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  1. #1
    Senior Member reason's Avatar
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    Default Atheists Who Claim There is a God

    This should be fun.

    Let the domain of x be the set of all things. If God exists, then some x is God. If God does not exist, then no x is God. Simple:

    Theism: ∃x[Gx]

    In words: there exists a thing (∃x), and that thing is God (Gx).

    Atheism: ∀x[~Gx]

    In words: for all things (∀x), no thing is God (~Gx).

    Atheists often place the burden of proof on theists, because, atheists claim, "one cannot prove a negative." In this context, the term "prove" does not mean the same thing as it does in mathematics, but, instead, it means to verify empirically. Since it is impossible to empirically verify that every single thing is not God, then one cannot prove that no thing is God. However, in principle, only a single empirical verification is needed to prove that God exists. There is a logical asymmetry: in principle, atheism cannot be proven and theism can. The burden of proof, therefore, is on the theist.

    In the meantime, however, the atheist claims that every new thing we discover that is not God decreases the probability that God exists. Atheists claim the existence of God is highly improbable, because we have searched and searched and yet no thing discovered so far has been God. The structure of the argument is inductive, e.g.

    ~Ga, ~Gb, ~Gc, ~Gd ⊢ ∀x[~Gx]

    Atheists observe singular instances of things not being God (~Ga, ~Gb, etc.) and conclude that no thing is God (∀x[~Gx]). Like all inductions, the argument is strictly invalid, i.e. the truth of the conclusion is not necessary given true premises. Instead, the singular instances are said to make the conclusion more probable. In this case, the evidence appears to support or partially justify the claim that God does not exist. Each observation of something new that is not God, supports the conclusion even more.

    Let y be the degree to which a set of premises supports a conclusion (where 0 > y < 1). Appending y to the previous argument, we get a partial entailment:

    ~Ga, ~Gb, ~Gc, ~Gd ⊢yx[~Gx]

    The more y increases, the more ∀x[~Gx] is supported. In the limiting case, every thing has been observed not to be God, y equals 1, and the argument is purely deductive. In other words, in the hypothetical scenario in which our evidence exhausts all possibilities, the support for the conclusion becomes comprehensive. That said, this is impossible to achieve in practice, and hence the burden of proof is on the theist. I mention this limiting case to illustrate the relationship between induction and deduction.

    From here out, to keep things from getting too cluttered, I am going to refer to all observations of things that are not God as "the evidence" or just "e," and the claim that no thing is God will be "the hypothesis" or "h." The previous induction can now be restated:

    e ⊢y h

    To relate this idea of evidential suppor to probability, atheists rightly claim that the degree of support (y) which is given by the evidence (e) to the conclusion (h), is equal to the conditional probability of h given e.

    (1) e ⊢y h ⇔ p(h|e) = y

    Given the premises, the conclusion of a deductive argument must be true on pain of contradiction. That is, the deductive relation between the premises and conclusion is a necessary truth. It follows, that for any deduction, a corresponding material implication, with the premises as antecedent and the conclusion as consequent, will be a tautology.

    A ⊢ B ⇔ ⊢ A → B

    We can extend this principle to our partial entailment or induction.

    (2) e ⊢y h ⇔ ⊢y e → h

    And from (1) and (2) we get

    (3) ⊢y e → h ⇔ p(e → h) = y

    And from (1) and (3), we get

    (4) y = p(e → h) = p(h|e)

    That is, the degree of evidential support for the hypothesis is equal to the probability of e → h and the probability of h given e. So far, this agrees with the atheists intuition of how evidential support and probability behave.

    When changing the probability of the hypothesis in light of the evidence, it is necessary to also change the probability of all logical consequences of the hypothesis. The set of all logical consequences of the hypothesis has the same probability as the hypothesis, because they are logically equivalent. Now consider the following a valid deduction from the hypothesis.

    (5) h ⊢ e → h

    That is, it is impossible to update the probability of h in light of e without also updating the probability of e → h in light of e, however, the probability of e → h given e actually declines rather than rising:

    (6) p(e → h|e) < p(e → h)

    This result is necessary supposing the neither p(h) or p(e) are equal to 0 or 1. Since y is equal to the probability of e → h, it follows that after updating the probability of h in light of e, y actually decreases.

    This argument demonstrates something incredibly counter-intuitive. Supposing that the existence of God is initially assigned a probability greater than 0, it follows that as the probability that God does not exist increases, the evidential (or inductive) support that God does not exist actually decreases!

    Thus, by atheists own standards, they have no right to say that the evidence does not support the existence of God. In fact, every time they observe something and it is not God, the evidential support for the conclusion that some thing is God keeps growing even while its probability is decreasing. It's counter-intuitive but true: higher probability reduces evidential (or inductive) support!

    Alright, I'm done. Whew!
    A criticism that can be brought against everything ought not to be brought against anything.

