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The explanatory indispensability argument [a] is an argument in the philosophy of mathematics for the existence of mathematical objects.It claims that rationally we should believe in mathematical objects such as numbers because they are indispensable to scientific explanations of empirical phenomena.
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
For example, Karl Popper once wrote that "In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by 'proof' an argument which establishes once and for ever the truth of a theory." [23] [24] Albert Einstein said: The scientific theorist is not to be envied.
A priori ('from the earlier') and a posteriori ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. A priori knowledge is independent from any experience. Examples include mathematics, [i] tautologies and deduction from pure reason.
For example, anecdotal evidence from a friend about how to treat a certain disease constitutes empirical evidence that this treatment works but would not be considered scientific evidence. [ 38 ] [ 39 ] Others have argued that the traditional empiricist definition of empirical evidence as perceptual evidence is too narrow for much of scientific ...
For example, a scientific realist would argue that science must derive some ontological support for atoms from the outstanding phenomenological success of all the theories using them. Arguments for scientific realism often appeal to abductive reasoning or "inference to the best explanation" (Lipton, 2004). For instance, one argument commonly ...
It could be that our home galaxy, the Milky Way, is not an entirely hospitable galaxy for life, according to a scientific report last month that suggests other galaxies in the universe could host ...
Among his many arguments Hume also added another important slant to the debate about scientific method—that of the problem of induction. Hume argued that it requires inductive reasoning to arrive at the premises for the principle of inductive reasoning, and therefore the justification for inductive reasoning is a circular argument. [4]