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Gettier's Problems
Gettier's made up problems.

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Gettier's Problems

7
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Posted 04/25/08 - 09:39 PM:	#26
reincarnated wrote: There is a pun which has been doing the rounds in philosophy circles for the last 45 years. Perhaps the funniest aspect of this particular pun is that most philosophers don’t seem to get the joke. This pun is commonly known as The Gettier Problem, inaugurated in 1963 by the publication, by Edmund L. Gettier, of two classic cases of alleged “problems” which seem to cast doubt on either the soundness or the completeness of the traditional Justified True Belief (JTB) analysis of knowledge. A detailed, logical and rational analysis of the ambiguities inherent in these Gettier-type cases shows how the pun is constructed, and by disambiguating the Gettier argument we can show that the JTB analysis is in fact quite complete and quite sound. Disambiguation of these cases clearly reveals Gettier’s joke – but will philosophers see the funny side? For a full explanation see http://www.moving-finger.com/papers/gettier.pdf I want to go slowly and carefully through the analysis of case 1 (then maybe case 2 later). The author says that Smith believes the following two propositions: 1c) Jones will get the job 1d) Jones has 10 coins in his pocket The dubious proposition is: 1b) The man who will get the job has 10 coins in his pocket His next point is that we can interpret 1b in several ways. I note that these correspond roughly to Donellan's attributive/referential distinction. We can, on the one hand, understand 'the man' as Jones or, on the other, we can interpret it as whoever the man is who gets the job and has 10 coins in his pocket (this man is not necessarily Jones). The author proposes that we must interpret it in this second sense for the counterexample to work and Smith does not know this proposition. Apparently, he finds this obvious. I do not. If Smith believes that someone in particular will get the job and have 10 coins in his pocket, surely he is justified in believing that there is some man such that: a) he gets the job and b) he has 10 coins in his pocket. If he believes that a particular man satisfies some description, he should be justified in his belief in the existentially generalized proposition.

despinozist
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Posted 04/26/08 - 12:03 PM:	#27
I'm starting to side with the ambiguity argument much more now; however, I do not think the argument itself succeeds. What it does reveal, however, is that Gettier does not want you to look at the propositions as having any semantic content whatever. So, the what in which we interpret the propositions with respect to Smith's "actual beliefs" is not relevant. Gettier wants us to ignore all semantic wealth of the propositions, and he only wants us to look at them as strictly truth-functional linguistic objects. So there are two assumptions: (a) truth-functionality and semantics have a certain relationship that makes it so that semantics can be ignored (b) truth-functionality is more important to knowledge-claims than semantic concerns It's not that we could interpret the propositions in many ways; Gettier's argument is such that interpretation is irrelevant; this is how his argument prevails. So there is a pun, yes, but Gettier et al want you to believe that puns do not exist. All that matters is what is truth functional. Propositions do not have "interpretation."
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Posted 04/26/08 - 06:31 PM:	#28
It's not that we could interpret the propositions in many ways; Gettier's argument is such that interpretation is irrelevant; this is how his argument prevails. I disagree. The interpretation of 1b determines whether it's true or false. Jones doesn't get the job, so if 'the man' is parsed as Jones, the statement is false, and so it cannot be a counterexample to JTB.

