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Single Idea 9846
[filed under theme 18. Thought / E. Abstraction / 1. Abstract Thought
]
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.
Gist of Idea
Defining 'direction' by parallelism doesn't tell you whether direction is a line
Source
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §60) by Michael Dummett - Frege philosophy of mathematics Ch.11
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.126
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.
The
22 ideas
with the same theme
[general concepts not about concrete objects]:
9569
|
The origin of geometry started in sensation, then moved to calculation, and then to reason
[Proclus]
|
10503
|
We abstract forms from appearances, and acquire knowledge of immaterial things
[Aquinas]
|
10509
|
Understanding consists entirely of grasping abstracted species
[Aquinas]
|
5827
|
A species of thing is an abstract idea, and a word is a sign that refers to the idea
[Locke]
|
23648
|
First we notice and name attributes ('abstracting'); then we notice that subjects share them ('generalising')
[Reid]
|
6925
|
The new philosophy thinks of the concrete in a concrete (not a abstract) manner
[Feuerbach]
|
9078
|
The study of the nature of Abstract Ideas does not belong to logic, but to a different science
[Mill]
|
9080
|
General conceptions are a necessary preliminary to Induction
[Mill]
|
9846
|
Defining 'direction' by parallelism doesn't tell you whether direction is a line
[Dummett on Frege]
|
9030
|
Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item
[Price,HH]
|
9029
|
If ideas have to be images, then abstract ideas become a paradoxical problem
[Price,HH]
|
11102
|
Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms
[Quine]
|
17664
|
Each subject has an appropriate level of abstraction
[Armstrong]
|
9873
|
Abstract terms are acceptable as long as we know how they function linguistically
[Dummett]
|
10839
|
You can't infer a dog's abstract concepts from its behaviour
[Dummett]
|
9086
|
The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction
[Plantinga]
|
9087
|
Theists may see abstract objects as really divine thoughts
[Plantinga]
|
8901
|
Abstraction is usually explained either by example, or conflation, or abstraction, or negatively
[Lewis]
|
9144
|
Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology
[Fine,K, by Cook/Ebert]
|
8299
|
Abstractions are non-spatial, or dependent, or derived from concepts
[Lowe]
|
9609
|
The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars
[Brown,JR]
|
9611
|
'Abstract' nowadays means outside space and time, not concrete, not physical
[Brown,JR]
|