Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-21T02:32:50.538Z Has data issue: false hasContentIssue false
  • English
  • Français

Ramsey Sentences and the Meaning of Quantifiers

Published online by Cambridge University Press:  01 April 2022

Jaakko Hintikka
Jaakko Hintikka*
Affiliation:
Department of Philosophy, Boston University
Get access Rights & Permissions [Opens in a new window]

Extract

1. Ramsey Sentences and the Function of Theoretical Concepts. In his famous paper “Theories,” Frank Ramsey (1931, 212–236; 1978, Ch. 4) introduced a technique of examining a scientific theory by means of certain propositions, dubbed later “Ramsey Sentences.” They are the results of what is often called Ramsey elimination. This prima facie elimination is often presented as a method of dispensing with theoretical concepts in scientific theorizing. The idea is this: Assume that we are given a finitely axiomatized scientific theory

where O1, O2, … are the primitive observation terms (individual constants, predicate constants, function constants, etc.) of (1) and H1, H2, … its primitive theoretical terms. For simplicity, it will be assumed that (1) is a first-order theory. Since it is finitely axiomatizable, we may think of it as having the form of a single complex proposition, i.e., the conjunction of all the axioms. What can then be done is to generalize existentially with respect to (1). The result is a sentence of the form

In (2), the theoretical terms H1, H2, … do not occur any longer. They have been replaced by the variables X1, X2, … bound to initial existential quantifiers. In this sense at least, Ramsey sentences do effect on elimination. Unlike (1), (2) is not a first-order sentence but a second-order one.

Type
Research Article
Information
Philosophy of Science , Volume 65 , Issue 2 , June 1998 , pp. 289 - 305
Copyright
Copyright © Philosophy of Science Association 1998

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.)

Footnotes

†

Send requests for reprints to the author, Department of Philosophy, Boston University, 745 Commonwealth Avenue, Boston, MA 02215.

References

Ramsey, F. P. (1931), The Foundations of Mathematics and other Logical Essays. Edited by Braithwaite, R. B. London: Routledge and Kegan Paul.Google Scholar
Ramsey, F. P. (1978), Foundations: Essays in Philosophy, Logic, Mathematics and Economics. Edited by D. H. Mellor. Routledge and Kegan Paul.Google Scholar
Achinstein, P. (1968), Concepts of Science. Baltimore: The Johns Hopkins Press.Google Scholar
Carnap, R. (1966), Philosophical Foundations of Physics. New York: Basic Books.Google Scholar
Hintikka, J. (1995a), “Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematics”, in Hintikka, Jaakko (ed.), From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics. Dordrecht: Kluwer Academic, 21–44.CrossRefGoogle Scholar
Hintikka, J. (1995b), “What Is Elementary Logic?”, in Gavroglu, K. et al. (eds.), K. Gavroglu et al. Dordrecht: Kluwer Academic, 301–326.Google Scholar
Hintikka, J. (1996), The Principles of Mathematics Revisited. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Moore, G. H. (1988), “The Emergence of First-Order Logic”, in Aspray, William and Kitcher, Philip (eds.), History and Philosophy of Modern Mathematics. Minneapolis: University of Minnesota Press, 95–135.Google Scholar
Newman, M. H. A. (1928), “Mr. Russell's Causal Theory of Perception”, Mind 37: 137–148.CrossRefGoogle Scholar
Papineau, D. (1996), “Theory-dependent Terms”, Philosophy of Science 63: 1–20.CrossRefGoogle Scholar
Russell, B. (1931), “Critical Notice of F. P. Ramsey, The Foundations of Mathematics and Other Essays”, The Foundations of Mathematics and Other Essays 40: 476–482.Google Scholar
Sahlin, N.-E. (1990), The Philosophy of F. P. Ramsey, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Sneed, J. D. (1971), The Logical Structure of Mathematical Physics. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Stegmüller, W. (1970), Theorie und Erfahrung (Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie, Band II). Berlin: Springer-Verlag. (See chapter 7.)Google Scholar
Tuomela, R. (1973), Theoretical Concepts. Wien: Springer-Verlag.CrossRefGoogle Scholar
van Benthem, J. (1978), “Ramsey Eliminability”, Studia Logica 37: 321–336.CrossRefGoogle Scholar
van Fraassen, B. (1997), “Structure and Perspective: Philosophical Perplexity and Paradox”, in Dalla Chiara, M. L. et al. (eds.), M. L. Dalla Chiara et al. Dordrecht: Kluwer Academic, 511–530.Google Scholar