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Thread: On Probability

  1. #11
    Senior Member reason's Avatar
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    Here I go again.

    The wikipedia article on truth states that there are 'differing claims on [what] constitutes truth' and 'whether truth is subjective, relative, objective, or absolute'. The article goes on explain that there are 'major theories of truth', such as correspondence theory, coherence theory, consensus theory and pragmatic theory, each with its own proponents, and states that 'theories of truth continue to be debated'. But what is being debated? This "debate" is framed as though theories of truth are competing, but are they? I do not think so.

    If two scientific theories compete then they are expected to contradict one another, but theories of truth do not. The word 'post' can refer to 'a piece of wood or other material set upright into the ground to serve as a marker or support', 'a starting point at a racetrack', or perhaps 'an electronic message sent to a newsgroup or forum'. It would, however, seem very strange to call these alternatives meanings 'theories of post', and yet that seems to be exactly what has been done in regard to truth.

    Suppose that a scientist is interested in finding theories which correspond to the facts, and by convention she labels such theories 'true'. One day a philosopher comes to watch the scientist, and asks the scientist whether she has had any success finding true theories. The scientists is careful not to make any guaruntees, but answers that she has been successful. At this point the philosopher kindly informs the scientist that her theories could not possibly be true, because they have not yet been agreed upon. The scientist would perhaps be confused. Even if we suppose the philosopher later convinced her of the consensus theory of truth, then should the scientist revise the aim of her investigations so to find theories which everyone agrees upon? No, the original aim was the discovery of theories which correspond to the facts, and that aim can remain even if the scientist no longer labels such theories 'true'. Nothing depended upon the meanings of particular words.

    If the "theories of truth" are competing in any capacity then it is not in regard to the essential meaning of the word 'true', but as competing proposals for the adoption of a convention. With this in mind the most sensible "theory of truth" is the correspondence theory, because when most people say 'P is true' they mean something like 'P corresponds to the facts' or 'P accurately describes reality.' The alternatives to the correspondence theory only proliferate confusion and miscommunication.

    Given that a true theory is one which corresponds to the facts, there are some kind of sentences which cannot be true. For example, the setence 'every x is y' cannot be true, because the letters x and y are variables i.e. there can be no correspondence to the facts because there is nothing for the facts to correspond to. The letters must be interpreted before the sentence can correspond to the facts, as in the sentence 'every raven is black'. Another example of a sentence which cannot be true is any sentence featuring a pronoun, such as 'he is a black raven'. The pronoun 'he' is a variable, and without any context in which it can be interpreted the sentence cannot be true.

    In life the decisions we make depend upon what we think is true: we organise our activities around those beliefs in the hope of achieving our desired ends. One thing which we cannot do is act as though a sentence with variables in it is true, because such a sentence cannot correspond to the facts. Here arises a problem for anyone who believes that our decisions depend upon what we think is probably true, because sentences asserting probabilities always include variables, cannot correspond to the facts and, therefore, cannot be true.

    Let the probability of rolling a 'five' with a die be 1/6, and imagine the following sequence of rolls:

    four, two, six, four, three, one, five, one, two, two, ... ad infinitum

    My contention here is the sentence 'the probability of rolling a "five" is 1/6' can be more accurately written 'the probability of roll x being a "five" is 1/6', or in other words, the probability of obtaining a 'five' by random selection from this sequence is 1/6.

    However, the sentence 'the probability of roll x being a "five" is 1/6' contains a variable, and therefore, cannot correspond to the facts. In conseuquence, it is not possible to make decisions based on any sentence asserting probability -- no sentence which can correspond to the facts can be probable, since no sentence asserting a probability can correspond to the facts. The phrase 'probably true' does not make sense. The variable x must be interpreted before the sentence can be intelligibly said to be true or false. However, such an interpretation would result in a sentence like 'the probability of the sixth roll being a "five" is 1/6', which is false. There was only one sixth role, and for a sequence with one member the probability that it is a 'five' is either 1 or 0 i.e. true or false.

    Hopefully that is a little clearer.
    A criticism that can be brought against everything ought not to be brought against anything.

  2. #12
    pathwise dependent FDG's Avatar
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    That's a philosophical objection I had in mind since I first came into contact with probability. It's actually one of the best lame excuses to spend a lot of time playing the lottery and the like: after all, if you actually win, the probability of winning is one.
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  3. #13
    Occasional Member Evan's Avatar
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    Quote Originally Posted by reason View Post
    However, the sentence 'the probability of roll x being a "five" is 1/6' contains a variable, and therefore, cannot correspond to the facts. In conseuquence, it is not possible to make decisions based on any sentence asserting probability -- no sentence which can correspond to the facts can be probable, since no sentence asserting a probability can correspond to the facts. The phrase 'probably true' does not make sense.
    i get your point but who cares about truth if you define it that way? people are using a differently defined 'truth' when they say "probably true". they're not wrong. "x is probably true" really means something like "i have a model in my head of how i believe the world works with some functions relating objects in the model to each other. if i apply all of those functions to the current state of the model, the next state is x. i am assuming that this model will correspond to the world."

    inference is useful. if you want to change some words around in the definition so that it doesn't say anything about truth, that's fine. i have a feeling that's as far as you'd want to go anyway.

    and what exactly are "facts"?

    also, what if someone said "x is probably going to be true" instead of "x is probably true"?

