Ideas from 'Letters to Bentley' by Isaac Newton [1692], by Theme Structure

[found in 'Philosophical Writings' by Newton,Isaac [CUP 2004,0-521-53848-3]].

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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
We can talk of 'innumerable number', about the infinite points on a line
                        Full Idea: If any man shall take the words number and sum in a larger sense, to understand things which are numberless and sumless (such as the infinite points on a line), I could allow him the contradictious phrase 'innumerable number' without absurdity.
                        From: Isaac Newton (Letters to Bentley [1692], 1693.02.25)
                        A reaction: [compressed] I take the key point here to be the phrase of taking number 'in a larger sense'. Like the word 'atom' in physics, the word 'number' retains its traditional reference, but has considerably shifted its scope. Amateurs must live with this.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Not all infinites are equal
                        Full Idea: It is an error that all infinites are equal.
                        From: Isaac Newton (Letters to Bentley [1692], 1693.01.17)
                        A reaction: There follows a discussion of the mathematicians' view of infinity. Cantor was not the first to notice that there is more than one sort of of infinity.
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The principles of my treatise are designed to fit with a belief in God
                        Full Idea: When I wrote my treatise about our system, I had an eye upon such principles as might work with considering men, for the belief of a deity.
                        From: Isaac Newton (Letters to Bentley [1692], 1692.12.10)
                        A reaction: Harré quotes this, and it shows that the rather passive view of nature Newton developed was to be supplemented by the active power of God. Without God, we need a more active view of nature.
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
I do not pretend to know the cause of gravity
                        Full Idea: You sometimes speak of gravity as essential and inherent in matter. Pray do no ascribe that notion to me; for the cause of gravity is what I do not pretend to know.
                        From: Isaac Newton (Letters to Bentley [1692], 1693.01.17)
                        A reaction: I take science to be a two-stage operation - first we discern the regularities, and then we explain them. Evolution was spotted, then explained by Darwin. Cancer from cigarettes was spotted, but hasn't been explained. Regularity is the beginning.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
That gravity should be innate and essential to matter is absurd
                        Full Idea: That gravity should be innate, inherent and essential to matter ...is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.
                        From: Isaac Newton (Letters to Bentley [1692], 1693.02.25)
                        A reaction: He is replying to some sermons, and he pays vague lip service to a possible divine force. Nevertheless, this is thoroughgoing anti-essentialism, and he talks of external 'laws' in the next sentence. Newton still sought the cause of gravity.
The motions of the planets could only derive from an intelligent agent
                        Full Idea: The motions which the planets now have could not spring from any natural cause alone, but were impressed by an intelligent agent.
                        From: Isaac Newton (Letters to Bentley [1692], 1692.12.10)
                        A reaction: He is writing to a cleric, but seems to be quite sincere about this. Elsewhere he just says he doesn't know what causes gravity.