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Thread: My solution to the Gettier counterexamples

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    The Dude's Avatar Praeses
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    Default My solution to the Gettier counterexamples

    So I guess not everyone is familiar with the Gettier counterexamples or why they are important. Let me first explain it then, so that you understand what this thread is about:

    Edmund Gettier posited a few objections against the traditional definition of knowledge. For centuries, knowledge had been defined as the following structure:

    1. Person P believes S.
    2. Belief S corresponds to fact S.
    3. Person P knows S.

    This is what's known as the tripartite analysis of knowledge. Essentially it comes down to the following: if Bob believes that the apple is round, and the apple is in fact round, then Bob knows that the apple is round.

    Gettier managed to come up with a few examples, however, that fulfill all of the above three requirements but still make us disinclined to speak of knowledge. Consider the following:

    1) Bob looks at the clock and deducts that it's 12 o clock in the afternoon. Unbeknownst to Bob, the clock is broken. But, coincidentally, it is 12 o clock. Does Bob know that it is? We would not say so.

    2) Jack believes that Pete will get the job, and Jack knows that Pete has 10 dollars in his pocket. So, Jack is justified in saying: I believe that the person who gets the job has 10 dollars in his pocket. However, pete doesn't get the job. Jack gets the job. And Jack turns out to have 10 dollars in his pocket that he wasn't aware of. Was Jack's original statement justified? Not so much.

    3) Joe drives through Iowa and sees a series of red barns dotted around the countryside. He comes home and says "I saw some red barns on the way home." In fact, most of the barns turned out to be a facade, except say, two of them. Does Joe know that he saw barns? We would not be inclined to say so.

    Now there have been a serious amount of attempts to resolve the Gettier counterexamples. Fred Dretske showed up with contextualism, Robert Nozick with truth-tracking, etc. It seems to me though, that the solution is actually not that difficult: since all knowledge is expressed in language, and all language is intentioned towards a certain object, all knowledge is by definition intentioned towards a certain object. And so the solution is: if a claim was based on the wrong object, it is not knowledge.

    Consider this example from the first Transformers movie, slightly paraphrased to make it fit:

    Dad Witwicky looks out the window of his son's bedroom and sees the entire backyard trashed and power lines broken. The electrical transformer is sparking, and so dad says: "Honey, we have a transformer problem." Of course, he does have a transformer problem: he cannot see the four actual transformers, ie Optimus Prime, Bumblebee etc, hidden around the house right below his field of vision. The reason the entire backyard got trashed was precisely due to Transformers and so his statement ironically does an accurate job at describing the situation. But it's not knowledge: clearly he's talking about the electrical device known as a transformer and not about the gargantuan alien species hiding around his house.

    So what if we adapt the original tripartite definition to the following structure:

    1) Person P claims S.
    2) Claim S is intentioned towards Object R.
    3) Object R corresponds with Claim S.
    4) Person P knows S.

    Now to some this may be too vague, and I get why. Because let's use the example of Joe in Iowa who sees barns. Whether or not the barns exist doesn't change his personal experience that he saw what he perceived to be barns. You could say according to my definition he doesn't know that there are barns because the barns he refers to don't consist entirely of barns but also of fake facades. But what difference would that make in Joe's experience? And I will concede to that. But I will also say this: as long as Joe simply talks about having seen barns, we aren't talking about whether or not he knows there are. He is simply confirming a sensory experience when he talks about what he saw. So perhaps we will also need to consider this: only when Joe says that he knows that there are barns along the road he travelled down are we able to test the validity of his claims.

    If he says that he knows he saw barns he means either
    1) He knows that he had a sensory experience
    2) He knows that the objects are barns

    The former we can't dispute. There is no way for us to put it to the test and therefore we have to take him at his word. The latter however can be confirmed. That he saw what he perceived to be barns is indisputable, whether or not they are barns is not. So then the following structure reveals itself:

    1) Person P claims knowledge S in explicit (or implicit uncontroversial) language.
    2) Knowledge claim S is intended towards a certain object R.
    3) Object R corresponds with knowledge claim S.
    4) Person P knows knowledge claim S.

