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Single Idea 8311
[filed under theme 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
]
Full Idea
If 2 is a particular, 'adding' it to itself can, it would seem, only leave us with 2, not another number. (If 'Socrates + Socrates' denotes anything, it most plausibly just denotes Socrates).
Gist of Idea
If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2
Source
E.J. Lowe (The Possibility of Metaphysics [1998], 10.7)
Book Ref
Lowe,E.J.: 'The Possibility of Metaphysics' [OUP 2001], p.224
A Reaction
This suggest Kant's claim that arithmetical sums are synthetic (Idea 5558). It is a nice question why, when you put two 2s together, they come up with something new. Addition is movement. Among patterns, or along abstract sequences.
Related Ideas
Idea 5558
7+5=12 is not analytic, because 12 is not contained in 7 or 5 or their combination [Kant]
Idea 9974
Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle]
The
34 ideas
with the same theme
[reasons for believing maths entities exists]:
16150
|
One is, so numbers exist, so endless numbers exist, and each one must partake of being
[Plato]
|
9863
|
We aim for elevated discussion of pure numbers, not attaching them to physical objects
[Plato]
|
9864
|
In pure numbers, all ones are equal, with no internal parts
[Plato]
|
8727
|
Geometry is not an activity, but the study of unchanging knowledge
[Plato]
|
10216
|
We master arithmetic by knowing all the numbers in our soul
[Plato]
|
13738
|
It is a simple truth that the objects of mathematics have being, of some sort
[Aristotle]
|
13874
|
Numbers seem to be objects because they exactly fit the inference patterns for identities
[Frege]
|
13875
|
Frege's platonism proposes that objects are what singular terms refer to
[Frege, by Wright,C]
|
7731
|
How can numbers be external (one pair of boots is two boots), or subjective (and so relative)?
[Frege, by Weiner]
|
7737
|
Identities refer to objects, so numbers must be objects
[Frege, by Weiner]
|
8635
|
Numbers are not physical, and not ideas - they are objective and non-sensible
[Frege]
|
8652
|
Numbers are objects, because they can take the definite article, and can't be plurals
[Frege]
|
9580
|
Our concepts recognise existing relations, they don't change them
[Frege]
|
9589
|
Numbers are not real like the sea, but (crucially) they are still objective
[Frege]
|
10303
|
Restricted Platonism is just an ideal projection of a domain of thought
[Bernays]
|
10043
|
Mathematical objects are as essential as physical objects are for perception
[Gödel]
|
10490
|
Mathematics isn't surprising, given that we experience many objects as abstract
[Boolos]
|
12328
|
Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic
[Badiou]
|
13869
|
Number platonism says that natural number is a sortal concept
[Wright,C]
|
10021
|
It is claimed that numbers are objects which essentially represent cardinality quantifiers
[Hodes]
|
10022
|
Numerical terms can't really stand for quantifiers, because that would make them first-level
[Hodes]
|
8757
|
The Indispensability Argument is the only serious ground for the existence of mathematical entities
[Field,H]
|
10200
|
We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false)
[Shapiro]
|
10210
|
If mathematical objects are accepted, then a number of standard principles will follow
[Shapiro]
|
10215
|
Platonists claim we can state the essence of a number without reference to the others
[Shapiro]
|
10233
|
Platonism must accept that the Peano Axioms could all be false
[Shapiro]
|
8298
|
Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa
[Lowe]
|
8311
|
If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2
[Lowe]
|
9606
|
The irrationality of root-2 was achieved by intellect, not experience
[Brown,JR]
|
4241
|
If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects
[Lowe]
|
9183
|
Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist
[Williamson]
|
10003
|
Why is arithmetic hard to learn, but then becomes easy?
[Hofweber]
|
13741
|
If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers'
[Schaffer,J]
|
23622
|
We can only mentally construct potential infinities, but maths needs actual infinities
[Hossack]
|