despinozist
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Posted 04/26/08 - 08:24 PM:	#29
7 wrote: I disagree. The interpretation of 1b determines whether it's true or false. Jones doesn't get the job, so if 'the man' is parsed as Jones, the statement is false, and so it cannot be a counterexample to JTB. Think of it this way: there's a fact-machine that Smith's belief is processed through. After Smith has the belief, who he means by "The man..." is irrelevant because the facts turn out a certain way. We cannot "play with history." Another way to look at it is this: in a nearby possible world, Smith's belief "The man..." does involve Smith getting the job, Jones not getting the job, them both having ten coins in their pockets while Smith doesn't know this fact about himself. The interpretation cannot matter because one cannot "interpret away" their both being, having ten coins, and Smith getting the job while believing "The man..." will get the job based off of the wrong justification. The idea is that "The man..." becomes its own truth-functional monster, regardless of the physical evidence ("Jones has...") given to Smith. We can look at it like this: (1) Jones has ten coins in his pocket and he will get he job. (2) The man, who is Jones, who will get the job has ten coins in his pocket. (3) There is exactly one x such that x is a man, x will get the job, and x has ten coins in his pocket. (1) is false and does not count as a relevant counterexample, as we'll all agree. (2) is the same way. But Gettier wants us to buy (3) which is a justified true logical inference (belief). (3) is a proposition about the "x as male gender" or "a subject of the male gender." Even if we accept that Smith always means (2), (3) is still a possible belief that Gettier wants you to accept that Smith "sees the entailment of" and subsequently believes. Your argument is that Smith necessarily means (2), which doesn't qualify; Gettier wants us to accept (3). You must be able to explain why Smith can't just be talking about gender. In a more extreme sense, look at it this way: Smith is a raging sexist, and he only thinks men ought to get the kind of job he's a candidate for.
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Posted 04/27/08 - 10:26 AM:	#30
Think of it this way: there's a fact-machine that Smith's belief is processed through. After Smith has the belief, who he means by "The man..." is irrelevant because the facts turn out a certain way. We cannot "play with history." Another way to look at it is this: in a nearby possible world, Smith's belief "The man..." does involve Smith getting the job, Jones not getting the job, them both having ten coins in their pockets while Smith doesn't know this fact about himself. The interpretation cannot matter because one cannot "interpret away" their both being, having ten coins, and Smith getting the job while believing "The man..." will get the job based off of the wrong justification. The idea is that "The man..." becomes its own truth-functional monster, regardless of the physical evidence ("Jones has...") given to Smith. I don't understand. By this I mean not that I disagree, but that I do not know what you're arguing. We can look at it like this: (1) Jones has ten coins in his pocket and he will get he job. (2) The man, who is Jones, who will get the job has ten coins in his pocket. (3) There is exactly one x such that x is a man, x will get the job, and x has ten coins in his pocket. (1) is false and does not count as a relevant counterexample, as we'll all agree. (2) is the same way. But Gettier wants us to buy (3) which is a justified true logical inference (belief). (3) is a proposition about the "x as male gender" or "a subject of the male gender." Even if we accept that Smith always means (2), (3) is still a possible belief that Gettier wants you to accept that Smith "sees the entailment of" and subsequently believes. Your argument is that Smith necessarily means (2), which doesn't qualify; Gettier wants us to accept (3). My argument is not that Smith necessarily believes 2. First of all, I was quite clear that the counterexample is the existentially generalized belief, not the one that has 'the man' functioning as a placeholder for 'Jones.' I know that 2 doesn't qualify and 3 does. Second, I haven't commented on the necessity of belief. I don't know how that subject ever came up. He doesn't necessarily have to believe anything. For the counterexample to work, all Gettier needs is for him to have a justified, true belief that is not knowledge. He doesn't need to necessarily have that belief in the given epistemic circumstances. That he has it in this instance is stipulated by the example. There's no argument as to what belief he has. You must be able to explain why Smith can't just be talking about gender. In a more extreme sense, look at it this way: Smith is a raging sexist, and he only thinks men ought to get the kind of job he's a candidate for. I don't know what you mean.

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Posted 04/29/08 - 06:38 PM:	#31
Is this discussion over?

