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Single Idea 17312

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers ]

Full Idea

Being the successor of the successor of 0 is more explanatory than being predecessor of 3 of the nature of 2, since it mirrors more closely the method by which 2 is constructed from a basic entity, 0, and a relation (successor) taken as primitive.

Gist of Idea

It is more explanatory if you show how a number is constructed from basic entities and relations

Source

Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.4)

Book Ref

'Metaphysical Grounding', ed/tr. Correia,F/Schnieder,B [CUP 2012], p.199

A Reaction

This assumes numbers are 'constructed', which they are in the axiomatised system of Peano Arithmetic, but presumably the numbers were given in ordinary experience before 'construction' occurred to anyone. Nevertheless, I really like this.

Related Idea

The 48 ideas from Kathrin Koslicki

15110 An essence and what merely follow from it are distinct [Koslicki]
15111 In demonstration, the explanatory order must mirror the causal order of the phenomena [Koslicki]
15112 If an object exists, then its essential properties are necessary [Koslicki]
15115 In a demonstration the middle term explains, by being part of the definition [Koslicki]
15118 A successful Aristotelian 'definition' is what sciences produces after an investigation [Koslicki]
15116 Essences cause necessary features, and definitions describe those necessary features [Koslicki]
15113 Individuals are perceived, but demonstration and definition require universals [Koslicki]
15114 Discovering the Aristotelian essence of thunder will tell us why thunder occurs [Koslicki]
15117 Greek uses the same word for 'cause' and 'explanation' [Koslicki]
24065 Structured wholes are united by the teamwork needed for their capacities [Koslicki]
24066 The form explains kind, structure, unity and activity [Koslicki]
24067 Hylomorphic compounds need an individual form for transworld identity [Koslicki]
24069 Much metaphysical debate concerns what is fundamental, rather than what exists [Koslicki]
17439 There is no deep reason why we count carrots but not asparagus [Koslicki]
17435 Objects do not naturally form countable units [Koslicki]
17433 We can still count squares, even if they overlap [Koslicki]
17434 We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
17436 We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki]
14497 The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki]
14495 I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki]
14496 Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki]
13266 Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki]
14498 For three-dimensionalist parthood must be a three-place relation, including times [Koslicki]
14500 Wholes are entities distinct from their parts, and have different properties [Koslicki]
14501 'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki]
13264 If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki]
13258 The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki]
13281 Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki]
13283 The parts may be the same type as the whole, like a building made of buildings [Koslicki]
13280 Statue and clay differ in modal and temporal properties, and in constitution [Koslicki]
13279 There are at least six versions of constitution being identity [Koslicki]
13284 Should vernacular classifications ever be counted as natural kind terms? [Koslicki]
13285 Natural kinds support inductive inferences, from previous samples to the next one [Koslicki]
13287 Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki]
13286 There are apparently no scientific laws concerning biological species [Koslicki]
14504 The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki]
14505 Some questions concern mathematical entities, rather than whole structures [Koslicki]
14506 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki]
13288 Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki]
13289 Structures have positions, constituent types and number, and some invariable parts [Koslicki]
17311 Real definitions don't just single out a thing; they must also explain its essence [Koslicki]
17312 It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
17309 For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki]
17313 Modern views want essences just to individuate things across worlds and times [Koslicki]
17314 The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki]
17315 We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki]
17316 We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]
17317 A good explanation captures the real-world dependence among the phenomena [Koslicki]