1,383 research outputs found
Introducing Formalism in Economics: The Growth Model of John von Neumann
The objective is to interpret John von Neumann's growth model as a decisive step of the forthcoming formalist revolution of the 1950s in economics. This model gave rise to an impressive variety of comments about its classical or neoclassical underpinnings. We go beyond this traditional criterion and interpret rather this model as the manifestation of von Neumann's involvement in the formalist programme of mathematician David Hilbert. We discuss the impact of Kurt Gödelâs discoveries on this programme. We show that the growth model reflects the pragmatic turn of the formalist programme after Gödel and proposes the extension of modern axiomatisation to economics..Von Neumann, Growth model, Formalist revolution, Mathematical formalism, Axiomatics
Axiomatic method and the law
Whether an axiomatic approach to law is possible and useful today has to be perceived as unanswered. Perception of the axiomatic method among lawyers, however, is clouded by misunderstanding. Clarifying them may generate new discussion about the axiomatization of legal theories
Axiomatics for the external numbers of nonstandard analysis
Neutrices are additive subgroups of a nonstandard model of the real numbers.
An external number is the algebraic sum of a nonstandard real number and a
neutrix. Due to the stability by some shifts, external numbers may be seen as
mathematical models for orders of magnitude. The algebraic properties of
external numbers gave rise to the so-called solids, which are extensions of
ordered fields, having a restricted distributivity law. However, necessary and
sufficient conditions can be given for distributivity to hold. In this article
we develop an axiomatics for the external numbers. The axioms are similar to,
but mostly somewhat weaker than the axioms for the real numbers and deal with
algebraic rules, Dedekind completeness and the Archimedean property. A
structure satisfying these axioms is called a complete arithmetical solid. We
show that the external numbers form a complete arithmetical solid, implying the
consistency of the axioms presented. We also show that the set of precise
elements (elements with minimal magnitude) has a built-in nonstandard model of
the rationals. Indeed the set of precise elements is situated between the
nonstandard rationals and the nonstandard reals whereas the set of non-precise
numbers is completely determined
Electric/magnetic reciprocity in premetric electrodynamics with and without magnetic charge, and the complex electromagnetic field
We extend an axiomatic approach to classical electrodynamics, which we
developed recently, to the case of non-vanishing magnetic charge. Then two
axioms, namely those of the existence of the Lorentz force (Axiom 2) and of
magnetic flux conservation (Axiom 3) have to be generalized. Electric/magnetic
reciprocity constitutes a guiding principle for this undertaking. The extension
of the axioms can be implemented at a premetric stage, i.e., when metric and
connection of spacetime don't play a role. Complex Riemann-Silberstein fields
of the form have a natural place in the
theory, independent of the Hodge duality mapping defined by any particular
metric.Comment: 13 pages in latex, 3 references added, text slightly revise
Locus configurations and -systems
We present a new family of the locus configurations which is not related to
-systems thus giving the answer to one of the questions raised in
\cite{V1} about the relation between the generalised quantum Calogero-Moser
systems and special solutions of the generalised WDVV equations. As a
by-product we have new examples of the hyperbolic equations satisfying the
Huygens' principle in the narrow Hadamard's sense. Another result is new
multiparameter families of -systems which gives new solutions of the
generalised WDVV equation.Comment: 12 page
A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests
The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive
axiomatics of the space-time geometry that uses light rays and freely falling
particles with high velocity, is replaced by several constructions with low
velocity particles only. For that purpose we describe in a space-time with a
conformal structure and an arbitrary path structure the radial acceleration, a
Coriolis acceleration and the zig-zag construction. Each of these quantities
give effects whose requirement to vanish can be taken as alternative version of
the compatibility axiom of EPS. The procedural advantage lies in the fact, that
one can make null-experiments and that one only needs low velocity particles to
test the compatibility axiom. We show in addition that Perlick's standard clock
can exist in a Weyl space only.Comment: to appear in Gen.Rel.Gra
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