Is Gettier's First Example Flawed? Christoph Schmidt-Petri, Konstanz 1. Introduction: what does Smith believe? 1.1. The 'Gettier counterexamples' (Gettier 19631) to the tripartite account of propositional knowledge are generally taken to show that not every instance of justified true belief constitutes knowledge. I argue that Gettier's famous first example fails to establish this conclusion. I claim to show that the example violates the belief condition of the tripartite account. Of course, if Smith does not believe that (1) the man who will get the job has ten coins in his pocket it should not be surprising that he does not know it either, as Gettier correctly claims. But as the three conditions are not satisfied, the tripartite account is not refuted. 1.2. My analysis exploits the distinction between 'attributive' and 'referential' uses of a definite description introduced by Donnellan (Donnellan 1966). According to Donnellan, 'the F' in a statement of the form 'the F is G' (here: (1) 'the man who will get the job has ten coins in his pocket') can be used attributively in order to attribute the property of G-hood to whatever object satisfies the description (is the F); or referentially, serving as one contextually adequate way of establishing reference to an independently identified object with the intention of making an assertion about that object, namely, that it is G. I consequently take beliefs involving descriptions to have the following truth conditions: if the description is intended referentially, the belief is singular, and the object referred to figures in it as 'constituent'. It is true iff this object is G. Understood attributively, as in Russell's original account, it has to be analysed as an existential statement (i.e. as: ∃x (Fx & ∀y (Fy y=x) & Gx)), and that is true iff there exists some object that is both the unique F and also G. This object, however, does not enter the truth conditions of the thought that would also be true if in its stead some other object had been both the unique F, and G. Now, to know (or believe) that the F is G, as a referential proposition, is to know (believe) of the object that actually is the F that it is G. To know (believe) an attributive proposition instead is to know (believe) that there exists some object – the identity of which one need not (but may have) an opinion about – such that this object is both the unique F and G. Both of these cases can properly be reported as 'knowing that the F is G'. 1.3. The Gettier example to which I would now like to apply this distinction is the following: Smith is justified in believing that Jones will get the job they have both applied for, and he also has a justified and true belief that Jones has ten coins in his pocket. So apparently Smith's belief in the following would be justified: (1) The man who will get the job has ten coins in his pocket. But should, unexpectedly, Smith himself get the job, and should he himself coincidentally and unbeknownst to him have ten coins in his pocket too, (1) is true, even though one proposition from which it had initially been deduced is false. 1 All unannotated quotations are from the first example of this paper. Now apparently i) (1) is true, ii) Smith believes it, and iii) Smith is justified in believing it.2 The three conditions for knowledge as justified true belief seem satisfied. Yet, Gettier continues, certainly this is not an instance of knowledge since Smith's belief "is true in virtue of the coins in Smith's pocket, while Smith does not know how many coins are in Smith's pocket, and bases his belief in [(1)] on a count of the coins in Jones's pocket, whom he falsely believes to be the man who will get the job." My methodological Leitmotiv is the question what exactly it is that Smith believes but does not know. Given Donnellan's distinction, (1) could represent several distinct referential or even an attributive belief. Which one of these does Smith believe? I shall argue that he believes none of them. 2. The referential reading: he can't believe it Let us first look at the referential reading. Following Donnellan, 'the man who will get the job' could, in this context, be used either to refer to Smith, to whom it applies, or to Jones, to whom it does not apply; only the former reading is interesting here. Yet we are told that Smith has been informed that Jones is the person to whom the description applies, and that Smith neither believes that he himself will get the job, nor that he has ten coins in his pocket. So, maybe quite obviously, Smith can't believe (1) if understood referentially to him. 3. The attributive reading: if only he had believed! 3.1. This section is based on the intuition that Smith does not have to believe/know that he will get the job for him to be able to believe/know that the man who will get the job has ten coins in his pocket, even if that should turn out to be him; for instance in case he had the 'attributive' belief (Russell 1905) that whoever will get the job has ten coins in his pocket: (2) ∃x (x will get the job & ∀y (y will get the job x = y) & x has ten coins in his pocket) 3 If so, Smith's ignorance of the fact that he will get the job clearly does not provide sufficient explanation for his ignorance of (1): if Smith could believe or know (2) without believing that he will get the job, then, logically, the fact that he does not believe that he will get the job is not conclusive evidence for his not knowing (2). (2), however, is just one way of reading (1) and thus Smith could know (1) despite this ignorance. But we said that Smith does not know (1). 2 The 'Principle of Deducibility of Justification' (PDJ) asserts that "for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q." My argument does not need to question this principle. Deductive closure of beliefs is not required by the tripartite account. 