17612
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Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
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Full Idea:
I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers.
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From:
Richard Dedekind (Continuity and Irrational Numbers [1872], §1)
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A reaction:
Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting?
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10502
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We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
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Full Idea:
I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things.
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From:
Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
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A reaction:
[compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer.
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16784
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Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P]
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Full Idea:
The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties.
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From:
Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6
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A reaction:
If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea.
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10501
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A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P]
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Full Idea:
If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles.
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From:
Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
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A reaction:
[compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power.
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23221
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The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish]
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Full Idea:
Sensitive and rational matter …makes not only the Brain, but all Thoughts, Conceptions, Imaginations, Fancy, Understanding, Memory, Remembrance, and whatsoever motions are in the Head or Brain.
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From:
Margaret Cavendish (Philosophical Letters [1664], p.185), quoted by Matthew Cobb - The Idea of the Brain 2
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A reaction:
Judging by the date of this, and that she is a Cavendish, the influence of Hobbes must be strong, which was brave in 1664. A very strong statement of reductive physicalism, making sure that nothing is left out.
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