Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Structuralism Reconsidered' and 'Philosophical Letters'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

5 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

9390	Logic guides thinking, but it isn't a substitute for it [Rumfitt]
	Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking.
	From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13)
	A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy.

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 / B. Unity of Objects / 3. Unity Problems / e. Vague objects

9389	Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
	Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept.
	From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5)
	A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy.

17. Mind and Body / E. Mind as Physical / 1. Physical Mind

23221	The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish]
	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.
	From: Margaret Cavendish (Philosophical Letters [1664], p.185), quoted by Matthew Cobb - The Idea of the Brain 2
	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.