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Gettier's Problems
Gettier's made up problems.

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Gettier's Problems

despinozist
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Posted 03/18/08 - 04:13 PM: Subject: Gettier's Problems	#1
Hello, new here. I'm taking an epistemology class, and I've, naturally, been introduced to Gettier's two counterexamples to justified true belief. You might suspect this thread is an attempt at a thesis for a paper, but at the moment, I cannot say it is. I do not know what my professor will assign because the semester is only half-way done. (He gives paper assignments 2 weeks before they're due.) In any event, my point. I do not think Gettier's two page refutation of JTB is plausible. The first counterexample goes like this. As far as Smith KNOWS (saw into his pocket, the employer said, "Yeah, he's gonna get it", etc): (1) Jones (a man) has 10 coins in his pocket & Jones' (same man) likelihood of getting the job is imminent. Gettier believes (1) entails the following. (2) The man [who has 10 coins in his pocket] [will get the job]. Now, I'm rubbed the wrong way about this. First, the second-order properties of Jones in (1) become displaced and assumed to apply to all men in an equivocal way. Why do I say this? Well, obviously, "The man" in (2) is an existential particular by use. But it is presumed, in so far as Gettier's problem goes, to function as a knowledge-claim universal. That is, upon conclusion, when Smith turns out the be WRONG (thus not displaying knowledge and therefore no Justification), the inference (2) cleverly presumes that the existential particular is now a universal (for Smith to be wrong about). My argument is that (2) does not lose the property "Jones" in so far as Smith's knowledge is concerned. The inference (2) still contains "(Jones,) The man who...etc" However, Gettier just drops the noun clause ("Jones,") for convenience. But this loses important and pertinant information as to Smith's knowledge-claim. Therefore, when Smith turns out to be wrong, he turned out to be wrong about just (1), and (2) is utterly irrelevant (or just a rephrasing of (1), possibly with an attempt to deceive, that has the same meaning). The inference, I feel, is just a waste of text in the already brief essay by Gettier. (2) is the same as (1), though Gettier likes to believe it isn't, and therefore it is not applicable to justifying Gettier's counterargument against Smith's knowledge. (1) turned out to be false; Smith believed it to be true, and it was justified given what Smith learnt. The primary point here is that Smith does not satisfy JTB because proposition p was false, not that he wasn't justified in believing that p. He was always justified: p was, throughout the scenario (1), and never (2) (as if implying that "the man" could be Smith or Jones or Carl; right, right, I get it. We're speaking of a local universal domain. In any event, Smith or Jones is not a knowledge claim). This leads me to my second counter argument: the status of OR knowledge and Gettier's second "counterexample." If someone claims to know that "It is raining outside or it is snowing outside," would you call this a sufficient knowledge-claim? Of course not! It's a logical truth, and it says nothing about the world. It is justified by virtue of the rules of logic, but the rules of logic justify no POSITIVE claims about the world. The law of noncontradiction does not tell us what the thing is, only that you won't find it in the same spatio-temporal location/logical space as a thing of a contradictory nature; the law of identity only asserts that a thing is itself without premises (but we're arguing!); excluded middle is a fork (as we've just witnessed; by inference: "It is raining or it is not raining" leaves us inquiring further: So is it raining? "Well, it's either raining or it's snowing"--hopeless!); Humean skeptics show us that rational entailment is just a sham when concerning matters of fact, etc. So, the second counterexample. (1) Jones owns a Ford. (1) is true, Smith accepts/believes/knows (1), and is justified, in whatever way you want to build the story, in believing (1). Smith, by disjunctive inclusion, builds the following list. (2) Jones owns a Ford, or Brown is in city A. (3) Jones owns a Ford, or Brown is in city B. (4) Jones owns a Ford, or Brown is in city C. Gettier seems to believe Smith is justified in believing this. However, he gives little to no argument except the implicit one that logic somehow makes positive claims about knowledge. ("I know A is A by the law of identity."--no you don't, it's a rule, not a fact!", etc) (1) turns out to be false, but (3) turns out to be true because Brown happens to be, for whatever reason, in city B. Of course, Smith does not actually know this. It just happens to be the case; thus, (3) is true in a rather random way. However, in the first place, is the disjunction a knowledge claim about the state of affairs? Keep in mind that we're talking strictly about (3) as a propositional knowledge-claim. (Students in my class couldn't wrap their minds around how 3 turned out to be true.) So the point is, even if (3) is true, propositions like [A v B] are not knowledge claims. So let's look at inclusive and exclusive. (5) Jones owns a Ford or Brown is in city B, or both. Easily, this entire propositional claim would be false. One of the conjuncts in the conjunction would be false; therefore, the whole proposition would fall through. (6) Jones owns a Ford or Brown is in city B, but not both. (6.1) (FvB)&-(F&B) This is obviously the proposition Gettier is using. But what about the intuitiveness of us using inclusive OR propositions? Open inspection of Smith's claims,--wait, there is no inspection! Gettier just assumes (6) is the intuitive claim. But what reason do we have to automatically accept that (5) could not