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Ideas for 'A Résumé of Metaphysics', 'Marx' and 'Grundlagen der Arithmetik (Foundations)'

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10 ideas

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta

8647	Not all objects are spatial; 4 can still be an object, despite lacking spatial co-ordinates [Frege]
	Full Idea: To give spatial co-ordinates for the number four makes no sense; but the only conclusion to be drawn from that is, that 4 is not a spatial object, not that it is not an object at all. Not every object has a place.
	From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §61)
	A reaction: This is the modern philosophical concept of an 'object', though I find such talk very peculiar. It sounds like extreme Platonism, though this is usually denied. This is how logicians seem to see the world.

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

10309	Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale]
	Full Idea: Frege's argument for abstract objects is: 1) singular terms in true expressions must denote objects, 2) numerals function as singular terms, 3) there must exist numbers denoted by those expressions.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Bob Hale - Abstract Objects Ch.1
	A reaction: [compressed] Given that most of the singular term usages can be rephrased adjectively, this strikes me as a weak argument, though Hale pins his whole book on it.

10550	Frege establishes abstract objects independently from concrete ones, by falling under a concept [Frege, by Dummett]
	Full Idea: For Frege it is legitimate, in order to establish the existence of a certain number, to cite a concept under which only abstract objects fall, and in such a way guarantee the existence of the number quite independently of what concrete objects there are.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
	A reaction: This approach of Frege's got into trouble with Russell's Paradox, which gave a concept under which nothing could fall. It strikes me as misguided even without that problem. I say abstracta are rooted in the concrete.

9. Objects / A. Existence of Objects / 3. Objects in Thought

8785	For Frege, objects just are what singular terms refer to [Frege, by Hale/Wright]
	Full Idea: In Frege's 'Grundlagen' objects, as distinct from entities of other types (properties, relations, or various functions), just are what (actual or possible) singular terms refer to.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by B Hale / C Wright - Logicism in the 21st Century 2
	A reaction: This seems to be the key claim that results in twentieth century metaphysics being done through analysis of language. The culmination is, of course, a denial of metaphysics, and then an eventual realisation that Frege was wrong.

10278	Without concepts we would not have any objects [Frege, by Shapiro]
	Full Idea: Frege is known for the idea that we do not have objects without concepts. Without concepts, there is nothing - no thing - to count.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stewart Shapiro - Philosophy of Mathematics 8.4
	A reaction: A very helpful clarification. Thinking about the probable mental life of higher and lower animals, the proposal seems extremely plausible. Dogs have some concepts, slugs have none, so slugs do not exist in a world of objects. I like it.

9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation

17432	Frege's universe comes already divided into objects [Frege, by Koslicki]
	Full Idea: Frege's universe is one that comes already divided into objects.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1
	A reaction: Nice to have this spelled out. I get frustrated with metaphysics built on logic, with domains of objects, without worry about where all these objects came from. They're axiomatic, it seems. She cites Geach as having a universe of 'goo'.

9. Objects / F. Identity among Objects / 1. Concept of Identity

16022	The idea of a criterion of identity was introduced by Frege [Frege, by Noonan]
	Full Idea: The notion of a criterion of identity was introduced into philosophical terminology in Frege's 'Grundlagen', and was strong emphasised in Wittgenstein's 'Philosophical Investigations'.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Harold Noonan - Identity §4
	A reaction: For Frege a thing can only have an intrinsic identity if it can participate in an equality relation. For abstract objects (such as directions or numbers) the relation is an equivalence. The general idea is that identical objects must relate in some way.

11100	Frege's algorithm of identity is the law of putting equals for equals [Frege, by Quine]
	Full Idea: Frege's algorithm of identity is the law of putting equals for equals.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Willard Quine - Identity, Ostension, and Hypostasis 4
	A reaction: Quine, and most modern philosophers, seem to accept universal substitutivity as a sufficient condition for identity. But you then get the problem of coextensionality (renate/cordate), which can only be solved by introducing modality.

9. Objects / F. Identity among Objects / 3. Relative Identity

12153	Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry on Frege]
	Full Idea: Frege's position is that 'being the same F as' splits up into a general relation and an assertion about the referent ('being the same' and 'being an F'). This is what Geach denies, when he says there is no such thing as being 'just the same'.
	From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by John Perry - The Same F I
	A reaction: It looks as if you can take your pick - whether two things are perfectly identical, or whether they are identical in some respect. Get an unambiguous proposition before you begin the discussion. Identify referents, not kinds of identity, says Perry.

9. Objects / F. Identity among Objects / 6. Identity between Objects

9853	Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett]
	Full Idea: Part of Frege's profound new idea of identity is that the criteria for identity of objects of a given kind is not a consequence of the way that kind of object is characterised, but has to be expressly stipulated as part of that characterisation.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.13
	A reaction: This makes identity a relative concept, rather than an instrinsic concept. Does a unique object have an identity? Do properties have intrinsic identity conditions, making them usable to identify two objects. Deep waters. Has Frege muddied them?