The Leibnizian Cosmological Argument

(1)  (Premise) Every contingent fact has an explanation.

(2)   (Premise) There is a contingent fact that includes all other contingent facts.

(3)  Therefore, there is an explanation of this fact. (1 and 2)

(4)   (Premise) An explanation of the totality of contingent facts would have to be in terms of the activity of a necessarily existing being.

(5)   There is an explanation of the totality of contingent facts in terms of the activity of a necessarily existing being. (3 and 4)

(6)   (Premise) Any necessary existing being whose activity explains the totality of contingent facts is God.

(7)   God exists. (5 and 6)

 

The Principle of Sufficient Reason

PSR: Every contingent fact has an explanation.

CP: Every contingent thing (event or object) has a cause.

 

If we add the claim that ultimately every explanation of a contingent thing’s existence must be causal, the PSR implies the CP. 

Arguments for the PSR:

None of these are satisfactory.  So we opt for another one, a causal one in which possibilities are grounded in the powers of things.  But this yields a CP and a PSR.

 

Arguments against the PSR:

 

(11)           No necessary proposition explains a contingent proposition.  (Premise.)

(12)           No contingent proposition explains itself.  (Premise.)

(13)           If a proposition explains a conjunction, it explains every conjunct.  (Premise.)

(14)           A proposition q only explains a proposition p if q is true.  (Premise.)

(15)           There is a Big Conjunctive Contingent Fact (BCCF) which is the conjunction of all true contingent propositions, perhaps with logical redundancies removed, and the BCCF is contingent.  (Premise.)

(16)           Suppose the PSR holds.  (For reductio.)

(17)           Then, the BCCF has an explanation, q.  (By (15) and (16).)

(18)           The proposition q is not necessary.  (By (11) and (15) and as the conjunction of true contingent propositions is contingent.)

(19)           Therefore, q is a contingent true proposition.  (By (14) and (18).)

(20)           Thus, q is a conjunct in the BCCF.  (By (15) and (19).)

(21)           Thus, q explains itself.  (By (13), (15), (17) and (19).)

(22)           But q does not explain itself.  (By (12) and (19).)

(23)           Thus, q does and does not explain itself, which is absurd.  Hence, the PSR is false.