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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]