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On Tue, 1 Oct 2024 15:51:36 +0000, Thomas Koenig wrote:It's worth remembering that mathematical proofs always start at a base - a set of axioms. And these axioms are assumed, not proven.
David Brown <david.brown@hesbynett.no> schrieb:Indeed, Units of forward progress in Math are done with formal
>Science is not a religion.>
>
And as someone (whose name I have forgotten) once said, "Science is
about unanswered questions. Religion is about unquestioned answers."
That is the ideal of science - scientific hypotheses are proposed.
They have to be falsifiable (i.e. you have to be able to do experiments
which could, in theory, prove the hypothesis wrong). You can never
_prove_ a hypothesis, you can only fail to disprove it, and then it
will gradually tend to become accepted. In other words, you try
to make predictions, and if those predictions fail, then the theory
is in trouble.
>
For example, Einstein's General Theory of Relativity was never
proven, it was found by a very large number of experiments by a
very large number of people that it could not be disproven, so
people generally accept it. But people still try to think of
experiments which might show a deviation, and keep trying for it.
>
Same for quantum mechanics. Whatever you think of it
philosophically, it has been shown to be remarkably accurate
at predicting actual behavior.
>
Mathematics is not a sciene under this definition, by the way.
proofs.
I think you need evidence, justification, and a good basis for proposing something before it can even be called a "conjecture" in science. You don't start off with a conjecture - you start with an idea, and have a long way to go to reach a "scientific theory", passing through "conjecture" and "hypothesis" on the way.>The colloquial person thinks theory and conjecture are
The main problem is with people who try to sell something as
science which isn't, of which there are also many examples.
essentially equal. As in: "I just invented this theory".
No, you just: "Invented a conjecture." you have to have
substantial evidence to go from conjecture to theory.
Or even in hard sciences - scientists are humans too, and some of them get their statistics wildly wrong."Scientific Marxism" is one such example. It is sometimes hardOr politics....
for an outsider to differentiate between actual scientific theories
which have been tested, and people just claiming that "the science
says so" when they have not been applying the scientific method
faithfully, either through ignorance or through bad intent.
>
There is also the problem of many people not knowing statistics well
enough and misapplying it, for example in social or medical science.
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