possibly be the claim Smith was making? My point is this: I do not think Gettier added enough rigor to his paper, and thus, without this added inspection, his arguments become ineffectual. Another Gettier counterexample deals with Fred, Sam, and a room (kinky). (1) Sam is in the room. (1) is true (Sam has a twin brother who's visible in the room, but Sam is hiding somewhere in it), Fred accepts/believes (1), and Fred is justified (Fred sees Tim, Sam's twin, believing he's in fact Sam). Give that Fred has a sufficiently impaired recognizability faculty is the only way in which this counterexample MIGHT work. However, how is Fred justified in his belief that Sam is in the room? Oh, he sees Tim. So we've got a circular justification issue. My beliefs justify whatever evidence I receive and whatever evidence I receive justify my beliefs, regardless of the matters of fact. This is called dogmatism. Fred does not see Sam; he seems Tim. His justification is absent. Again, this counterexample is worthless. Any thoughts? Edited by despinozist on 03/18/08 - 04:31 PM
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Posted 03/19/08 - 03:40 PM:	#2
despinozist, I only scanned your post above. I'll read it more carefully later when I have time. I think that I agree with what you've said anout the equivocation. Meanwhile, here's an analysis of this issue that I wrote in a post in the forum once before: My own analysis of this �Gettier problem� is this: the confusion is caused by switching the referent signified by �man.� Smith�s belief that the �man� who will get the job has ten coins in his pocket means that Smith believes that Jones will get the job and Jones has ten coins in his pocket. In Smith�s sentence, �man� refers uniquely to Jones--not to anybody who happens to be a �man.� The fact that the other �man� (Smith himself as it turns out) who gets the job also happens to have ten coins in his pocket is an irrelevant coincidence. The confusion is caused by blatant equivocation about the referent of �man.� First �man� refers to Jones, then suddenly �man� refers to Smith. This is equivocation. By the way, I've noticed also in other Gettier-like problems that the equivocation or referent switch is where the issue lies. Cheers. jd
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despinozist
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Posted 03/19/08 - 11:35 PM:	#3
Thank you! I've re-written the post and put it on my blog. What I wrote originally (up there) is largely incoherent and rambling. I think the problem arises when attempting to "step outside" and look objectively at the inferences. Yeah, from the observer's perspective (usually an analytic philosopher), we can say the Jones statement entails the The man statement. But we are talking about the subjective contents of a person's mind. Philosophy aside, I need justificatory purpose for such an inference. We can't just say "suppose this inference" and carry on as if we're still talking about a human beings knowledge-claims (even if internal; I think assuming the subjective contents of one's mind requires even more justification). Basically, if Smith would never actually make such an inference in any real sense, then the inference as a philosophical argument is pointless. I suppose I'm taking a rather Moorean stance on this. I do not demand that we look at the inference from a commonsensical perspective, but why must we alienate ourselves, beyond humanity, in order justify an argument against a knowledge-claim that arguably would never arise in the first place. It seems strikingly close to a straw-man argument against knowledge. You're right. The way I put it is this. Smith is entitled, based on his evidence, to make a propositional knowledge-claim about Jones and Jones alone. Any rephrasing of the proposition never loses its domain of discourse. "The man" is a property of Jones, and Jones alone, as far as Smith's knowledge allows, and that is the case until he finds out that he himself (Smith) actually got the job. In that case, Smith was wrong about the first proposition, and the second proposition is just irrelevant if considered as a Gettier-inference. If considered as a rephrasing of the first, then Smith is wrong about that one as well. In that case, JTB was never satisfied, by definition, and Gettier never refuted a case of JTB. Of course, I do not argue for JTB. It's just that by definition, Gettier's problems seem to be irrelevant.
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Posted 03/29/08 - 02:32 AM:	#4
So the point is, even if (3) is true, propositions like [A v B] are not knowledge claims. So let's look at inclusive and exclusive. (5) Jones owns a Ford or Brown is in city B, or both. Easily, this entire propositional claim would be false. One of the conjuncts in the conjunction would be false; therefore, the whole proposition would fall through. What conjunction? This is the formula (A v B) with v being the inclusive or we find in a standard propositional truth table. Clearly, by checking the table, one can verify that the disjunction is true if at least one of its disjuncts is. Brown is in city b, so it's true.

despinozist
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Posted 03/29/08 - 06:08 AM:	#5
I got mixed up. I already addressed that in a revising of the paper. I was referring to inclusive or but thinking [A v B] & -[ A & B ] not [A v B] v [A & B]. A "conjunct" would have been in the former. Edited by despinozist on 03/29/08 - 07:50 AM
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Posted 03/29/08 - 06:16 AM:	#6
I see. You don't have to write out the second formula. (A v B) is enough because it covers when both are true. BTW, why don't you post the paper on this thread?

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Posted 03/29/08 - 06:23 AM:	#7
Of course, you don't have to write out the first formula, either. (A & B) is enough.

