Gettier problem

The Gettier problem, in the field of epistemology, is a landmark philosophical problem with our understanding of knowledge. Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called "Gettier-cases") challenged the long-held justified true belief (or JTB) account of knowledge. On the JTB account, knowledge is equivalent to justified true belief, and if all three conditions (justification, truth, and belief) are met of a given claim, then we have knowledge of that proposition. In his three-page 1963 paper, titled "Is Justified True Belief Knowledge?", Gettier showed, by means of two counterexamples, that there were cases where individuals had justified true belief of a claim, but still failed to know it. Thus, Gettier claimed to have showed that the JTB account was inadequate—it could not account for all of knowledge. The JTB account was first credited to Plato, though Plato argued against this very account of knowledge in the Theaetetus (210a).

The term "Gettier problem", or "Gettier case", or even the adjective "Gettiered", is sometimes used to describe any case in epistemology that purports to repudiate the JTB account.

Responses to Gettier's paper have been numerous. Some rejected Gettier's examples, while others sought to adjust the JTB account to blunt the force of counterexamples. Gettier problems have even found their way into experiments, where the intuitive responses of people of varying demographics to Gettier cases have been studied.

History

The question of what constitutes "knowledge" is as old as philosophy itself. Its earliest instances are found in Plato's dialogues, notably Meno (97a–98b) and Theaetetus. Gettier himself was not even the first to raise the problem named after him; its existence is known to have been acknowledged by both Alexius Meinong and Bertrand Russell. The latter discussed it in his book Human knowledge: Its scope and limits.

Russell's case, called the stopped clock case, goes as follows:[1] Alice sees a clock that reads two o'clock, and believes that the time is two o'clock. It is in fact two o'clock. There's a problem, however: unknown to Alice, the clock she's looking at stopped twelve hours ago. Alice thus has an accidentally true, justified belief. Russell provides an answer of his own to the problem. Edmund Gettier's formulation of the problem was important as it coincided with the rise of the sort of philosophical naturalism promoted by W.V.O. Quine and others, and was used as a justification for a shift towards externalist theories of justification.[2] John L. Pollock and Joseph Cruz have stated that the Gettier problem has "fundamentally altered the character of contemporary epistemology" and has become "a central problem of epistemology since it poses a clear barrier to analyzing knowledge".[3]

Alvin Plantinga rejects the historical analysis:

According to the inherited lore of the epistemological tribe, the JTB [justified true belief] account enjoyed the status of epistemological orthodoxy until 1963, when it was shattered by Edmund Gettier... Of course there is an interesting historical irony here: it isn't easy to find many really explicit statements of a JTB analysis of knowledge prior to Gettier. It is almost as if a distinguished critic created a tradition in the very act of destroying it.[4]

Despite this, Plantinga does accept that some philosophers before Gettier have advanced a JTB account of knowledge, specifically C. I. Lewis and A. J. Ayer.[4]

Knowledge as justified true belief

The JTB account of knowledge is the claim that knowledge can be conceptually analyzed as justified true belief, which is to say that the meaning of sentences such as "Smith knows that it rained today" can be given with the following set of conditions, which are necessary and sufficient for knowledge to obtain:

A subject S knows that a proposition P is true if and only if:
  1. P is true, and
  2. S believes that P is true, and
  3. S is justified in believing that P is true

This account of knowledge is what Gettier subjected to criticism.

Gettier's two original counterexamples

Gettier's paper used counterexamples (see also thought experiment) to argue that there are cases of beliefs that are both true and justified—therefore satisfying all three conditions for knowledge on the JTB account—but that do not appear to be genuine cases of knowledge. Gettier, therefore, argued that his counterexamples show that the JTB account of knowledge is false, and thus that a different conceptual analysis is needed to correctly track what we mean by "knowledge".

