Abstract
If we accept certain Peircean commitments, Gettier’s two cases are not cases of justified true belief because the beliefs are not true. On the Peircean view, propositions are sign substitutes, or “representamens.” In typical cases of thought about the world, propositions represent facts. In each of Gettier’s examples, we have a case in which a person S believes some proposition p, there is some fact F* such that were p to represent F* to S then p would be true, and yet p does not represent F* to S but some other fact F of which p is false. Since truth is a property of propositions with respect to their representational function, it follows that the belief is not true. Although an examination of Gettier’s two cases, this essay is not a defense of the justified true belief (JTB) analysis of knowledge, for there are objections to the JTB analysis other than Gettier’s two cases. Rather, Gettier’s two cases are of particular interest for the light they shed on the nature of truth and representation.
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Notes
As I shall explain later, although all propositions are statements, not all statements are propositions, even if they have the same grammatical structure as a proposition.
The literature on the Gettier problem is vast. For a monographic exposition of the Gettier problem, see Hetherington (2016); for an edited volume collecting diverse perspectives on it, see Hetherington (2019). Since I focus only on Gettier’s two cases, I do not consider cases without a false lemma. Though the considerations here can be generalized to such cases as the broken clock, doing so requires motivating claims that stand outside the scope of this essay. Persons familiar with the literature will recognize a similarity between the account offered here and the positions defended by Mizrahi (2016, 2017), Jacquette (1996), and Heathcote (2006, 2012, 2014a, 2014b), though there are crucial differences. Mizrahi denies “we are in a position to say…whether the beliefs are true or not” (2016, p. 32) whereas I contend the beliefs are not true. Jacquette and Heathcote concede the beliefs are true, only the evidence which constitutes the justification is not evidence of the very state of affairs that makes the belief true. I hold that the beliefs are not true because the propositional contents of the beliefs do not represent the facts which would make them true, independently of the justificatory profile of the belief.
Citations in square brackets follow the standard apparatus of Peirce scholarship, where the title is abbreviated, the number before the colon refers to the volume, and the number after the colon refers to the page number (or in the case of the Collected Papers, the number before the period is the volume number and the number after the period is the paragraph number), and these are followed by the year of publication or composition of the work in which the quotation appears.
Peirce remarks, “I use the term ‘object’ in the sense in which obiectum was first made a substantive early in the XIIIth century;…I mean anything that comes before thought or the mind in any usual sense” (Peirce and Welby, 1977, p. 69 [SS 69, 1908]).
In some late works, Peirce distinguishes between the immediate object and the dynamical object (see, e.g., Peirce, 1998, pp. 482 and 498 [EP 2:482, 1908, and EP 2:498, 1909]), although his conception of them is a matter of some dispute. He seems to have wanted the distinction to explain how illusions can nevertheless be representations of objects as well as to account of the fact that when (say) one sees an apple sitting on the counter one sees only a side of the apple (the immediate object) rather than the whole thing (the dynamical object). Moreover, it is not clear whether the immediate objects are something like Fregean senses or whether they are parts of real objects. As the exegetical question of the precise nature of Peirce’s distinction does not bear directly on the present analysis, I set it aside in favor the distinction between the immediate and ultimate referent of the sign, though see, most recently, Hilpinen (2019), Bellucci (2015, 2018a, passim), and Wilson (2017a).
I should note that a Peircean index is not quite the same as what contemporary philosophers of language call an indexical. As noted earlier, a Peircean index is a sign that stands in some existential relationship to its object, such as a weathervane. An indexical is a word or term whose referent changes depending on the context of utterance. For instance, if I say “I am a person” the indexical “I” refers to me whereas if you say “I am a person” the indexical “I” refers to you. Nevertheless, an indexical such as “here” will typically function like a Peircean index insofar as it will cause the hearer to attend to the location indicated by the utterer.
Peirce’s robust account is more complex than this brief presentation suggests. I am here focused on propositions which have singular referring terms or phrases, such as proper names (Smith) or definite descriptions (the man who will get the job), since these cases are the most pertinent to Gettier’s examples. On the fuller account, Peirce holds that the subject of a proposition “if not an index is a precept prescribing the conditions under which an index is to be had” (Peirce 1998, p. 168 [EP 2:168, 1903]). For instance, he claims that some woman is adored by every Catholic means that “a well-disposed person with sufficient means could find an index whose object should be a woman such that allowing an ill-disposed person to select an index whose object should be a Catholic, that Catholic would adore that woman” (ibid.). Peirce takes a game-theoretic approach to quantification on which “some” and “every” function as precepts prescribing conditions under which some object is selected (see Pietarinen, 2006, Ch. 3, 2014). Atkin (2005) explains that Peirce recognizes three classes of indexicals (the index, the sub-index, and the precept) each one of which may be either genuine or degenerate.
