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Even though Popper is clearly not a relativist, Sokal and Bricmont discuss falsifiability because they see postmodernist epistemological relativism as a reaction to Popper's description of falsifiability, and more generally, to his theory of science.
Popper argues that science should adopt a methodology based on falsifiability, because no number of experiments can ever prove a theory, but a reproducible experiment or observation can refute one. According to Popper: "non-reproducible single occurrences are of no significance to science.
Popper held that it is the least likely, or most easily falsifiable, or simplest theory (attributes which he identified as all the same thing) that explains known facts that one should rationally prefer.
Falsifiability is the demarcation criterion proposed by Popper as opposed to verificationism: "statements or systems of statements, in order to be ranked as scientific, must be capable of conflicting with possible, or conceivable observations." [19]
Furthermore, Popper defended his critical rationalism as a normative and methodological theory, that explains how objective, and thus mind-independent, knowledge ought to work. [13] Hungarian philosopher Imre Lakatos built upon the theory by rephrasing the problem of demarcation as the problem of normative appraisal. Lakatos' and Popper's aims ...
In Popper's philosophy of science, scientific statements are always provisional, they have limits of application, and they could always be wrong. If a statement cannot even in principle be proved wrong, it cannot be a scientific statement. Thus, in Popper's eyes, the falsifiability criterion clearly demarcates "science" from "non-science". This ...
He saw falsifiability as the cornerstone of critical rationalism, his theory of science. As a key notion in the separation of science from non-science, it has featured prominently in many scientific controversies and applications, even being used as legal precedent. (This page incorporates text from the Wikipedia, namely Falsifiability
This led Popper to his falsifiability criterion. Popper wrote about critical rationalism in many works, including: The Logic of Scientific Discovery (1934/1959), [ 1 ] The Open Society and Its Enemies (1945), [ 2 ] Conjectures and Refutations (1963), [ 3 ] Unended Quest (1976), [ 4 ] and The Myth of the Framework (1994).