Gettier's case is based on two counterexamples to the JTB analysis. Both of them rely on the established claim (under JTB) that justification is preserved by entailment, and the further claim that such applies significantly, or can be applied there coherently to the "stipulation" attributed to Smith's putative "belief" in the case of this particular counter-example: that is, that if Smith is justified in believing P, and Smith realizes that the truth of P entails the truth of Q, then Smith would also be justified in believing Q. Gettier calls these counterexamples "Case I" and "Case II":

Case I

Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition: (d) Jones is the man who will get the job, and Jones has ten coins in his pocket.
Smith's evidence for (d) might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones's pocket ten minutes ago. Proposition (d) entails: (e) The man who will get the job has ten coins in his pocket.
Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.
But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is then true, though proposition (d), from which Smith inferred (e), is false. In our example, then, all of the following are true: (i) (e) is true, (ii) Smith believes that (e) is true, and (iii) Smith is justified in believing that (e) is true. But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith's pocket, while Smith does not know how many coins are in Smith's pocket, and bases his belief in (e) on a count of the coins in Jones's pocket, whom he falsely believes to be the man who will get the job.

Case II

Smith, it is claimed by the hidden interlocutor, has a justified belief that "Jones owns a Ford". Smith therefore (justifiably) concludes (by the rule of disjunction introduction) that "Jones owns a Ford, or Brown is in Barcelona", even though Smith has no knowledge whatsoever about the location of Brown.
In fact, Jones does not own a Ford, but by sheer coincidence, Brown really is in Barcelona. Again, Smith had a belief that was true and justified, but not knowledge.

False premises

In both of Gettier's actual examples (see also counterfactual conditional), the justified true belief came about, if Smith's purported claims are disputable, as the result of entailment (but see also material conditional) from justified false beliefs that "Jones will get the job" (in case I), and that "Jones owns a Ford" (in case II). This led some early responses to Gettier to conclude that the definition of knowledge could be easily adjusted, so that knowledge was justified true belief that does not depend on false premises.

More general Gettier-style problems

In a 1966 scenario known as "The sheep in the field", Roderick Chisholm asks us to imagine that someone is standing outside a field looking at something that looks like a sheep (although in fact it is a dog disguised as a sheep). They believe there is a sheep in the field, and in fact they are right because there is a sheep behind the hill in the middle of the field. Hence, they have a justified true belief that there is a sheep in the field. But is that belief knowledge? A similar problem which seeks to be more plausible called the "Cow in the Field" appears in Martin Cohen's book 101 Philosophy Problems, where it is supposed that a farmer checking up on his favourite cow confuses a piece of black and white paper caught up in a distant bush for his cow. However, since the animal actually is in the field, but hidden in a hollow, again, the farmer has a justified, true belief which seems nonetheless not to qualify as "knowledge".

Another scenario by Brian Skyrms is "The Pyromaniac",[5] in which a struck match lights not for the reasons the pyromaniac imagines but because of some unknown "Q radiation".

A different perspective on the issue is given by Alvin Goldman in the "fake barns" scenario (crediting Carl Ginet with the example).[6] In this one, a man is driving in the countryside, and sees what looks exactly like a barn. Accordingly, he thinks that he is seeing a barn. In fact, that is what he is doing. But what he does not know is that the neighborhood generally consists of many fake barns — barn facades designed to look exactly like real barns when viewed from the road, as in the case of a visit in the countryside by Catherine II of Russia, just to please her. Since if he had been looking at one of them, he would have been unable to tell the difference, his "knowledge" that he was looking at a barn would seem to be poorly founded. A similar process appears in Robert A. Heinlein's Stranger in a Strange Land as an example of Fair Witness behavior.

The "no false premises" (or "no false lemmas") solution which was proposed early in the discussion proved to be somewhat problematic, as more general Gettier-style problems were then constructed or contrived in which the justified true belief does not seem to be the result of a chain of reasoning from a justified false belief.

For example:

After arranging to meet with Mark for help with homework, Luke arrives at the appointed time and place. Walking into Mark's office Luke clearly sees Mark at his desk; Luke immediately forms the belief "Mark is in the room. He can help me with my logic homework". Luke is justified in his belief; he clearly sees Mark at his desk. In fact, it's not Mark that Luke saw; it was a marvelous hologram, perfect in every respect, giving the appearance of Mark diligently grading papers at his desk. Nevertheless, Mark is in the room; he is crouched under his desk reading Frege. Luke's belief that Mark is in the room is true (he is in the room, under his desk) and justified (Mark's hologram is giving the appearance of Mark hard at work).

