respect to p would be, to use Smart’s felicitous expression in a different context (Reference Smart1956, p. 349), an instance of superstitious rule-worship.

Here is an analogy (which might be isomorphic to the case of Thelma and her seat belt in the previous section). Let us assume that the goal of the security check in an airport is to prevent harm to the passengers, the crew, and the aircraft of each departing flight. A popular strategy to achieve this goal is to have the passengers screened by X-ray machines or some such devices. Now if, as a matter of fact, passenger B. J. Ortcutt carries no weapons or explosive material, then, as a matter of fact, it is all right not to subject him to the screening. Moreover, if the security guard knows that Ortcutt carries nothing harmful, then the guard may easily come to know that it is all right to waive the security check for him. Admittedly, it does not happen too often that the security guard knows that Ortcutt is clean without having actually screened him; but this does not affect the moral of the story: (knowledge of) the proposition that Ortcutt carries nothing harmful entails (knowledge of) the proposition that there is no need to screen Ortcutt. To deny this is either to say that there are important things other than the immunity of this particular flight, or to attach some intrinsic importance to adhering to a policy. To insist on screening Ortcutt while knowing that he is clean would be insisting on a ritual with little or no purpose.

Of course one may think of undesirable consequences of dogmatism, despite the truth of what one is dogmatic about: perhaps dogmatism makes us less amiable, less tolerant to others’ tastes; perhaps it propels the society towards a less open one – and these may be considered bad for reasons other than missing the truth of the particular proposition with respect to which one is dogmatic.Footnote ¹⁹ This may give us good reasons for erring on the side of caution and avoid dogmatism in all cases; but such worries are irrelevant in the eye of Kripke’s subject who values having true beliefs (and avoid having false ones) above anything else.

6. Residual Doubts

This, then, is my solution to – or, rather, dissolution of – the dogmatism paradox as originally presented by Kripke. To put it bluntly: in the situation described by Kripke, it is OK for the subject to be dogmatic with respect to what he knows. In this final section I shall try to make my solution look more palatable.

First and foremost, the solution depends on Kripke’s crucial premise that the subject A wishes, above anything else, to avoid losing his true belief or gaining a false one. I do not endorse such an attitude towards truth, neither do I think that it is always a rational one. Gaining a false and paltry belief, or losing a true and trivial one, about a friend of yours may save a valuable friendship. To give another case: would it not be rational, or even outright morally obligatory, to opt for losing your true beliefs concerning Metallica’s discography, or gaining false beliefs concerning arcane issues in algebraic topology, if the Devil offers you the saving of the lives of nine fatally sick children in return?Footnote ²⁰

Even if we forget about friendship and morality and restrict our attention to purely epistemic issues, it is not clear that the subject’s preference, as described by Kripke, is reasonable – it is not crystal clear whether and to what extent true belief is of fundamental epistemic value, and here one might think that it is required of a believed truth that it must be believed ‘aptly and virtuously’ (Sosa, Reference Sosa and Greco2004, p. 320; see also Sosa, Reference Sosa, Fairweather and Zagzebski2001).

Secondly, common wisdom has it that dogmatism is irrational or even immoral, and that open-mindedness is a requirement of rationality, perhaps even a moral obligation as well. I think this platitude takes open-mindedness and dogmatism to be character traits, so that we hear of open-mindedness as a virtue – an epistemic or intellectual virtue (perhaps a moral one as well). Now I surmise that the sense of paradoxicality caused by the conclusion of Kripke’s (i)–(vi) argument results partly from sensing a tension between two ideas: the cliché that open-mindedness is an epistemic virtue, and the argument that dogmatism may occasionally help us keeping true beliefs and protect us from false ones. Having in mind that my solution concerns only with particular pieces of true beliefs, and then against the background of the subject’s peculiar preference, may make it appear less contrary to common sense.

Moreover, virtue epistemology may come to my help from a different angle. In recent years some virtue epistemologists have argued against the long-standing conviction that open-mindedness is an epistemic virtue. Thus, Carter and Gordon (Reference Carter and Gordon2014) argue that open-mindedness has no significant connection to truth – they argue that it is not particularly truth-conducive.Footnote ²¹ Baehr (Reference Baehr2011) argues, among other things, that some modes of open-mindedness are in fact intellectually vicious. Fantl (Reference Fantl2018), who also examines the ethical consequences of closing one’s mind, falls into this broad category. Such investigations may somehow modify our way of looking at open-mindedness with unconditional affection, hence, by implication, lessen the weirdness of prescribing dogmatism in particular cases. Besides, we may come to think of Kripke, with his work of the early 1970s on the dogmatism paradox, as anticipating some topics in virtue epistemology which began to flourish only a couple of decades afterwards.Footnote ²²

7. Appendix: A Knowledge Version of the Paradox?

Above I argued that it is all right for the subject A to be dogmatic with respect to a proposition p if he knows that p. In my argument I made essential use of Kripke’s assumption that A’s all-embracing concern is to avoid losing true beliefs or gaining false ones. Now one may ask what happens if A wishes above all else to avoid losing his knowledge. Here I briefly examine this issue.Footnote ²³

Two preliminary comments are in order. First, I think that Kripke’s seminal contribution is important enough to be examined in detail in its original format. Apart from its originality, it has the clear advantage over a great majority of second-hand reports that it makes explicit reference to the subject’s preference instead of simply asserting, as a premise of the paradoxical argument, that one should disregard misleading evidence.Footnote ²⁴ Secondly, one noticeable aspect of Kripke’s original paradox is that it is quite minimal in its presumptions, and this, I believe, adds to its allure. In discussing a knowledge version, one may thereby reduce some of the charm of the original version.

