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Dean, Walter (2014) Models and computability. Philosophia Mathematica, 22 (2). pp. 143-166. doi:10.1093/philmat/nkt035 ISSN 0031-8019.
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Official URL: http://dx.doi.org/10.1093/philmat/nkt035
Abstract
Computationalism holds that our grasp of notions like ‘computable function’ can be used to account for our putative ability to refer to the stan- dard model of arithmetic. Tennenbaum’s Theorem has been repeatedly invoked in service of this claim. I will argue that not only do the relevant class of arguments fail, but that the result itself is most naturally under- stood as having the opposite of a reference-fixing effect — i.e., rather than securing the determinacy of number-theoretic reference, Tennenbaum’s Theorem points towards a sense in which portions of our computational vocabulary should be regarded as model-relative.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | B Philosophy. Psychology. Religion > BC Logic | ||||
| Divisions: | Faculty of Social Sciences > Philosophy | ||||
| Journal or Publication Title: | Philosophia Mathematica | ||||
| Publisher: | Oxford University Press | ||||
| ISSN: | 0031-8019 | ||||
| Official Date: | 2014 | ||||
| Dates: |
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| Volume: | 22 | ||||
| Number: | 2 | ||||
| Page Range: | pp. 143-166 | ||||
| DOI: | 10.1093/philmat/nkt035 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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