despinozist
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Posted 03/29/08 - 08:40 AM:	#8
Here's a link to my rewrite about Gettier Case II. http://nerdfiles.net/2008/03/29/rethinking-gettie... Edited by despinozist on 03/29/08 - 08:45 AM
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Posted 03/31/08 - 02:06 PM:	#9
Hi, new here too... I think I've two things to say on the original post (which deserves more time from me... sorry). 1. One problem that is apparent here is that it is assumed that we (must?) believe all logical consequences of any of our occurent beliefs. Thus the existential generalisation in case 1, from Jones to 'a man with 10 coins...' (btw I haven't the article to hand, but I thought it was 'a man' not 'the man' - no matter the point's the same) is a consequential belief that Smith 'logically' must have. Now from a philo of mind perspective these are of course two very different beliefs, even though associated, and it is by no means certain that Smith does hold the second belief. This is another way of putting the 'equivocation' view. But I think this is a mind problem separate from the epistemological one, since.... 2. If we accept that Smith HAS made the existential generalisation and DOES hold the occurent belief that 'a man with 10 coins will get the job', then we get to precisely the point that Gettier was making - his belief is true and justified, yet we would be disinclined to call it knowledge. Why? We are inclined to blame the wobble in the justification, but another way of looking at it is the way the later epistemologists did - the proposition is JTB only by luck. And the long search ever since to find anti-Gettier clauses to add to JTB is really a way of strengthening the chain of justification, derivation and evidence that can support knowledge as opposed to just-lucky JTB. (And, just to be pedantic, but possibly to be helpful to a serious philo student... a compound proposition formed by the OR operator is a disjunction not a conjunction, and the elements are disjuncts. Sorry.... I hate correcting even more than being corrected)
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Posted 04/17/08 - 11:24 PM:	#10
Hey there, It is almost agreed in contemporary epistemology that the Gettier problems are, in fact, counter examples to JTB theory of knowledge. Here's why. According to JTB S has knowledge that p iff a. S believes that p b. p (p is true) c. S is justified in believing that p. Gettier introduces the first counter example somewhat as follows. Suppose Smith has strong inductive evidence that (1) Jones has 10 coins in his pocket & It is highly probable that Jones is going to get the job. (the evidence can be as strong as you want it to be, and the probability can be extremely high that Jones is going to get the job. Maybe Jones has more than enough qualifications for the job and all the higher ups in the company that Jones is trying for agree that Jones is the best candidate etc.) From (1) Smith infers the following: (2) The man that will get the job has 10 coins in his pockets. The induction from (1) to (2) is valid, it's going from a particular to an existential instantiation. Here's the proof: (1) Jones has 10 coins in his pocket & It is highly probable that Jones is going to get the job. (1') It is highly probable that Jones is going to get the job. (2) The man that will get the job has 10 coins in his pocket. (ie, there is some man, such that there is only one man, and that man will get the job, and that man will have 10 coins in his pocket). Now Smith believes that (2), and also has justification that (2). It just has to be true for the belief that (2) to count as knowledge. Suppose that Jones doesn't get the job, he was going to get the job and things were looking good, but Jones dies of a tragic freak accident. So the job is given to the next candidate, Bob. And Bob just happens to have 10 coins in his pocket. So, (2) is true and according to JTB Smith has knowledge that (2) is true, but intuitively Smith does not have knowledge. His belief turns out to be true just by luck. Thus JTB is not sufficient for knowledge. So the project that most epistemologists have now is to either discard JTB, or add another condition to JTB. Most philosophers prefer the latter, but so far all attempts have been met with Gettier style examples.

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Posted 04/18/08 - 03:29 AM:	#11
The point of this thread is to show that the Gettier-type problems are not true counterexamples, not to restate what can be read from a Wikipedia article or the paper itself. Look, the mainline arguments are the following. Counter I Smith cannot make the inference “Jones has” to “The man has” without maintaining all the properties and referent (Jones) of the first conjunction-proposition. The inference itself is the problem. (1) I cannot imagine why in any real world scenario he’d make anything like it, and even if he did, it would be peculiar. Thus, Gettier can be accused of committing what I call Platonic Language. The inference itself, so stated, is contrived and too Form-like to be seriously considered. (2) Smith is not epistemically entitled to make any inference not necessarily referring to Jones. So Jones is thinking “some man, such that there is only one man”; well, is he not still thinking of Jones? Yes, the inference is valid for us, as observers of Smith’s situation, but for Smith, he’d need justification to at all include himself as a possibility of getting the job, which is what his inference (2) implies. “Smith’s evidence for (d) might be that the president of the company assured him that Jones would in the end be selected”; here, he receives possibly the strongest evidence available. So why would he still believe he’s even a likely candidate? My hunch is that we must further assume that Smith is the most optimistic thinker on the planet in order to accept his inference (2). That being said, wouldn’t most of us consider jettisoning, rather than making awkward and for-the-sake-of-argument inferences? Counter II “Jones owns a Ford, or Brown is in Barcelona” is logically equivalent to “If Jones does not own a Ford, then Brown is in Barcelona”. (1:Assum.) FvB (2:Provisional Assum.) -F (3:Provisional Assum.) -B (4: DeMorgan’s) -(-F&-B) (5:Conj) -F&-B (6:Conj) [-(-F&-B)] & [-F&-B] (6:Reductio) B (7:Conditional Proof) -F->B (1:Assum) -F -> B (2:Prov. Assum) -(FvB) (3: DeMorgan’s) -F&-B (4:Conj. Out) -F (5:Conj. Out) -B (6:Modus) B (7:Conj) -B&B (8:Reductio) FvB So, I pull the “possible worlds” card. In a nearby possible world, Smith says (2) “If Jones does not own a Ford, then Brown is in Barcelona.” I highly doubt I even need to play the possible worlds card since Gettier is making awkward inferences and brute-forcing logic