Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-24T18:30:36.957Z Has data issue: false hasContentIssue false
  • English
  • Français

Reference to Abstract Entities

Published online by Cambridge University Press:  01 January 2020

Edward Oldfield
Edward Oldfield*
Affiliation:
University of Wisconsin, Madison
Get access Rights & Permissions [Opens in a new window]

Extract

Platonism, considered as a philosophy of mathematics, can be formulated in two interestingly different ways. Strong platonism holds that numerals, for example, refer to certain non-physical, non-mental entities. Weak platonism holds only that numerals uniquely apply to certain non-physical, non-mental entities. (Of course, there may even be weaker views that deserve to be called ‘platonistic.’

The distinction between referring to an object and uniquely applying to an object may be illustrated as follows. If there is a tallest person and I say, ‘the tallest person is over seven feet tall,’ without knowing who that person is, then my use of ‘the tallest person’ uniquely applies to someone, but it does not refer to anyone. The distinction is at least as old as Russell, for we might put his views in our terms by saying that for Russell only logically proper names refer to things, while ordinary proper names and definite descriptions at best uniquely apply to things.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 11 , Issue 3 , September 1981 , pp. 425 - 438
Copyright
Copyright © The Authors 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benacerraf, Paul ‘Mathematical Truth,’ Journal of Philosophy 70 (1973), 661-79.CrossRefGoogle Scholar
Benacerraf, Paul ‘What Numbers Could Not Be,’ Philosophical Review 74 (1965), 47-73.CrossRefGoogle Scholar
Burge, Tyler ‘Belief De Re,’ Journal of Philosophy 74 (1977), 338-62.CrossRefGoogle Scholar
Burge, Tyler ‘Belief and Synonymy,’ Journal of Philosophy 75 (1978), 119-38.10.2307/2025424CrossRefGoogle Scholar
Carnap, Rudolf Meaning and Necessity (Chicago 1956).Google Scholar
Cartwright, Richard ‘Propositions,’ in Butler, R.J. ed., Analytical Philosophy First Series, (Oxford 1966).Google Scholar
Frege, Gottlob The Foundations of Arithmetic, trans. by Austin, J.L. (New York 1950).Google Scholar
Frege, Gottlob ‘The Thought,’ in Strawson, P.F. ed., Philosophical Logic, (Oxford 1967).Google Scholar
Geach, Peter and Black, Max eds., Translations from the Philosophical Writings of Gottlob Frege (Oxford 1970).Google Scholar
Jubien, Michael ‘Ontology and Mathematical Truth,’ Noûs 11 (1977) 133-50.Google Scholar
Kaplan, David ‘Bob and Carol and Ted and Alice,’ in Jaakko Hintikka et. al., eds., Approaches to Natural Language (Dordrecht 1973).CrossRefGoogle Scholar
Kaplan, David ‘Demonstratives,’ (xeroxed 1977).Google Scholar
Kripke, Saul ‘Naming and Necessity,’ in Donald Davidson and Gilbert Harman, eds., Semantics of Natural Language (Dordrecht 1972).CrossRefGoogle Scholar
Parsons, Terence ‘Frege's Hierarchies of Indirect Senses,’ (xeroxed 1977).Google Scholar
Perry, John ‘Frege on Demonstratives,’ Philosophical Review 86 (1977) 474-97.CrossRefGoogle Scholar
Russell, Bertrand The Principles of Mathematics (New York 1903).Google Scholar
Russell, Bertrand ‘Lectures on Logical Atomism,’ reprinted in Logic and Knowledge, ed. by Marsh, R. (London 1956).Google Scholar