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2 I added References, and some detail into the form of Argument.
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consider the following argument, this might steer your mind to some conclusion.

Suppose that It is not impossible for something to come into being without a cause. Then, consequently, if it is not impossible then it is possible for something to come into being without a cause. Now, if it is possible for something to come into being without a cause, then there is a World W1 such that in it there are event that come into being without a cause. Consequently, if there is a world in which events come into being without a cause, then it is not impossible for something to come into being without a cause. Similarly, if it is not impossible for something to come into existence without a cause, then it is possible for something to come into existence without a cause in W1. Therefore, there is a W2 accessible to W1 such that in it thing come into existence without a cause. Following the same reasoning one can deduce our world is a world such that in which things come into being without a cause. However, that is not what we observe. Therefore, by the negation of consequent it is not the case that it is possible for things to come into being without a cause.

The above aregument I gave is modally valid. That is, it is a valid modal argument. Since developement of Modal Logic is a recent phenomenon, Russell's modal conception was not as sophisticated to realise the deductive impossibility of the notion that things can come into being without a cause. That is why, perhaps, he followed Hume and threw the bathwater with the baby. Though, I have immence respect for Russell, especially for his contributions to analytic philosophy, he is not beyond reproach.

  • For more information about modal logic refer to this article of Stanford

  • Refer to Kripkean semantics for more information on non-possible world semantic.

consider the following argument, this might steer your mind to some conclusion.

Suppose that It is not impossible for something to come into being without a cause. Then, consequently, if it is not impossible then it is possible for something to come into being without a cause. Now, if it is possible for something to come into being without a cause, then there is a World W1 such that in it there are event that come into being without a cause. Consequently, if there is a world in which events come into being without a cause, then it is not impossible for something to come into being without a cause. Similarly, if it is not impossible for something to come into existence without a cause, then it is possible for something to come into existence without a cause in W1. Therefore, there is a W2 accessible to W1 such that in it thing come into existence without a cause. Following the same reasoning one can deduce our world is a world such that in which things come into being without a cause. However, that is not what we observe. Therefore, by the negation of consequent it is not the case that it is possible for things to come into being without a cause.

The above aregument I gave is modally valid. That is, it is a valid modal argument. Since developement of Modal Logic is a recent phenomenon, Russell's modal conception was not as sophisticated to realise the deductive impossibility of the notion that things can come into being without a cause. That is why, perhaps, he followed Hume and threw the bathwater with the baby. Though, I have immence respect for Russell, especially for his contributions to analytic philosophy, he is not beyond reproach.

consider the following argument, this might steer your mind to some conclusion.

Suppose that It is not impossible for something to come into being without a cause. Then, consequently, if it is not impossible then it is possible for something to come into being without a cause. Now, if it is possible for something to come into being without a cause, then there is a World W1 such that in it there are event that come into being without a cause. Consequently, if there is a world in which events come into being without a cause, then it is not impossible for something to come into being without a cause. Similarly, if it is not impossible for something to come into existence without a cause, then it is possible for something to come into existence without a cause in W1. Therefore, there is a W2 accessible to W1 such that in it thing come into existence without a cause. Following the same reasoning one can deduce our world is a world such that in which things come into being without a cause. However, that is not what we observe. Therefore, by the negation of consequent it is not the case that it is possible for things to come into being without a cause.

The above aregument I gave is modally valid. That is, it is a valid modal argument. Since developement of Modal Logic is a recent phenomenon, Russell's modal conception was not as sophisticated to realise the deductive impossibility of the notion that things can come into being without a cause. That is why, perhaps, he followed Hume and threw the bathwater with the baby. Though, I have immence respect for Russell, especially for his contributions to analytic philosophy, he is not beyond reproach.

  • For more information about modal logic refer to this article of Stanford

  • Refer to Kripkean semantics for more information on non-possible world semantic.

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source | link

consider the following argument, this might steer your mind to some conclusion.

Suppose that It is not impossible for something to come into being without a cause. Then, consequently, if it is not impossible then it is possible for something to come into being without a cause. Now, if it is possible for something to come into being without a cause, then there is a World W1 such that in it there are event that come into being without a cause. Consequently, if there is a world in which events come into being without a cause, then it is not impossible for something to come into being without a cause. Similarly, if it is not impossible for something to come into existence without a cause, then it is possible for something to come into existence without a cause in W1. Therefore, there is a W2 accessible to W1 such that in it thing come into existence without a cause. Following the same reasoning one can deduce our world is a world such that in which things come into being without a cause. However, that is not what we observe. Therefore, by the negation of consequent it is not the case that it is possible for things to come into being without a cause.

The above aregument I gave is modally valid. That is, it is a valid modal argument. Since developement of Modal Logic is a recent phenomenon, Russell's modal conception was not as sophisticated to realise the deductive impossibility of the notion that things can come into being without a cause. That is why, perhaps, he followed Hume and threw the bathwater with the baby. Though, I have immence respect for Russell, especially for his contributions to analytic philosophy, he is not beyond reproach.