into the way the mind thinks. Perhaps not a possible world? I say it is logically possible for Smith to actually utter (2). If he can’t, I’d sure like to see why it is that he can’t. Anyway, my point is this, given the logically equivalent item (2): why would Smith at all consider Jones’ ownership of a Ford consequentially relevant to Brown’s being in Barcelona? More generally, how in any way is Brown’s being in Barcelona conditioned by Jones’ owning or not owning of a Ford? Which kind of “OR” proposition is this? Inclusive or Exclusive? In either case, why would Smith feel entitled to know if Brown is in Barcelona? Sure, the inference is logically possible, but Smith is epistemically restricted to his own evidence. Either OR-type highlights the awkwardness of the inference; he couldn’t possibly think himself justified in saying anything about actual Brown’s location. He can only rattle off a list of possibilities; this does not implicate knowledge. The propositions are neither true nor false, but meaningless for Smith; thus, they are useless to Gettier’s project. Smith’s being right in the end is irrelevant because he had no epistemic justification for his inference, only rule-logical justification. Well, if he’s going to play the rules of logic that way, as said earlier, it must be further argued why Smith cannot, in the first place, utter (2) (the If…Then… proposition). Edited by despinozist on 04/18/08 - 03:41 AM
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Posted 04/18/08 - 03:49 PM:	#12
Response to Counter 1. Why can't Smith make the inference from "Jones has" to "The man has", presumably Jones is a man, and this is a simple case of existential introduction. Smith is making a deductive, valid inference. Unless existential introduction is somehow a bad inference; but I have my doubts. We make existential introduction inferences all the time, we might think about a particular object in the world and state a sentence that makes use of an existential introduction. For example, I think "Edwin the elephant has only three legs", so I state "There is some elephant that has three legs", everyone hearing the sentence understands this a generalization about some particular elephant. It would be extremely bazaar if we said that "your inference from what you were thinking, to what you said was not a good inference". You might think it was a bad inference if it was inductive, but it's deductive, which makes the Gettier cases all the more problematic. Second Smith is aloud to make an inference not necessarily referring to Jones. Why? consider this example: Jones is a student. Somone is a student. Smith has hands. Someone has hands. It's easy to think of a dialogue where we make these inferences in philosophical arguments. Smith argues that nobody is a student. So, it is not the case that someone is a student. April remembers that Jones is a student. So, she thinks "well someone is a student, since jones is." from the simple premise that Jones is a student, April constructs an argument to the effect that it is false that it is not the case that someone is a student. April wins the argument. Doesn't she? Edited by rayzer on 04/18/08 - 03:54 PM

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Posted 04/18/08 - 05:00 PM:	#13
I readily accept existential introduction (EI); however, what I do not accept is it implicating knowledge-claims into some domain of discourse that is not epistemically valid. Of course April wins the argument; when she is thinking "someone is a student," here evidence is Jones. Her basis for raising her counter is that she's seen that Jones is a student. So, [-VxSx] is contradicted by [ExSj]. That's perfectly fine because April always had Jones in mind. This Gettier case is quite different. Not only is existential introduction made, but it is made in such a way where no true referent is held. At whatever time t during the Gettier Case I, Smith's inference of "The man" becomes vacuous. It literally means, before we are told that Smith actually gets the job, (1) Smith has ten coins in his pocket and he will get the job. (2) Jones has ten coins in his pocket and he will get the job. The point is that "the man" is too general; Smith's epistemic justification only entitles him to making "The man" statement while maintaining Jones as a property of Man. Thus, if someone says: (3) Socrates is a man (3.1) Ms (3.2) ExMx (EI) We cannot expect this person to also mean "Plato is a man." The statement was uttered by Socrates. Logically, the inference is fine. There is some man such that at least one man exists is satisfied. But this does not mean that every possible man is accounted for or even considered. Smith's belief is Justified True Logical Inference, not Justified True Belief. You can believe that "someone is a man," but that is not knowledge unless you can have that proposition track back to your initial particular. Like on the witness stand: "Yeah, I saw someone rob that house"--"but did you see Tim rob the house?"--"I can't say Tim exactly, but my evidence leads me to believe someone actually did enter the house." Smith's case is that he's inferred through EI, but he's only justified in believing Jones and only Jones, not "The man." Now we can backtrack in categories; so, Smith is entitled to say "a person of a certain gender will get the job." This would imply, since we can switch categories at will, that we can be JTB-no fourth condition in many cases. My argument here is that the fourth condition must be that the belief tracks. Now I'm thinking about the gender thing... I wish people would emphasize the nature of ontological categories in this jazz.
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Posted 04/19/08 - 12:58 AM:	#14
I'm still not convinced, my friend. I understand your point, "The man" Smith has in mind in Jones, but the proposition "The man..." remains true whether smith has Jones in mind or not. According to your thesis, Smith is only epistemically aloud to make an general inference from a particular to a general existential introduction if he has a particular in mind. I agree, but that existential generalization remains a True Justified Logical Inference that Smith believes, So It's not exactly clear why it's not a JTB. It seems to me that you're actually introducing a new version of what counts for knowledge; that is to say a fourth condition. Smith should be able to track the truth of his belief. The question isn't whether Gettier's counter examples are good or not, they are good counter examples to JTB. But you're version is adding a fourth condition to JTB; it's essentially a truth tracking theory. But I'm not entirely sure truth tracking is necessary, or suffiecient for knowledge. I'll elaborate this in the future but right now I have homework to do.

