Editing Scientific theory (section)

==About theories==

===Theories as axioms===
The [[logical positivism|logical positivists]] thought of scientific theories as statements in a [[formal language]]. [[First-order logic]] is an example of a formal language. The logical positivists envisaged a similar scientific language. In addition to scientific theories, the language also included observation sentences ("the sun rises in the east"), definitions, and mathematical statements. The phenomena explained by the theories, if they could not be directly observed by the senses (for example, [[atom]]s and [[radio waves]]), were treated as theoretical concepts. In this view, theories function as [[axioms]]: predicted observations are derived from the theories much like [[theorems]] are derived in [[Euclidean geometry]]. However, the predictions are then tested against reality to verify the predictions, and the "axioms" can be revised as a direct result.{{citation needed|date=March 2023}}

The phrase "[[received view of theories|the received view of theories]]" is used to describe this approach. Terms commonly associated with it are "[[linguistic]]" (because theories are components of a language) and "[[syntactic]]" (because a language has rules about how symbols can be strung together). Problems in defining this kind of language precisely, e.g., are objects seen in microscopes observed or are they theoretical objects, led to the effective demise of logical positivism in the 1970s.{{citation needed|date=March 2023}}

===Theories as models===
{{main|Scientific model}}

The [[semantic view of theories]], which identifies scientific theories with [[scientific model|models]] rather than [[proposition]]s, has replaced the received view as the dominant position in theory formulation in the philosophy of science.<ref>{{cite journal |last1=Suppe |first1=Frederick |year=1998 |title=Understanding Scientific Theories: An Assessment of Developments, 1969–1998 |journal=Philosophy of Science |volume=67 |pages=S102–S115 |url=https://www.princeton.edu/~hhalvors/teaching/phi520_f2012/Suppe_2000.pdf |access-date=14 February 2013 |doi=10.1086/392812|s2cid=37361274 }}</ref><ref>{{cite journal |last1=Halvorson |first1=Hans |year=2012 |title=What Scientific Theories Could Not Be |journal=Philosophy of Science |volume=79 |issue=2 |pages=183–206 |url=https://www.princeton.edu/~hhalvors/teaching/phi520_f2012/halvorson2012.pdf |access-date=14 February 2013 |doi=10.1086/664745|citeseerx=10.1.1.692.8455 |s2cid=37897853 }}</ref><ref>{{cite journal |last1=Frigg |first1=Roman |year=2006 |title=Scientific Representation and the Semantic View of Theories |journal=Theoria |volume=55 |issue=2 |pages=183–206 |url=http://philsci-archive.pitt.edu/2926/1/Scientific_Representation.pdf |access-date=14 February 2013}}</ref> A model is a logical framework intended to represent reality (a "model of reality"), similar to the way that a map is a graphical model that represents the territory of a city or country.<ref>Hacking, Ian (1983). ''Representing and Intervening. Introductory Topics in the Philosophy of Natural Science''. Cambridge University Press.</ref><ref>Box, George E.P. & Draper, N.R. (1987). ''Empirical Model-Building and Response Surfaces.'' Wiley. p. 424</ref>

[[File:Perihelio.svg|thumb|right|[[Apsidal precession|Precession]] of the [[perihelion]] of [[Mercury (planet)|Mercury]] (exaggerated). The deviation in Mercury's position from the Newtonian prediction is about 43 [[Second of arc|arc-seconds]] (about two-thirds of 1/60 of a [[Degree (angle)|degree]]) per century.<ref>{{cite journal|author1=Lorenzo Iorio|title=On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging|doi=10.1051/0004-6361:20047155|year=2005|journal=Astronomy and Astrophysics|volume=433|issue=1|pages=385–93|arxiv=gr-qc/0406041|bibcode=2005A&A...433..385I|s2cid=1546486}}</ref><ref>Myles Standish, Jet Propulsion Laboratory (1998)</ref>]]

In this approach, theories are a specific category of models that fulfil the necessary criteria (see [[#Characteristics of theories|above]]). One can use language to describe a model; however, the theory is the model (or a collection of similar models), and not the description of the model. A model of the [[Solar System]], for example, might consist of abstract objects that represent the Sun and the planets. These objects have associated properties, e.g., positions, velocities, and masses. The model parameters, e.g., Newton's Law of Gravitation, determine how the positions and velocities change with time. This model can then be tested to see whether it accurately predicts future observations; astronomers can verify that the positions of the model's objects over time match the actual positions of the planets. For most planets, the Newtonian model's predictions are accurate; for [[Mercury (planet)|Mercury]], it is slightly inaccurate and the model of [[general relativity]] must be used instead.{{citation needed|date=March 2023}}

The word "[[semantic]]" refers to the way that a model represents the real world. The representation (literally, "re-presentation") describes particular aspects of a phenomenon or the manner of interaction among a set of phenomena. For instance, a scale model of a house or of the Solar System is clearly not an actual house or an actual Solar System; the aspects of an actual house or the actual Solar System represented in a scale model are, only in certain limited ways, representative of the actual entity. A scale model of a house is not a house; but to someone who wants to ''learn about'' houses, analogous to a scientist who wants to understand reality, a sufficiently detailed scale model may suffice.