Again, it seems as though Luke does not "know" that Mark is in the room, even though it is claimed he has a justified true belief that Mark is in the room, but it is not nearly so clear that the perceptual belief that "Mark is in the room" was inferred from any premises at all, let alone any false ones, nor led to significant conclusions on its own; Luke did not seem to be reasoning about anything; "Mark is in the room" seems to have been part of what he seemed to see.

To save the "no false lemmas" solution, one must logically say that Luke's inference from sensory data does not count as a justified belief unless he consciously or unconsciously considers the possibilities of deception and self-deception. A justified version of Luke's thought process, by that logic, might go like this:

  1. That looks to me like Mark in the room.
  2. No factor, right now, could deceive me on this point.
  3. Therefore, I can safely ignore that possibility.
  4. "Mark is in the room" (or, "I can safely treat that as Mark").

The second line counts as a false premise. However, by the previous argument, this suggests we have fewer justified beliefs than we think we do.

Responses to Gettier

The Gettier problem is formally a problem in first-order logic, but the introduction by Gettier of terms such as believes and knows moves the discussion into the field of epistemology. Here, the sound (true) arguments ascribed to Smith then need also to be valid (believed) and convincing (justified) if they are to issue in real-world discussion about justified true belief. [7]

Responses to Gettier problems have fallen into one of three categories:

One response, therefore, is that in none of the above cases was the belief justified because it is impossible to justify anything that is not true. Conversely, the fact that a proposition turns out to be untrue is proof that it was not sufficiently justified in the first place. Under this interpretation the JTB definition of knowledge survives. This shifts the problem to a definition of justification, rather than knowledge. Another view is that justification and non-justification are not in binary opposition. Instead, justification is a matter of degree, with an idea being more or less justified. This account of justification is supported by mainstream philosophers such as Paul Boghossian [8] and Stephen Hicks. In common sense usage, an idea can not only be more justified or less justified, but it can also partially justified (Smith's boss told him X) and partially unjustified (Smith's boss is a liar). Gettier's cases involve propositions that were true, believed, but which had weak justification. In case 1, the premise that the testimony of Smith's boss is "strong evidence" is rejected. The case itself depends on the boss being either wrong or deceitful (Jones did not get the job) and therefore unreliable. In case 2, Smith again has accepted a questionable idea (Jones owns a Ford) with unspecified justification. Without justification, both cases do not undermine the JTB account of knowledge.

Other epistemologists accept Gettier's conclusion. Their responses to the Gettier problem, therefore, consist of trying to find alternative analyses of knowledge. They have struggled to discover and agree upon as a beginning any single notion of truth, or belief, or justifying which is wholly and obviously accepted. Truth, belief, and justifying have not yet been satisfactorily defined, so that JTB (justified true belief) may be defined satisfactorily is still problematical, on account or otherwise of Gettier's examples. Gettier, for many years a professor at University of Massachusetts Amherst later also was interested in the epistemic logic of Hintikka, a Finnish philosopher at Boston University, who published Knowledge and Belief in 1962.

Fourth condition (JTB+G) approaches

The most common direction for this sort of response to take is what might be called a "JTB+G" analysis: that is, an analysis based on finding some fourth condition—a "no-Gettier-problem" condition—which, when added to the conditions of justification, truth, and belief, will yield a set of necessary and jointly sufficient conditions.

Goldman's causal theory

One such response is that of Alvin Goldman (1967), who suggested the addition of a causal condition: a subject's belief is justified, for Goldman, only if the truth of a belief has caused the subject to have that belief (in the appropriate way); and for a justified true belief to count as knowledge, the subject must also be able to "correctly reconstruct" (mentally) that causal chain. Goldman's analysis would rule out Gettier cases in that Smith's beliefs are not caused by the truths of those beliefs; it is merely accidental that Smith's beliefs in the Gettier cases happen to be true, or that the prediction made by Smith: " The winner of the job will have 10 coins", on the basis of his putative belief, (see also bundling) came true in this one case. This theory is challenged by the difficulty of giving a principled explanation of how an appropriate causal relationship differs from an inappropriate one (without the circular response of saying that the appropriate sort of causal relationship is the knowledge-producing one); or retreating to a position in which justified true belief is weakly defined as the consensus of learned opinion. The latter would be useful, but not as useful nor desirable as the unchanging definitions of scientific concepts such as momentum. Thus, adopting a causal response to the Gettier problem usually requires one to adopt (as Goldman gladly does) some form of reliabilism about justification. See Goldmans Theory of justification.

Lehrer–Paxson's defeasibility condition

Keith Lehrer and Thomas Paxson (1969) proposed another response, by adding a defeasibility condition to the JTB analysis. On their account, knowledge is undefeated justified true belief — which is to say that a justified true belief counts as knowledge if and only if it is also the case that there is no further truth that, had the subject known it, would have defeated her present justification for the belief. (Thus, for example, Smith's justification for believing that the person who will get the job has ten coins in his pocket is his justified belief that Jones will get the job, combined with his justified belief that Jones has ten coins in his pocket. But if Smith had known the truth that Jones will not get the job, that would have defeated the justification for his belief.) However, many critics (such as Marshall Swain [1974]) have argued that the notion of a defeater fact cannot be made precise enough to rule out the Gettier cases without also ruling out a priori cases of knowledge .

Pragmatism

Pragmatism was developed as a philosophical doctrine by C.S.Peirce and William James (1842–1910). In Peirce's view, truth is nominally defined as a sign's correspondence to its object, and pragmatically defined as the ideal final opinion to which sufficient investigation would lead sooner or later. James' epistemological model of truth was that which works in the way of belief, and a belief was true if in the long run it worked for all of us, and guided us expeditiously through our semihospitable world. Peirce argued that metaphysics could be cleaned up by a pragmatic approach.

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object.[9]

From a pragmatic viewpoint of the kind often ascribed to James, defining on a particular occasion whether a particular belief can rightly be said to be both true and justified is seen as no more than an exercise in pedantry, but being able to discern whether that belief led to fruitful outcomes is a fruitful enterprise. Peirce emphasized fallibilism, considered the assertion of absolute certainty a barrier to inquiry,[10] and in 1901 defined truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth."[11] In other words, any unqualified assertion is likely to be at least a little wrong or, if right, still right for not entirely the right reasons. Therefore one is more veracious by being Socratic, including a recognition of one's own ignorance and knowing one may be proved wrong. This is the case, even though in practical matters one sometimes must act, if one is to act at all, with decision and complete confidence.[12]

Revisions of JTB approaches

The difficulties involved in producing a viable fourth condition have led to claims that attempting to repair the JTB account is a deficient strategy. For example, one might argue that what the Gettier problem shows is not the need for a fourth independent condition in addition to the original three, but rather that the attempt to build up an account of knowledging by conjoining a set of independent conditions was misguided from the outset. Those who have adopted this approach generally argue that epistemological terms like justification, evidence, certainty, etc. should be analyzed in terms of a primitive notion of knowledge, rather than vice versa. Knowledge is understood as factive, that is, as embodying a sort of epistemological "tie" between a truth and a belief. The JTB account is then criticized for trying to get and encapsulate the factivity of knowledge "on the cheap," as it were, or via a circular argument, by replacing an irreducible notion of factivity with the conjunction of some of the properties that accompany it (in particular, truth and justification). Of course, the introduction of irreducible primitives into a philosophical theory is always problematical (some would say a sign of desperation), and such anti-reductionist accounts are unlikely to please those who have other reasons to hold fast to the method behind JTB+G accounts.

Fred Dretske's conclusive reasons and Robert Nozick's truth-tracking

Fred Dretske (1971) developed an account of knowledge which he called "conclusive reasons", revived by Robert Nozick as what he called the subjunctive or truth-tracking account (1981). Nozick's formulation posits that proposition P is an instance of knowledge when:

  1. p is true
  2. S believes that p
  3. if p were true, S would believe that p
  4. if p weren't true, S wouldn't believe that p

Nozick's definition is intended to preserve Goldman's intuition that Gettier cases should be ruled out by disacknowledging "accidentally" true justified beliefs, but without risking the potentially onerous consequences of building a causal requirement into the analysis. This tactic though, invites the riposte that Nozick's account merely hides the problem and does not solve it, for it leaves open the question of why Smith would not have had his belief if it had been false. The most promising answer seems to be that it is because Smith's belief was caused by the truth of what he believes; but that puts us back in the causalist camp.