  2. #2
    royal member Rasofy's Avatar
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    I guess scientologists shouldn't be playing with math.
    Quote Originally Posted by reason View Post
    Thus, by atheists own standards, they have no right to say that the evidence does not support the existence of God. In fact, every time they observe something and it is not God, the evidential support for the conclusion that some thing is God keeps growing.
    From nothing to nowhere!
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    A man builds. A parasite asks 'Where is my share?'
    A man creates. A parasite says, 'What will the neighbors think?'
    A man invents. A parasite says, 'Watch out, or you might tread on the toes of God... '


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  3. #3
    Senior Member Jessica's Avatar
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    There is no probability of god's existence in my mind.

    That is to say, it's not assigned greater than zero, it is zero. I could be wrong, but that doesn't equate to doubt so much as being an admittance of fallibility.
    I have a (new) blog here.

    You should do these: JohariNohari

  4. #4
    Une Femme est une femme paperoceans's Avatar
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    TL;DR
    Between that cigarillo and sticking my finger down my throat to see if I could DT, I feel like puking RN.

    Read my Blog.

  5. #5
    Ginkgo
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    Quote Originally Posted by reason View Post
    This should be fun.



    In the meantime, however, the atheist claims that every new thing we discover that is not God decreases the probability that God exists. Atheists claim the existence of God is highly improbable, because we have searched and searched and yet no thing discovered so far has been God. The structure of the argument is inductive, e.g.

    ~Ga, ~Gb, ~Gc, ~Gd ⊢ ∀x[~Gx]


    If the number of things in existence is infinite, isn't that moot?

  6. #6
    null Jonny's Avatar
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    I'm sorry but this makes very little sense to me.


    Firstly, you present a straw argument here:

    In the meantime, however, the atheist claims that every new thing we discover that is not God decreases the probability that God exists.
    This is simply untrue. What atheists claim is that each new thing that we learn which is in direct conflict with the prevailing religious thoughts and texts serves as evidence that such thoughts and texts do not present truth, and that any conclusions drawn from them are questionable. Essentially, the argument is something akin to: You believe in B because you trust C; however, here is some evidence that C is not trustworthy. Et cetera.


    Secondly, as Ginkgo pointed out above, if the universe is indeed infinite, then any finite amount of information about it cannot be represented as a percentage of the whole amount of information available. As such, no matter what we know, it would not affect the conditional probability of God's existence, at least in a very abstract sense of the term God.


    Lastly, I'm having difficultly following your usage of the logical symbols above. In particular, the inference symbol (⊢) is used in a manner with which I am not familiar. Care to clarify?


    Let me end by saying that, as an Atheist, I resign myself to the fact that I can never know for certain if God exists or doesn't exist. However, for me it seems very likely that any talk of God by members of our species is based on pure conjecture and fantasy, and that anyone claiming to have truth is simply being presumptuous.
    [SIGPIC][/SIGPIC]

  7. #7
    resonance entropie's Avatar
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    Quote Originally Posted by reason View Post

    Atheists often place the burden of proof on theists, because, atheists claim, "one cannot prove a negative." In this context, the term "prove" does not mean the same thing as it does in mathematics, but, instead, it means to verify empirically. Since it is impossible to empirically verify that every single thing is not God, then one cannot prove that no thing is God. However, in principle, only a single empirical verification is needed to prove that God exists. There is a logical asymmetry: in principle, atheism cannot be proven and theism can. The burden of proof, therefore, is on the theist.


    Thats not completly correct; valid empirical verification in experimental physics following the concept of empirical research means that an experiment can be repeated several times and that it can be executed backwards. Even if you can prove a given outcome several times, this is no proof for a fact to be true. It needs several years of research, isolating all possible side effects, which could have led to the result, before an answer is taken for granted. And after that this answer is only taken for so long as granted, until proven otherwise.

    In the meantime, however, the atheist claims that every new thing we discover that is not God decreases the probability that God exists. Atheists claim the existence of God is highly improbable, because we have searched and searched and yet no thing discovered so far has been God. The structure of the argument is inductive, e.g.

    ~Ga, ~Gb, ~Gc, ~Gd ⊢ ∀x[~Gx]
    This is a failure of definition. A rationalist can say that the probability of Gods existence decreases by finding evidence against it. An atheist tho believes that there is no God. He has made the conscious choice to deny a Gods existence and he is like the theist a believer and no rationalist.


    Atheists observe singular instances of things not being God (~Ga, ~Gb, etc.) and conclude that no thing is God (∀x[~Gx]). Like all inductions, the argument is strictly invalid, i.e. the truth of the conclusion is not necessary given true premises. Instead, the singular instances are said to make the conclusion more probable. In this case, the evidence appears to support or partially justify the claim that God does not exist. Each observation of something new that is not God, supports the conclusion even more.

