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Single Idea 9569
[filed under theme 18. Thought / E. Abstraction / 1. Abstract Thought
]
Full Idea
It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason.
Gist of Idea
The origin of geometry started in sensation, then moved to calculation, and then to reason
Source
Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55
Book Ref
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.282
A Reaction
The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths.
The
22 ideas
with the same theme
[general concepts not about concrete objects]:
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9569
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The origin of geometry started in sensation, then moved to calculation, and then to reason
[Proclus]
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10503
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We abstract forms from appearances, and acquire knowledge of immaterial things
[Aquinas]
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10509
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Understanding consists entirely of grasping abstracted species
[Aquinas]
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5827
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A species of thing is an abstract idea, and a word is a sign that refers to the idea
[Locke]
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23648
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First we notice and name attributes ('abstracting'); then we notice that subjects share them ('generalising')
[Reid]
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6925
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The new philosophy thinks of the concrete in a concrete (not a abstract) manner
[Feuerbach]
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9078
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The study of the nature of Abstract Ideas does not belong to logic, but to a different science
[Mill]
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9080
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General conceptions are a necessary preliminary to Induction
[Mill]
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9846
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Defining 'direction' by parallelism doesn't tell you whether direction is a line
[Dummett on Frege]
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9030
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Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item
[Price,HH]
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9029
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If ideas have to be images, then abstract ideas become a paradoxical problem
[Price,HH]
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11102
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Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms
[Quine]
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17664
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Each subject has an appropriate level of abstraction
[Armstrong]
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9873
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Abstract terms are acceptable as long as we know how they function linguistically
[Dummett]
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10839
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You can't infer a dog's abstract concepts from its behaviour
[Dummett]
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9086
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The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction
[Plantinga]
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9087
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Theists may see abstract objects as really divine thoughts
[Plantinga]
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8901
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Abstraction is usually explained either by example, or conflation, or abstraction, or negatively
[Lewis]
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9144
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Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology
[Fine,K, by Cook/Ebert]
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8299
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Abstractions are non-spatial, or dependent, or derived from concepts
[Lowe]
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9609
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The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars
[Brown,JR]
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9611
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'Abstract' nowadays means outside space and time, not concrete, not physical
[Brown,JR]
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