Criticisms and counter examples (notably the Grandma case) prompted a revision, which resulted in the alteration of (3) and (4) to limit themselves to the same method (i.e. vision):

  1. p is true
  2. S believes that p
  3. if p were true, S (using M) would believe that p
  4. if p weren't true, S (using method M) wouldn't believe that p

Saul Kripke has pointed out that this view remains problematic and uses a counterexample called the Fake Barn Country example, which describes a certain locality containing a number of fake barns or facades of barns. In the midst of these fake barns is one real barn, which is painted red. There is one more piece of crucial information for this example: the fake barns cannot be painted red.

Jones is driving along the highway, looks up and happens to see the real barn, and so forms the belief

Though Jones has gotten lucky, he could have just as easily been deceived and not have known it. Therefore it doesn't fulfill premise 4, for if Jones saw a fake barn he wouldn't have any idea it was a fake barn. So this is not knowledge.

An alternate example is if Jones looks up and forms the belief

According to Nozick's view this fulfills all four premises. Therefore this is knowledge, since Jones couldn't have been wrong, since the fake barns cannot be painted red. This is a troubling account however, since it seems the first statement I see a barn can be inferred from I see a red barn; however by Nozick's view the first belief is not knowledge and the second is knowledge.

Richard Kirkham's skepticism

Richard Kirkham has proposed that it is best to start with a definition of knowledge so strong that giving a counterexample to it is logically impossible. Whether it can be weakened without becoming subject to a counterexample should then be checked. He concludes that there will always be a counterexample to any definition of knowledge in which the believer's evidence does not logically necessitate the belief. Since in most cases the believer's evidence does not necessitate a belief, Kirkham embraces skepticism about knowledge. He notes that a belief can still be rational even if it is not an item of knowledge. (see also: fallibilism)

Attempts to dissolve the problem

One might respond to Gettier by finding a way to avoid his conclusion(s) in the first place. However, it can hardly be argued that knowledge is justified true belief if there are cases that are justified true belief without being knowledge; thus, those who want to avoid Gettier's conclusions have to find some way to defuse Gettier's counterexamples. In order to do so, within the parameters of the particular counter-example or exemplar, they must then either accept that

  1. Gettier's cases are not really cases of justified true belief, or
  2. Gettier's cases really are cases of knowledge after all,

or, demonstrate a case in which it is possible to circumvent surrender to the exemplar by eliminating any necessity for it to be considered that JTB apply in just those areas that Gettier has rendered obscure, without thereby lessening the force of JTB to apply in those cases where it actually is crucial. Then, though Gettier's cases stipulate that Smith has a certain belief and that his belief is true, it seems that in order to propose (1), one must argue that Gettier, (or, that is, the writer responsible for the particular form of words on this present occasion known as case (1), and who makes assertion's about Smith's "putative" beliefs), goes wrong because he has the wrong notion of justification. Such an argument often depends on an externalist account on which "justification" is understood in such a way that whether or not a belief is "justified" depends not just on the internal state of the believer, but also on how that internal state is related to the outside world. Externalist accounts typically are constructed such that Smith's putative beliefs in Case I and Case II are not really justified (even though it seems to Smith that they are), because his beliefs are not lined up with the world in the right way, or that it is possible to show that it is invalid to assert that "Smith" has any significant "particular" belief at all, in terms of JTB or otherwise. Such accounts, of course, face the same burden as causalist responses to Gettier: they have to explain what sort of relationship between the world and the believer counts as a justificatory relationship.

Those who accept (2) are by far in the minority in analytic philosophy; generally those who are willing to accept it are those who have independent reasons to say that more things count as knowledge than the intuitions that led to the JTB account would acknowledge. Chief among these are epistemic minimalists such as Crispin Sartwell, who hold that all true belief, including both Gettier's cases and lucky guesses, counts as knowledge.