    I think that particularly the explicit formulation of a knowledge claim is important. Knowledge is otherwise too vague. If someone simply reports a sensory experience, we can't claim they know anything about what they say. If Bob simply reports that the clock in the first example points at 12 o clock, then we can't claim he knows anything (other than that he knows he had a sensory experience of this clock). Only when he explicitly states, or makes it implicity clear, that he knows that it is 12 o clock, then we can see if the object he based his claim on is capable of reproducing that claim. Obviously at 12:01 it won't be able to.

    What I'm looking for is some feedback, preferably counterexamples, as to why I could be wrong. It seems odd to me that so many established academics have not yet devised a solution, yet this one seems so obvious. Is that because a counterexample is readily available? I can't seem to immediately think of one.

    Any response would be appreciated.
    Last edited by The Dude; July 03, 2011 at 10:46 AM. Reason: Expanded the original concept with further thought

  2. #2

    Default Re: My solution to the Gettier counterexamples

    What I see are examples of limited knowledge, in each case facts are known but other vital attributes which belong to the entire body of fact are not present. E.g. jack didn’t know he had $10 in his pocket, however it turns out he did. A case of delayed knowledge which caused misrepresentation of the facts.

    1) Bob looks at the clock and deducts that it's 12 o clock in the afternoon. Unbeknownst to Bob, the clock is broken. But, coincidentally, it is 12 o clock. Does Bob know that it is? We would not say so.
    Bob does know that it is 12 o clock in the afternoon at that point, but as soon as some time elapses the clock will no longer deliver knowledge and bob will know it is wrong even without looking at another timepiece ~ because time will continue to elapse and the clock will not have changed.

    With the red barn facades, one would estimate there to be full barns as that is the norm, it is merely assumed knowledge accordingly.

    In each case I can see no reason why a given fact or set of facts do not exist, and hence the belief is correct. However to make assumptions concerning what is hidden remains a belief until otherwise known. Its all in the method of knowledge ascertainment, if there are no assumptions made there only remains fact, ergo beliefs are factless when based in assumption and true when not.

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    CarbEast's Avatar Senator
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    Default Re: My solution to the Gettier counterexamples

    It appears to me that the whole idea of Gettier counterexamples is just a play on contrasts between two aspects of knowledge - a model on which a conception of a certain part of reality is made and a conclusion that is being derived from that model. The idea here is that even a fundamentally wrong model can produce exactly the same result as a valid one, although not necessarily in every possible case.

    Your approach to solution for this problem seems to be based on making the statement about known fact as clear, precise and detailed as possible and as such to expose a certain part of the model, making it in a way a part of conclusion itself. And it works in the particular cases mentioned in your examples. The problem with that approach is that at certain level of abstraction you can avoid any number of additional constraints on part of clearness and detailedness and still have a paradoxical result.

    Consider this example. A person is solving an arithmetic problem for his test. The problem is 4 ÷ 2 = ?. On his particular test sheet the division symbol isn't clearly typed, so he takes it for minus. He writes 2 as his answer, which is incidentally also the correct one. But did he actually have knowledge of the right answer for this problem?

    In this particular example all the conditions you mentioned (1) Person P claims knowledge S in explicit (or implicit uncontroversial) language, 2) Knowledge claim S is intended towards a certain object R, 3) Object R corresponds with knowledge claim S. 4) Person P knows knowledge claim S), yet knowledge still doesn't seem to be there.

    I suppose the whole hassle with counterexamples could be avoided if the thought model was made a part of the knowledge structure in first place. The thing is, conclusions (facts) alone, especially if they are put in words of human language don't have any separate, autonomous meaning.
    Last edited by CarbEast; July 09, 2011 at 03:03 AM.

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    Default Re: My solution to the Gettier counterexamples

    I don't get it. What's object R? It seems like you're just saying "Joe gets to have knowledge of the barn because 'barn' here in natural language refers to his mental image of the barn". But Joe's mental image of the barn is not in fact the barn, and so natural language here does not refer to mental images of barns, but barns. If john saw something that looked like a barn and pointed to an area where there in fact was a barn but intended to point at the non-barn, then John doesn't know there is a barn there. Even though he has justified true belief that there's a barn there.