Now, what would a knowledge version of the paradox look like? In the original presentation of the paradox, Kripke talks about A’s concern for losing true beliefs or gaining false ones. Nonetheless, it may seem that he could have formulated his argument for a subject who wishes, above all else, to avoid losing his knowledge. In fact, in a 21st-century appendix to the original paper, Kripke switches without comment from true-belief talk to knowledge talk (p. 49, n. 28, my italics):

In order to have a knowledge version, the most obvious change to be made in the original (i)–(vi) argument is in the assumption concerning the subject’s desire: here we will assume that A knows that p and wishes, above all else, not to lose this piece of knowledge. Now A may lose his knowledge that p in at least two ways: (a) losing his belief that p, (b) losing his justification for p. Therefore, following his desire, A has to take measures in at least two dimensions. First, concerning (a), we already have the original argument with conclusion (vi):

Second, concerning (b), we need a new application of premise (v): previously the relevant consequence C was our familiar gaining a false belief or losing a true one, and the relevant action T was accepting Footnote ²⁶ evidence against p. We now take C to be losing knowledge. (Note that while in the original version we had a disjunction – gaining a false belief or losing a true one – here there is no obvious corresponding alteration.) And now it is not clear how to proceed.

In the original argument, we had Kripke’s elaboration on his premise (ii): he had defined ‘misleading’ as leads to a false conclusion. A couple of lines afterwards he tells us what specific false conclusion a misleading evidence against a true proposition p leads to: it leads to ‘the false conclusion that not-p’ (p. 43). So, according to Kripke, by accepting evidence against p the subject A is led to gain the false belief that not-p. Assuming that A is reflective enough, we may infer that he loses his true belief that p.Footnote ²⁷ Hence, although premise (iii) tells us that A knows that p, the process of losing this knowledge seems to be this: A simply loses his belief that p. Evidently, the process has nothing to do with A’s justification for p. Thus, in the context of Kripke’s paradox, it is not clear how accepting misleading evidence leads to losing a piece of knowledge, as opposed to simply losing a true belief.

Eager to find a knowledge version of the paradox, we may think of the following idea. Conceivably, in the aftermath of an epistemological enquiry, one may hold that dogmatism with respect to p destroys A’s knowledge that p by virtue of the effect of dogmatism on A’s justification for p.Footnote ²⁸ One who finds this thought appealing may subscribe to the following thesis, perhaps here functioning as a supplement to premise (iv) of Kripke’s original argument:

Recall that by now the subject is supposed to be aware of (vi),Footnote ²⁹ so that he knows that he should perform the following action, prescribed by (vi):

But it follows from (θ) that taking t – i.e., adopting dogmatism with respect to p – leads to losing the knowledge that p. Therefore, by (v), A should resolve not to take t.Footnote ³⁰ So we have the following rather complicated ‘should’-statement (with a new roman numeral):

Do we have a paradox now? Note that what we have in (vi) and (vii) is not exactly a pair of the form ‘A should X’ and ‘A should not-X’; instead, it is of the form ‘A should X’ and ‘A should resolve not to X’. Yet even this milder form puts A in a predicament, more so if understood in a subjective sense of ‘should’: if A sees the situation in a way that he should perform an action X, how on earth could he resolve not to perform X?Footnote ³¹

Yet I think there is no genuine paradox here. In a genuine paradox we are faced with an unacceptable or at least a strange conclusion while it is not initially clear where the argument has gone wrong or which of the premises are to be blamed. In the present case, however, what we have is an overt clash between an epistemological thesis (θ), and A’s overarching desire not to lose his knowledge. And I find it clear that the culprit is the desire: if A has already subscribed to the thesis that having an open mind is necessary for maintaining one’s knowledge (and recall that we need to assume that A does believe in (θ) – see my footnote 30), then he cannot reasonably decide to keep his knowledge via closing his mind to all counterevidence. That is to say, a rational agent who believes in (θ) cannot act upon his desire to maintain his knowledge no matter what. He simply has to give up that desire, or at least not to act upon it.

But let me say, in conclusion, that I find this a truly desperate move. My main argument – which I described briefly in this appendix – is that the Kripkean conception of misleadingness, with its effect on replacing belief in p by belief in not-p while leaving the justification for p intact, does not allow a knowledge version, as opposed to a true-belief version, of his dogmatism paradox.Footnote ³²