Skip to main content
Log in

Idealization in Applied First-Order Logic

Synthese Aims and scope Submit manuscript

Abstract

Applying first-order logic to derive the consequences of laws that are only approximately true of empirical phenomena involves idealization of a kind that is akin to applying arithmetic to calculate the area of a rectangular surface from approximate measures of the lengths of its sides. Errors in the data, in the exactness of the lengths in one case and in the exactness of the laws in the other, are in some measure transmitted to the consequences deduced from them, and the aim of a theory of idealization is to describe this process. The present paper makes a start on this in the case of applied first-order logic, and relates it to Plato's picture of a world or model of 'appearances' in which laws are only approximately true, but which to some extent resembles an ideal world or model in which they are exactly true.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Adams, E. W.: 1966, 'On the Nature and Purpose of Measurement', Synthese 16, 125-69.

    Article  Google Scholar 

  • Adams, E. W.: 1973, 'The Naive Conception of the Topology of the Surface of a Body', in P. Suppes (ed.), Space, Time and Geometry, D. Reidel Publishing Co., Dordrecht, pp. 402-24.

    Google Scholar 

  • Adams, E. W.: 1974, 'The Logic of “Almost All”', Journal of Philosophical Logic 3, 3-17.

    Article  Google Scholar 

  • Adams, E. W.: 1975, The Logic of Conditionals, an Application of Probability to Deductive Logic, D. Reidel and Co., Dordrecht.

    Google Scholar 

  • Adams, E. W.: 1986, 'On the Dimensionality of Surfaces, Solids and Spaces', Erkenntnis 24, 137-201.

    Article  Google Scholar 

  • Adams, E. W.: 1986, 'Continuity and Idealizability of Approximate Generalizations', Synthese 67, 439-76.

    Article  Google Scholar 

  • Adams, E. W.: 1988, 'A Note on Solidity', Australasian Journal of Philosophy 66(4), 512-16.

    Article  Google Scholar 

  • Adams, E. W.: 1993, 'Classical Physical Abstraction', Erkenntnis 38, 145-67.

    Article  Google Scholar 

  • Adams, 1996, 'Topology, Empiricism, and Operationalism', The Monist 79(1), 1-20.

    Google Scholar 

  • Adams, E. W. and I. F. Carlstrom: 1979, 'Representing Approximate Ordering and Equivalence Relations', Journal of Mathematical Psychology 19, 182-207.

    Article  Google Scholar 

  • Adams, W. Y. and E. W. Adams: 1987, 'Purpose and Scientific Concept Formation', British Journal for the Philosophy of Science 38, 419-40.

    Google Scholar 

  • Adams, W. Y. and E. W. Adams: 1991, Archaeological Typology and Practical Reality, Cambridge University Press, Cambridge.

    Google Scholar 

  • Carlstrom, I. F.: 1975, 'Truth and Entailment for a Vague Quantifier', Synthese 30, 461-95.

    Article  Google Scholar 

  • Carlstrom, I. F.: 1990, 'A Truth Functional Logic for Near-Universal Generalizations', Journal of Philosophical Logic 19, 379-405.

    Article  Google Scholar 

  • Craig, W.: 1965, 'Boolean Notions Extended to Higher Dimensions', in J. Addison et al. (1965), The Theory of Models, North-Holland, Amsterdam, pp. 55-69.

    Google Scholar 

  • Heath, T. H.: 1956, The Thirteen Rooks of Euclid's Elements, Vol. 1, Dover Publications, Inc., New York.

    Google Scholar 

  • Hilbert, D.: 1956, Grundlagen der Geometrie, Eighth Edition, with revisions and supplements by P. Bernays, Stuttgart.

  • Luce, R. D.: 1956, 'Semiorders and a Theory of Utility Discrimination', Econometrica 24, 178-91.

    Article  Google Scholar 

  • Plato: 1945, The Republic of Plato, translated and with introduction by F. D. Cornford, Oxford University Press, New York and London.

    Google Scholar 

  • Tarski, A.: 1959, 'What is Elementary Geometry?', in L. Henkin, P. Suppes, and A. Tarski (eds.), The Axiomatic Method with Special Reference to Geometry and Physics, North-Holland Publishing Company, Amsterdam.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Adams, E.W. Idealization in Applied First-Order Logic. Synthese 117, 331–354 (1998). https://doi.org/10.1023/A:1005090932292

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005090932292

Keywords

Navigation