The Inclusion Problem in Epistemology: The Case of the Gettier Cases (2 of 3)

Post Two of Three (Post 1)

The contemporary engagement with Gettier’s counterexamples builds off of Gettier’s actual discussion. So, it will be useful to rehearse what was actually done in his classic (1963). Recall that in his original paper Gettier argued that the following conditional is false by way of providing counterexamples: If x has a justified true belief that p, then x knows that p. He also, importantly, assumed the following about the nature of justification in order to set up his counterexamples.

Closure: If x is justified in believing that p, and x is justified in believing that if p, then q, then x is justified in believing that q.

Fallibility: It is possible for x to be justified in believing that p, even though p is false.

With these assumptions in place, his original examples have the following profiles.

Ten-Coins Case:

  1. Jones is the man who will get the job, and Jones has ten coins in his pocket.
  2. So, the man who will get the job has ten coins in his pocket.
  • Smith has strong evidence for (1), and he believes that on the basis of his evidence.
  • Smith infers (2) from (1) and has justification for (2) by deduction from (1) and Closure.
  • The fact that Smith has ten coins in his pocket and that Smith will get the job, rather than Jones, is what makes (2) true.

From (a)-(c) Smith has a justified true belief in (2). But many people have the intuition that Smith does not know that the man who will get the job has ten coins in his pocket, even though he has a justified true belief.

Ford or Barcelona Case:

  1. Jones owns a Ford.
  2. So, either Jones owns a Ford or Brown is in Barcelona.
  • Smith has strong evidence for (1), and he believes (1) on the basis of his evidence.
  • Smith infers (2) from (1) and has justification for (2) by deduction from (1) and Closure.
  • The fact that Brown is in Barcelona is what makes (2) true, since it turns out that Jones does not own a Ford.

From (a)-(c) Smith has a justified true belief in (2). But many people have the intuition that Smith does not know that either Jones owns a Ford or Brown is in Barcelona, even though he has a justified true belief.

Some Contemporary Non-Western Traditions on Gettier’s Cases:

Jaysankar Shaw, extrapolating for the Nyāya School, shows how it would handle both counterexamples. He carefully uses the original examples and discusses in detail the responses. Here I offer a quote concerning each, and my own rendering of what the main argument is.

Ten-Coins Case:

With respect to the [The Ten-Coins Case] of Gettier, the Nyāya philosophers such as Udayana would claim that the conclusion of this inference is false. Therefore, it cannot be a case of knowledge. The belief or the cognition of Smith expressed by the sentence ‘The person who will get the job has ten coins in his pocket’ can be expressed in the following way: ‘The person who will get the job presented under the mode of being identical with Jones has ten coins in his pocket’. This is due to the fact that the conclusion is derived from the belief that Jones is the person who will get the job, and Jones has ten coins in his pocket. Since Smith got the job and has ten coins in his pockets, the belief of Smith is false. Since this sentence can be used to express different beliefs, we are not simply concerned with the truth of the sentence, but with the belief expressed by this sentence. In this case the belief it expresses is false. (Shaw 2015: 93, emphasis added)

The Argument:

  1. JTB is about belief.
  2. The phrase ‘the man with ten coins in his pocket’ can be used to capture two distinct beliefs; one that has Jones as the referent and the other that has Smith as the referent.
  3. Smith’s belief is about Jones, not himself.
  4. So, although the sentence expresses a true belief, it is not Smith’s true belief, since Smith’s belief is about Jones.
  5. If the belief that is actually expressed by ‘the man with ten coins in his pocket’ is not Smith’s belief, then we don’t have a case of justified true belief that is not knowledge, rather we have a case of justified false belief that is not knowledge.
  6. So, Gettier’s ten coins case is not a counterexample to knowledge according to the Nyāya.

