194 CLARKE AND SPINOZA. [CHAP. XIII. 



The latter of these is the proposition which Dr. Clarke proves. 

 As, by the above analysis, all the propositions represented by the 

 literal symbols x, y, z, p, q, are determined as absolutely true or 

 false, it is needless to inquire into the existence of any further re- 

 lations connecting those propositions together. 



Another proof is given of Prop, n., which for brevity I pass 

 over. It may be observed, that the " impossibility of infinite 

 succession," the proof of which forms a part of Clarke's argu- 

 ment, has commonly been assumed as a fundamental principle of 

 metaphysics, and extended to other questions than that of causa- 

 tion. Aristotle applies it to establish the necessity of first prin- 

 ciples of demonstration;* the necessity of an end (the good), in 

 human actions, &c.| There is, perhaps, no principle more fre- 

 quently referred to in his writings. By the schoolmen it was 

 similarly applied to prove the impossibility of an infinite subor- 

 dination of genera and species, and hence the necessary existence 

 of universals. Apparently the impossibility of our forming a 

 definite and complete conception of an infinite series, i. e. of 

 comprehending it as a whole, has been confounded with a logical 

 inconsistency, or contradiction in the idea itself. 



8. The analysis of the following argument depends upon the 

 theory of Primary Propositions. 



PROPOSITION III. 

 That unchangeable and independent Being must be self-existent. 



The premises are : 



1 . Every being must either have come into existence out of 

 nothing, or it must have been produced by some external cause, 

 or it must be self-existent. 



2. No being has come into existence out of nothing. 



3. The unchangeable and independent Being has not been 

 produced by an external cause. 



For the symbolical expression of the above, let us assume, 



* Metaphysics, III. 4 ; Anal. Post. I. 19, et seq. 

 f Nic. Ethics, Book I. Cap. n. 



