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remote. Its calculations are based on the assumption that in 
the remotest regions two and two make four ; and if any region 
existed in which they did not make four but five, the whole of 
its apparatus of calculation would be subverted. Next, the 
assertion that two and two make four and not five, is a truth 
self-evident to the mind as soon as it is capable of compre- 
hending the terms. It is marvellous that any man should have 
made such a statement. What is two? 1 + 1. What is four ? 
1 + 1 + 1 + 1. What is five? l+l + l + l + l. It is 
therefore evident that the proposition 2 + 2, i.e. (1 + 1) + (1 + 1) 
must make 4, i.e. 1 + 1 + 1 + 1, and not five, i.e. 1 + 1+1 
+ 1 + 1, must be valid for all thought, all space, and all time, 
and that to affirm the contrary is to assert the possibility of 
contradictions being true. It follows, therefore, that all our 
knowledge is not relative. 
9. If all our knowledge is only relative and phenomenal, on 
what does our belief in the existence of an external universe 
rest ? It will be answered, on experience. But what renders 
such experience valid? How do we know that any sensation 
or mental conception has anything to correspond to it outside 
our minds? This cannot be the result of experience alone, for 
all that we are actually cognizant of are certain mental states. 
1 et our belief in the reality of an external world is so strong, 
that it cannot be shaken by any amount of reasoning. More- 
over, it is no mere result of a balance of probabilities, but it is 
a firm and ultimate persuasion, on which it is impossible to 
avoid acting. It the alternative of idealism or materialism were 
presented to our minds as a matter of abstract reasoning, the 
balance of the evidence would turn in favour of idealism. Still 
we cannot help believing in the reality of an external world, 
and we shall continue to do so despite of all philosophy. 
10. To say that this belief is derived from experience is to 
beg the question at issue, because there must be something to 
give validity to the primary experience ; and which has enabled 
us to infer from some primary act of sensation, the externality 
of the cause producing it. The only possible account of our 
belief is, that there must be some principle in the mind (be it 
what it may) independent of sensation, which compels us to 
believe in the externality of the cause producing it. This 
power may be called into activity by an act of sensation; but it 
is impossible that it can be its mere result. Such beliefs the 
mind pronounces to have a universal validity. Of a similar 
character are the great truths which lie at the foundations of 
our reasonings. It is impossible to conceive of them as true in 
one place and not true in another. It is impossible, therefore, 