    Maybe I'm misunderstanding you though.

  5. #5

    Default Re: My solution to the Gettier counterexamples

    Consider this example. A person is solving an arithmetic problem for his test. The problem is 4 ÷ 2 = ?. On his particular test sheet the division symbol isn't clearly typed, so he takes it for minus. He writes 2 as his answer, which is incidentally also the correct one. But did he actually have knowledge of the right answer for this problem?
    No he got the answer right purely by accident because it’s the same answer for division or subtraction.

    I appreciate there may be ways to utilise this, but I’d say getting the method right will always yield superior results.

    ..interesting puzzle though
    Formerly quetzalcoatl. Proud leader of STW3 and member of the RTR, FATW and QNS teams.

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    Denny Crane!'s Avatar Comes Rei Militaris
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    Default Re: My solution to the Gettier counterexamples

    I like this as a response.

    Pragmatism
    Pragmatism was developed as a philosophical doctrine by chiefly C.S.Peirce and William James (1842–1910). In Peirce's view, truth is nominally defined as a sign's correspondence to its object, and pragmatically defined as the ideal final opinion to which sufficient investigation would lead sooner or later. James' epistemological model of truth was that which works in the way of belief, and a belief was true if in the long run it worked for all of us, and guided us expeditiously through our semihospitable world. Peirce argued that metaphysics could be cleaned up by a pragmatic approach.
    Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object.[4]
    From a pragmatic viewpoint of the kind often ascribed to James, defining on a particular occasion whether a particular belief can rightly be said to be both true and justified is seen as no more than an exercise in pedantry, but being able to discern whether that belief led to fruitful outcomes is a fruitful enterprise. Peirce emphasized fallibilism, considered the assertion of absolute certainty a barrier to inquiry,[5] and in 1901 defined truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.".[6] In other words, any unqualified assertion is likely to be at least a little wrong or, if right, still right for not entirely the right reasons; so one is more veracious by being Socratic and including a recognition of one's own ignorance, though in practical matters one sometimes must act, if one is to act at all, with decision and complete confidence of supposed knowledge even though one may end up proven wrong.[7]

  7. #7

    Default Re: My solution to the Gettier counterexamples

    ^^ sounds about right to me.

    thanks!
    Formerly quetzalcoatl. Proud leader of STW3 and member of the RTR, FATW and QNS teams.

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    Justice and Mercy's Avatar Praefectus
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    Default Re: My solution to the Gettier counterexamples

    The solution is very simple: Words do not mean their definitions.

    Concepts include the existents which they designate.

    But it's not knowledge: clearly he's talking about the electrical device known as a transformer and not about the gargantuan alien species hiding around his house.
    Uh-huh.

    Well... you solved it there. He's referring to something particular, and that's the meaning of his statement.



    Gettier sucks, Rand is awesome. Solved.

    As to your solution, you're turning "knowledge" into a meaningless husk. What we're asking here is when we might consider our conclusions, like "I see a barn," true.
    Last edited by Justice and Mercy; August 25, 2011 at 04:11 PM.
    The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State. - James Madison

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    Denny Crane!'s Avatar Comes Rei Militaris
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    Default Re: My solution to the Gettier counterexamples

    Do you have to reference Rand in every post? Touch of hyperbole there but it almost seems true.

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    Justice and Mercy's Avatar Praefectus
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Denny Crane! View Post
    Do you have to reference Rand in every post?
    When it's relevant.

    Here it most certainly is, since I just finished reading "Introduction to Objectivist Epistemology" which deals mostly with concepts and how they are formed.

    Since I do know the solution to this problem, and since I owe that knowledge exclusively to Ayn Rand (not that I'm saying I never would've figured it out on my own, but that's unlikely because before reading Ayn Rand I considered philosophy a bunch of useless ), I make sure to proudly pay that debt. You'll note that I tend to do the same with other intellectuals, namely the Austrian economists and their predecessors. I think that it's tragic that Ayn Rand's philosophy, especially her epistemology, is so largely ignored. Worse yet, simply by posting these things I subject myself and Ayn Rand to a wide range of vile insults.



