PhilSci Archive

Standard Formalization

Ketland, Jeffrey (2022) Standard Formalization. [Preprint]

This is the latest version of this item.


Download (957kB) | Preview


A \emph{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 $\in$). Patrick Suppes (\cite{sup92}) 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 \emph{mathematicized}, one must specify the underlying \emph{applied mathematics base theory}, which the physical axioms live on top of. Second, such theories are typically \emph{geometric}, concerning quantities or trajectories in space/time: so, one must specify the underlying \emph{physical geometry}. Third, the differential equations involved generally refer to \emph{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 $\R$-valued quantities $Q$ (that is, scalar fields), defined on $n$ (``spatial'' or ``temporal'') dimensions, taken to be isomorphic to the usual Euclidean space $\R^n$. 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.

Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Ketland, Jeffreyjeffreyketland@gmail.com0000-0002-5128-4387
Keywords: Formalization of scientific theories
Subjects: General Issues > Structure of Theories
Depositing User: Dr Jeffrey Ketland
Date Deposited: 27 Feb 2023 15:40
Last Modified: 27 Feb 2023 15:40
Item ID: 21795
Subjects: General Issues > Structure of Theories
Date: 6 May 2022

Available Versions of this Item

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item