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Full Idea
Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1.
Gist of Idea
Dedekind cuts lead to the bizarre idea that there are many different number 1's
Source
Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
Book Ref
-: 'Philosophical Studies' [-], p.386
A Reaction
See Idea 10572.
Related Idea
Idea 10572 A cut between rational numbers creates and defines an irrational number [Dedekind]
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |