Theory of Physical Theories |

**Metatheories in General** > s.a. correlations [classification of theories];
physical theories [frameworks, theories of everything].

* __Semantic view__: According to the semantic view
of scientific theories, theories are classes of models.

* __Change of level__: When
going from one physical theory to a deeper one, the singularities at the former
level tend to be dissolved (see atomic
stability from classical to quantum mechanics).

* __Types of theories__: Einstein [@ London Times 1919] distinguished
between theories of principles, and theories of constructs (principle and constructive theories).

* __Examples__: The PPN formalism
(> see modified newtonian gravity).

@ __References__: Giere PhSc(94)jun
[cognitive structure]; Smith BJPS(98)
[approximate truth]; Halvorson SHPMP(04)qp/03 [insert,
state
space and information theory]; D'Agostini phy/04-conf
[probabilistic reasoning]; 't Hooft IJMPA(08)-a0707 [grand
view]; Matravers CP(07);
Allen a1101 [statistical counting and stochastic fluctuations]; French & Vickers BJPS(11) [ontological status]; Halvorson PhSc(12) [against the semantic view of theories]; Jaroszkiewicz a1501 [generalized propositions and a classification scheme for theories].

@ __Equivalence of theories__: Weatherall a1411 [and Newtonian gravity vs geometrized Newtonian gravity]; Barrett & Halvorson a1506 [definitional, Morita and categorical equivalence]; > s.a. Einstein Algebras.

@ __Relationships, types__: Baumann PhSc(05)jan
[re "better theories"]; Page a0712-proc [Bayesian
meta-theories, "sensible quantum mechanics", and quantum cosmology]; Van Camp SHPMP(11) [types of theories, explanation, and quantum mechanics]; Bény & Osborne a1403 [renormalization and effectively indistinguishable microscopic theories]; Oriti a1705-in [principle of proliferation of theories, and non-empirical theory assessment].

> __Related topics__:
see category theory and physics; Deformations; Theory [theory space].

**Structure of Theories** > s.a. computation; Explanations; history of physics; Interpretation
of a Theory; logic; Physical Laws.

* __Idea__: A physical theory consists of a mathematical formalism and an interpretation (definition of symbols, measurement assignments, concepts and principles, ontology).

* __Method__: Knowledge in
physics comes from interplay of theory and experiment; In the theory, one simplifies
systems and considers simple,
closed ones, supposes that observers are not important, identifies the simplest
measurements,
e.g., *m*, *l*, *t*, and sets up the mathematical description of the models;
Later, one tries to get rid of ideal elements by making them dynamical, or
giving a natural choice (Leibniz's principle of sufficient reason).

* __Ideal elements__: Formal
element which are contingent (a different choice is possible) and play a role
in the evolution of the physical degrees of freedom but
are non-dynamical, absolute;
__Examples__: Correspondence observables-operators,
time, inner product in insert; Number of spacetime dimensions, topology in
general relativity; Preferred class of inertial observers in pre-general-relativity
physics; >
s.a. general relativity; inertia.

* __Structure__: A theory
has a lattice of propositions (including assumptions), structural equations
and equations
of other origin, about some structure which constitutes a model (or metaphor)
for the systems under consideration [P Duhem considered the metaphor itself
as an educational tool, not a part of science, while J Bernstein and J Ziman
view them as an integral part of science, @ pw(00)nov];
As with any metaphor, a key issue is to establish how far each theory can go;
Theories can be regarded as organized into hierarchies in
many cases, with higher levels sometimes called 'paradigms' and lower-level
models encoding more specific or concrete hypotheses.

* __Evolution__: In the hierarchical
point of view, higher-level theory change may be driven by the impact of evidence
on lower levels.

@ __Books__: Holton & Roller 58; Ripley 64 [simple]; Cooper 68; Tonti 76; Shive & Weber
82 [II]; Sklar 85; Pavšič 01-gq/06 [overview]; Helland 09.

