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Single Idea 10684
[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
]
Full Idea
I take the real numbers to be just lengths.
Gist of Idea
I take the real numbers to be just lengths
Source
Keith Hossack (Plurals and Complexes [2000], 9)
Book Ref
-: 'British Soc for the Philosophy of Science' [-], p.432
A Reaction
I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged.
The
29 ideas
from Keith Hossack
23621
|
Numbers are properties, not sets (because numbers are magnitudes)
[Hossack]
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23622
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We can only mentally construct potential infinities, but maths needs actual infinities
[Hossack]
|
23623
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Predicativism says only predicated sets exist
[Hossack]
|
23624
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The iterative conception has to appropriate Replacement, to justify the ordinals
[Hossack]
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23625
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Limitation of Size justifies Replacement, but then has to appropriate Power Set
[Hossack]
|
23626
|
Transfinite ordinals are needed in proof theory, and for recursive functions and computability
[Hossack]
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23627
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'Before' and 'after' are not two relations, but one relation with two orders
[Hossack]
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23628
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The connective 'and' can have an order-sensitive meaning, as 'and then'
[Hossack]
|
10666
|
Plural reference will refer to complex facts without postulating complex things
[Hossack]
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10664
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Complex particulars are either masses, or composites, or sets
[Hossack]
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10665
|
Leibniz's Law argues against atomism - water is wet, unlike water molecules
[Hossack]
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10663
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A thought can refer to many things, but only predicate a universal and affirm a state of affairs
[Hossack]
|
10668
|
We are committed to a 'group' of children, if they are sitting in a circle
[Hossack]
|
10669
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Plural reference is just an abbreviation when properties are distributive, but not otherwise
[Hossack]
|
10671
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Plural definite descriptions pick out the largest class of things that fit the description
[Hossack]
|
10673
|
Plural language can discuss without inconsistency things that are not members of themselves
[Hossack]
|
10675
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A plural comprehension principle says there are some things one of which meets some condition
[Hossack]
|
10674
|
A plural language gives a single comprehensive induction axiom for arithmetic
[Hossack]
|
10676
|
The Axiom of Choice is a non-logical principle of set-theory
[Hossack]
|
10677
|
Extensional mereology needs two definitions and two axioms
[Hossack]
|
10678
|
The relation of composition is indispensable to the part-whole relation for individuals
[Hossack]
|
10682
|
The fusion of five rectangles can decompose into more than five parts that are rectangles
[Hossack]
|
10681
|
In arithmetic singularists need sets as the instantiator of numeric properties
[Hossack]
|
10680
|
The theory of the transfinite needs the ordinal numbers
[Hossack]
|
10684
|
I take the real numbers to be just lengths
[Hossack]
|
10683
|
We could ignore space, and just talk of the shape of matter
[Hossack]
|
10685
|
Set theory is the science of infinity
[Hossack]
|
10686
|
The Axiom of Choice guarantees a one-one correspondence from sets to ordinals
[Hossack]
|
10687
|
Maybe we reduce sets to ordinals, rather than the other way round
[Hossack]
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