3 Another example would be the candidate with the most votes (the actual person), who does not have to believe/know that she herself is the candidate with the most votes in order to know that the candidate with the most votes wins the election. Is Gettier's First Example Flawed? Christoph Schmidt-Petri 318 3.2. That Smith has an additional and mistaken belief about who will get the job is irrelevant for this attributive belief; and accordingly the answer to: 'of whom was Smith thinking in believing (2)?' would have had to be: 'of no-one in particular' – existential statements, in the logical sense, never refer to any object. Most people however would add, hesitantly, that Smith does have Jones 'in the back of his mind' in some sense. This tends to push us back to the referential reading in which the description refers to Jones. But Smith's ignorance about who gets the job would only have mattered had (1) been intended, first, referentially rather than attributively, and secondly, referentially to Smith – but Smith certainly doesn'tt have either of these referential beliefs (cf. §2). So it seems Smith does not have the referential belief, and assuming he has the attributive belief his ignorance of who gets the job would not have mattered for knowledge of (1). What is more, Gettier's story seems to suggest he has both a referential belief and an attributive belief, in some sense or other. What, finally, is the role of the coins? 4. But he couldn't have believed it! 4.1. In fact, a conclusive reason why Smith does not seem to hold an existential belief like (2) is that he does not know about the coins in his pocket. It seems that in order for him to believe that whoever will get the job has ten coins in his pocket, knowledge of the coins is required since, logically, either of Smith or Jones could get the job. The central – and so far unjustified – claim here is that unless Smith believes of himself that he has ten coins in his pocket he cannot plausibly be understood to believe that whoever will get the job has ten coins in his pocket, given that he is well aware of the fact that he could get the job. A justification of this claim will have to wait for the next section, but the underlying intuition is this. If you claim to believe something of some unspecified element of a set of things (but of no element in particular, i.e. 'attributively'), then, unless you think that what you know serves to determine this element (the coins serving to determine who will get the job), you will have to believe of all the elements whatever what you claim to believe of this unspecified element for your claimed belief to hold up as belief (rather than just as a claimed belief, that is, a belief that you claim to have but do not actually have 4 ). My argument here may be taken to mirror Gettier's (implicit) reasoning for his claim that Smith does not know (1) – just replace know for believe in what follows to get Gettier's version: in order to believe (2), that is, that whoever will get the job has ten coins in his pocket, Smith has to believe that whoever could get the job has ten coins in his pocket. Both Jones and Smith could get the job, but Smith only knows of Jones that he has ten coins in his pocket, thus, Smith does not believe of whoever could get the job that he has ten coins in his pocket. It follows that he does not believe that whoever will get the job has ten coins in his pocket – he could not, since for that he would have to believe it of himself as well. Hence he does not believe that the man who will get the job has ten coins in his pocket, whoever that may be. 4.1. So, that Smith does not know about the coins in his pocket is not the reason why he does not know (2) even though he does justifiably and truly believe it – as Gettier 4 This is not as unusual as it might appear. For instance, think of the number of people who, on one occasion or other, claim that they believe in God. claims – no, it is the reason why he cannot even believe (2). The right explanation, then, of why Smith does not know (1) is not to be found in the insufficiency of the tripartite account of knowledge, it is simply that he does not even believe it – but belief is required for knowledge. In other words, what is wrong with (1) is that it cannot be read as a (justified) true belief of Smith, not that it cannot be read as knowledge – but that follows immediately. 5. The claim justified 5.1. I will now argue that if Smith were not thus required to know about the coins to believe (1), then he could also have known it – but we concurred with Gettier that Smith does not know. Hence he must be required to know about the coins, in this sense, even by Gettier. For the purpose of this 'reductio' argument let us assume that it were not required that Smith had to know of the coins in his pocket to have the belief (2). And it seems indeed that this is possible: without believing of himself that he has ten coins in his pocket it generally is still possible for Smith to believe that the man who will get the job has ten coins in his pocket (in the attributive sense) even if that should turn out to be him. For instance, he learns that the numerologists-board members want to pick the person with ten coins in his pocket. In such a case Smith could believe (1) attributively despite ignorance of the coins in his pocket (as long as he is ignorant about who actually gets the job). But here is the rub: under these circumstances, one is not barred from saying quite literally: 'Smith knew that the man who will get the job has ten coins in his pocket', maybe but not even necessarily continuing with 'he just did not know that that man would be him', and/or with 'he just did not know that he had ten coins in his pocket' and thus to attribute knowledge of (1) to Smith. That is to say, by not requiring that Smith has to be aware of the coins in his pocket it is actually possible to attribute belief and knowledge of (1) to Smith. (Of course additional knowledge of the coins in his pocket would not turn that piece of knowledge into ignorance either.) 