The account being given here is not the causal theory of reference, for it is not an account of how names come to refer to their objects but an account of how signs direct the interpreting mind to their objects. It bears mentioning that propositions may refer to objects indirectly through other signs not in the mind, and in such cases there is a still a chain of representations. In spite of my sop to Cerberus, semiosis does not just occur in a human mind. A functioning weathervane represents the wind’s direction. The judgment “the wind is blowing southerly” represents the wind’s direction through the weathervane. If the weathervane is rusted and stuck in place, the proposition fails to represent the wind’s direction and so is not true, even if the wind is blowing southerly. This suggests how the proposal on offer here might be extended to other Gettier cases, such as the broken clock.
These points raise diverse problems for various sorts of propositions. What shall we make of propositions about no longer existing objects, imaginary objects, future contingents, and counterfactuals? Peirce does have replies to these worries, but a consideration of them is beyond the scope of the present essay. For some of Peirce’s comments on the matters, in the order just listed, see: Peirce (1986, pp. 336–337 [W 3:336–337, 1878], 1998, p. 209 [EP 2:209, 1903], 1998, p. 358 [EP 2:358, 1905], 1958, pp. 380–382 [CP 8.380–382, 1913]). See also the works mentioned in fn. 12.
Again, I set aside the complications mentioned in the previous footnote.
For simplicity’s sake, I am here taking object to be an ordinary physical object, but Peirce would allow that a percept could be the object. Now if one were suffering an illusion and were to judge the chair is red when it is in fact yellow, the judgment might be true of the percept qua immediate referent but false of the physical object represented by the illusory percept, i.e., the ultimate referent. I set those complications aside as beyond the focus on the present essay.
That Peirce is congenial to a correspondence theory of truth broadly speaking is defended in the scholarly literature by Migotti (1998), Atkins (2010), Lane (2018), and Legg (2019). Misak (1991/2004, 1999) defends a deflationary account of Peirce’s theory of truth, and note that deflationists may accept the correspondence platitude; see, e.g., Horwich (1999).
One anonymous reviewer has made the thought-provoking observation that, as Donnellan (1966) notes, definite descriptions may be used attributively or referentially. When used attributively, “the man who will get the job has ten coins in his pocket” states something about whoever will get the job. When used referentially, the definite description calls attention to a person or thing, enabling someone to pick out that thing. Peirce never draws this distinction, but it is a consequence of his other commitments that definite descriptions may be used in these two ways. Moreover, it is interesting to reflect on Gettier’s cases in light of Donnellan’s distinction and Peirce’s semiotics. In Gettier’s first case, the definite description “the man who will get the job” virtually functions as an index of Jones, since it takes the subject place of the proper name Jones (as Atkin (2005) explains, definite descriptions are genuine “precept” indexes—see also fn. 10). Hence, it is used referentially, and as such the statement is not true since Jones will not get the job. But now consider two other cases: (A) a man awakes and declares for no reason that the man who will get the job has ten coins in his pocket and (B) the hiring manager knows each of Jones and Smith has ten coins in his pockets but does not know whom the CEO will choose and so asserts that regardless, the man who will get the job has ten coins in his pocket. In (A), the definite description is used attributively. But on Peirce’s view, (A) is a not a proposition but an imitation of a proposition. Hence, the statement is not true. The story with respect to (B) is more complex. The assertion is a logical interpretant of (I) either (a) Jones will get the job or (b) Smith will get the job and (II) (a) Jones has ten coins in his pocket and (b) Smith has ten coins in his pocket. (Ia) and (IIa) imply the man who will get the job has ten coins in his pocket, as do (Ib) and (IIb), leading to the conclusion (III) (a) the man who will get the job has ten coins in his pocket or (b) the man who will get the job has ten coins in his pocket. By tautology, (III) implies (IV) the man who will get the job has ten coins in his pocket. Now the definite descriptions in (IIIa) and (IIIb) function referentially, for the same reason that the definite description does in Gettier’s first case. However, the definite description in (IV) appears to function attributively insofar as no definite individual is indicated. But on Peirce’s view, it is in fact an index that functions referentially insofar as it refers to the collection Jones-or-Smith (as Atkin 2005, p. 165, explains, on Peirce’s view the referent of an index may be either an individual or a collection). Hence, provided Smith or Jones is hired, the hiring manager’s assertion is true and nongettierized. But if the CEO should happen to hire Brown out of the blue and Brown happens to have ten coins in his pocket, the hiring manager’s belief is not true since “the man who will get the job” refers to the Jones-or-Smith collection and not to Brown.
For instance, perhaps someone asks Smith what kind of car Jones owns. Not having considered the matter before, Jones thinks: Well, I have always seen Jones driving a Ford, so that must be the kind of car he owns.
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Atkins, R.K. A Peircean examination of Gettier’s two cases. Synthese 199, 12945–12961 (2021). https://doi.org/10.1007/s11229-021-03361-8
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DOI: https://doi.org/10.1007/s11229-021-03361-8