despinozist
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Posted 04/29/08 - 09:19 PM:	#32
I'm reconsidering yours and the other philosopher's arguments/clarifications, studying for finals, writing two papers, and reading the Donellan essay "Reference and Definite Descriptions." I'll have something to say in a few days perhaps. But as a first reaction, I cannot say that I can really give a reply since a majority of what I have said is going by misunderstood. Either it is an inadequacy on my part, or I am just plain wrong. In truth, I am not trying to defend Gettier, but I am trying to obtain the most accurate interpretation and understanding of his argument so that I might refute it or stumble upon a fourth condition for JTB with a considerable degree of plausibility.
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Posted 05/04/08 - 05:46 AM:	#33
despinozist wrote: I want to go slowly and carefully through the analysis of case 1 (then maybe case 2 later). The author says that Smith believes the following two propositions: 1c) Jones will get the job 1d) Jones has 10 coins in his pocket The dubious proposition is: 1b) The man who will get the job has 10 coins in his pocket His next point is that we can interpret 1b in several ways. I note that these correspond roughly to Donellan's attributive/referential distinction. We can, on the one hand, understand 'the man' as Jones or, on the other, we can interpret it as whoever the man is who gets the job and has 10 coins in his pocket (this man is not necessarily Jones). The author proposes that we must interpret it in this second sense for the counterexample to work and Smith does not know this proposition. Apparently, he finds this obvious. I do not. OK, let’s try to work through it. We start with two propositions: (1a) Jones is the man who will get the job, and Jones has ten coins in his pocket. (1b) The man who will get the job has ten coins in his pocket. Now, the truth of (1a) entails the truth of (1b). In other words, if (1a) is true then it follows that (1b) is also true. However the REVERSE is NOT the case – the truth of (1b) does NOT entail the truth of (1a). If (1b) is true, then it follows there are a whole host of propositions similar to but not identical with (1a), any one (but ONLY one) of which could be true, such as (1e) “Evans will get the job, and Evans has 10 coins in his pocket”, or even (1h) “I have no idea which man will get the job, but he will have 10 coins in his pocket”. The meaning of (1b) is therefore ambiguous, there are many different and mutually exclusive unambiguous propositions, any one of which could be entailed by (1b) – but we have no idea which one. Now, Gettier’s argument hinges on the truth of (1b). But we have seen already that (1b) is ambiguous, and it is this very ambiguity which Gettier exploits. In Gettier’s example, Smith (not Jones) gets the job, and coincidentally Smith has 10 coins in his pocket. Proposition (1b) is therefore true, and since (following Gettier) the truth of proposition (1b) is entailed by the truth of proposition (1a), and we agree that Smith believes (1a) to be true, it follows (according to JTB) that all of the conditions are satisfied to allow us to conclude that Smith knew that he would get the job, and yet he clearly did NOT know that he would get the job! Why does Gettier’s argument appear to succeed? Because it exploits the ambiguity in (1b), in the same way that the expression “fruit flies like a banana” might seem to imply that we can have flying bananas – when in fact the true meaning is quite different. The absurdity of the expression “fruit flies like a banana” exploits the ambiguities in meaning of the words used, just as the absurdity in Gettier’s argument exploits the ambiguities in meaning of the words used in proposition (1b). despinozist wrote: If Smith believes that someone in particular will get the job and have 10 coins in his pocket, surely he is justified in believing that there is some man such that: a) he gets the job and b) he has 10 coins in his pocket. If he believes that a particular man satisfies some description, he should be justified in his belief in the existentially generalized proposition. Yes – this is in effect saying that the truth of (1a) entails the truth of (1b). What you call an existentially generalized proposition I call an ambiguous proposition. despinozist wrote: I'm starting to side with the ambiguity argument much more now; however, I do not think the argument itself succeeds. What it does reveal, however, is that Gettier does not want you to look at the propositions as having any semantic content whatever. Well of course he doesn’t. Just like the magician does not want to reveal the secret of his magic tricks – Gettier does not want to interpret his proposition as having any particular semantic content because once we start to do that we are on the road to revealing the ambiguity and the pun. Given that Gettier’s objective is to cast doubt on the reliability of JTB, it is quite natural that he wants to avoid any semantic analysis of his propositions. despinozist wrote: So there is a pun, yes, but Gettier et al want you to believe that puns do not exist. I refer you to “fruit flies like a banana” despinozist wrote: All that matters is what is truth functional. Propositions do not have "interpretation." Gettier would love this to be the case, and this is how he has hoodwinked a generation of philosophers.
_____________________ �If one pays attention to the concepts being employed, rather than the words being used, the resolution of this problem is simple.� (Stuart Burns)