5.2. So, in addition to the irrelevance of the ignorance about who gets the job, whether Smith knows about the coins in his pocket or not really does not matter for the attributive belief either – provided Smith actually believes (2) as here we assume he does. But the problem for Gettier's story is that clearly Gettier does not want to attribute knowledge to Smith! If we assume the above claim (cf. §4) to be false, there is no ignorance, but Gettier obviously requires this ignorance. Hence it must be true. 5.3. Note, importantly, that if you accept that ignorance of the coins does not show that Smith necessarily does not know (2), nor that knowledge of them implies knowledge of (2), as surely you have to, then it can no longer simply be stipulated that Smith does believe (2) and would know (1) in case he knew about the coins. Independent argument is now required to establish that Smith does believe (2) in the first place since we know that ignorance of the coins in his pocket does not suffice to show that he does not know (2) if he did believe (2), as Gettier wants us to believe. (Ignorance about who will get the job does not matter anyway since the belief is attributive). We need a good reason to think that in this case, ignorance about the coins in his pocket suffices to establish that Smith does not know – as we all want to say – since it does not do so generally (given belief in (2)). My analysis provides this reason, whereas Gettier's story provides none. Is Gettier's First Example Flawed? Christoph Schmidt-Petri 319 6. How the Example Works 6.1. Supposing that Russell's theory of descriptions has not entered the subconscious of most readers of this example the description in Smith's alleged belief (1) will initially be understood as applying 'referentially' to either Jones or Smith. The reader is thus faced with two possible readings of (1) representable as: (1) Jones is the man who will get the job, and Jones has ten coins in his pocket, or (2) Smith is the man who will get the job, and Smith has ten coins in his pockets. Note that (1) can be taken to paraphrase (3) from Smith's perspective (who "...sees the entailment [of (1) from (3)] ... and accepts [(1)]..."), and to paraphrase (4) from the reader's perspective, but not vice versa. Unlike Smith, the reader has the correct information about who will get the job, and also knows that Smith has ten coins in his pocket. Smith himself clearly does not believe (4) while he seems to believe (3). So Smith neither has justified true belief in (3) (which is false) nor in (4) (which he does not believe). But then, the reader rightly wonders, how could he have justified true belief in (1)? Thus in the second step the attributive belief (2) enters the scene as the third and last possible reading of (1) and is then adopted by elimination. 6.2. The common understanding is that Smith believes (2) but does not know (1), the reason for this ignorance being that he neither knows about his ten coins nor about the job he is about to get. But if Smith actually did believe (2), I argued above, none of this need matter for knowledge. But clearly here it does. My conclusion was that Smith, for the same reason for which he does not believe (4), does not believe (2) either – the coins in his pocket. This explains why his ignorance matters, but the counterexample is dissolved. The rationale behind the common reading is somewhat twisted, deriving from the overriding desire to attribute some belief to Smith, and preferably a justified and true one at that. From the possible true beliefs (2) and (4) on offer (2) has major advantages over (4). As argued, Smith does not have to know that he gets the job to believe (2), but he does to believe (4). That by itself would eliminate (4). Furthermore (2), unlike (4), is justified by assumption (PDJ and existential generalisation5), and the reader thinks that clearly it cannot be contradictory to attribute a belief to Smith which he is justified to hold. Clearly, if already he is justified in believing (2) at the very least he might believe it. 5 Gettier never says that Smith performs an existential generalisation. The fact that he could, and would be justified in so doing, does not suffice to establish that he does. Nonetheless a contradiction arises from the supposition that Smith does believe (2). Thus it is concluded that Smith cannot know (1) despite (the possibility of) justified true belief in (2). What is more, the ignorance about the coins also affects (4) so there is really no reason to believe that Smith knows either of these. This conclusion is not doubted since anyway expected. 7. Justified True Beliefs, anyone? Smith takes (1) to express (3) and that the reader takes (1) to express (2) or (4). Given these beliefs of Smith, for him, belief in the truth of (1) and hence its acceptance is perfectly legitimate (hence the J: he is 'justified'). So Smith accepts the sentence (1) because he believes the proposition (3) and believes (1) to express that proposition (he mistakenly thinks that the man who will get the job is Jones) – he believes (1) to be true. And indeed (1) is true (hence the T: his 'belief is true'). Given the beliefs of the reader, her acceptance of (1) is equally legitimate. When the reader accepts (1) she believes both (2) and (4) which she knows to be expressed (ambiguously) by (1) – she has better information than Smith about who gets the job (required for (4)), and she also knows about the coins in Smith's pocket (required for both (4) and (2)). Yet Smith's belief (3) is a sufficient reason for his acceptance of (1). It is due to rashly identifying this belief in the truth of (1) with belief in what (1) expresses that Smith was therefore thought to believe (1) too (hence the B: 'belief'), and thus (2) (since (3) and (4) are clearly out for him). But acceptance clearly is not an infallible guide to belief. It is Smith's acceptance of (1) that is mistaken and based on the 'wrong reasons' (his false belief (3)) – these still help to rationalise the problem. But Smith does not have the 'wrong reasons' for his belief in (1) since he does not believe (1) at all, even though he believes (1), the sentence, to be true. Smith does not have a justified true belief in (1). A fortiori he does not have a justified true belief that is not knowledge. Hence Gettier's first example is flawed. Literature Gettier, E. L. 1963 "Is Justified True Belief Knowledge?", Analysis 23, 121-123. Available at: http://www.ditext.com/gettier/gettier.html Russell, B. 1905 "On Denoting", Mind 14, 479-493. Donnellan, K. 1966 "Reference and Definite Descriptions", The Philosophical Review 75, 281-304.