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**Continu’ous time goes by Russell.**
*(English)*
Zbl 1113.03012

Summary: Russell and Walker proposed different ways of constructing instants from events. For an explanation of “time as a continuum,” S. K. Thomason [J. Philos. Log. 13, 85–96 (1984; Zbl 0556.03005)] favored Walker’s construction. The present article shows that Russell’s construction [B. Russell, Our knowledge of the external world. Chicago etc.: Open Court (1914; JFM 45.0122.03)] fares as well. To this end, a mathematical characterization problem is solved which corresponds to the characterization problem that Thomason solved with regard to Walker’s construction. It is shown how to characterize those event structures (formally, interval orders) which, through Russell’s construction of instants, become linear orders isomorphic to a given (or, deriving, to some – nontrivial ordered) real interval. As tools, separate characterizations for each of resulting (i) Dedekind completeness, (ii) separability, (iii) plurality of elements, (iv) existence of certain endpoints are provided. Denseness is characterized to replace Russell’s erroneous attempt. Somewhat minimal nonconstructive principles needed are exhibited, and some alternative approaches are surveyed.

### MSC:

03A05 | Philosophical and critical aspects of logic and foundations |

01A60 | History of mathematics in the 20th century |

03E25 | Axiom of choice and related propositions |

06A05 | Total orders |