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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12191
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Counterfactuals are true if logical or natural laws imply the consequence [Goodman, by McFetridge]
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Full Idea:
Goodman's central idea was: 'If that match had been scratched, it would have lighted' is true if there are suitable truths from which, with the antecedent, the consequent can be inferred by means of a logical, or more typically natural, law.
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From:
report of Nelson Goodman (The Problem of Counterfactual Conditionals [1947]) by Ian McFetridge - Logical Necessity: Some Issues §4
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A reaction:
Goodman then discusses the problem of identifying the natural laws, and identifying the suitable truths. I'm inclined to think counterfactuals are vaguer than that; they are plausible if coherent reasons can be offered for the inference.
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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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