Experimental research

Some early work in the field of experimental philosophy suggested that traditional intuitions about Gettier cases might vary cross-culturally.[13] However, subsequent studies have consistently failed to replicate these results, finding instead of that participants from different cultures do share the traditional intuition.[14][15][16] Indeed, more recent studies have actually been providing evidence for the opposite hypothesis, that people from a variety of different cultures have surprisingly similar intuitions in these cases.[17]

Notes

  1. ↑ 'Conditions of Knowledge' (1965). Chicago: Scott, Foresman
  2. ↑ Timothy McGrew (2007), Internalism and Externalism, Abingdon, Oxon: Routledge, chapter 1
  3. ↑ John L. Pollock; Joseph Cruz (1999), Contemporary theories of knowledge, Lanham, Md: Rowman & Littlefield Publishers, pp. 13–14, ISBN 0-8476-8936-0, 0847689360
  4. 1 2 Alvin Plantinga (1992). Warrant: The Current Debate. Oxford University Press. pp. 6–7. ISBN 0-19-507862-4.
  5. ↑ Skyrms, Brian (22 June 1967). "The Explication of 'X knows that p'". The Journal of Philosophy. 64 (12): 373–389. JSTOR 2024269. doi:10.2307/2024269.
  6. ↑ Goldman, Alvin I. (18 November 1976). "Discrimination and Perceptual Knowledge". The Journal of Philosophy. 73 (20): 771–791. JSTOR 2025679. doi:10.2307/2025679.
  7. ↑ James Pryor. Theory of Knowledge - The Gettier Problem (archive)
  8. ↑ Paul Boghossian (2007), Fear of Knowledge: Against relativism and constructivism, Oxford, UK: Clarendon Press, Chapter 7, p 95-101.
  9. ↑ See p. 481 in Peirce, C. S. (1905), "Issues of Pragmaticism", The Monist, vol. 15, pp. 481–499, Google Book Search Beta Eprint, Internet Archive Eprint. Reprinted in Collected Papers of Charles Sanders Peirce v. 5 paragraphs 438–463, see 438, and in Charles S. Peirce: Selected Writings, pp. 203–226)
  10. ↑ Peirce, C. S. (1899), "F.R.L." [First Rule of Logic], unpaginated manuscript, c. 1899, CP 1.135–140. Eprint Archived January 6, 2012, at the Wayback Machine..
  11. ↑ Peirce, C.S. (1901), "Truth and Falsity and Error" (in part), pp. 718–720 in J.M. Baldwin. ed., Dictionary of Philosophy and Psychology, vol. 2. Reprinted, CP 5.565–573.
  12. ↑ Peirce, C.S. (1898), "Philosophy and the Conduct of Life", Lecture 1 of the Cambridge (MA) Conferences Lectures, published in Collected Papers of Charles Sanders Peirce v. 1, paragraphs 616–48 in part and in Reasoning and the Logic of Things, Ketner (ed., intro.) and Putnam (intro., commentary), 105–22, reprinted in The Essential Peirce, v. 2, 27–41.
  13. ↑ Weinberg, Jonathan M.; Nichols, Shaun; Stich, Stephen (Spring–Fall 2001). "Normativity and Epistemic Intuitions". Philosophical Topics. 29 (1–2): 429–460. doi:10.5840/philtopics2001291/217.
  14. ↑ Kim, Minsun; Yuan, Yuan (2015). "No cross-cultural differences in the Gettier car case intuition: A replication study of Weinberg et al. 2001". Episteme. 12 (3): 355–361. doi:10.1017/epi.2015.17.
  15. ↑ Seyedsayamdost, Hamid (2014). "On Normativity and Epistemic Intuitions: Failure of Replication". Episteme. 12 (1): 95–116. doi:10.1017/epi.2014.27.
  16. ↑ Nagel, Jennifer (November 2012). "Intuitions and Experiments: A Defense of the Case Method in Epistemology". Philosophy and Phenomenological Research. 85 (3): 495–527. doi:10.1111/j.1933-1592.2012.00634.x.
  17. ↑ Machery, Edouard; Stich, Stephen; Rose, David; Chatterjee, Amita; Karasawa, Kaori; Struchiner, Noel; Sirker, Smita; Usui, Naoki; Hashimoto, Takaaki (August 2015). "Gettier Across Cultures". Noûs. doi:10.1111/nous.12110.

References

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