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was previously pure negation, is assumed to be something 
carried on without limits, or for ever. We assume its actual 
existence, although we can never realize it. Thus our infinite 
becomes our highest conceivable finite conception plus x ad 
infinitum. The constitution of our minds compels us to assume 
that infinity exists, as in number, duration, and extension. 
Still, however, we are unable to create any distinct image or 
conception in our minds. If we call it by the term conception, 
we can only correctly designate it an indefinite one, which 
the mind is unable to realize. Are mathematicians able to 
make their infinites a subject of reasoning as a positive idea ? 
They can only reason about infinity by representing it by a 
finite symbol. It has been replied that when we thus conceive 
of an object without limits, we are guilty of the absurdity of 
asserting that we conceive of it as having limits. The truth 
is we have no definite conception in our minds at all. What 
other minds can do I cannot say, but I am wholly unable to 
form a positive conception of an unlimited thing. 
Let us illustrate the subject in the concrete. What do I 
mean when I apply the term infinity to number, duration, or 
extension ? I take the highest conceivable number, and deny 
that it represents the possible limits of number. I then 
assume the existence of number beyond it, and that for ever. 
I call this an infinite number, but I have no direct conception 
of that portion of it which lies beyond the limits of the finite. 
All that I can distinctly image to the mind is a direct concep- 
tion and a negation. All I can do is to postulate the existence 
of an infinite number. Still I am as far as ever from being able 
to form a conception of what infinite number is ; because all 
finite number with which I am acquainted has limit. It may 
be said that it is still number. I reply that the denial of limit 
to number takes away an essential portion of the original con- 
ception. Mathematicians have methods for approximating 
the value of infinite numbers; but it is well known that 
such processes can only be carried on by the use of sym- 
bols, which represent infinity under the image of finitenes3. 
It follows, therefore, that although we are capable of postulating 
the existence of an infinite number, in doing which we 
advance a stage beyond the conception of the non-finite, we 
view it as something beyond the limits of our power to 
image it directly to the mind, and that it can only enter as a 
factor in any rational process, when the unknown quantity 
is capable of being represented by a finite symbol. 
This will be apparent from an analysis of our conception of 
space. It is that of simple extension. We can only image 
it to our minds under some form of limitation. Still, while 
