Richard Dawkins, among other atheists attempts to use an informal argument based on the principle of mathematical induction to show that science will someday manage to answer all questions leaving no room for God in the universe. The principle of mathematical induction is a rigorous way of showing that a hypothesis Ht holds true at all possible times t. Such an argument takes the following steps:

It is easily seen that such an argument contains, hidden deep within, a series of logic errors which, when brought to light, show Dawkins' so called "proof" by mathematical induction to be demonstrably and transparently fallacious. Firstly, it is obvious from the sequential nature of the principle of mathematical induction that it assumes scientific determinism to hold true. That is, it assumes that the universe has always behaved in a consistent fashion will and always continue to do so. Furthermore, scientific determinism assumes that the state of the universe at a given time can always be predicted given enough information at a previous point in time. The reader will note that such an assumption has, embedded within it, a further assumption that God does not exist since it does not allow in any way for interference with the interaction of the universe beyond the scope of the laws of nature. Hence, it can now be seen that, hidden layers deep, within Dawkins' argument against the existence of God there is an assumption that God does not exist, which leads to a circular argument and and easy disproof with Godels theorem.

Put more simply, it is simply preposterous to prove the non-existence of God by first assuming that God does not exist. Indeed, if such an argument were true one could prove in an entirely similar way that, since God's existence has not yet been disproven, the hypothesis set arguing that there are currently more counter-arguments to God refuting hypotheses than at any time before, under mathematical induction, shows that eventually all God refuting hypotheses can be assumed false. Hence, Dawkins must surely be forced to concede that, under his assumptions, there exists no hypothesis which can possibly refute the existence of God. Of course this argument is equally flawed to Dawkins' original argument, and hence not applicable to the questions at hand, however it does serve to demonstrate the nature of the circular arguments which arise from Dawkins' arguments.

- Show that the hypothesis holds at time t = 1. ie. H1 is true.
- Assume the hypothesis holds Ht holds true at time t. This obviously holds for some t since it was previously shown for t = 1.
- Show, using the previous assumption, that the hypothesis Ht+1 holds true at time t+1.

It is easily seen that such an argument contains, hidden deep within, a series of logic errors which, when brought to light, show Dawkins' so called "proof" by mathematical induction to be demonstrably and transparently fallacious. Firstly, it is obvious from the sequential nature of the principle of mathematical induction that it assumes scientific determinism to hold true. That is, it assumes that the universe has always behaved in a consistent fashion will and always continue to do so. Furthermore, scientific determinism assumes that the state of the universe at a given time can always be predicted given enough information at a previous point in time. The reader will note that such an assumption has, embedded within it, a further assumption that God does not exist since it does not allow in any way for interference with the interaction of the universe beyond the scope of the laws of nature. Hence, it can now be seen that, hidden layers deep, within Dawkins' argument against the existence of God there is an assumption that God does not exist, which leads to a circular argument and and easy disproof with Godels theorem.

Put more simply, it is simply preposterous to prove the non-existence of God by first assuming that God does not exist. Indeed, if such an argument were true one could prove in an entirely similar way that, since God's existence has not yet been disproven, the hypothesis set arguing that there are currently more counter-arguments to God refuting hypotheses than at any time before, under mathematical induction, shows that eventually all God refuting hypotheses can be assumed false. Hence, Dawkins must surely be forced to concede that, under his assumptions, there exists no hypothesis which can possibly refute the existence of God. Of course this argument is equally flawed to Dawkins' original argument, and hence not applicable to the questions at hand, however it does serve to demonstrate the nature of the circular arguments which arise from Dawkins' arguments.

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