The differences between law, theory and theorem

What is a law? And a theory? What are the theorems? These concepts are handled daily in academic fields, institutes and universities, but sometimes we are not clear about the differences and what each one of them means. Are theories and laws irrefutable? What is a theorem based on to be considered as such?

In this article we explain what is the meaning of concepts such as law, theory and theorem, and what are their main differences.

• It may interest you: "The 4 main types of science (and their research fields)"

What is a theorem?

A theorem is made up of a proposition or statement whose validity or "truth" can be demonstrated within a logical framework. and from the inclusion of axioms or other theorems that have been previously validated or demonstrated.

The axioms or axiomatic sets are propositions or statements so evident that it is considered that they do not need any demonstration to be considered as valid. For example, when we want to play a game of chess, the rules of this game constitute a system axiomatic, since both participants take its validity for granted without it being questioned in any way. moment.

In order to consider a theorem valid, it must be demonstrated by means of a procedure and some inference rules, which are used to deduce from one or several premises (affirmations or ideas that serve as the basis for reasoning and a subsequent deduction), a conclusion valid. However, until a statement is not proven, it is defined as the name of hypothesis or conjecture.

In mathematics, for example, a theorem is proved true by applying logical arguments and operations.. One of the best known, the Pythagorean theorem, states that in any right triangle (the one that has an angle of 90º) its hypotenuse (the longest side) can be calculated in relation to the value of its legs (the sides that form the angle of 90º).

What is a theory?

A theory is a logically structured system of knowledge, established from a set of axioms, empirical data, and postulates., whose objective is to record under what conditions certain assumptions are generated; that is, trying to describe, explain and understand a part of objective reality or a particular scientific field.

Theories can be developed starting from different starting points: with conjectures, which are suppositions or ideas that do not have empirical support, that is, they are not supported by the observation; and the hypotheses, which are supported by different observations and empirical data. However, a theory cannot be inferred solely from one or several axioms within a logical system, as it happens with theorems.

The function of a theory is to explain reality (or at least part of it), to answer basic questions (such as what, how, when or where the phenomenon that one tries to understand and explain occurs) and to order said reality in a series of concepts and ideas that are understandable and accessible.

The set of rules from which a theory is constituted must be capable of describing and predicting the behavior of a specific system.. For example, Charles Darwin's theory of evolution, explains how living things have a specific origin and change and evolve slowly, and how These changes cause different species to emerge from the same ancestor, in what he came to call selection. natural.

In science, theories are built using the hypothetical-deductive system or method, which is made up of the following steps:

• The phenomenon to be studied is observed.

• One or several hypotheses are generated to explain this phenomenon.

• Taking the hypothesis(es) as a starting point, the most basic consequences or statements are deduced.

• Said affirmations are verified and validated by comparing them with the empirical data that emanate from observation and experience.

Law: definition and characteristics

By law we understand a rule, a norm or a set of norms, which describe the relationships that exist between the components that intervene in a phenomenon. or a particular system. Although in popular culture it is common to think that laws are a kind of universal and absolute truths (above theories), this is not exactly the case.

Laws, in the field of science, must be invariable rules (which cannot be modified), universal (which must be valid for all the elements of the phenomenon it describes) and necessary (which must suffice by themselves to describe the phenomenon in question). However, a law is considered as a particular rule, present in all theories (hence its universality), not as a higher-rank assumption.

For example, in a science like physics, there are multiple theories that explain certain phenomena and realities; the theory of quantum mechanics (which explains the nature of the smallest), the theory of relativity special or the theory of general relativity (both necessary to explain the nature of the most big). All of them share a common law: the conservation of energy, as a particular and universal rule in all three theories.

With everything, laws maintain their provisional status and can be rebutted, since in science there is nothing absolute or written in stone, and any statement, whether it is a theory or a law, can be dismantled with the necessary evidence and the relevant demonstration.

Differences between theorem, theory and law

The differences between the concepts of theorem, theory and law can be somewhat blurred, but let's look at some of them.

As far as the difference between a theorem and a theory is concerned, the following should be noted: while theory can be defined in Based on a pattern of natural events or phenomena that cannot be proved using an axiom or set of basic statements, the Theorem is a proposition of an event or a phenomenon that is determined from a group of axioms, within a framework or criterion. logical.

Another subtle difference between theory and law is that, although both are based on hypotheses and empirical data, Theory is established to explain an observed phenomenon, while laws seek to describe said phenomenon.. For example, Kepler described mathematically the movement of the planets in their orbits around the sun, formulating the well-known Kepler Laws; however, they do not provide an explanation of planetary motions.

Finally, it is worth noting a basic difference between the concepts of theorem and law, and that is that the theorem is made up of provable propositions (through axioms, in a logical system); and, for its part, a law is made up of a series of established, constant and invariable rules, based on observations and empirical data that can be validated or refuted.

Bibliographic references:

• Acevedo-Diaz, J. A., Vázquez-Alonso, Á., Manassero-Mas, M. A., & Acevedo-Romero, P. (2007). Consensus on the nature of science: epistemological aspects. Eureka Magazine on teaching and popularizing science, 4(2), 202-225.

• Chalmers, A. F., Villate, J. TO. P., Máñez, P. L., & Sedeno, E. Q. (2000). What is that thing called science?. Madrid: XXI century.