  4. #14
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    Does this thread remind anyone else of Gary Oldman constantly flipping a coin (and landing "heads") in "Rosencrantz and Guildenstern Are Dead"?
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  5. #15
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    Quote Originally Posted by PinkPiranha View Post
    Does this thread remind anyone else of Gary Oldman constantly flipping a coin (and landing "heads") in "Rosencrantz and Guildenstern Are Dead"?
    Sort of. In the sense that I'd rather be looking at anything else and yet for some reason I won't.
    I don't wanna!

  6. #16
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    May I recommend that the original poster do some research into Bayesian vs. Frequentist schools of thought in statistics. It might address some of your thoughts.

  7. #17
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    Quote Originally Posted by Bluesman View Post
    May I recommend that the original poster do some research into Bayesian vs. Frequentist schools of thought in statistics. It might address some of your thoughts.
    You may, though you needn't. I am aware of the Bayesian vs. Frequentist thing, though do not quite understand of why there is a 'vs' in the middle of the two.

    Anyway, even my recent restatement is flawed, in several ways. I am still working on these ideas, and they just keep getting more and more interesting. At this moment in time I am primarily concerned with "frequentism", but plan to come to Bayesianism later.
    A criticism that can be brought against everything ought not to be brought against anything.

  8. #18
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    This: Monty Hall problem - Wikipedia, the free encyclopedia is so completely and utterly confounding to me, that I am humbled by my intellectual incapacities.
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  9. #19
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    If you strip away all the fanciness, Monty Hall boils down to the fact that the host eliminates one of the wrong answers. His guess is not random.

    So, what started out for you as a 1 in 3 guess becomes a 1 in 2 guess, if you decide to switch doors. If you do not switch doors, your guess still remains in its original 1 in 3 flavor, despite the host removing a door.

    Hah, don't know if that makes it any clearer!
    Last edited by Udog; 09-05-2008 at 10:36 PM. Reason: Changed the wording

  10. #20

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    Quote Originally Posted by reason View Post
    My contention here is the sentence 'the probability of rolling a "five" is 1/6' can be more accurately written 'the probability of roll x being a "five" is 1/6', or in other words, the probability of obtaining a 'five' by random selection from this sequence is 1/6.

    However, the sentence 'the probability of roll x being a "five" is 1/6' contains a variable, and therefore, cannot correspond to the facts. In conseuquence, it is not possible to make decisions based on any sentence asserting probability -- no sentence which can correspond to the facts can be probable, since no sentence asserting a probability can correspond to the facts. The phrase 'probably true' does not make sense. The variable x must be interpreted before the sentence can be intelligibly said to be true or false. However, such an interpretation would result in a sentence like 'the probability of the sixth roll being a "five" is 1/6', which is false. There was only one sixth role, and for a sequence with one member the probability that it is a 'five' is either 1 or 0 i.e. true or false.

    Hopefully that is a little clearer.
    Quote Originally Posted by reason View Post
    Anyway, even my recent restatement is flawed, in several ways. I am still working on these ideas, and they just keep getting more and more interesting. At this moment in time I am primarily concerned with "frequentism", but plan to come to Bayesianism later.
    Perhaps, I can rephraze what I believe you are trying to say, and we can see if we are in agreement.

    In a frequentist intepretation of probability, the "probability" of a particular outcome of an event is defined to be its long-run reltive frequency. That is the percentage of an infinite number of runs of identical but independent events that have the outcome in question.

    However, at any given time, only a finite number of events will have transpired (and in reality these events are not identical and indepedent). That means, the the long-run relative frequency remains nothing more than a guess.

    Probability, however is a profoundly useful concept. One that is absolutely required in the science and engineering discuplines.

    Quote Originally Posted by Bluesman View Post
    May I recommend that the original poster do some research into Bayesian vs. Frequentist schools of thought in statistics. It might address some of your thoughts.
    Quote Originally Posted by CaptainChick View Post
    This: Monty Hall problem - Wikipedia, the free encyclopedia is so completely and utterly confounding to me, that I am humbled by my intellectual incapacities.
    We've covered similar issues earlier (shameless self-promotion):
    Simple Puzzles to Stump People
    http://www.typologycentral.com/forum...bayesians.html

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