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Posted 04/20/08 - 06:57 PM:	#15
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 Edited by reincarnated on 04/20/08 - 07:02 PM
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Posted 04/20/08 - 07:27 PM:	#16
That's what I've been saying! Smith believes "Jones has" because the property of Jones MUST track for Smith (i.e. predicate-logic: Mj). Sure, the proposition is TRUE by existential introduction for the purposes of "God's eye view," but for Smith, the proposition must necessarily include Jones and not himself. (a) Jones is necessarily the referent for Smith but not necessarily for us. Now, the question must be asked: What is the relationship of JTB and an external observer? Further, how can we say that because "the man" is imposed on Smith that he believes it? Yes, it is TRUE, I reiterate, for us reading the paper because we can play with logical inference, but we are talking about a supposedly real person with Internal Beliefs. We cannot just play some logical ninjitsu while expecting someone to hold necessarily generalizations (Existential Introduction) as their beliefs. Sure, the new proposition ("The Man...") is True and (Logically) Justified...but does Smith actually believe it? Gettier says "suppose Smith sees the entailment"... THIS is what needs an argument, and Gettier does not provide it. In what way does he see its entailment? Why does he see it? What reason does he have for "seeing" it? Did he actually make it himself (Smith), or is Gettier just imposing it for the sake of argument? At the end, after successfully winning the job, would Smith reflect on his proposition and count himself as having had known it? Is that a philosophical question? Or can only external minds judge the knowledge of others? Can a mind never judge its own knowledge? Again, the proposition of case I is certainly true and logically justified, but "I agree, but that existential generalization remains a True Justified Logical Inference that Smith believes..." In what way does he believe it? It's never stated in the paper that he believes it, only that he sees the entailment. Furthermore, my argument still stands; recognize the gist of it: Smith has made a generalization (by EI); in order to make such a generalization, it has to be a true generalization. It has to be a statement about the state of affairs which encompasses more than just a particular. However, my argument has been that Smith's belief MUST TRACK. Why do I say this? Well, what has Smith made an Existential Introduction about? Well, he's made one based off of a particular. Generally existential quantifiers stand for "some," "at least one," etc. Now, consider the (vague) situation Gettier set up. For all we know, Smith and Jones are the only candidates for the job. My argument has been that Smith cannot possibly be considering himself as the likely candidate to get it. The evidence for Jones is too strong. Thus, Gettier makes, and Smith "sees," entailment based on EXACTLY ONE token, and only one token. For Smith's knowledge-claim proposition, not only MUST his belief track, but the entailed proposition ("The man...") can only function as a grammatical transposition. Not only must his belief track, but his belief cannot do anything but (as far as we, as outside observers can tell) zero in on Jones. Okay, ignore this... It's possible they're not the only ones. However, I still think issue needs to be raised with the nature of existential introduction. I suppose we could say "Jones, Smith, and only other men were applying for a job." I do not think the Gettier argument works, however, if Jones and Smith are the ONLY men applying. Furthermore, whoever founded the idea that "beliefs" and "logic" correspond at all? Couldn't beliefs simply be expressions of one's attitude? That said, one's attitude could toss off any old list for Case II, and if Brown were not located at any city on that finite list? This is not the point, though. I would grant that beliefs will be subjected to truth and falsity, but who established the notions of truth and falsity necessarily are governed by the rules of logical inference. I suppose I may come off as a Humean Skeptic here, but, they're OUR rules of logical inference. Who's to say our beliefs must answer to our logic rather than our logic to our beliefs? Edited by despinozist on 04/20/08 - 07:51 PM
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Posted 04/20/08 - 08:05 PM:	#17
That second argument in that paper fails to understand how disjunction inclusion propositions work. Smith is justified in believing P; now he has a proposition going. By disjunctive inclusion, Smith gets P or Q. -P is the case; therefore, Q. By logic, this is how it works: P or Q -P Therefore, Q However, Smith was never justified in believing Q. He caught its truth by accident. However, if you accept that later evidence governs Smith's JTB, the falsity of P (by logic) somehow (outside of Smith's mind) determines that Q is true. Smith never sees this intimate relationship between P and Q, but in order for him to infer Q at all he must see that P and Q are related in some way. The idea Gettier wants to get across is that Smith got P or Q and believed that by disjunctive inclusion. Who knows why people would believe a whole disjunctive argument; it's not "believable" in principle. It's a dichotomous context builder. Disjunctive inclusion INCREASES the number of those you possibly believe; believing a disjunctive proposition itself requires that one explain how the disjuncts are related. Even then, believing the proposition on the whole makes the belief a tautology. For a believer, a tautology can never become falsified. The OR-proposition for Smith becomes a tautology. If you consider the OR proposition as Inclusive or Exclusive, this would require you to ask why Smith would feel epistemically justified in believing P&Q or, exclusively, Not-[P&Q]. Considering these form of OR-propositions, Smith's epistemic justified becomes empty. He has no justified at all for considering that P& Brown is wherever is at all entitled to his knowledge. Edited by despinozist on 04/20/08 - 08:11 PM
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Posted 04/20/08 - 09:02 PM:	#18
despinozist wrote: Smith is justified in believing P; now he has a proposition going. By disjunctive inclusion, Smith gets P or Q. -P is the case; therefore, Q. By logic, this is how it works: P or Q -P Therefore, Q The simple logical argument fails to capture the nuances of Smith's belief - that's where the ambiguity comes in and that is how Gettier's pun succeeds. If we say that "P or Q", this may be interpreted in several ways (in terms of Smith's belief) as follows: Smith either (a) believes that P and has no particular belief about Q; or (b) believes that Q and has no particular beliefs about P; or (c) has NO particular belief about the truth of either P or Q, but for some inexplicable reasons believes that one of these is true. In fact in this case (a) is true and both (b) and (c) are false. But all three (a), (b) and (c) are compatible with the simpler (and hence ambiguous) logical statement "P or Q". Gettier's argument exploits the ambiguity in meaning of "P or Q", that's where the pun comes in.
