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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 67 ideas from 'The Possibility of Metaphysics'

16414 Science needs metaphysics to weed out its presuppositions [Lowe, by Hofweber]
16063 Metaphysical necessity is logical necessity 'broadly construed' [Lowe, by Lynch/Glasgow]
8258 Two of the main rivals for the foundations of ontology are substances, and facts or states-of-affairs [Lowe]
9414 Metaphysics is the mapping of possibilities [Lowe, by Mumford]
8260 Logical necessity can be 'strict' (laws), or 'narrow' (laws and definitions), or 'broad' (all logical worlds) [Lowe]
8267 Perhaps concrete objects are entities which are in space-time and subject to causality [Lowe]
8265 Our commitment to the existence of objects should depend on their explanatory value [Lowe]
8262 How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe]
8263 An object is an entity which has identity-conditions [Lowe]
8266 Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
8268 Some things (such as electrons) can be countable, while lacking proper identity [Lowe]
8269 Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe]
8270 Events are changes or non-changes in properties and relations of persisting objects [Lowe]
8271 An object 'endures' if it is always wholly present, and 'perdures' if different parts exist at different times [Lowe]
8272 How can you identify temporal parts of tomatoes without referring to tomatoes? [Lowe]
8273 Is 'the Thames is broad in London' relational, or adverbial, or segmental? [Lowe]
8275 Objects are entities with full identity-conditions, but there are entities other than objects [Lowe]
8276 Properties or qualities are essentially adjectival, not objectual [Lowe]
8279 The identity of composite objects isn't fixed by original composition, because how do you identify the origin? [Lowe]
8280 While space may just be appearance, time and change can't be, because the appearances change [Lowe]
8283 Ontological categories are not natural kinds: the latter can only be distinguished using the former [Lowe]
8281 Heraclitus says change is new creation, and Spinoza that it is just phases of the one substance [Lowe]
8282 Only metaphysics can decide whether identity survives through change [Lowe]
8284 The top division of categories is either abstract/concrete, or universal/particular, or necessary/contingent [Lowe]
8286 Tropes cannot have clear identity-conditions, so they are not objects [Lowe]
8285 I prefer 'modes' to 'tropes', because it emphasises their dependence [Lowe]
8288 Sortal terms for universals involve a substance, whereas adjectival terms do not [Lowe]
8292 Diversity of two tigers is their difference in space-time; difference of matter is a consequence [Lowe]
8291 Individuation principles identify what kind it is; identity criteria distinguish items of the same kind [Lowe]
8290 One view is that two objects of the same type are only distinguished by differing in matter [Lowe]
8289 The idea that Cartesian souls are made of some ghostly 'immaterial' stuff is quite unwarranted [Lowe]
8293 Real universals are needed to explain laws of nature [Lowe]
8294 How can tropes depend on objects for their identity, if objects are just bundles of tropes? [Lowe]
8296 Does a ball snug in plaster have one trope, or two which coincide? [Lowe]
8295 Why cannot a trope float off and join another bundle? [Lowe]
16127 Metaphysics tells us what there could be, rather than what there is [Lowe]
16131 The metaphysically possible is what acceptable principles and categories will permit [Lowe]
16128 A 'substance' is an object which doesn't depend for existence on other objects [Lowe]
16130 To be an object at all requires identity-conditions [Lowe]
15079 'Conceptual' necessity is narrow logical necessity, true because of concepts and logical laws [Lowe]
8298 Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe]
8297 Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
8299 Abstractions are non-spatial, or dependent, or derived from concepts [Lowe]
8300 Perhaps possession of causal power is the hallmark of existence (and a reason to deny the void) [Lowe]
8301 Some abstractions exist despite lacking causal powers, because explanation needs them [Lowe]
8302 Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
8306 You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe]
8305 A clear idea of the kind of an object must precede a criterion of identity for it [Lowe]
8303 Criteria of identity cannot individuate objects, because they are shared among different types [Lowe]
8307 Particulars are instantiations, and universals are instantiables [Lowe]
8308 Events are ontologically indispensable for singular causal explanations [Lowe]
8310 Does the existence of numbers matter, in the way space, time and persons do? [Lowe]
8309 A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe]
8311 If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]
8312 It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe]
8313 Facts are needed for truth-making and causation, but they seem to lack identity criteria [Lowe]
8314 Are facts wholly abstract, or can they contain some concrete constituents? [Lowe]
8315 Maybe facts are just true propositions [Lowe]
8316 Facts cannot be wholly abstract if they enter into causal relations [Lowe]
8317 To cite facts as the elements in causation is to confuse states of affairs with states of objects [Lowe]
8318 The problem with the structured complex view of facts is what binds the constituents [Lowe]
8319 One-to-one correspondence would need countable, individuable items [Lowe]
8320 Does every abstract possible world exist in every possible world? [Lowe]
8321 All possible worlds contain abstracta (e.g. numbers), which means they contain concrete objects [Lowe]
8322 I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe]
8323 It is whimsical to try to count facts - how many facts did I learn before breakfast? [Lowe]
13122 Lowe divides things into universals and particulars, then kinds and properties, and abstract/concrete [Lowe, by Westerhoff]