====Differences between theory and model====
{{main|Conceptual model}}
Several commentators<ref>For example, Reese & Overto (1970); Lerner (1998); also Lerner & Teti (2005), in the context of modeling human behavior.</ref> have stated that the distinguishing characteristic of theories is that they are explanatory as well as descriptive, while models are only descriptive (although still predictive in a more limited sense). Philosopher [[Stephen Pepper]] also distinguished between theories and models and said in 1948 that general models and theories are predicated on a "root" metaphor that constrains how scientists theorize and model a phenomenon and thus arrive at testable hypotheses.{{citation needed|date=March 2023}}

Engineering practice makes a distinction between "mathematical models" and "physical models"; the cost of fabricating a physical model can be minimized by first creating a mathematical model using a computer software package, such as a [[computer-aided design]] tool. The component parts are each themselves modelled, and the fabrication tolerances are specified. An [[exploded view drawing]] is used to lay out the fabrication sequence. Simulation packages for displaying each of the subassemblies allow the parts to be rotated, and magnified, in realistic detail. Software packages for creating the bill of materials for construction allow subcontractors to specialize in assembly processes, which spreads the cost of manufacturing machinery among multiple customers. See: [[Computer-aided engineering]], [[Computer-aided manufacturing]], and [[3D printing]]{{citation needed|date=March 2023}}

===Assumptions in formulating theories===
An assumption (or [[axiom]]) is a statement that is accepted without evidence. For example, assumptions can be used as premises in a logical argument. [[Isaac Asimov]] described assumptions as follows:

<blockquote>...it is incorrect to speak of an assumption as either true or false, since there is no way of proving it to be either (If there were, it would no longer be an assumption). It is better to consider assumptions as either useful or useless, depending on whether deductions made from them correspond to reality...Since we must start somewhere, we must have assumptions, but at least let us have as few assumptions as possible.<ref>Isaac Asimov, ''Understanding Physics'' (1966) pp. 4–5.</ref></blockquote>

Certain assumptions are necessary for all empirical claims (e.g. the assumption that [[reality]] exists). However, theories do not generally make assumptions in the conventional sense (statements accepted without evidence). While assumptions are often incorporated during the formation of new theories, these are either supported by evidence (such as from previously existing theories) or the evidence is produced in the course of validating the theory. This may be as simple as observing that the theory makes accurate predictions, which is evidence that any assumptions made at the outset are correct or approximately correct under the conditions tested.{{citation needed|date=March 2023}}

Conventional assumptions, without evidence, may be used if the theory is only intended to apply when the assumption is valid (or approximately valid). For example, the [[special theory of relativity]] assumes an [[inertial frame of reference]]. The theory makes accurate predictions when the assumption is valid, and does not make accurate predictions when the assumption is not valid. Such assumptions are often the point with which older theories are succeeded by new ones (the [[general theory of relativity]] works in non-inertial reference frames as well).

The term "assumption" is actually broader than its standard use, etymologically speaking. The Oxford English Dictionary (OED) and online Wiktionary indicate its Latin source as ''assumere'' ("accept, to take to oneself, adopt, usurp"), which is a conjunction of ''ad-'' ("to, towards, at") and ''sumere'' (to take). The root survives, with shifted meanings, in the Italian ''assumere'' and Spanish ''sumir''. The first sense of "assume" in the OED is "to take unto (oneself), receive, accept, adopt". The term was originally employed in religious contexts as in "to receive up into heaven", especially "the reception of the Virgin Mary into heaven, with body preserved from corruption", (1297 CE) but it was also simply used to refer to "receive into association" or "adopt into partnership". Moreover, other senses of assumere included (i) "investing oneself with (an attribute)", (ii) "to undertake" (especially in Law), (iii) "to take to oneself in appearance only, to pretend to possess", and (iv) "to suppose a thing to be" (all senses from OED entry on "assume"; the OED entry for "assumption" is almost perfectly symmetrical in senses). Thus, "assumption" connotes other associations than the contemporary standard sense of "that which is assumed or taken for granted; a supposition, postulate" (only the 11th of 12 senses of "assumption", and the 10th of 11 senses of "assume").