4 ideas
| 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. |
| 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. |
| 8130 | Qualities of experience are just representational aspects of experience ('Representationalism') [Harman, by Burge] |
| Full Idea: Harman defended what came to be known as 'representationalism' - the view that qualitative aspects of experience are nothing other than representational aspects. | |
| From: report of Gilbert Harman (The Intrinsic Quality of Experience [1990]) by Tyler Burge - Philosophy of Mind: 1950-2000 p.459 | |
| A reaction: Functionalists like Harman have a fairly intractable problem with the qualities of experience, and this may be clutching at straws. What does 'represent' mean? How is the representation achieved? Why that particular quale? |
| 22251 | Liberalism may fail because it neglects the shared nature of what we pursue and protect [Haldane] |
| Full Idea: I am interested in the claim that liberalism fails inasmuch as it neglects, and cannot accommodate, the fact that some or all of the goods we pursue, and which a system of rights is concerned to protect, are goods possessed in common. | |
| From: John Haldane (The Individual, the State, and the Common Good [1996], III) | |
| A reaction: It depends how individualistic we take liberalism to be. Extreme individualism (Nozick) strikes me as crazy. If 'we' erect a statue to some dubious politicians, it might be presented as a common good, but actually be despised by many. |