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18. Thought / E. Abstraction / 2. Abstracta by Selection

[mental acts which create abstract concepts]

22 ideas
You can't abstract natural properties to make Forms - objects and attributes are defined together [Aristotle]
We learn primitives and universals by induction from perceptions [Aristotle]
Mathematics can be abstracted from sensible matter, and from individual intelligible matter [Aquinas]
A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham]
Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis]
We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]
Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor]
Frege accepts abstraction to the concept of all sets equipollent to a given one [Tait on Frege]
We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI]
A 'felt familiarity' with universals is more primitive than abstraction [Price,HH]
Our understanding of 'dog' or 'house' arises from a repeated experience of concomitances [Price,HH]
The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH]
Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta]
Abstractionism claims that instances provide criteria for what is shared [Fodor]
To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K]
We should define abstraction in general, with number abstraction taken as a special case [Fine,K]
Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
Simple types can be apprehended through their tokens, via abstraction [Shapiro]
The old debate classified representations as abstract, not entities [Burgess/Rosen]
The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen]