11.21 What Differentiates Science from Beliefs?

11.21.1 What is a Scientific Theory?
Generally, a scientific theory is constructed from elementary theorems that consist in empirical data about observable phenomena. A scientific theory is used as a plausible general principle, or body of principles, offered to explain a phenomenon.

A scientific theory is a deductive theory in that its content is based on some formal system of logic, and that some of its elementary theorems are taken as axioms. In a deductive theory, any sentence which is a logical consequence of one or more of the axioms is also a sentence of that theory.

Theories whose subject matter consists not in empirical data, but rather in ideas are in the realm of philosophical theories, are in contrast with scientific theories. At least some of the elementary theorems of a philosophical theory are statements whose truth cannot necessarily be scientifically tested through empirical observation.

11.21.1.1 Theories as Models
Theories are constructed to explain, predict, and master phenomena. A scientific theory can be thought of as a model of reality, and its statements as axioms of some axiomatic system. The aim of this construction is to create a formal system for which reality is the only model.

11.21.1.2 Description and Prediction
Stephen Hawking in “A Brief History of Time” states, “A theory is a good theory if it satisfies two requirements:

• It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements
• It must make definite predictions about the results of future observations.”

He goes on to state, “Any physical theory is always provisional, in the sense that it is only a hypothesis; you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.”

11.21.1.3 Assumptions to Formulate a Theory
In “Understanding Physics”, Asimov spoke of theories as “arguments” where one deduces a “scheme,” or model. Arguments, or theories, always begin with some premises —”arbitrary elements” as Hawking calls them— which are here described as “assumptions”. An assumption according to Asimov is… something accepted without proof, and it is incorrect to speak of an assumption as either true or false, since there is no way of proving it to be either. It is better to consider assumptions as either useful or useless, depending on whether deductions made from them corresponded to reality.

11.21.1.4 Examples

Special Theory of Relativity
Albert Einstein put forth his “Special Theory of Relativity” by taking two phenomena that had been observed —that the “addition of velocities” is valid (Galilean transformation), and that light did not appear to have an “addition of velocities” (Michelson-Morley experiment). He assumed both observations to be correct, and formulated his theory, based on these assumptions, by simply altering the Galilean transformation to accommodate the lack of addition of velocities with regard to the speed of light. The model created in his theory is, therefore, based on the assumption that the speed of light is a constant.

Ptolemy
In Ptolemy’s planetary model, the earth was at the centre, the planets and the sun made circular orbits around the earth, and the stars were on a sphere outside of the orbits of the planet and the earth. Retrograde motion of the planets was explained by smaller circular orbits of individual planets. Mathematical calculations could be made that predicted, to a great degree of accuracy, where the planets would be. His model of the planetary system survived for over 1500 years until the time of Copernicus. In conclusion, a theory is a “model of reality” that explains certain scientific facts; yet the theory may not be a satisfactory picture of reality. Another, more acceptable, theory can later replace the previous model, as when the Copernican theory replaced the Ptolemaic theory. Or a new theory can be used to modify an older theory as when Einstein modified Newtonian mechanics (which is still used for computing planetary orbits or modelling spacecraft trajectories) with his theories of relativity.

11.21.2 Differences Between Theory and Model
Central to the nature of models, from general models to scale models, is the use of representation to describe 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 a solar system is clearly not an actual house or an actual solar system; the aspects of an actual house or an actual solar system represented in a scale model are, only in certain limited ways, representative of the actual entity. The important difference between theories and models is that the first is explanatory as well as descriptive, while the second is only descriptive.

11.21.3 Characteristics
In a famous comment on a paper someone showed him, Wolfgang Pauli captured the difference between scientific and unscientific thought by saying, “This isn’t right. It’s not even wrong.”

11.21.4 Criterions

11.21.4.1 Essential Criteria
The defining characteristic of a scientific theory is that it makes falsifiable or testable predictions. The relevance and specificity of those predictions determine how potentially useful the theory is. A would-be theory that makes no predictions that can be observed is not a useful theory. Predictions not sufficiently specific to be tested are similarly not useful. In both cases, the term “theory” is inapplicable.

In practice a body of descriptions of knowledge is usually only called a theory once it has a minimum empirical basis, according to certain criteria:

• It is consistent with pre-existing theory
• It is supported by many strands of evidence ensuring it is probably a good approximation, if not totally correct.

11.21.4.2 Non-Essential Criteria
Additionally, a theory is generally only taken seriously if:

• It is tentative, correctable, and dynamic in allowing for changes as new facts are discovered, rather than asserting certainty
• It is the most parsimonious explanation, sparing in proposed entities or explanations —commonly referred to as passing the Occam’s razor test.

Theories do not have to be perfectly accurate to be scientifically useful. The predictions made by Classical mechanics are known to be inaccurate, but they are sufficiently good approximations in most circumstances. For this reason they are still very useful and widely used in place of more accurate but mathematically difficult theories.

11.21.4.3 Criterion for Scientific Status
Karl Popper described the characteristics of a scientific theory as follows:It is easy to obtain confirmations, or verifications, for nearly every theory

1. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory —an event which would have refuted the theory
2. Every “good” scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is
3. A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory but a vice
4. Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability
5. Confirming evidence should not count except when it is the result of a genuine test of the theory
6. Some genuinely testable theories, when found to be false, are still upheld by their admirers —for example by introducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation
7. One can sum up all this by saying that according to Popper, the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.

According to Kitcher, good scientific theories must have three features:

1. Unity: “A science should be unified. Good theories consist of just one problem-solving strategy, or a small family of problem-solving strategies, that can be applied to a wide range of problems”
2. Fecundity: “A great scientific theory, like Newton’s, opens up new areas of research…. Because a theory presents a new way of looking at the world, it can lead us to ask new questions, and so to embark on new and fruitful lines of inquiry
3. Auxiliary hypotheses that are independently testable: “An auxiliary hypothesis ought to be testable independently of the particular problem it is introduced to solve, independently of the theory it is designed to save”.

11.21.4.4 In Physics
In physics the term theory is used for a mathematical framework —derived from a small set of basic postulates— which is capable of producing experimental predictions for a given category of physical systems.

11.21.5 Pedagogical Definition
A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are reliable accounts of the real world.

11.21.6 The Term Theoretical
The term “theoretical” is sometimes informally used instead of “hypothetical” to describe a result that is predicted by theory but has not yet been adequately tested by observation or experiment. It is not uncommon for a theory to produce predictions that are later confirmed, or proven incorrect by experiment. A prediction proved incorrect by experiment demonstrates that the hypothesis is invalid. This either means the theory is incorrect, or the experimental conjecture was wrong, and the theory did not predict the hypothesis.

11.21.7 Scientific Laws
Scientific laws are similar to scientific theories in that they are principles that can be used to predict the behaviour of the natural world. Both scientific laws and scientific theories are typically well-supported by observations and/or experimental evidence. Usually scientific laws refer to rules for how nature will behave under certain conditions. Scientific theories are explanations of how nature works, and why it exhibits certain characteristics.

11.21.8 Arguments Relating to the Definition and Limits of Science
Critiques, such as those based on the distinction between theory and fact, are often levelled against unifying concepts within scientific disciplines. Principles such as uniformitarianism, Occam’s Razor or parsimony, and the Copernican principle are claimed to be the result of a bias within science toward philosophical naturalism, which is equated by many creationists with atheism. In countering this claim, philosophers of science use the term methodological naturalism to refer to the long standing convention in science of the scientific method. The methodological assumption is that observable events in nature are explained only by natural causes, without assuming the existence or non-existence of the supernatural. Therefore supernatural explanations for such events are outside the realm of science. Creationists claim that supernatural explanations should not be excluded, and that scientific work is paradigmatically close-minded.

11.21.9 Definitions

• Fact: In science, an observation that has been repeatedly confirmed and, for all practical purposes, is accepted as “true.” Truth in science, however, is never final, and what is accepted as a fact today may be modified or even discarded tomorrow
• Hypothesis: A tentative statement about the natural world leading to deductions that can be tested. If the deductions are verified, it becomes more probable that the hypothesis is correct. If the deductions are incorrect, the original hypothesis can be abandoned or modified
• Law: A descriptive generalization about how some aspect of the natural world behaves under stated circumstances
• Theory: In science, a well-substantiated explanation of some aspect of the natural world that can incorporate facts, laws, inferences, and tested hypotheses
• Limitations of the scientific endeavour: In science, explanations are limited to those based on observations and experiments that can be substantiated by other scientists.

11.21.10 Theory vs. Fact
The argument that evolution is a theory, not a fact, has often been made against the exclusive teaching of evolution. The argument is related to a common misconception about the technical meaning of “theory” that is used by scientists. In science, “theory” usually means “a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena.”.