despinozist
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Posted 05/04/08 - 11:53 AM:	#34
I'm sorry, but I do not think the "fruit flies like a banana" comparison is apt. It is a pun, but it is also a simile. Thus, by being figurative, it losing its basis for comparison. Attributing "flying like a banana" to a fruit can mean "flying like bananas biologically fly" (which they don't), "flying like the banana flew that I saw get tossed into the air yesterday," etc, etc. Ultimately, the figurative sense plays on "flying." The Gettier case is not a figurative statement, and you cannot look at either interpretation of it (semantic or truth-functional) as being figurative. It's attributive-referential, as I will later point out. Thanks for mentioning Donellan's essay, 7. Yes – this is in effect saying that the truth of (1a) entails the truth of (1b). What you call an existentially generalized proposition I call an ambiguous proposition. You might call it this, but nevertheless, the proposition is true, justified, and could be believed by Smith or anyone he might pass that proposition (1b) to. Your argument that it is ambiguous is noteworthy, but it's about as noteworthy as regards JTB as statistics data with marginalization errors. Existential Introduction uses a particular to generalize. It is a valid form of reasoning by most modern logicians' standards. (Pa -> ExPx) This is the inference Smith makes. It is a logically valid inference. This is all Gettier wants you to look at, that of being logically valid. Thus, it becomes a Justified True Logical Inference. Gettier wants you to believe (a) that it is possible for Smith to believe it, (B) that if Smith were to believe it, it would be a kosher belief, and (c) that truth-functionality makes, in this case and in many cases of our lives, semantic content irrelevant (even though semantic content is there--this is your ambiguity argument). Ultimately, your "ambiguity argument" translates into our need to look at the semantic content of any proposition. However, upon analysis, there's no reason to see why a proposition cannot both (a) have semantic content and (b) have truth-functional parameters which condition its truth or falsity. Gettier wants us to look at (b), as I've said numerous times already, and ignore, for the moment, (a). I do not need to be told anymore the notion of "puns." I get the notion of ambiguity. I hope now that I have laid out (a) and (b), the argument will not be reiterated that the proposition (1b) is "ambiguous" or a "pun." That much has been understood for sometime now. What is not "ambiguous" is the jump from particular (Jones) to generalized (man). Your beef with ambiguity does not come from seeing that Smith made the inference. Your beef comes from the possibility of what Smith could have meant (semantic content, pun, etc). He, ultimately, had to have been something. Gettier would like you to look at only the truth-functionality of the situation; that is, (a) Smith believes "The man who will get the job has ten coins in his pocket" in strictly truth-functional terms with respect to the properties so stated (that of "man-ness," "getting the job," and "coin possession." We have trouble with this because we know and feel that Smith must have someone in mind. Keith Donellan's attributive-referential distinction gives us a clear view of the problem here. Gettier wants us to look at the proposition in the attributive sense. He wants us to see Smith has making a proposition in which some such man will be attributed with the properties of "getting the job" and "coin possession." Our problem is with the referential sense that Smith does not satisfy. Smith, with your (1b), could not be referring to any man. However, by Existential Instantiation, when people make propositions of the sort (1b), we expect them to have a referent in mind. So we can look at the proposition as attributive or as referential. What are the criteria for saying that we ought to look at it in one sense rather than the other? In short, Why should we even care about ambiguity (which pertains to reference) when Smith is talking about the attributive sense? And if your argument is "Gettier didn't mean that," then I am interpreting at the moment that he did. So, I'd like to understand how my interpretation is wrong. Now, Existential Instantiation/Elimination is trickier. (ExPx -> Pa) And it pertains to our problem of the attributive sense. We consider this a valid line of reasoning. Given the context of the situation, look at it this way: Smith is asked by the secretary, just on a whim of hers, "Who do you think will get the job?" Smith says, "The man who will get the job has ten coins in his pocket." For whatever reason, this secretary also knows that Jones has ten coins in his pocket, and, let us further suppose that she does have evidence of this property of coin possession that pertaining to Smith. She cheerfully smiles in response, and the office becomes silent. Now we are faced with the problem you guys raise; and this is the problem in its most proper sense. Between Smith and Jones, this secretary cannot use existential instantiation to infer the right man who bears ten coins and who will get the job. She has equal evidence for both; what is not conveyed to her is Smith's evidence for Jones getting the job; this information, which is vital, is not captured in