Ketland, Jeffrey (2022) Standard Formalization. [Preprint]
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Abstract
A \emph{standard formalization} of a scientific theory is a system of axioms for that theory in a firstorder language (possibly manysorted; 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 difficultat 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, ``textbook'') formalizations: for the simple harmonic oscillator equation in onedimension and for the Laplace equation in two dimensions.
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Item Type:  Preprint  

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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  
URI:  http://philsciarchive.pitt.edu/id/eprint/21795 
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Standard Formalization. (deposited 09 May 2022 04:07)
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