9879
|
NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett]
|
|
Full Idea:
Quine's New Foundations system of set theory, devised with no model in mind, but on the basis of a hunch that a purely formal restriction on the comprehension axiom would block all contradictions.
|
|
From:
report of Willard Quine (New Foundations for Mathematical Logic [1937]) by Michael Dummett - Frege philosophy of mathematics Ch.18
|
|
A reaction:
The point is that Quine (who had an ontological preference for 'desert landscapes') attempted to do without an ontological commitment to objects (and their subsequent models), with a purely formal system. Quine's NF is not now highly regarded.
|
10502
|
We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
|
|
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.
|
|
From:
Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
|
|
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.
|
16784
|
Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P]
|
|
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.
|
|
From:
Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6
|
|
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.
|
10501
|
A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P]
|
|
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.
|
|
From:
Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5)
|
|
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.
|