Editing Scientific method (section)

==Heuristics==

=== Confirmation theory ===

During the course of history, one theory has succeeded another, and some have suggested further work while others have seemed content just to explain the phenomena. The reasons why one theory has replaced another are not always obvious or simple. The philosophy of science includes the question: ''What criteria are satisfied by a 'good' theory''. This question has a long history, and many scientists, as well as philosophers, have considered it. The objective is to be able to choose one theory as preferable to another without introducing [[cognitive bias]].<ref name=Kuhn>
[[Thomas Kuhn]] formally stated this need for the "norms for rational theory choice". One of his discussions is reprinted in {{cite book |title=The Road since Structure: Philosophical Essays, 1970–1993 |author=Thomas S Kuhn |chapter-url=https://books.google.com/books?id=sXufWLnPp94C&pg=PA208 |pages=208 ''ff'' |chapter=Chapter 9: Rationality and Theory Choice  |editor=James Conant, John Haugeland |edition=2nd |publisher=University of Chicago Press |isbn=0226457990 |date=2002-11-01}}
</ref> Though different thinkers emphasize different aspects,{{efn-lg|Differing accounts of which elements constitute a ''good theory'': 
* Kuhn (1977) identified: accuracy; consistency (both internal and with other relevant currently accepted theories); scope (its consequences should extend beyond the data it is required to explain); simplicity (organizing otherwise confused and isolated phenomena); fruitfulness (for further research);<ref>Kuhn, T.S. (1977) Objectivity, Value Judgment, and Theory Choice. In: Kuhn, T.S., Ed., The Essential Tension—Selected Studies in Scientific Tradition and Change, The University of Chicago Press, Chicago, 320–339.</ref>
* Colyvan (2001) listed simplicity/parsimony, unificatory/explanatory power, boldness/fruitfulness, and elegance;<ref name=Colyvan>
{{cite book |title=The Indispensability of Mathematics |author=Mark Colyvan |url=https://books.google.com/books?id=OBs-TSFopLkC&pg=PA78 |pages=78–79 |isbn=0195166612 |year=2001 |publisher=Oxford University Press}}
</ref>
* Weinert (2004) noted the recurring theme of invariance;{{efn-lg|name=invariantTheme|Friedel Weinert in ''The Scientist as Philosopher'' (2004) noted the theme of invariance as a fundamental aspect of a scientific account of reality in many writings from around 1900 onward, such as works by [[Henri Poincaré]] (1902), [[Ernst Cassirer]] (1920), [[Max Born]] (1949 and 1953), [[Paul Dirac]] (1958), [[Olivier Costa de Beauregard]] (1966), [[Eugene Wigner]] (1967), [[Lawrence Sklar]] (1974), [[Michael Friedman (philosopher)|Michael Friedman]] (1983), [[John D. Norton]] (1992), [[Nicholas Maxwell]] (1993), [[Alan Cook (physicist)|Alan Cook]] (1994), [[Alistair Cameron Crombie]] (1994), [[Margaret Morrison (philosopher)|Margaret Morrison]] (1995), [[Richard Feynman]] (1997), [[Robert Nozick]] (2001), and [[Tim Maudlin]] (2002).<ref name="Weinert 2004">{{Cite book |last=Weinert |first=Friedel |title=The Scientist as Philosopher: Philosophical Consequences of Great Scientific Discoveries |date=2004 |publisher=[[Springer-Verlag]] |isbn=3540205802 |location=Berlin; New York |pages=62–74 (72) |chapter=Invariance and reality |doi=10.1007/b138529 |oclc=53434974|url=https://cds.cern.ch/record/828852 }}</ref> — [[David Deutsch|Deutsch]] in a 2009 TED talk proclaimed that "the search for hard-to-vary explanations is the origin of all progress".<ref name="DD_TED" />}}
* [[Stephen Hawking|Hawking]] (2010): simplicity/parsimony, unificatory/explanatory power, and elegance, but did not mention fruitfulness.<ref name=Hawking>
{{cite book |title=The Grand Design |pages=51–52 |chapter=What is reality? |isbn=978-0553907070 |year=2010 |publisher=Random House Digital, Inc |chapter-url=https://books.google.com/books?id=RoO9jkV-yzIC&pg=PA51 |author1=Stephen Hawking |author2=Leonard Mlodinow }} See also: [[model-dependent realism]].
</ref> 
}} a good theory:

*is accurate ''(the trivial element)'';
*is consistent, both internally and with other relevant currently accepted theories;
*has explanatory power, meaning its consequences extend beyond the data it is required to explain;
*has unificatory power; as in its organizing otherwise confused and isolated phenomena
*and is fruitful for further research.