    Let y be the degree to which a set of premises supports a conclusion (where 0 > y < 1). Appending y to the previous argument, we get a partial entailment:

    ~Ga, ~Gb, ~Gc, ~Gd ⊢yx[~Gx]
    I think your fixation on a mathematical proof does cloud the reality of Atheism even further. As I said an atheist is no more than a believer. He has made the conscious choice to deny that deities exist, his opinion has to be treated like the opinion of a theist. It is an opinion of belief and not based on scientific evidence.

    Scientifically inductions do not exist. This of course a matter of argument and depends on the interpretation, but from my personal view induction does not exist as well. If I was to trust in induction to exist, I would on the same time need to believe things like religious intervention, in which a deity induces an idea into a humans head. Since I am a an agnostic, who believes that thinking about philosophy and religion is a major waste of time, I cant support the existence of induction.

    Gnosis in general is the meaning that religious people have a sort of enlightened knowledge about things that others dont have. Agnosis is the disbelief that such an enlightened knowledge would exist. The greek letter A- in the beginning is always used to present an opposing opinion but on the same premise. Which means that the agnostic doesnt rule out the possibility that there may be more to things than mankind does know, but he is convinced as well that this applies for all mankind and religious people are no exception to this rule.

    The more y increases, the more ∀x[~Gx] is supported. In the limiting case, every thing has been observed not to be God, y equals 1, and the argument is purely deductive. In other words, in the hypothetical scenario in which our evidence exhausts all possibilities, the support for the conclusion becomes comprehensive. That said, this is impossible to achieve in practice, and hence the burden of proof is on the theist. I mention this limiting case to illustrate the relationship between induction and deduction.

    From here out, to keep things from getting too cluttered, I am going to refer to all observations of things that are not God as "the evidence" or just "e," and the claim that no thing is God will be "the hypothesis" or "h." The previous induction can now be restated:

    e ⊢y h

    To relate this idea of evidential suppor to probability, atheists rightly claim that the degree of support (y) which is given by the evidence (e) to the conclusion (h), is equal to the conditional probability of h given e.

    (1) e ⊢y h ⇔ p(h|e) = y
    As I stated, I dont believe in induction and things already have become a bit cluttered, I am not completly able to follow anymore.

    This argument demonstrates something incredibly counter-intuitive. Supposing that the existence of God is initially assigned a probability greater than 0, it follows that as the probability that God does not exist increases, the evidential (or inductive) support that God does not exist actually decreases!
    If you believe in induction, the word counter-intuitive basically shouldnt exist no more, cause then everything could be intuitively deduced some how. When I read your sentence correctly, it says that if we assume God exists, then facts speaking in favor of that assumption do increase the probability of Gods existence. Thats true but that could have been said easier.

    Thus, by atheists own standards, they have no right to say that the evidence does not support the existence of God. In fact, every time they observe something and it is not God, the evidential support for the conclusion that some thing is God keeps growing even while its probability is decreasing. It's counter-intuitive but true: higher probability reduces evidential (or inductive) support!

    Alright, I'm done. Whew!
    The last sentence makes no logical sense to me. You basically say, when the probability of Gods existence decreases, Atheists have no right to believe in his non-existence ? You lost me.

    One thing is for sure tho, if you take the right from Atheists to not believe in a God, you have to take the right from Theists who do believe as well.

    The rest is only words...
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  8. #8
    null Jonny's Avatar
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    I'm replying a second time to address something apart from the specific topic you presented in this thread. In particular, this regards your method for presenting your thoughts to those around you, and how that presentation affects your ability to respond to criticism. Judging from the formatting, length, and overall appearance of your post, I would imagine that you felt this idea was particularly significant; and, if I may project a bit here, it seems as though you might have experienced a great deal of satisfaction with your accomplishment.

    However, of particular note is the certainty with which you covey these ideas. Rather than offering them up as a work in progress, or perhaps even asking for criticism, you present them as truth, and in this way you prime your future state to emotionally reject such criticisms. This isn't to say that you would be incapable of seeing the fault in your reasoning, only that it would be emotionally more difficult since you displayed such a confidence with them when you first presented them.

    I might recommend that you structure future arguments in a way that, if anything, downplays your confidence in them. This method tends to be more conducive to a learning environment, and allows you to more easily accept the ideas of others without the emotional turmoil.
    [SIGPIC][/SIGPIC]

  9. #9
    Senior Member NegativeZero's Avatar
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    Tip: try posting this without the logical notation.
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  10. #10
    Nips away your dignity Fluffywolf's Avatar
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    I'll teach you something funny about logic and I'll keep it very simple.

    If obtained knowledge/all existing knowledge is <1 then if x*2=10, x could be said to be 5, but what if x is only 2.5 and you've overlooked z completely?

    What z you say? Well, that's something we don't know, do we? Obtained knowledge / All existing knowledge is after all <1.
    ~Self-depricating Megalomaniacal Superwolf

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