Two roads to the successor axiom.
Most accounts of our knowledge of the successor axiom claim that this is based on the procedure of adding one. While they usually don't claim to provide an account of how children actually acquire this knowledge, one may well think that this is how they get that knowledge. I argue that when we look...
| Publicado en: | Synthese Vol. 197; no. 3; pp. 1241 - 1262 |
|---|---|
| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Mar2020
|
| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=142270100&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 142270100 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Mar2020 vid: 197 iid: 3 pid: 237 pub: Springer Nature artinfo: ui: 142270100 10.1007/s11229-018-1752-5 ppf: 1241 ppct: 21 formats: fmt: – @attributes: type: T – @attributes: type: P size: 455KB tig: atl: Two roads to the successor axiom. aug: au: Buijsman, Stefan affil: Filosofiska Institutionen, Stockholm University, Universitetsvägen 10D, 106 91, Stockholm, Sweden su: Number systems Executive succession Natural numbers Axioms sug: subj: Number systems Executive succession Natural numbers Axioms keyword: Arithmetical cognition Epistemology Number concepts Successor axiom ab: Most accounts of our knowledge of the successor axiom claim that this is based on the procedure of adding one. While they usually don't claim to provide an account of how children actually acquire this knowledge, one may well think that this is how they get that knowledge. I argue that when we look at children's responses in interviews, the time when they learn the successor axiom and the intermediate learning stages they find themselves in, that there is an empirically viable alternative. I argue that they could also learn it on the basis of a method that has to do with the structure of the numeral system. Specifically, that they (1) use the syntactic structure of the numeral system and (2) attend to the leftmost digits, the one with the highest place-value. Children can learn that this is a reliable method of forming larger numbers by combining two elements. First, a grasp of the syntactic structure of the numeral system. That way they know that the leftmost digit receives the highest value. Second, an interpretation of numerals as designating cardinal values, so that they also realise that increasing or adding digits on the lefthand side of a numeral produces a larger number. There are thus two, currently equally well-supported, ways in which children might learn that there are infinitely many natural numbers. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2020. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2020 holdings: @attributes: islocal: N |
|---|