In trying to look for such theories, scientists will, given a lack of guidance by empirical evidence, try to adhere to:

*parsimony in causal explanations 
*and look for invariant observations.
*Scientists will sometimes also list the very subjective criteria of "formal elegance" which can indicate multiple different things.

The goal here is to make the choice between theories less arbitrary. Nonetheless, these criteria contain subjective elements, and should be considered [[heuristics]] rather than a definitive.{{efn-lg|name=Pars_and_El|...Hawking & Mlodinow on criteria for a good theory: "The above criteria are obviously subjective. Elegance, for example, is not something easily measured, but it is highly prized among scientists." The idea of 'too baroque' is connected to 'simplicity': "a theory jammed with fudge factors is not very elegant. To paraphrase Einstein, a theory should be as simple as possible, but not simpler".<ref name=Hawking/> See also:<ref name=Baker/>}} Also, criteria such as these do not necessarily decide between alternative theories. Quoting [[Alexander Bird|Bird]]:<ref name=Bird>
{{cite encyclopedia |date= Aug 11, 2011 |author=Bird, Alexander |title=§4.1 Methodological Incommensurability |encyclopedia=The Stanford Encyclopedia of Philosophy (Spring 2013 Edition) |editor=Edward N. Zalta |url= http://plato.stanford.edu/entries/thomas-kuhn/#4.1}}
</ref>

{{blockquote|"[Such criteria] cannot determine scientific choice. First, which features of a theory satisfy these criteria may be disputable (''e.g.'' does simplicity concern the ontological commitments of a theory or its mathematical form?). Secondly, these criteria are imprecise, and so there is room for disagreement about the degree to which they hold. Thirdly, there can be disagreement about how they are to be weighted relative to one another, especially when they conflict."}}

It also is debatable whether existing scientific theories satisfy all these criteria, which may represent goals not yet achieved. For example, explanatory power over all existing observations is satisfied by no one theory at the moment.<ref name=Realism>
See {{cite book |title=The Grand Design |author1=Stephen Hawking |author2=Leonard Mlodinow |url=https://books.google.com/books?id=RoO9jkV-yzIC&pg=PA9 |page=8 |quote=It is a whole family of different theories, each of which is a good description of observations only in some range of physical situations...But just as there is no map that is a good representation of the earth's entire surface, there is no single theory that is a good representation of observations in all situations. |isbn=978-0553907070 |year=2010 |publisher=Random House Digital, Inc}}
</ref><ref name=Davies>
{{cite web |title=Epistemological pluralism |author=E Brian Davies |url=http://philsci-archive.pitt.edu/3083/1/EP3single.doc |work=PhilSci Archive |year=2006 | page=4 | quote=Whatever might be the ultimate goals of some scientists, science, as it is currently practised, depends on multiple overlapping descriptions of the world, each of which has a domain of applicability. In some cases this domain is very large, but in others quite small.}}
</ref>

==== Parsimony ====

The [[wikt:desiderata|desiderata]] of a "good" theory have been debated for centuries, going back perhaps even earlier than [[Occam's razor]],{{efn|Occam's razor, sometimes referred to as "ontological parsimony", is roughly stated as: Given a choice between two theories, the simplest is the best. This suggestion commonly is attributed to William of Ockham in the 14th-century, although it probably predates him.<ref name=Baker/>}} which is often taken as an attribute of a good theory. Science tries to be simple. When gathered data supports multiple explanations, the most simple explanation for phenomena or the most simple formation of a theory is recommended by the principle of parsimony.{{sfnp|Gauch|2003|p=269}} Scientists go as far as to call simple proofs of complex statements ''beautiful''.

{{Blockquote| quote=We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.|source=Isaac Newton, ''Philosophiæ Naturalis Principia Mathematica (1723 [3rd ed.])''<ref name="principia" />}}

The concept of parsimony should not be held to imply complete frugality in the pursuit of scientific truth. The general process starts at the opposite end of there being a vast number of potential explanations and general disorder. An example can be seen in [[Paul Krugman]]'s process, who makes explicit to "dare to be silly". He writes that in his work on new theories of international trade he [[literature review|reviewed prior work]] with an open frame of mind and broadened his initial viewpoint even in unlikely directions. Once he had a sufficient body of ideas, he would try to simplify and thus find what worked among what did not. Specific to Krugman here was to "question the question". He recognised that prior work had applied erroneous models to already present evidence, commenting that "intelligent commentary was ignored".{{refn | name=Krugman|{{cite journal | last=Krugman | first=Paul | title=How I Work | journal=The American Economist | publisher=Sage Publications, Inc. | volume=37 | issue=2 | year=1993 | issn=0569-4345 | jstor=25603965 | pages=25–31 | doi=10.1177/056943459303700204 }} ...I have already implicitly given my four basic rules for research. Let me now state them explicitly, then explain. Here are the rules: 
# Listen to the Gentiles
# Question the question
# Dare to be silly
# Simplify, simplify
<!--credit to q:Science-->}} Thus touching on the need to bridge the common bias against other circles of thought.{{sfnp | Fleck | 1979 | p=27}}

==== Elegance ====

Occam's razor might fall under the heading of "simple elegance", but it is arguable that ''parsimony'' and ''elegance'' pull in different directions. Introducing additional elements could simplify theory formulation, whereas simplifying a theory's ontology might lead to increased syntactical complexity.<ref name=Baker>
{{cite encyclopedia |author=Baker, Alan |title=Simplicity |encyclopedia=The Stanford Encyclopedia of Philosophy (Summer 2011 Edition) |editor=Edward N. Zalta |url=http://plato.stanford.edu/archives/sum2011/entries/simplicity/ |date=Feb 25, 2010}}
</ref>

Sometimes ad-hoc modifications of a failing idea may also be dismissed as lacking "formal elegance". This appeal to what may be called "aesthetic" is hard to characterise, but essentially about a sort of familiarity. Though, argument based on "elegance" is contentious and over-reliance on familiarity will breed stagnation.<ref name=Colyvan/>

==== Invariance ====

Principles of invariance have been a theme in scientific writing, and especially physics, since at least the early 20th century.{{efn-lg|name=invariantTheme}} The basic idea here is that good structures to look for are those independent of perspective, an idea that has featured earlier of course for example in [[Mill's Methods]] of difference and agreement—methods that would be referred back to in the context of contrast and invariance.<ref name="O&H 1995">{{cite journal | last1=van Overwalle | first1=Frank J. | last2=Heylighen | first2=Francis P. | title=Relating covariation information to causal dimensions through principles of contrast and invariance | journal=European Journal of Social Psychology | volume=25 | issue=4 | date=1995 | issn=0046-2772 | doi=10.1002/ejsp.2420250407 | pages=435–455 | url=http://pcp.vub.ac.be/Papers/Contrast&Invariance.html| url-access=subscription }}</ref> But as tends to be the case, there is a difference between something being a basic consideration and something being given weight. Principles of invariance have only been given weight in the wake of Einstein's theories of relativity, which reduced everything to relations and were thereby fundamentally unchangeable, unable to be varied.<ref name="Wigner1967"/>{{efn |name=WeinertEddingtonEinstein}} As [[David Deutsch]] put it in 2009: "the search for hard-to-vary explanations is the origin of all progress".<ref name="DD_TED">{{Cite AV media | time=15:05min | url=https://www.ted.com/talks/david_deutsch_a_new_way_to_explain_explanation | title=A new way to explain explanation |date=October 2009 | last=Deutsch | first=David | publisher=TED talk | access-date=16 September 2018 | archive-date=4 November 2018 | archive-url=https://web.archive.org/web/20181104012430/https://www.ted.com/talks/david_deutsch_a_new_way_to_explain_explanation |url-status=live }} Also available from [https://www.youtube.com/watch?v=folTvNDL08A YouTube] {{Webarchive|url=https://web.archive.org/web/20221108112725/https://www.youtube.com/watch?v=folTvNDL08A |date=8 November 2022 }}.</ref>