the proposition. This is the nature of generalizations; we all know this. Most Asians become "math nerds"; most blacks become "basketball stars"; etc, etc. But it is quite different in this case: for the secretary, the proposition is not ambiguous insofar as the properties go. For her, she can only look at the properties of coin possession and getting the job. Being a man is by default true because they are both men. For her, she is tying "coin possession" and "job getting" together. Consider "men" as the universe of discourse. Now, being a man is just assumed. But we've gone to far, your arguments are with the meaning Smith had. I've already raised my argument: We must reconcile "truth-functionality" with "semantic content." You might say "Gettier ignores semantic content," but so what? You are ignoring truth-functionality. Are they mutually exclusive? You say "Gettier would love this to be the case..." Where is your justification for saying that Gettier is wrong about investigating these propositions only in terms of truth-functionality? Edited by despinozist on 05/04/08 - 12:08 PM
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Posted 05/05/08 - 12:39 AM:	#35
OK, let’s try to work through it. We start with two propositions: (1a) Jones is the man who will get the job, and Jones has ten coins in his pocket. (1b) The man who will get the job has ten coins in his pocket. Now, the truth of (1a) entails the truth of (1b). In other words, if (1a) is true then it follows that (1b) is also true. However the REVERSE is NOT the case – the truth of (1b) does NOT entail the truth of (1a). If (1b) is true, then it follows there are a whole host of propositions similar to but not identical with (1a), any one (but ONLY one) of which could be true, such as (1e) “Evans will get the job, and Evans has 10 coins in his pocket”, or even (1h) “I have no idea which man will get the job, but he will have 10 coins in his pocket”. The meaning of (1b) is therefore ambiguous, there are many different and mutually exclusive unambiguous propositions, any one of which could be entailed by (1b) – but we have no idea which one. Now, Gettier’s argument hinges on the truth of (1b). But we have seen already that (1b) is ambiguous, and it is this very ambiguity which Gettier exploits. In Gettier’s example, Smith (not Jones) gets the job, and coincidentally Smith has 10 coins in his pocket. Proposition (1b) is therefore true, and since (following Gettier) the truth of proposition (1b) is entailed by the truth of proposition (1a), and we agree that Smith believes (1a) to be true, it follows (according to JTB) that all of the conditions are satisfied to allow us to conclude that Smith knew that he would get the job, and yet he clearly did NOT know that he would get the job! Why does Gettier’s argument appear to succeed? Because it exploits the ambiguity in (1b), in the same way that the expression “fruit flies like a banana” might seem to imply that we can have flying bananas – when in fact the true meaning is quite different. The absurdity of the expression “fruit flies like a banana” exploits the ambiguities in meaning of the words used, just as the absurdity in Gettier’s argument exploits the ambiguities in meaning of the words used in proposition (1b). (1b) is ambiguous, true. It can be interpreted in the following ways: (1c) Jones is the man who will get the job and he has 10 coins in his pocket (1d) x is the man who will get the job and he has 10 coins in his pocket, where x is some particular man, other than Jones, such as Evans. (1e) There is a man such that he will get the job and he has 10 coins in his pocket. Gettier wants (1e). This is the existentially generalized version. It is true if there is some man (Jones, Evans, me, etc) who gets the job and has 10 coins in his pocket. Gettier's point is that if Smith is justified in believing (1a), then he is justified in believing (1e), and (1e) is true, so (1e) is a JTB. Do you think that it's false that if (1a) is justified, then (1e) is justified? That is, do you think that if one belief is justified, the existential generalization of that belief might fail to be justified? If that is not your objection, I fail to see what it could possibly be. The ambiguity of (1b) is not vicious. (1b) can easily be pinned down to a definite statement which preserves Gettier's argument. Yes – this is in effect saying that the truth of (1a) entails the truth of (1b). What you call an existentially generalized proposition I call an ambiguous proposition. It's not ambiguous. He believes: Ex[(Mx & 10x) & Jx] where M is the predicate "is a man," 10 is the predicate "has 10 coins in his pocket," and J is "will get the job." Edited by 7 on 05/05/08 - 12:46 AM

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Posted 05/15/08 - 05:16 PM:	#36
IMO you only really know something if you have absolute proof.

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Posted 05/15/08 - 06:15 PM:	#37
Neodymion wrote: IMO you only really know something if you have absolute proof. The list of things that you really know, then, must be pretty short. What do you claim to know that you have absolute proof about? Cheers. jd
_____________________ OTOH I might be exhaustively wrong about everything I've ever thought--with the possible exception of this sentence.

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