Monday, February 15, 2010

The Third Way in Syllogistic Form


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I. The Text (ST I.2.3c)


"The third way is taken from possibility and necessity, and runs thus. We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence — which is absurd. Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary. But every necessary thing either has its necessity caused by another, or not. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes. Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God."






II. The Argument in Syllogistic Format:
P1A) If everything is contingent, i.e., possible to be and not to be (c), then at one time there would have been nothing in existence (o).
P2A) Now if at one time there would have been nothing in existence (o), even now there would be nothing in existence (n).    
CA) Therefore, if everything is contingent (c), then even now there would be nothing in existence (n).

P1B) If everything is contingent (c), then even now there would be nothing in existence (n).
P2B) It is false that even now nothing is in existence (~n).                                                                                                                                      
CB) Therefore, not all beings are contingent, but there must exist something the existence of which is necessary (~c). 

P1C) There are necessary things (~c).
P2C) If there are necessary things (~c), then their necessity is either caused by another, or not caused by another (a     ~a)
P3C) If it is caused by another (a), then there must be an uncaused necessary being (g).
P4C) If it is not caused by another (~a), then there must be an uncaused necessary being (g).                                                                        
CC) Therefore, there is an uncaused necessary being, not receiving its necessity from another, but rather causing in others their necessity; this all men speak of as God (g).

III. The Argument in Symbolic Format:
P1A: c  ®    o
P2A: o   ®   n      
CA: \c   ®    n        

P1B: c   ®   n
P2B: ~n                
CB: \~c

P1C: ~c
P2C: ~c  ®   (a     ~a)
P3C: a   ®     g
P4C: ~a   ®    g     
CC: \g

IV. Legend
P1A:, P1B:, etc. = "Premise 1 of argument A," "Premise 1 of argument B," etc.
CA, CB, CC = "Conclusion of argument A," "Conclusion of argument B," etc.
x = It is true that x.
~x  = "it is false that x"
x ® y = "if x (is true), then y (is true)."
xy = "either x (is true), or y (is true), but not both."
\x "Therefore, x (is true)."
c = "Everything is contingent."
o = "Once there was nothing in existence."
n = "Now there is nothing in existence."
a = "The necessity of a necessary being is caused by another."
g = "There is an uncaused necessary being, whom all speak of as God."




V. See also:
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