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Posted 04/20/08 - 09:36 PM:	#19
Keep in mind, however, the beginning of Gettier Case II: "Suppose that Smith has strong evidence" etc... Yes, Gettier was going for economy. My epistemology professor adds to that brief "strong evidence" statement with "add evidence you want--maybe Smith sees Jones drive a Ford everyday for five years." Gettier is really leaving it up to the audience to build the story here; that's one of my own possible refutations: overall vagueness and Platonicity. But that's beside the point. "strong evidence" for believing P means that your (b) and (c) are irrelevant. Smith believes P because he is justified in believing his evidence for P. The proposition "P v Q" is produced because of P's truth, as far as Smith IS JUSTIFIED, and because of disjunctive inclusive. Smith doesn't believe P or Q without basis. He believes P; therefore, he believes P or Q. He's not justified in believing just Q at all. He's only justified in believing: (1) P alone. (2) P or Q. (3) P or Z. (4) and so on. (b) and (c) are not compatible because they ignore Gettier's description of "strong evidence" for P. Do not lose sight of what P is standing for: it stands for "Jones owns a Ford." That isn't arbitrary and interchangeable with Q. It's the basis for "Jones owns a Ford, or Brown is in..." This logical disjunction must be viewed as a WHOLE. Smith believes the WHOLE, or Smith believes ONLY the P part. Thus, Smith's ultimate belief is P v Q, not P v Q on the basis of P or P v Q on the basis of Q. It's just P v Q. Generally, my beef is that propositions of the OR-type ("P v Q") are not truly knowledge-claims; more specifically, I do not see how Jones owning a Ford is related to Brown's location. Why? Well, Gettier is forcing logic onto Smith's thinking. So, why can I not force that "P v Q" is logically equiavlent to "-P > Q"? That accepted, we can ask: How is Jones owning a Ford consequentially relevant to Brown's location?
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Posted 04/21/08 - 01:46 AM:	#20
despinozist wrote: "strong evidence" for believing P means that your (b) and (c) are irrelevant. With respect, I think you are missing my point entirely. When the statement "P or Q" is translated into possible beliefs that Smith COULD hold (ie beliefs consistent with the statement "P or Q") then there are at least 3 possible and mutually exclusive beliefs that Smith could hold - these are (a), (b) and (c) in my last post. In fact Smith holds only one of these 3 beliefs (belief (a)). The statement "P or Q" is therefore AMBIGUOUS in terms of Smith's actual beliefs. despinozist wrote: Smith doesn't believe P or Q without basis. He believes P; therefore, he believes P or Q. Agreed - but when the statement "P or Q" is translated back into Smith's beliefs, we see that it has 3 possible meanings (as explained in my previous post), only ONE of which is true (the other two meanings are false). What Smith actually believes is "that P is true, but he has no particular beliefs about the truth or falsity of Q", hence it follows "that P or Q". However it is NOT possible to work backwards - we cannot conclude from the statement "that P or Q" which particular meaning Smith has in his head (either (a) (b) or (c) in my previous post). "P or Q" thus has ambiguity in meaning when translated back to Smith's belief - and this ambiguity leads to the uncertainty and the pun, which is what is exploited by Gettier. Edited by reincarnated on 04/21/08 - 04:05 AM
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Posted 04/21/08 - 08:49 AM:	#21
I'm understanding your point better now. I think, though, is not that I've been "missing it," but that I actively deny it. It calls for what I deny to be relevant: I deny the notion of "God's eye view" and "retrospection." God's eye view allows us to think in terms of how the resultant propositions ("The man..."; "P or Q"; etc) relate to Smith's cognition. Since the point of Gettier's argument is that knowledge is stumbled upon by luck and chance, my point is this: There is no relationship between the ultimate true propositions and Smith's internal beliefs. So, I feel, the question of "if Smith were to write his beliefs down, walk away for a week, and come back--would he know which belief he held to make the inference?" is irrelevant. It's a God's eye view question that only we can ask because we are observing the situation. The point of the second Gettier problem is not that Smith should be held epistemically accountable to what he meant. My statement that he gets P or Q from just P is just that; and that (a) is the only closely relevant option you gave. However, once P or Q is established, (a), (b) and (c) are all equally irrelevant. Gettier's point is that Smith believes P or Q, but the disconnect in epistemic justification comes when he makes the logical inference. He is justified in making the inference, and thus justified in holding P or Q. P or Q has a separate epistemic quality to it. Yet, your argument is that because of this, Smith should be able to tie P or Q back to P as its basis. Now this is true, and Smith himself very well could. We cannot because we are in God-mode and engaged in retrospection. Now, Smith is not equally epistemically justified in P or Q as he is in P (it's just a logical inference). I actively deny your claim of "working backwards" because (b) and (c) are not even possible for Smith; yet they are possible for us, I agree. Smith believes P or Q and he is at least aware of P in his cognition. Being aware of P is one thing, and being justified by P to make an inference is another. Smith is aware of P in his cognition, always--ambiguity comes for us, but not for Smith. What I want to do is stop this "God's eye view" argument which presupposes Platonicity. It does not matter that it's ambiguous for us that P or Q, on paper, might not tie back to P as the justification. It nevertheless does for Smith. Translating meaning back to Smith cannot be raised as an argument against Gettier because Smith believes, ultimately, "P or Q" and is aware of P. Ask Smith, he'll say "I see P or Q on basis of P." Smith necessarily opts for (a). Now, if you're saying that we're more important in determining what constitutes knowledge as opposed to Smith's internal judgment or determining ground, I'd like to see that premise. It seems to be the implicit premise working here: "we cannot conclude from the statement "that P or Q" which particular meaning Smith has in his head" Why would we do this if we know that Smith had "P or Q is justified on basis on P by disjunctive inclusion" in his cognition? In what way are we "working backwards" with proposition P or Q? You are trying to tie meaning back to Smith's belief, but there is no meaning beyond the simple fact that an OR proposition is true. Looking for meaning behind P or Q is going about it wrongly, I feel, because Gettier is trying to show that Smith is wrong about P or Q; not that he's wrong about P or Q because he was wrong about any of the disjuncts. The disjuncts are irrelevant meaning-wise and justification-wise. Smith is justified to make P or Q by disjunction inclusion not by evidence of P or Q. Smith believes P or Q because of logical manipulation. Therefore, P's meaning and justification is irrelevant so is Q's, yet the fact still remains that Smith is aware of how he got P or Q in the first place. I've gone about this redundantly. Please do not take it as condescension on my part, but I'm just restating points so that I can better grasp the problems we here concern ourselves with. Edited by despinozist on 04/21/08 - 08:54 AM
