Page:Carroll - Euclid and His Modern Rivals.djvu/123

.] And here I notice a singular mental process. 'Two material bodies,' we are told, 'cannot occupy the same space. We are thus led to recognise a third property common to all bodies: every body has position.' (p. 3.) The word thus is what I want to call your special attention to: for I confess I can see no such sequence of thought as it would seem to imply. Suppose bodies could occupy the same space: wouldn't they have 'position' just as much as if they couldn't? Does an orange—to take the favourite logical entity—lose its position because another orange most uncivilly insists on permeating it and occupying the same portion of Space? But if not, what is the meaning of 'thus'? As Artemus Ward would say, 'why this thusness?'

Nie. I can't say.

Min. A little further on I find a 'therefore' which is equally shadowy. The writer's logical ideas—in spite of his actually introducing a 'Digression on Logic'—are, I fear, a little vague. He says 'If we bring different points together into the same position, they will never give us anything but a point; we never obtain any extension. We cannot, therefore, say that Space is made up of points' (p. 6). I venture to say that there is no such sequence as 'therefore' seems to imply: he has made the whole argument null and void by using the words 'into the same position.'

Nie. I do not understand you.

Min. I will put it in another way. The real reason why you cannot construct Space of points is that they have no size: if they had size you could do it. But, under