Wisdom

143 In order Post Date: Mon, 4 Aug 2008 15:04:39 +0000
According to these principles, geometry is a science which makes its pure ideas sensible by a phenomenal re presentation. This representation is necessary so long as geometry is a human science, and man is subject to phe nomena ; but geometry in itself and in all its purity has no need of such representations. 143 In order that this doctrine may seem less strange, and may be more readily accepted, I will ask, whether pure spirits possess the science .

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St Thomas calls them phantasmata Post Date: Mon, 4 Aug 2008 15:18:24 +0000
of geometry? We must answer in the affirmative ; for, otherwise we should be forced to conclude that God, the author of the universe and greatest of geometricians, does not know geometry. Does God, then, have these representations, by the aid of which we imagine extension ? No ; these representations are a sort of continuation of sensibility which God has not ; they are the exercise of the internal sense, which is not found in God. St Thomas calls them phantasmata, and says they are not found in God, or in pure spirits, nor even in the soul separated from the body.

Autor of the post: Undefined

There is nothing absolute Post Date: Mon, 4 Aug 2008 15:36:11 +0000
Therefore, the science of geometry is possible, and does really exist without sensible representations, and, consequently, we may distinguish two extensions, the one phenomenal, and the other real, with out thereby destroying either the phenomenon or the re ality, so long as we admit the correspondence between them ; so long as we do not break the thread which unites our being with those around us ; so long as the conditions of our being harmonize with those of the external world. (32) 144 THE preceding doctrine will seem much more prob able if we reflect that all purely intellectual perceptions of extension may be reduced to the knowledge of order and relation. There is nothing absolute in the eyes of science, not even of mathematical science.

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We can not even form Post Date: Mon, 4 Aug 2008 15:47:31 +0000
The absolute, in rela tion to extension, is an ignorant fancy which the observa tion of the phenomena is sufficient to dissipate. In the order of appearances there are no absolute mag nitudes ; all are relations. We can not even form an idea of a magnitude, unless with reference to another which serves for a measure.

Autor of the post: Undefined

The number is a fixed Post Date: Mon, 4 Aug 2008 15:58:05 +0000
The absolute is found only in num- her, and never in extension ; a magnitude is absolute, not in itself, but only by being numbered. A surface two feet square, presents two distinct ideas ; the number of its parts, and the kind of parts. The number is a fixed idea, bub the kind is purely relative.

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If I arn asked Post Date: Mon, 4 Aug 2008 16:13:55 +0000
I will try to make this clearer. 145 When I speak of a surface four feet square, the number four is a simple, fixed, and unchangeable idea; but I can explain a square foot only by relations. If I arn asked what is a square foot, I can answer only by com parison with a square rod or a square inch ; but if I am again asked what is a square rod or a square inch, I am again forced to recur to other measures which are greater or smaller ; I can nowhere find a fixed magnitude.

Autor of the post: Undefined

Shall we take for our Post Date: Mon, 4 Aug 2008 16:30:25 +0000
146 If there were some fixed measure it might be some dimension of the body, my hand, or foot, or arm. But who does not see that the dimensions of my body are not a uni versal measure, and that the hands, or feet, or arms, of all men are not equal? And even in the same individual they are subject to a thousand changes more or less per ceptible. Shall we take for our fixed measure the radius of the earth, or of a heavenly body ? But one has no claim to preference before the other.

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But even astronomers regard these Post Date: Mon, 4 Aug 2008 16:47:54 +0000
Every one knows that astronomers take sometimes the radius of the earth, and sometimes the radius of its orbit as the unity of mea sure. If we suppose these radii to be greater or smaller, can we not equally in either case take them as the mea sure ? They are preferred because they do not change. But even astronomers regard these magnitudes as purely relative, and at one time consider them infinitely large, at another infinitely small, according to the point of view from which they look at them.

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What idea should we Post Date: Mon, 4 Aug 2008 17:00:55 +0000
The radius of the earth s orbit is considered infinite in comparison with a small ine quality on the earth s surface, and infinitely small when compared with the distance of the fixed stars. We can form no idea of these measures except by com parison with those in constant use. What idea should we have of the magnitude of the radius of the earth if we did not know how many million measures it is equal to ? What idea should we have in turn of these measures if we had nothing constant to which we could refer them ? 147 There is something absolute in magnitudes, it may be objected ; for a foot is a certain length which we both see and touch, and cannot be greater or smaller ; the sur face of a square yard is in like manner something definite which we see and which we touch ; and the same may be applied to solids.

Autor of the post: Undefined

I appeal tc experience Post Date: Mon, 4 Aug 2008 17:20:36 +0000
There is no necessity of going farther to find that which is so clearly presented to us in sensible intuition. This objection supposes that there is something fixed and constant in intuition ; this is false. I appeal tc experience.

Autor of the post: Undefined

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