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This book explores the premise that a physical theory is an
interpretation of the analytico-canonical formalism. Throughout the
text, the investigation stresses that classical mechanics in its
Lagrangian formulation is the formal backbone of theoretical
physics. The authors start from a presentation of the
analytico-canonical formalism for classical mechanics, and its
applications in electromagnetism, Schroedinger's quantum mechanics,
and field theories such as general relativity and gauge field
theories, up to the Higgs mechanism. The analysis uses the main
criterion used by physicists for a theory: to formulate a physical
theory we write down a Lagrangian for it. A physical theory is a
particular instance of the Lagrangian functional. So, there is
already an unified physical theory. One only has to specify the
corresponding Lagrangian (or Lagrangian density); the dynamical
equations are the associated Euler-Lagrange equations. The theory
of Suppes predicates as the main tool in the axiomatization and
examples from the usual theories in physics. For applications, a
whole plethora of results from logic that lead to interesting, and
sometimes unexpected, consequences. This volume looks at where our
physics happen and which mathematical universe we require for the
description of our concrete physical events. It also explores if we
use the constructive universe or if we need set-theoretically
generic spacetimes.
Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.
This book explores the premise that a physical theory is an
interpretation of the analytico-canonical formalism. Throughout the
text, the investigation stresses that classical mechanics in its
Lagrangian formulation is the formal backbone of theoretical
physics. The authors start from a presentation of the
analytico-canonical formalism for classical mechanics, and its
applications in electromagnetism, Schroedinger's quantum mechanics,
and field theories such as general relativity and gauge field
theories, up to the Higgs mechanism. The analysis uses the main
criterion used by physicists for a theory: to formulate a physical
theory we write down a Lagrangian for it. A physical theory is a
particular instance of the Lagrangian functional. So, there is
already an unified physical theory. One only has to specify the
corresponding Lagrangian (or Lagrangian density); the dynamical
equations are the associated Euler-Lagrange equations. The theory
of Suppes predicates as the main tool in the axiomatization and
examples from the usual theories in physics. For applications, a
whole plethora of results from logic that lead to interesting, and
sometimes unexpected, consequences. This volume looks at where our
physics happen and which mathematical universe we require for the
description of our concrete physical events. It also explores if we
use the constructive universe or if we need set-theoretically
generic spacetimes.
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