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Full Idea
The prime numbers are more fundamental than the even numbers, and than the composite non-prime numbers. The result that all numbers uniquely decompose into a product of prime numbers is called the 'Fundamental Theorem of Arithmetic'.
Gist of Idea
The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes
Source
Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 13.4.2)
Book Ref
Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.329
A Reaction
I could have used this example in my thesis, which defended the view that essences are the fundamentals of explanation, even in abstract theoretical realms.
| 13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
| 9865 | Daily arithmetic counts unequal things, but pure arithmetic equalises them [Plato] |
| 16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| 21665 | The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber] |