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Thus, complex hypotheses must predict data much better than do simple hypotheses before researchers reject the simple hypotheses. Recent advances employ information theory, a close cousin of likelihood, which uses Occam's razor in the same way. The choice of the "shortest tree" relative to a not-so-short tree under any optimality criterion ...
Another foundational assumption to quantum mechanics is that of free will, [92] which has been argued to be foundational to the scientific method as a whole. [93] Bell acknowledged that abandoning this assumption would both allow for the maintenance of determinism as well as locality. [94]
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is uniformly isotropic and homogeneous when viewed on a large enough scale, since the forces are expected to act equally throughout the universe on a large scale, and should, therefore, produce no observable inequalities in the large-scale structuring over the course ...
Hutton's Unconformity at Jedburgh. Above: John Clerk of Eldin's 1787 illustration. Below: 2003 photograph. Uniformitarianism, also known as the Doctrine of Uniformity or the Uniformitarian Principle, [1] is the assumption that the same natural laws and processes that operate in our present-day scientific observations have always operated in the universe in the past and apply everywhere in the ...
They are called the strong law of large numbers and the weak law of large numbers. [ 16 ] [ 1 ] Stated for the case where X 1 , X 2 , ... is an infinite sequence of independent and identically distributed (i.i.d.) Lebesgue integrable random variables with expected value E( X 1 ) = E( X 2 ) = ... = μ , both versions of the law state that the ...
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause [1] attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα ( axíōma ), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
Modus tollens (also known as "the law of contrapositive") is a deductive rule of inference. It validates an argument that has as premises a conditional statement (formula) and the negation of the consequent ( ¬ Q {\displaystyle \lnot Q} ) and as conclusion the negation of the antecedent ( ¬ P {\displaystyle \lnot P} ).