AIMS, ETC., OF SCIENTIFIC THOUGHT. i 79 



matieal physics, which requires of most men a good deal of careful 

 study to understand it accurately. 



Let us pass on to consider, with all the reverence which it demands, 

 another opinion, held by great numbers of the philosophers who have 

 lived in the brightening ages of Europe : the opinion that, at the basis 

 of the natural order, there is something which we can know to be un- 

 reasonable, to evade the processes of human thought. The opinion is 

 set forth first by Kant, so far as I know, in the form of his famous 

 doctrine of the antinomies or contradictions, a later form \ of which I 

 will endeavor to explain to you. It is said, then, that space must 

 either be infinite or have a boundary. Now, you cannot conceive 

 infinite space ; and you cannot conceive that there should be any end 

 to it. Here, then, are two things, one of which must be true, while 

 each of them is inconceivable; so that our thoughts about space 

 are hedged in, as it were, by a contradiction. Again, it is said that 

 matter must either be infinitely divisible, or must consist of small 

 particles incapable of further division. Now, you cannot conceive a 

 piece of matter, divided into an infinite number of parts, while, on the 

 other hand, you cannot conceive a piece of matter, however small, 

 which absolutely cannot be divided into two pieces ; for, however great 

 the forces are which join the parts of it together, you can imagine 

 stronger forces able to tear it in pieces. Here, again, there are two 

 statements, one of which must be true, while each of them is sepa- 

 rately inconceivable ; so that our thoughts about matter also are 

 hedged in by a contradiction. There are several other cases of the 

 same thing, but I have selected these two as instructive examples. 

 And the conclusion to which philosophers were led by the contempla- 

 tion of them was, that on every side, when we approach the limits of 

 existence, a contradiction must stare us in the face. The doctrine has 

 been developed and extended by the great successors of Kant ; and 

 this unreasonable, or unknowable, which is also called the absolute 

 and the unconditioned, has been set forth in various ways as that 

 which we know to be the true basis of all things. As I said be- 

 fore, I approach this doctrine with all the reverence which should be 

 felt for that which has guided the thoughts of so many of the wisest 

 of mankind. Nevertheless, I shall endeavor to show that, in these 

 cases of supposed contradiction, there is always something which we 

 do not know now, but of which we cannot be sure that we shall 

 be ignorant next year. The doctrine is an attempt to found a 

 positive statement upon this ignorance, which can hardly be re- 

 garded as justifiable. Spinoza said, " A free man thinks of nothing 

 so little as of death;" it seems to me we may parallel this max- 

 im in the case of thought, and say, "A wise man only remem- 

 bers his ignorance in order to destroy it." A boundary is that 



1 That of Mr. Herbert Spencer, " First Principles." I believe Kant himself would 

 have admitted that the antinomies do not exist for the empiricist. 



