display all the ideas for this combination of texts
18 ideas
| 8620 | Thought is the same everywhere, and the laws of thought do not vary [Frege] |
| Full Idea: Thought is in essentials the same everywhere: it is not true that there are different kinds of laws of thought to suit the different kinds of objects thought about. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro) | |
| A reaction: Different kinds of thinker might also be candidates for different laws of thought. I'm unsure of Frege's grounds for this claim; most continental philosophers would probably reject it. |
| 9870 | Early Frege takes the extensions of concepts for granted [Frege, by Dummett] |
| Full Idea: In the 'Grundlagen' Frege takes the notion of the extension of a concept for granted as unproblematic. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.16 | |
| A reaction: This comfortable notion was undermined by Russell's discovery of a concept which couldn't have an extension. Maybe we could defeat the Russell problem (and return to Frege's common sense) by denying that sets are objects. |
| 13878 | Concepts are, precisely, the references of predicates [Frege, by Wright,C] |
| Full Idea: For Frege concepts are, precisely, the Bedeutungen of predicates. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 1.iv | |
| A reaction: On p.17 Wright challenges Frege's right to make that assumption. |
| 7736 | A concept is a non-psychological one-place function asserting something of an object [Frege, by Weiner] |
| Full Idea: A concept is a one-place function - something that can be asserted of an object - as found in 'Earth is a planet' and 'Venus is a planet'. This notion of concept does not belong to psychology at all. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4 | |
| A reaction: This doesn't seem to leave room for the concept of the object or substance of which the something is asserted. In 'x is a planet' we need a concept of what x is. But then Frege will reduce the reference to a set of descriptions (i.e. functions). |
| 17430 | Fregean concepts have precise boundaries and universal applicability [Frege, by Koslicki] |
| Full Idea: Both precise boundaries and universal applicability are built into the very notion of a Fregean concept from the outset, while isolation and non-arbitrary division are additional criteria imposed on concepts. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1 | |
| A reaction: The latter two criteria are for concepts which create counting units. |
| 8622 | Psychological accounts of concepts are subjective, and ultimately destroy truth [Frege] |
| Full Idea: Defining concepts psychologically, in terms of the nature of the human mind, makes everything subjective, and if we follow it through to the end, does away with truth. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro) | |
| A reaction: This is the reason for Frege's passionate opposition to psychological approaches to thought. The problem, though, is to give an account in which the fixity of truth connects to the fluctuations of mental life. How does it do that?? |
| 8651 | A concept is a possible predicate of a singular judgement [Frege] |
| Full Idea: A concept is for me that which can be predicate of a singular judgement-content. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §66 n) | |
| A reaction: This seems intuitively odd, given that a predicate could (in principle) be of almost infinite complexity, whereas I would be reluctant to call anything a 'concept' if it couldn't be grasped by a single action of a normal conscious mind. |
| 9846 | Defining 'direction' by parallelism doesn't tell you whether direction is a line [Dummett on Frege] |
| Full Idea: The stipulation that the direction of a line a is to be the same as that of a line b just in case a is parallel to b does not determine whether the direction of a line is itself a line or something quite different. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §60) by Michael Dummett - Frege philosophy of mathematics Ch.11 | |
| A reaction: Nice point. Maybe not being able to say exactly what something is is either a symptom of nonsense, and simply a symptom that we are dealing with an abstract concept. If abstractions don't exist, they don't need individuation criteria. |
| 9976 | Frege accepts abstraction to the concept of all sets equipollent to a given one [Tait on Frege] |
| Full Idea: Frege's own conception of abstraction (although he disapproves of the term) is in agreement with the view that abstracting from the particular nature of the elements of M would yield the concept under which fall all sets equipollent to M. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by William W. Tait - Frege versus Cantor and Dedekind III | |
| A reaction: Nice! This shows how difficult it is to slough off the concept of abstractionism and live with purely logical concepts of it. If we 'construct' a set, then there is a process of creation to be explained; we can't just think of platonic givens. |
| 10803 | Frege himself abstracts away from tone and color [Yablo on Frege] |
| Full Idea: Frege himself abstracts away from tone and color. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stephen Yablo - Carving Content at the Joints §3 | |