Ford or Barcelona Case:

With respect to the [Ford or Barcelona Case] of Gettier, it is a case of belief, truth and justification, but not a case of justified true belief, where justification is a qualifier of true belief. The belief (or cognition) expressed by the sentence ‘Jones owns a Ford or Brown is in Barcelona’ is true by virtue of the fact that Brown happens to be in Barcelona. Since it is deduced from the premise ‘Jones owns a Ford’ it is in accordance with the rules of logic. If ‘justification’ means ‘being derived from premise(s) by applying the rules of logic’, then it has justification… [T]his counterexample of Gettier’s lacks justified true belief, although it is true and has justification. This is analogous to the truth of the sentence ‘The man with a red iron mask is in this room’. This sentence cannot be claimed to be true by virtue of having a man in this room, an iron mask in this room and a red object in this room. Hence from the Nyāya point of view, justification is a qualifier of true belief. Here justification means some sort of guarantee for its truth. (Shaw 2015: 93, emphasis added)

The Argument:

  1. There is a difference between (i) justified true belief and (ii) true belief qualified by justification.
  2. When Smith believes that either Jones owns a Ford or Brown is in Barcelona, he has (i) a justified true belief and not (ii) a true belief qualified by justification.
  3. Just as the sentence ‘the man with the red iron mask is in the room’ is not made true by a room with a man, an iron mask, and a red object, a proposition is not a piece of knowledge because it is a justified true belief, rather it has to be a true belief qualified by justification.
  4. So, the Ford or Barcelona Case is not a counterexample to the JTB theory of knowledge.

 

Bo Mou, extrapolating for the Mohist School, carefully shows how the Mohist would handle the Ten-Coins case. His work relies on the Mohist treatment of a kind of inference pattern known as Parallel Inference. I cannot go into detail here on it, but see his (2016) “How the Validity of the Parallel Inference is Possible: From the Ancient Mohist Diagnosis to a Modern Logical Treatment of its Semantic-Syntactic Structure.

[F]rom the later Mohist “semantic-sensibility” perspective, we can identify where the problem would emerge: when Gettier takes it that the referring expression in (2) refers to Smith […], the inference from (1) to (2) fails to observe the law of identity with regard to the double reference: the subject expression of (1) and (2) need to maintain the same semantic-whole referent (Jones as a whole person) and the same specific-part referent (the specific attribute of getting the job) for the sake of the validity of the inference from (1) to (2); however, although (1) and (2) maintain the same specific-part referent they fail to maintain the same semantic-whole referent: the semantic-whole referent of (1) is Jones, while the semantic-whole referent of (2) is shifted to Smith … in other words, from the later Mohist “semantic-sensibility” perspective, Gettier’s argument has yet to maintain the due semantic-sensibility of talking about the same object (while pointing to the same specific-part referent, i.e., the attribute of getting the job): in (1), Jones is talked about, while in (2) Smith is talked about; it is not a legitimate shift from what is talked about in (1) to what is talked in (2) because it fails to observe the law of identity and maintain the consistency in this connection for the sake of validity of the parallel inference…. Consequently, the inference from (1) to (2) becomes deductively invalid. (Mou forthcoming: 4-5)

The Argument:

  1. If Smith has a justified true belief, then the inference from ‘Jones will get the job’ to ‘the man with the ten coins in his pocket will get the job’, must be valid for justification to be transferred.
  2. According to the Mohist tradition the inference is valid only if it preserves the identity relation across parts and wholes.
  3. Smith is the referent of ‘The man who will get the job’. Jones is the referent of ‘the man that has ten coins in his pocket’. So, the part-whole identity relation is not preserved.
  4. So, the inference is not deductively valid.

 

References

  • Mou, B. 2016a. How the Validity of the Parallel Inference is Possible: From the Ancient Mohist Diagnose to a Modern Logical Treatment of its Semantic-Syntactic Structure. History and Philosophy of Logic. DOI: 10.1080/01445340.2016.1169150
  • Mou, B. 2016b. The Gettier Problem and a Daoist-Mohist Approach: How Their Constructive Engagement Is Possible. (u.p.s) Forthcoming.
  • Shaw, J. 2015. The Relevance of Indian Epistemology to Contemporary Western Philosophy. In P. Bilimoria & M. Hemmingsen (eds.) Comparative Philosophy and J.L. Shaw. Dordrecht: Sophia Studies in Cross-Cultural Philosophy of Traditions and Cultures 13: 83-101.

Anand Jayprakash Vaidya is Associate Professor of Philosophy and Director of the Center for Comparative Philosophy at San Jose University in California. His interests include the epistemology of intuition, perception and modality, the metaphysics of logic, critical thinking, the capabilities approach to justice, the philosophy of economics, and cross-cultural and multi-disciplinary public philosophy.

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