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Posted 04/21/08 - 10:48 PM:	#22
despinozist wrote: I'm understanding your point better now. I think, though, is not that I've been "missing it," but that I actively deny it. It calls for what I deny to be relevant: I deny the notion of "God's eye view" and "retrospection." God's eye view allows us to think in terms of how the resultant propositions ("The man..."; "P or Q"; etc) relate to Smith's cognition. Since the point of Gettier's argument is that knowledge is stumbled upon by luck and chance, my point is this: There is no relationship between the ultimate true propositions and Smith's internal beliefs. So, I feel, the question of "if Smith were to write his beliefs down, walk away for a week, and come back--would he know which belief he held to make the inference?" is irrelevant. It's a God's eye view question that only we can ask because we are observing the situation. It seems we are still talking at cross-purposes. Gettier’s approach is to take the premise “P or Q” at face value, and his argument is based on taking the premise “P or Q” to derive certain conclusions about Smith’s beliefs . However, as we have seen, “P or Q” is ambiguous (in terms of Smith’s actual beliefs), therefore if we use “P or Q” to derive conclusions about Smith’s beliefs we may end up with incorrect conclusions (because of the ambiguity in meaning). This is exactly what the Gettier argument boils down to. Gettier starts with an unambiguous true premise (such as “Smith believes that P, but he has no particular beliefs about Q” ), converts this to another true but this time ambiguous premise (such as “Smith believes that either P or Q” ), and on the basis of this ambiguous premise concludes (from JTB) that Smith possesses knowledge but based on a false belief. Gettier’s conclusion (that Smith possesses knowledge but based on a false belief) is thus clearly a false conclusion simply because it is based on an ambiguous premise. The pun is exposed, and I can laugh at the joke – I hope you can also see the joke now?
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Posted 04/23/08 - 09:23 PM:	#23
I see the problem we face. I'm not sure why you seem to contrast the inferred belief "P or Q" with Smith's "actual beliefs." The inferred belief is not something to "derive" anything from; thus, the concern for ambiguity is something that is being imposed on the final belief. It is the ultimate belief Smith holds; it is the belief he fails to satisfy JTB for. For Case I, it is not the case that Smith triumphs because he always holds (or tracks Jones) with proposition "The man (who is Jones)..." The point Gettier is making is this: by existential introduction, Smith has inferred P. Now, Smith believes P. But Smith does not seem to have had knowledge after the fact because (a) he did not know he had ten coins in his own pocket, and (b) he actually got the job yet he is "a man." The point is that Smith believes "A being of a certain gender has ten coins in its pockets and will get the job." The emphasis is that Smith now has a belief about gender. So Ex(Mx&Tx&Jx) is his belief. There is such an x that x is a man, that x has ten coins in his pocket, and that x will get the job. His belief is no longer about Jones, Evans, or whoever: it is about gender. There's no ambiguity. This is exactly why Gettier discussed the issue of inference earlier in the paper. He's speaking of, truly, Justified True Logical Inference. Gettier's implicit assumption is that Logical Inference and Beliefs correspond. And when we logically infer something through predicate calculus, we necessarily believe that resultant proposition. Again, the ambiguity concern is not an issue for case II. Smith believes P v Q, P v F, P v Z on grounds of P alone. We cannot play revolving disjuncts here. Smith inferred P v Q, P v F, P v Z all equally based on the truth of P alone. P's truth transfers into all three equally. They are all true on grounds of P alone. The right hand disjuncts are not even a consideration for Smith, they're stabs in the dark. They cannot both be "unknown" because no truth would be transmitted. Smith isn't going in with all luck. He's got strong evidence and believes P. For Smith, P is true. P's truth makes the propositions all possible truths. It's not that we accepted that Smith held an OR-belief with two unknowns that makes JTB. It's that Smith turned out to be right about logically inferred belief which, though true, must be false knowledge for Smith because the evidence he based the belief on was actually false. Now of course, Smith would say, had he not inferred the OR-beliefs, "So I was wrong, sue me." But by Justified True Logical Inference, he had knowledge but in an awkward way. This awkwardness comes from the fact that logical inferences seem to cause a disconnect between our causal evidence for JTB. Gettier seems to be making a distinction between Justified True Belief in Evidence and Justified True Belief in Logical Inference. The latter is attacked in the paper; the inferences are attacked, not "The man (who is Jones)" but "The man qua man..." nor is "Jones owns a Ford" but rather "Jones owns a Ford or Brown is in Barcelona." It is the WHOLE and FINAL proposition that does not pass JTB. Yes, they are ambiguous in the sense that their referents seem to be "lost," but once the inference is made Jones-evidence becomes irrelevant. Smith is believing in ambiguous propositions, and those propositions are beliefs. Think of this "Jones owns a Ford or Brown is in Barcelona" is itself a belief. Don't even consider the disjuncts singularly. The whole proposition is a belief. "A man will get the job who has ten coins in his pocket" is itself a belief, regardless of the male candidates. These are the beliefs that seem to fail to be knowledge because of the holes in JTB when logical inference is made. The ambiguity argument is not a concern at all. Edited by despinozist on 04/23/08 - 09:41 PM
