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[B] A theory or hypothesis is falsifiable if it can be logically contradicted by an empirical test. Popper emphasized the asymmetry created by the relation of a universal law with basic observation statements [ C ] and contrasted falsifiability to the intuitively similar concept of verifiability that was then current in logical positivism .
Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. The practical feasibility of observing a reproducible series of such counterexamples if they do exist. In short, a hypothesis is testable if there is a possibility of deciding whether it is true or false based on experimentation by anyone.
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
The statistical proof is the Bayesian demonstration that one hypothesis has a higher (weak, strong, positive) likelihood. [13] There is considerable debate if the Bayesian method aligns with Karl Poppers method of proof of falsification, where some have suggested that "...there is no such thing as "accepting" hypotheses at all.
It makes falsifiable predictions with consistent accuracy across a broad area of scientific inquiry (such as mechanics). It is well-supported by many independent strands of evidence, rather than a single foundation. It is consistent with preexisting experimental results and at least as accurate in its predictions as are any preexisting theories.
According to it, scientific inquiry proceeds by formulating a hypothesis in a form that can be falsifiable, using a test on observable data where the outcome is not yet known. A test outcome that could have and does run contrary to predictions of the hypothesis is taken as a falsification of the hypothesis.
The hypothesis of Andreas Cellarius, showing the planetary motions in eccentric and epicyclical orbits. A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or ...
Both the hypothesis and its negation are thought to be consistent with the axioms of ZFC. [31] Many noteworthy discoveries have preceded the establishment of the continuum hypothesis. In 1877, Cantor introduced the diagonal argument to prove that the cardinality of two finite sets is equal, by putting them into a one-to-one correspondence . [ 32 ]