An example here can be found in one of [[Einstein's thought experiments#Falling painters and accelerating elevators|Einstein's thought experiments]]. The one of a lab suspended in empty space is an example of a useful invariant observation. He imagined the absence of gravity and an experimenter free floating in the lab. — If now an entity pulls the lab upwards, accelerating uniformly, the experimenter would perceive the resulting force as gravity. The entity however would feel the work needed to accelerate the lab continuously.{{efn| name=WeinertEddingtonEinstein |[[Arthur Eddington]], 1920: "The relativity theory of physics reduces everything to relations; that is to say, it is structure, not material, which counts." — Weinert, giving the Einstein example and quoting: "Eddington, Space, Time and Gravitation (1920), 197"<ref name="Weinert 2004"/>}} Through this experiment Einstein was able to equate gravitational and inertial mass; something unexplained by Newton's laws, and an early but "powerful argument for a generalised postulate of relativity".<ref name="Einstein1916">{{cite book|last1=Einstein|first1=Albert|title=Relativity: The Special and the General Theory|date=1961|publisher=Crown Publishers, Inc.|location=New York|isbn=978-0-517-88441-6|edition=15th|pages=75–79}}</ref>

{{Blockquote|quote=The feature, which suggests reality, is always some kind of invariance of a structure independent of the aspect, the projection.|source=[[Max Born]], 'Physical Reality' (1953), 149 — as quoted by Weinert (2004)<ref name="Weinert 2004"/>}}

The discussion on [[invariance (physics)|invariance]] in physics is often had in the more specific context of [[symmetry (physics)|symmetry]].<ref name="Wigner1967">{{cite book | last=Wigner | first=Eugene Paul | date=1967 | title=Symmetries and reflections | publisher=Indiana University Press | page=15}} : Wigner also differentiates between geometrical invariance principles, and the "new" ones that arose in the wake of Einstein's theories of relativity that he calls dynamic invariance principles.</ref> The Einstein example above, in the parlance of Mill would be an agreement between two values. In the context of invariance, it is a variable that remains unchanged through some kind of transformation or change in perspective. And discussion focused on symmetry would view the two perspectives as systems that share a relevant aspect and are therefore symmetrical.

Related principles here are [[falsifiability]] and [[testability]]. The opposite of something being ''hard-to-vary'' are theories that resist falsification—a frustration that was expressed colourfully by [[Wolfgang Pauli]] as them being "[[not even wrong]]". The importance of scientific theories to be falsifiable finds especial emphasis in the philosophy of Karl Popper. The broader view here is testability, since it includes the former and allows for additional practical considerations.<ref>{{cite book |last=Keuth |first=Herbert |author-link=:de:Herbert Keuth |chapter=From falsifiability to testability |title=The philosophy of Karl Popper |date=2004 |orig-year=Published in German 2000 |edition=1st English |location=Cambridge, UK; New York |publisher=[[Cambridge University Press]] |pages=[https://books.google.com/books?id=wxzoBfQYhYAC&pg=PA48 48–49] |chapter-url=https://books.google.com/books?id=wxzoBfQYhYAC&pg=PA48 |isbn=9780521548304 |oclc=54503549 |quote=Consequently, the ''universal statements'', which are contradicted by the basic statements, ''are not strictly refutable''. Like singular statements and probability statements, they are empirically testable, but their tests do not have certain, definite results, do not result in strict verification or falsification but only in temporary acceptance or rejection.}}</ref><ref name="l921">{{cite book | last=Krantz | first=S.G. | title=Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical | publisher=Mathematical Association of America | series=MAA spectrum | year=2005 | isbn=978-0-88385-554-6 | url=https://books.google.com/books?id=8mBdvAjk_gQC | access-date=29 August 2024 | page=194}}</ref>