    EDIT: Oh, and do you disagree with the Objectivist position on this issue? Would you like me to explain in more detail?
    The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State. - James Madison

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    Denny Crane!'s Avatar Comes Rei Militaris
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Justice and Mercy View Post
    When it's relevant.

    Here it most certainly is, since I just finished reading "Introduction to Objectivist Epistemology" which deals mostly with concepts and how they are formed.

    Since I do know the solution to this problem, and since I owe that knowledge exclusively to Ayn Rand (not that I'm saying I never would've figured it out on my own, but that's unlikely because before reading Ayn Rand I considered philosophy a bunch of useless ), I make sure to proudly pay that debt. You'll note that I tend to do the same with other intellectuals, namely the Austrian economists and their predecessors. I think that it's tragic that Ayn Rand's philosophy, especially her epistemology, is so largely ignored. Worse yet, simply by posting these things I subject myself and Ayn Rand to a wide range of vile insults.



    EDIT: Oh, and do you disagree with the Objectivist position on this issue? Would you like me to explain in more detail?
    Oh no I don't think I disagree actually I think the pragmatist position fits quite well with this no?

    Perhaps we should have a Rand thread. I'm alone in most of my friends (ones interested in this kinda stuff that is) that hasn't actually read Rand or at least not much of it. Perhaps I should.

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    Justice and Mercy's Avatar Praefectus
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Denny Crane! View Post
    Oh no I don't think I disagree actually I think the pragmatist position fits quite well with this no?
    Emphatically: No.

    "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief,"

    What's being asked comes BEFORE science. Before we can practice science, we must first figure out what "truth" is and how to best discover it. This, in fact, is almost explicitly a non-answer. When trying to define "truth" how can you resort, in that definition, "a tendency to bring scientific belief"?

    "which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth."

    So: Truth includes the admission (if implicit) that a statement is inaccurate.
    The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State. - James Madison

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    Denny Crane!'s Avatar Comes Rei Militaris
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    Default Re: My solution to the Gettier counterexamples

    Consider this which surely must be in accordance with objectivism, done a little reading and a little paraphrasing here:

    ‘we may define the real as that whose characters are independent of what anybody may think them to be.’

    In other words there are objective truths outside of subjective ideas and thoughts.

    But ultimately we perceive these truths through our own limited perceptions and thus whilst objective truths exist we must understand that we have a concept of truth and it is only through a pragmatic maxim that we can gather if our understanding of that truth is valid.

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    Justice and Mercy's Avatar Praefectus
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Denny Crane! View Post
    Consider this which surely must be in accordance with objectivism, done a little reading and a little paraphrasing here:

    ‘we may define the real as that whose characters are independent of what anybody may think them to be.’

    In other words there are objective truths outside of subjective ideas and thoughts.
    Sure, but it's at direct odds with pragmatist epistemology, which holds that things are "true" which are "useful." Thus, truth is ENTIRELY dependent on the subject, since what it deems as "useful" is becomes "true" based solely on that fact.

    But ultimately we perceive these truths through our own limited perceptions and thus whilst objective truths exist we must understand that we have a concept of truth and it is only through a pragmatic maxim that we can gather if our understanding of that truth is valid.
    What is meant by the bolded part there?
    The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State. - James Madison

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    Claudius Gothicus's Avatar Petit Burgués
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Denny Crane! View Post
    Perhaps we should have a Rand thread. I'm alone in most of my friends (ones interested in this kinda stuff that is) that hasn't actually read Rand or at least not much of it. Perhaps I should.
    Only if you enjoy neuronal self mutilation.

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    Justice and Mercy's Avatar Praefectus
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Claudius Gothicus View Post
    Only if you enjoy neuronal self mutilation.
    What a surprise! I say "Rand" and immediately the discussion stops and the insults begin.

    Nevermind the topic, did you hear what she said about that Hickman fellow?

