Combining Texts

All the ideas for 'works', 'Letters to De Vries' and 'Structuralism Reconsidered'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

8923	Numbers are identified by their main properties and relations, involving the successor function [MacBride]
	Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function.
	From: Fraser MacBride (Structuralism Reconsidered [2007], §1)
	A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique

8926	For mathematical objects to be positions, positions themselves must exist first [MacBride]
	Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right.
	From: Fraser MacBride (Structuralism Reconsidered [2007], §3)
	A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others.

9. Objects / D. Essence of Objects / 14. Knowledge of Essences

4869	Experience does not teach us any essences of things [Spinoza]
	Full Idea: Experience does not teach us any essences of things.
	From: Baruch de Spinoza (Letters to De Vries [1664], 1664?)
	A reaction: This, along with Leibniz's claim that experience cannot reveal necessities, may constitute a striking criticism of empiricism, but it invites the obvious reply 'so much the worse for essences'. An essence seems to be a theoretical concept, not a priori.

29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy

16713	Philosophers are the forefathers of heretics [Tertullian]
	Full Idea: Philosophers are the forefathers of heretics.
	From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2

29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism

6610	I believe because it is absurd [Tertullian]
	Full Idea: I believe because it is absurd ('Credo quia absurdum est').
	From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
	A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.