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Posted 04/24/08 - 12:09 AM:	#24
despinozist wrote: I'm not sure why you seem to contrast the inferred belief "P or Q" with Smith's "actual beliefs." Because, as I have tried to explain several times above, the meaning of “P or Q” is ambiguous when translated into Smith’s possible beliefs. despinozist wrote: The inferred belief is not something to "derive" anything from; thus, the concern for ambiguity is something that is being imposed on the final belief. It is the ultimate belief Smith holds; it is the belief he fails to satisfy JTB for. Gettier’s argument hinges on using “P or Q” to derive the conclusion (via JTB) that Smith allegedly knows something for which he has no justification. Getter’s argument works only because “P or Q” is ambiguous, it does not accurately and unambiguously portray Smith’s real belief, hence Gettier’s argument is invalid. despinozist wrote: Again, the ambiguity concern is not an issue for case II. Smith believes P v Q, P v F, P v Z on grounds of P alone. With respect, it seems again you are missing the point. “P v Q” is ambiguous (how many times do I have to say this?) in terms of Smith’s real belief. Let me try one more time to explain so that you might understand…. There are at least 3 possible and different beliefs that Smith could hold…. 1) Smith might believe that P is true, but has no belief about the truth or falsity of Q. This translates to “P v Q” 2) Alternatively, Smith might believe that Q is true, but has no belief about the truth or falsity of P. This is a VERY DIFFERENT BELIEF but low and behold, it also translates to “P v Q” 3) Alternatively, Smith might have no belief about the individual truth or falsity of either P or Q, but for some strange reason he believes that one or the other is true. This is again a VERY DIFFERENT BELIEF but low and behold, it also translates to “P v Q” Thus we have shown that three very different possible and mutually exclusive beliefs could be held by Smith, but all three of them are consistent with the premise “P v Q”. Conclusion: “P v Q” is ambiguous in terms of Smith’s beliefs. Now, Gettier's argument hinges on using the premise “P v Q” to derive conclusions about Smith's beliefs and his knowledge (via JTB). But because “P v Q” is an ambiguous premise in this case, it follows that Gettiers's argument is INVALID (in this case true premises do not lead to true conclusion, by virtue of the fact that the argument must implicitly assume unambiguity in the premises). I hope it is clear now?
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Posted 04/24/08 - 12:41 AM:	#25
1) Smith might believe that P is true, but has no belief about the truth or falsity of Q. This translates to “P v Q” It's not that he might believe that P is true; he does believe that P is true. This is the belief which triggered the capability of applying disjunctive inclusion. 2) Alternatively, Smith might believe that Q is true, but has no belief about the truth or falsity of P. This is a VERY DIFFERENT BELIEF but low and behold, it also translates to “P v Q” As said, we cannot play revolving disjuncts. He hung out with Jones and his Ford, got P. The question of him believing Q is irrelevant. He has no evidence for Q. He could never get P v Q if he started off with Q because he just rattled that off. You cannot look at the final belief and just interpret all the possibilities of its meaning while ignoring the history Gettier gave you. Whether or not the belief is ambiguous to us is not relevant. It cannot possibly be ambiguous to Smith because Smith saw the entailment in the first place. He made the list. Further, it actually cannot be ambiguous to us because we were just told what Smith initially believed and that he saw the entailment. We know Smith's story. P and Q are not equally possibly believable in terms of Smith's belief. We were told what he first believed. 3) Alternatively, Smith might have no belief about the individual truth or falsity of either P or Q, but for some strange reason he believes that one or the other is true. This is again a VERY DIFFERENT BELIEF but low and behold, it also translates to “P v Q” To accept this interpretation would mean we'd have to reject that Smith got evidence for P and then saw the entailment. Propositions have truth-functional assignments. The truth-functional assignment is what is being believed here. P = T (as far as Smith knows) Q = T or Q = F (doesn't matter either way because Smith has no evidence; in fact, this disjunct doesn't even need an assignment) * = of the OR P(t) v Q(t) yields TTT P(t) v Q(f) yields TTF This is what Gettier pulls on us in the end: P(f) v Q(t) yields FTT Smith believes in T; whether or not he believes P alone or Q alone is irrelevant to his beliefs. Tracking back to his atomic beliefs is NOT what Gettier cares about. Even IF Gettier were pulling a fast one like you say WHAT would that say about the truth-functional assignment to the OR? Why would Gettier leave a perfectly good TRUE or proposition just lying around? Your theory does not even account for the blatant facts of truth-functional assignment. Even if ambiguous, there's still a big fat OR-proposition sitting there with a big fat TRUE all over it. The catch is that it's possible that in the end: P(f) v Q(f) yields FFF This would mean that Jones actually does not own a Ford AND Brown is not in any of the cities Smith listed. But this is not the case; so after truth-functional assignment, Smith got a Justified (by logic), Truth-Functional Truth (not both false), Belief (belief in that truth functional assignment of ; the truth of the OR proposition itself) Look, I fully understand your argument, but I am saying it is wrong. I am saying that you are ignoring the history of Smith's evidence for P and that you are not acknowledging the nature of Gettier's strict adherence to truth-functional connectivity. Gettier’s argument hinges on using “P or Q” to derive the conclusion (via JTB) that Smith allegedly knows something for which he has no justification. You are really confusing me here. "[...] Smith does not know that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true." Smith is justified in every case; the argument Gettier advanced is that even though he wound up with a true justified belief, given that we know the history of the examples, we KNOW that he did not actually KNOW by JTB. The whole point is to show that even if you have JTB, you do not KNOW. Edited by despinozist on 04/24/08 - 01:13 AM
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