Philosophiehttps://kops.uni-konstanz.de:443/handle/123456789/402020-02-17T08:14:30Z2020-02-17T08:14:30ZTriangulating non-archimedean probabilityBrickhill, Hazelpop526189Horsten, Leonpop526276123456789/486512020-02-14T13:45:25Z2018-09Triangulating non-archimedean probability
Brickhill, Hazel; Horsten, Leon
We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.
2018-09Brickhill, HazelHorsten, Leon100We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.Cambridge University PressJOURNAL_ARTICLEeng10.1017/S17550203180000601755-02031755-0211519546113The Review of Symbolic Logic2020-02-14T14:45:25+01:00123456789/40The Review of Symbolic Logic ; 11 (2018), 3. - S. 519-546. - Cambridge University Press. - ISSN 1755-0203. - eISSN 1755-0211unknown2020-02-14T13:45:25ZtrueReasoning about Arbitrary Natural Numbers from a Carnapian PerspectiveHorsten, Leonpop526276Speranski, Stanislav O.123456789/486502020-02-14T13:40:55Z2019-08Reasoning about Arbitrary Natural Numbers from a Carnapian Perspective
Horsten, Leon; Speranski, Stanislav O.
Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.
2019-08Horsten, LeonSperanski, Stanislav O.100Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.SpringerJOURNAL_ARTICLEeng10.1007/s10992-018-9490-10022-36111573-0433685707484Journal of Philosophical Logic2020-02-14T14:40:55+01:00123456789/40Journal of Philosophical Logic ; 48 (2019), 4. - S. 685-707. - Springer. - ISSN 0022-3611. - eISSN 1573-0433true2020-02-14T13:40:55ZtrueHuman-Effective ComputabilityAntonutti Marfori, MariannaHorsten, Leonpop526276123456789/486492020-02-14T13:39:10Z2019-02-01Human-Effective Computability
Antonutti Marfori, Marianna; Horsten, Leon
We analyse Kreisel's notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church's thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.
2019-02-01Antonutti Marfori, MariannaHorsten, Leon100We analyse Kreisel's notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church's thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.Oxford University Press (OUP)JOURNAL_ARTICLEeng10.1093/philmat/nky0110031-80191744-64066187271Philosophia Mathematica2020-02-14T14:39:10+01:00123456789/40Philosophia Mathematica ; 27 (2019), 1. - S. 61-87. - Oxford University Press (OUP). - ISSN 0031-8019. - eISSN 1744-6406true2020-02-14T13:39:10ZtrueGeneric StructuresHorsten, Leonpop526276123456789/486482020-02-14T13:37:38Z2019-10-01Generic Structures
Horsten, Leon
In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.
2019-10-01Horsten, Leon100In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.Oxford University Press (OUP)JOURNAL_ARTICLEeng10.1093/philmat/nky0150031-80191744-6406362380273Philosophia Mathematica2020-02-14T14:37:38+01:00123456789/40Philosophia Mathematica ; 27 (2019), 3. - S. 362-380. - Oxford University Press (OUP). - ISSN 0031-8019. - eISSN 1744-6406true2020-02-14T13:37:38Ztrue