    Would you like to talk to us about "collective subjectivity" or any other such nonsense, or are you here solely to go off-topic?
    The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State. - James Madison

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    Denny Crane!'s Avatar Comes Rei Militaris
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Justice and Mercy View Post
    Sure, but it's at direct odds with pragmatist epistemology, which holds that things are "true" which are "useful." Thus, truth is ENTIRELY dependent on the subject, since what it deems as "useful" is becomes "true" based solely on that fact.
    You've fallen into the classic trap of what critics make of pragmatism but was a complete strawman of the pragmatist position, something which as a Rand supporter you surely must be tired of!

    What is meant by the bolded part there?
    I guess to say we must distinguish that we have beliefs and there are truths, do we always have a grasp of objective truths? This must surely be a constant search to understand how our beliefs in objective truths and realities are in accordance. This is where scientific methods come in handy.

    Quote Originally Posted by Claudius Gothicus View Post
    Only if you enjoy neuronal self mutilation.
    Well....I've been guilty of laughing at Rand and having a dig but I do have to accept that I haven't made a full enough study to be so down on the idea. Have you?

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    Justice and Mercy's Avatar Praefectus
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    Default Re: My solution to the Gettier counterexamples

    Quote Originally Posted by Denny Crane! View Post
    You've fallen into the classic trap of what critics make of pragmatism but was a complete strawman of the pragmatist position, something which as a Rand supporter you surely must be tired of!
    Well, go on then. What's is the strawman and what is it a confusion of?

    I guess to say we must distinguish that we have beliefs and there are truths, do we always have a grasp of objective truths? This must surely be a constant search to understand how our beliefs in objective truths and realities are in accordance. This is where scientific methods come in handy.
    Okay, but how can you do that without first coming up with a definition of "truth" seperate from scientific observation? First we have to understand what exactly we mean by the term. The pragmatists don't do that. They steal-concepts in order to evade doing so.
    The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State. - James Madison

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    Denny Crane!'s Avatar Comes Rei Militaris
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    Default Re: My solution to the Gettier counterexamples

    Oh damn I forgot the quote sorry!

    Many of James' best-turned phrases—truth's cash value (James 1907, p. 200) and the true is only the expedient in our way of thinking (James 1907, p. 222)— were taken out of context and caricatured in contemporary literature as representing the view where any idea with practical utility is true. William James wrote:

    It is high time to urge the use of a little imagination in philosophy. The unwillingness of some of our critics to read any but the silliest of possible meanings into our statements is as discreditable to their imaginations as anything I know in recent philosophic history. Schiller says the truth is that which 'works.' Thereupon he is treated as one who limits verification to the lowest material utilities. Dewey says truth is what gives 'satisfaction'! He is treated as one who believes in calling everything true which, if it were true, would be pleasant. (James 1907, p. 90)

    In reality, James asserts, the theory is a great deal more subtle. (See Dewey 1910 for a 'FAQ')
    The role of belief in representing reality is widely debated in pragmatism. Is a belief valid when it represents reality? Copying is one (and only one) genuine mode of knowing, (James 1907, p. 91). Are beliefs dispositions which qualify as true or false depending on how helpful they prove in inquiry and in action? Is it only in the struggle of intelligent organisms with the surrounding environment that beliefs acquire meaning? Does a belief only become true when it succeeds in this struggle? In Pragmatism nothing practical or useful is held to be necessarily true, nor is anything which helps to survive merely in the short term. For example, to believe my cheating spouse is faithful may help me feel better now, but it is certainly not useful from a more long-term perspective because it doesn't accord with the facts (and is therefore not true).

    Edit: I believe your second point is based on a misinterpretation of their position as stated in this quote. This quote which was supposed to be after the strawman accusation, sorry about that probably seemed flippant without a riposte.
    Last edited by Denny Crane!; August 25, 2011 at 06:20 PM.

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    Justice and Mercy's Avatar Praefectus
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    Default Re: My solution to the Gettier counterexamples

    So now the pragmatist position is the correspondence theory of truth? What, then, seperates the pragmatic theory of truth from the correspondence theory of truth? What is "new"?

    Further, how does this solve Gettier's problem, which specifically is meant to show a problem with the correspondence theory of truth?
    The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State. - James Madison

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