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or imagined. On the one hand it is assumed, and has been too 
hastily conceded, that as the conclusions of science are drawn 
by the aid of reason, therefore science is the exponent of 
reason, and its conclusions are necessary truths, to which the 
mind cannot do otherwise than assent without self-contradic- 
tion ; and the supernatural appears to be at variance with 
these conclusions. On the other hand, it is argued that the 
result of scientific thought being to establish the universality 
and continuity of law, there is no room left for will. And if 
this were true, it must entirely exclude God, and therefore, all 
religion, from the universe. 
16. I will briefly examine both these notions, and if it shall 
appear that there is no foundation for either, we may be con- 
tent to leave to science its legitimate position as one of the 
true modes of human thought ; neither the highest nor the 
lowest ; extending, indeed, into regions quite inaccessible by 
him who is enslaved to the ideas which the senses suggest, yet 
occupying a very small part of the whole realm into which 
the mental vision of reasonable man can penetrate. 
17. (I.) First, then, in order to ascertain whether, or to 
what extent, the conclusions of physical science ought to be 
invested with the authority of necessary truths, let us consider 
through what process the mind arrives at such conclusions. 
They are derived, we know, as deductions from certain 
primary assumptions as to material things, which the percep- 
tions of our bodily senses suggest. The process of logical 
reasoning by which the deductions are drawn, in all except the 
simplest and most obvious cases, is the science of mathematics; 
including both the science of abstract quantity and that of 
relations of abstract space, by means of which, combined, those 
conditions of quantity and space are determined, which define 
the various phenomena of nature. In these sciences, the funda- 
mental principles are not merely probable assumptions, or 
laws which require to be verified by the senses, they are pro- 
positions self-evident to reason, logical identities, which 
cannot be denied without a contradiction in terms. A world 
in which two and two made five (as has been supposed possible) 
must be a world in which the term “ two and two ” would 
not mean what we mean by it. And the result of mathema- 
tical investigation, however complicated, and though conducted 
by symbols by which the logical reasoning is so condensed as 
to be often obscured, if not entirely concealed, is yet nothing 
else than the comparison of different forms of identities which 
the reason thus determines to be equivalent. Thus far we are 
in the sphere of pure reason, and deal only with its relations ; 
and, except on the supposition of some error in the operations, 
anything contradictory to these conclusions is an absurdity. 