@ __General references__: Caianello RNC(92);
Foy qp/00 [logical
basis]; Tarantola & Mosegaard mp/00 [use
of inference]; Fellman et al a1001 [importance
of discourse]; Henderson et al PhSc(10)apr
[hierarchical Bayesian models]; Székely in(11)-a1101 [why-type questions]; Vignale 11; Fayer hp(12)jan [popular misunderstanding of the meaning of the word]; Weatherall a1206-ch ["puzzleball view", theories as networks of mutually interdependent principles and assumptions]; Wallace a1306 [inferential vs dynamical conceptions]; Coecke et al a1409 [mathematical theory of resources]; Curiel a1603 [kinematics and dynamics]; in Krizek a1707 [classification scheme].

@ __Evolution of theories__: Lederer a1510 [conflicting theories and scientific pluralism, example of high-temperature superconductivity].

**Construction of Theories** > s.a. Axioms
for Physical Theories; Models; Operationalism.

* __Approaches__: The main
distinction is between operational and deductive ones; The danger with an operational
approach is that one may get stuck with
technical difficulties and make little progress; The danger with
a deductive
approach is that progress in the right direction is more likely
to be impeded by idealizations.

* __Remark__: It is important
to understand which are the right variables; Which questions we can ask and
which make no sense (see Newton's laws, Einstein's
relativity, Bohr-Heisenberg principle).

@ __References__: Corry 04 [Hilbert and the axiomatization of physics]; Emch SHPMP(07);
Moldoveanu a1001-FQXi
[complete axiomatization of physics as an achievable goal]; Nguyen et al a1712 [the need for surplus structure].

> __Specific theories__:
see cosmology; particle
physics; etc.

**Criteria for Physical Theories** > s.a. Consistency;
Fine Tuning; Naturalness; Occam's Razor; paradigms; Simplicity.

* __Traditional__: Adequacy, i.e., verifiability / falsifiability, and good agreement with
experiment.

* __Stability under variations__: Often assumed as a dogma and not discussed
explicitly.

* __Also__: Accuracy, elegance
and simplicity (XX century aesthetic judgment), scope, symmetries.

* __Verifiability / Falsifiability__: 2015, Some theorists have called for a relaxation of the requirement for a scientific theory, in particular proponents of string theory and multiverse theory.

* __Beauty__: The sense
of what's natural or elegant is subjective, as can be seen in people's opinions
of various proposed explanations of the apparent cosmological acceleration.

* __Examples__: Issue of
whether Copernicus' theory of the Solar System was more "harmonious" and simpler
than Ptolemy's; Interpretation of positron in Dirac theory, according to "truth" of
knowledge at the time it was the proton (Dirac), according to "beauty" it
was not (Weyl).

* __On non-observable quantities__:
Around 1926, W Heisenberg advocated using only directly observable quantities
in the theory; The point of view was picked up by G Chew in his S-matrix approach
to quantum field theory.

@ __ General references__: Einstein JFI(36);
Mermin PT(00)mar
[elegance]; Norton SHPMP(00)
[Einstein and simplicity];
Falmagne FP(04) [meaningfulness + order-invariance];
Wells a1211 [consistency, and effective field theories];
Scorzato Syn(13)-a1402 [simplicity].

@ __Considerations on different types of theories__: Nelson AS(85);
Von Weizsäcker 85; Cushing 90; Tavakol BJPS(91)
[fragility]; Elby et al FP(93);
Barrett PhSc(03)dec
[our best physical theories are false]; Streater 07 ["lost causes"].

@ __Verifiability / Falsifiability__: Scott et al a1504 [giving up Falsifiability :-)]; Nemenman a1505, PT(15)oct [quantifying]; Hossenfelder blog(14)jul, Woit blog (14)jul, Ellis & Silk Nat(14)dec, blog sa(15)dec [defense of falsifiability]; Rovelli a1609-conf, Dawid a1702-ch [on non-empirical confirmation]; Curiel a1804 [Newtonian abduction].

@ __Stability__: Bouligand ARB(35);
Destouches ARB(35); Duhem 54;
Thom 67;
Vilela Mendes JPA(94).

@ __Beauty__: McAllister AS(98);
Tsallis PhyA(04) [beauty, truth and new ideas];
Martens SHPSA(09)
[beauty and simplicity as metaphors, Copernican theory];
Vignale 11;
Spratt & Elgammal a1410;
Wilczek 15;
Deser a1706 [elegance/simplicity and supergravity].

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send feedback and suggestions to bombelli at olemiss.edu – modified 22 apr 2018