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 Why Knowledge and Truth Are Different Things •dlaw Initiate Usergroup: Members Joined: Apr 27, 2012 Total Topics: 4 Total Posts: 35 #1 - Quote - Permalink Posted May 18, 2012 - 8:41 PM: Subject: Why Knowledge and Truth Are Different Things First, obvously, we have Gettier.http://en.wikipedia.org/wiki/Gettier_problemBeyond that, I think we can even quantify knowledge versus truth. Consider a "Three Doors Problem" with two goats and a new car distributed behind the doors. The Chooser chooses a door. "Monty" is required to open a different door, revealing a goat. A revealed car voids the game. The question is "what are the odds of the Chooser's getting the new car". As everyone knows, if a goat is revealed and the Chooser switches doors, his odds are 2/3 and if he doesn't, his odds are 1/3. Consider an example where the Chooser has chosen Door 2. Monty opens Door 1, revealing a goat. But before the Chooser makes his next move, he asks Monty: "Did you know where the car was?" If Monty says "no" the Chooser's odds are 50/50 of getting the car. He can stick or switch with equal outcomes. If Monty did know where the car was, the Chooser has the odds described above. But suppose Monty had knowledge of where the car was, but it was false. Even in that case, the Chooser has the same odds, so long as he reverses strategies. A belief that is true (Monty opens a door revealing a goat and doesn't spoil the game) but unjustified (Monty didn't really know anything) creates a different set of odds from a belief that is justified but untrue (Monty revealed a goat but had false knowledge), even though they are indistinguishable to the outside observer. Justified belief - knowledge - whether true or untrue, creates the same odds and they are different from the odds created by true belief that is unjustified. •AerosPyros potential philosopher Usergroup: Members Joined: Jan 28, 2010 Location: Aliso Viejo, California Total Topics: 45 Total Posts: 285 #2 - Quote - Permalink Posted May 20, 2012 - 6:30 PM: I believe that you are forgeting the part where Monty might have picked the door with the car. That would change the odds. But all jokes aside, it seems pretty obvious that thoughts in the brain are not always the same as the facts. •dlaw Initiate Usergroup: Members Joined: Apr 27, 2012 Total Topics: 4 Total Posts: 35 #3 - Quote - Permalink Posted May 21, 2012 - 5:25 PM: AerosPyros wrote:I believe that you are forgeting the part where Monty might have picked the door with the car. That would change the odds. But all jokes aside, it seems pretty obvious that thoughts in the brain are not always the same as the facts.No, those are included in the odds. Monty picks the car 1/3 of the time if he has no knowledge and 50% of the time if his knowledge is wrong. If Monty's knowledge is wrong a Chooser who sticks with his original choice wins 2/3 of the time. The point is that justified belief - right or wrong - changes outcomes while unjustified belief - even if it happens to be "true" (let's assume that Monty thinks he's not picking the door with the car, even if he has no basis for knowing whether or not he is, thus when he opens a door with a goat his belief is true but not justified) does not change the odds. The point is that it's a connection to reality that makes knowledge, not the truth of that connection. •jedaisoul exponent of reason Usergroup: Sponsors Joined: Aug 14, 2008 Location: UK Total Topics: 124 Total Posts: 3680 ♂ #4 - Quote - Permalink Posted May 25, 2012 - 10:10 AM: dlaw wrote:I think we can even quantify knowledge versus truth. There is no need. They are (usually) defined differently. Why would you define them to be the same thing? But if you did, they would by definition be indistinguishable! You seem to be suffering the delusuon that words in general, and "truth" and "knowledge" in particular, have an absolute meaning distinct from the meanings we attribut to them.dlaw wrote:Consider a "Three Doors Problem" with two goats and a new car distributed behind the doors. The Chooser chooses a door. "Monty" is required to open a different door, revealing a goat. A revealed car voids the game. The question is "what are the odds of the Chooser's getting the new car". As everyone knows, if a goat is revealed and the Chooser switches doors, his odds are 2/3 and if he doesn't, his odds are 1/3. I disagree. It seems to me that the "Monty Hall" problem (as described) is a statistical fallacy. Let me explain:1. The choser C has a 1/3 chance of initially picking a car. If he does, then Monty (M) is certain to pick a goat (probability 1). 2. If C initially picks a goat, M has a 1/2 chance of picking a goat.Therefore, the overall likelihood of M chosing a goat is 2/3. 