Standard Formalization

Axiomathes 32 (3):711-748 (2022)
  Copy   BIBTEX


A standard formalization of a scientific theory is a system of axioms for that theory in a first-order language (possibly many-sorted; possibly with the membership primitive $$\in$$ ). Suppes (in: Carvallo M (ed) Nature, cognition and system II. Kluwer, Dordrecht, 1992) expressed skepticism about whether there is a “simple or elegant method” for presenting mathematicized scientific theories in such a standard formalization, because they “assume a great deal of mathematics as part of their substructure”. The major difficulties amount to these. First, as the theories of interest are mathematicized, one must specify the underlying applied mathematics base theory, which the physical axioms live on top of. Second, such theories are typically geometric, concerning quantities or trajectories in space/time: so, one must specify the underlying physical geometry. Third, the differential equations involved generally refer to coordinate representations of these physical quantities with respect to some implicit coordinate chart, not to the original quantities. These issues may be resolved. Once this is done, constructing standard formalizations is not so difficult—at least for the theories where the mathematics has been worked out rigorously. Here we give what may be claimed to be a simple and elegant means of doing that. This is for mathematicized scientific theories comprising differential equations for $$\mathbb{R}$$ -valued quantities Q (that is, scalar fields), defined on n (“spatial” or “temporal”) dimensions, taken to be isomorphic to the usual Euclidean space $$\mathbb{R}^n$$. For illustration, I give standard (in a sense, “text-book”) formalizations: for the simple harmonic oscillator equation in one-dimension and for the Laplace equation in two dimensions.



    Upload a copy of this work     Papers currently archived: 91,349

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A System of Axioms for Minkowski Spacetime.Lorenzo Cocco & Joshua Babic - 2020 - Journal of Philosophical Logic 50 (1):149-185.
Limitations of formalization.Constantine Politis - 1965 - Philosophy of Science 32 (3/4):356-360.
A System of Axioms for Minkowski Spacetime.Lorenzo Cocco & Joshua Babic - 2020 - Journal of Philosophical Logic (1):1-37.
Traits essentiels d'une formalisation adéquate.Gheorghe-Ilie Farte - 2020 - Argumentum. Journal of the Seminar of Discursive Logic, Argumentation Theory and Rhetoric 18 (1):163-174.
A Simple Formalization And Proof For The Mutilated Chess Board.L. Paulson - 2001 - Logic Journal of the IGPL 9 (3):475-485.
Formalization and infinity.André Porto - 2008 - Manuscrito 31 (1):25-43.
Fine-tuning and the infrared bull’s-eye.John T. Roberts - 2012 - Philosophical Studies 160 (2):287-303.
Domains of Sciences, Universes of Discourse and Omega Arguments.Jose M. Saguillo - 1999 - History and Philosophy of Logic 20 (3-4):267-290.
Contexts, oracles, and relevance.Varol Akman & Mehmet Surav - 1995 - In Proceedings of the AAAI-95 Fall Symposium on Formalizing Context (AAAI Technical Report FS-95-02). Palo Alto, CA: Association for the Advancement of Artificial Intelligence Press. pp. 23-30.


Added to PP

22 (#690,757)

6 months
5 (#629,136)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
Philosophy of logic.Hilary Putnam - 1971 - London,: Allen & Unwin. Edited by Stephen Laurence & Cynthia Macdonald.

View all 47 references / Add more references