Axiomatic and Hypothetical-Deductive Methods in Science
Axiomatic Method
The axiomatic method aims for axiomatization, applying rigorously in formal sciences like logic and mathematics. It offers advantages in physical sciences and serves as an ideal in other knowledge branches. Complete objectivity is unattainable; no domain achieves total objectivity.
The idea of axiomatizing knowledge, present in Aristotle and mathematics, has been extended to logic and physics. Interest in axiomatization has grown.
An axiom signifies “recognition of validity,” representing a principle—a proposition from which other statements are deduced. An axiomatic system includes axioms and statements derived from them.
It is made up of a formalized system of signs.
Axioms are defined exclusively by being non-deductible from the system, not by evidence.
Axioms are laws, and rules are instructions on how to proceed.
With formalism and the distinction between laws and rules, deductibility is central to the system.
The system of statements is formulated along with the system of meaningful expressions.
Hypothetical-Deductive Method
The hypothetical-deductive method is a description of the scientific method.
An investigation begins with a problem, raising questions about the subject of study. These questions lead scientists to seek possible answers, forming hypotheses.
Building on Roger Bacon’s work, science was considered based on observing facts and repeated observation of comparable phenomena, using induction to extract general laws.
Karl Popper rejects deriving general laws from induction, arguing that scientists formulate general laws as hypotheses and use induction for interpolation, developing forecasts of individual phenomena based on these assumptions.
Central to this method is the falsifiability of scientific theories—the possibility of being refuted by experiment. In the hypothetical-deductive method, scientific theories can never be definitively proven, but at most remain uncontested.
The Problem of Demarcation
The problem of demarcation in the philosophy of science concerns defining the limits of “science.” Boundaries are established between scientific and nonscientific knowledge, science and pseudoscience, and science and religion.
- Postulate the need for building inductive theories worthy of scientific status.
- Start from observations and experiences.
- Use a verificationist criterion.
- Theories could be proved by experiments and/or observations, establishing their truth and scientific validity.
- Use a falsificationist criterion.
- This approach opposes the inductive and verificationist views.
- Recognize as scientific only theories capable of being subjected to tests that question their validity.