3. We know that the overall likelihood of C chosing a car first time is 1/3. I.e. C is 2/3 likely to have chosen a goat. But with a door now excluded, does he have a 2/3 chance that the car is behind the remaining door? Therefore he should change his choice? Nonsense.The flaw in this argument is that it compares the probabilities at different stages of the process. Yes, when he chose it there was a 1/3 chance that he had chosen the car. But when M excludes one of the doors, the probability that C's original choice was right changes. The liklihood that either of the remaining doors hides a car becomes 1/2. Now I'm not a statistician so I could well be wrong, but if so, why??? Edited by jedaisoul on May 25, 2012 - 11:41 AM •mclark Resident Usergroup: Sponsors Joined: Jun 18, 2011 Location: US Total Topics: 11 Total Posts: 351 #5 - Quote - Permalink Posted May 25, 2012 - 10:31 AM: In the classic formulation of the Monty Hall problem, Monty always:1) Picks one of the two doors that the chooser did not pick2) Knows where the car is3) Always picks a door with a goat, no matter whatUnder these terms, switching yields a 2/3rds chance of picking the car, and staying yields a 1/3rd chance of picking the car.If you modify the terms of the game, you should re-prove the probabilities, so we are not concerned that you are combining the answers to the classic scenario with a modified scenario which may have different answers. On May 25, 2012 - 11:20 AM, jedaisoul responded: Thanks for clarifying. I'll give it more thought... On May 25, 2012 - 11:36 AM, jedaisoul responded: Agreed. The MH problem was misquoted in the OP. so the flaw in it is irrelevant to MH. •ModernPlatonist It's a trap! Usergroup: Sponsors Joined: May 25, 2012 Location: Boston, MA, USA Total Topics: 2 Total Posts: 102 #6 - Quote - Permalink Posted May 25, 2012 - 3:27 PM: AerosPyros wrote:But all jokes aside, it seems pretty obvious that thoughts in the brain are not always the same as the facts.I think an important point to make right at the beginning is that thoughts are not in the brain. Thoughts are non-matterial, like the soul, so they reside in the mind or in the soul.Other than that, I think saying that there is such a thing as "false knowledge" is wrong. One can have a belief that they think is knowledge, but this does not make that knowledge so. So belief is not the same thing as truth, but knowledge is true, by definition. If we go by the classical definition of a thought (this can be equated with knowledge, to a point), it is conformity to ultimate reality, so by that definition it is impossible to have untrue knowledge (all knowledge is thought, by the way, but not all thought is knowledge). •dlaw Initiate Usergroup: Members Joined: Apr 27, 2012 Total Topics: 4 Total Posts: 35 #7 - Quote - Permalink Posted Jun 1, 2012 - 11:50 AM: jedaisoul wrote:There is no need. They are (usually) defined differently. Why would you define them to be the same thing? But if you did, they would by definition be indistinguishable! You seem to be suffering the delusuon that words in general, and "truth" and "knowledge" in particular, have an absolute meaning distinct from the meanings we attribut to them.I disagree. It seems to me that the "Monty Hall" problem (as described) is a statistical fallacy. Let me explain:1. The choser C has a 1/3 chance of initially picking a car. If he does, then Monty (M) is certain to pick a goat (probability 1). 2. If C initially picks a goat, M has a 1/2 chance of picking a goat.Therefore, the overall likelihood of M chosing a goat is 2/3. You're forgetting that Monty isn't picking doors by chance, but knows where the goats and car are distributed. If Monty is picking by chance, then he we have to include the instances where he spoils the game by revealing the car. jedaisoul wrote:3. We know that the overall likelihood of C chosing a car first time is 1/3. I.e. C is 2/3 likely to have chosen a goat. But with a door now excluded, does he have a 2/3 chance that the car is behind the remaining door? Therefore he should change his choice? Nonsense.In the instance where Monty was choosing at random and happened to reveal a goat, you'd be right. The Chooser's odds are 50/50, but your odds are somewhat confusing. Here's how it works:2/3 of the time, the Chooser chooses a door with a goat behind it. In those instances, "Random" Monty spoils the game 50% of the time and reveals a goat the other 50% of the time. (Meaning that "Random" Monty spoils the game 1/3 of the time, so we discount those instances as they leave the Chooser with no choice). This means that in 1/3 of the time, the Chooser will pick a goat door, Monty will reveal a goat and the car is behind the door the Chooser did not pick. 1/3 of the time, the Chooser picks the door with a car behind it, Monty inevitably reveals a goat and the car is behind the Chooser's original door. So with a "Random" Monty, a Chooser who sees Monty reveal a goat has a 50/50 shot at getting the car, whatever strategy (switch or stay) he uses. quote=jedaisoul]The flaw in this argument is that it compares the probabilities at different stages of the process. Yes, when he chose it there was a 1/3 chance that he had chosen the car. But when M excludes one of the doors, the probability that C's original choice was right changes. The liklihood that either of the remaining doors hides a car becomes 1/2. Now I'm not a statistician so I could well be wrong, but if so, why???