| A reaction: Gotcha! I have been searching for instances where Frege perpetrates psychological abstraction right in the heart of his theory. No one can avoid it, if they are in the business of trying to formulate new concepts. Reference ignores sense, and vice versa. |
| 9988 | If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege] |
| Full Idea: When from a set of two cats, one black and one white, we 'abstract' the number two as a set of pure units, the units are not black and white, respectively, and they are not cats. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §34) by William W. Tait - Frege versus Cantor and Dedekind XI | |
| A reaction: Well said. Frege is contemptuous of this approach, as if we were incapable of thinking of a black cat as anything other than as black or cat, when we can catch cats as 'food', or 'objects', or just plain 'countables'. |
| 9855 | Frege's logical abstaction identifies a common feature as the maximal set of equivalent objects [Frege, by Dummett] |
| Full Idea: Like psychological abstractionism, Frege's method (which we can call 'logical abstraction') aims at isolating what is in common between the members of any equivalent sets of objects, by identifying the feature with the maximal set of such objects. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.14 | |
| A reaction: [compressed] So Frege's approach to abstraction is a branch of the view that properties are sets. This view, in addition to being vulnerable to Russell's paradox, ignores the causal role of properties, making them all categorical (which is daft). |
| 10802 | Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first [Yablo on Frege] |
| Full Idea: Frege's discussion of 'direction' borders on incoherent. He claims that the equivalence of lines a and b and their directions being equal have the same content, which leads to the concept of direction, but we grasp the equivalence before the equality. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stephen Yablo - Carving Content at the Joints § 1 | |
| A reaction: [The Frege is in Grundlagen §64] Well said. The notion that we get the full concept of 'direction' from such paltry resources seems very weak. For a start, parallel lines exhibit two directions, not one. |
| 10525 | Frege put the idea of abstraction on a rigorous footing [Frege, by Fine,K] |
| Full Idea: It was Frege who first showed how the idea of abstraction could be put on a rigorous footing. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kit Fine - Precis of 'Limits of Abstraction' p.305 | |
| A reaction: This refers to the crucial landmark in philosophical thought about abstraction. The question is whether Frege had to narrow the concept of abstraction and abstract entities too severely, in order to achieve his rigour. |
| 10526 | Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K] |
| Full Idea: Fregean abstraction rests on initial items, taken to be related by an equivalence relation (e.g. parallelism, or equinumerosity), and then an operation for forming abstraction (e.g. direction or number), with identity related to their equivalence. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kit Fine - Precis of 'Limits of Abstraction' p.305 | |
| A reaction: [compressed] This is the best summary I have found of the modern theory of abstraction, as opposed to the nature of the abstracta themselves. A minimum of two items is needed to implement the process. |
| 10556 | We create new abstract concepts by carving up the content in a different way [Frege] |
| Full Idea: (In creating the concept of direction..) We carve up the content in a way different from the original way, and this yields us a new concept. ...It is a matter of drawing boundary lines that were not previously given. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64) | |
| A reaction: [second half in §88] 'Recarving' is now the useful shorthand for Frege's way of creating abstract concepts (rather than the old psychological way of ignoring some features of an object). |
| 9882 | You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables [Dummett on Frege] |
| Full Idea: Frege's root confusion (over abstraction by identity, and other things) was to believe that he could simultaneously fix the truth-conditions of such statements and the domain over which the individual variables were to range. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: This strikes me as a wonderfully penetrating criticism, but it also seems to me to threaten Dummett's whole programme of doing ontology through language. If a quantified sentences needs a domain, how do you first decide your domain? |
| 9881 | From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Frege, by Dummett] |
| Full Idea: Having rightly perceived that the fundamental class here was statements of identity between directions, Frege leapt to the conclusion that the basis for introducing new abstract terms consisted of determining the truth-conditions of identity-statements. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: This seems to be the modern view - that abstraction consists of the assertion of an equivalence principle. Dummett criticises Frege here (see Idea 9882). There always seems to be a chicken/egg problem. Why would the identity be asserted? |