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Single Idea 15910
[filed under theme 6. Mathematics / A. Nature of Mathematics / 1. Mathematics
]
Full Idea
Cantor believed he had discovered that between the finite and the 'Absolute', which is 'incomprehensible to the human understanding', there is a third category, which he called 'the transfinite'.
Gist of Idea
Cantor named the third realm between the finite and the Absolute the 'transfinite'
Source
report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.4
Book Ref
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.51
The
30 ideas
with the same theme
[discovered or invented, within or outside nature]:
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560
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Mathematical precision is only possible in immaterial things
[Aristotle]
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9076
|
Mathematics studies the domain of perceptible entities, but its subject-matter is not perceptible
[Aristotle]
|
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12377
|
Mathematics is concerned with forms, not with superficial properties
[Aristotle]
|
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2252
|
Surely maths is true even if I am dreaming?
[Descartes]
|
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2430
|
I can learn the concepts of duration and number just from observing my own thoughts
[Descartes]
|
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17185
|
Mathematics deals with the essences and properties of forms
[Spinoza]
|
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16918
|
Mathematics cannot proceed just by the analysis of concepts
[Kant]
|
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12427
|
All of mathematics is properties of the whole numbers
[Kronecker]
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15910
|
Cantor named the third realm between the finite and the Absolute the 'transfinite'
[Cantor, by Lavine]
|
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16869
|
To create order in mathematics we need a full system, guided by patterns of inference
[Frege]
|
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12456
|
I aim to establish certainty for mathematical methods
[Hilbert]
|
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12461
|
We believe all mathematical problems are solvable
[Hilbert]
|
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8717
|
Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted)
[Hilbert, by Friend]
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10059
|
In mathematic we are ignorant of both subject-matter and truth
[Russell]
|
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18119
|
Mathematics is a mental activity which does not use language
[Brouwer, by Bostock]
|
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10132
|
There can be no single consistent theory from which all mathematical truths can be derived
[Gödel, by George/Velleman]
|
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18281
|
In mathematics everything is algorithm and nothing is meaning
[Wittgenstein]
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9935
|
Mathematical truth is always compromising between ordinary language and sensible epistemology
[Benacerraf]
|
|
9812
|
In mathematics, if a problem can be formulated, it will eventually be solved
[Badiou]
|
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6298
|
Kitcher says maths is an idealisation of the world, and our operations in dealing with it
[Kitcher, by Resnik]
|
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12392
|
Mathematical a priorism is conceptualist, constructivist or realist
[Kitcher]
|
|
18078
|
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding
[Kitcher]
|
|
12426
|
The 'beauty' or 'interest' of mathematics is just explanatory power
[Kitcher]
|
|
9226
|
If mathematical theories conflict, it may just be that they have different subject matter
[Field,H]
|
|
6304
|
Mathematical realism says that maths exists, is largely true, and is independent of proofs
[Resnik]
|
|
10201
|
Virtually all of mathematics can be modeled in set theory
[Shapiro]
|
|
9604
|
Mathematics is the only place where we are sure we are right
[Brown,JR]
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4240
|
It might be argued that mathematics does not, or should not, aim at truth
[Lowe]
|
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10880
|
Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable)
[Clegg]
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15907
|
Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity
[Lavine]
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