[/quote]I think you're eliding the instances where Monty knows what he's choosing and where he doesn't know and picks at random. •dlaw Initiate Usergroup: Members Joined: Apr 27, 2012 Total Topics: 4 Total Posts: 35 #8 - Quote - Permalink Posted Jun 1, 2012 - 12:07 PM: mclark wrote:In the classic formulation of the Monty Hall problem, Monty always:1) Picks one of the two doors that the chooser did not pick2) Knows where the car is3) Always picks a door with a goat, no matter whatUnder these terms, switching yields a 2/3rds chance of picking the car, and staying yields a 1/3rd chance of picking the car.If you modify the terms of the game, you should re-prove the probabilities, so we are not concerned that you are combining the answers to the classic scenario with a modified scenario which may have different answers.Suppose a Monty with False Knowledge - that is, he thinks the car is somewhere it isn't. Let's say the car is behind Door 1 and Monty thinks it's behind Door 2. If the Chooser picks Door 3, Monty reveal Door 1 and spoil the game 100% of the time - so, 1/3 of the games are spoiled so far. If the Chooser picks Door 1, Monty will reveal Door 3 100% of the time, and so 1/3 of the time, a "stay" strategy will win the car for the Chooser. If the Chooser picks Door 2, Monty will think he has the choice of Doors 1 and 3, so 50% of the time he'll spoil the game by revealing Door 1 (we're up to 1/2 of the games spoiled) and 50% of the time he'll open Door 3, in which case (1/6 of the instances) a "switch" strategy would win. The point is that false knowledge still conveys real information and the interesting part is that you can often use unrelated data to make a judgment about whether knowledge is likely to be true or false, thus allowing false data act as if it's "true" by induction and deduction. •dlaw Initiate Usergroup: Members Joined: Apr 27, 2012 Total Topics: 4 Total Posts: 35 #9 - Quote - Permalink Posted Jun 1, 2012 - 12:39 PM: ModernPlatonist wrote:I think an important point to make right at the beginning is that thoughts are not in the brain. Thoughts are non-matterial, like the soul, so they reside in the mind or in the soul.Other than that, I think saying that there is such a thing as "false knowledge" is wrong. One can have a belief that they think is knowledge, but this does not make that knowledge so. So belief is not the same thing as truth, but knowledge is true, by definition. If we go by the classical definition of a thought (this can be equated with knowledge, to a point), it is conformity to ultimate reality, so by that definition it is impossible to have untrue knowledge (all knowledge is thought, by the way, but not all thought is knowledge).I don't think that thoughts are non-material, but they are ephemeral. Thoughts are interactions rather than states. I think I've demonstrated that false knowledge is real. Opinion, belief, action, and knowledge are not all that different. They are all communication of information - interaction. The argument that "belief" and "knowledge" are distinct things based on "truth"is a very weak one. Would an insightful and informative physical theory be merely "belief" because the physicist got a sign wrong, while a trivial observation would be "knowledge" simply because it was error-free? I think the more solid ground is to think of knowledge as 1) Something real independent - an interaction - independent of other realities. 2) Something different from whim or weak "belief" because of its overall correspondence with reality - whether true or untrue. That is, to the extent that it mimics the structure of other realities, it is knowledge. Note that in the Monty Hall example, the problem is so precise and constrained that Monty's false knowledge is as informative as his true knowledge because falsity creates a precise foil to reality. But in the mechanism of perception, this is not an uncommon situation. •mclark Resident Usergroup: Sponsors Joined: Jun 18, 2011 Location: US Total Topics: 11 Total Posts: 351 #10 - Quote - Permalink Posted Jun 1, 2012 - 1:32 PM: dlaw wrote:Let's say the car is behind Door 1...If the Chooser picks Door 1, Monty will reveal Door 3 100% of the time, and so 1/3 of the time, a "stay" strategy will win the car for the Chooser. If the chooser picks #1, the car appears, the game is won, and the only thing Monty does is shake the contestant's hand.

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