Settled Science?

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In the comment section of this post, I had occasion to return to one of my favourite memes. Sometimes I forget my own findings. So let me remind us — on a rainy day in May — that mathematics is no use in propping up the conceit of certain knowledge and settled science:

A commenter concludes in this instructive post about increasing evidence against claims of global warming:

So, contrary to what the alarmists keep shouting, the science is NOT “settled”.

To which I replied:

There is no such thing as “settled science”. Science is all about not being settled, being open to challenge and revision. He who appeals to “settled science” betrays that he does not understand how science works. Calling challengers “deniers” is a sure sign that the proponent is not aware of the fundamental methodological requirements of science.

Another commenter took up my denial of settled science with these words:

“There is no such thing as “settled science”.

There is however “settled science” mathematical proof that most of the algebra used in climate “science” is indisputably wrong.

My response:

Only definitional truth can ensure cognitive certainty. Science as an effort to learn more about the world in which we live is incapable of delivering cognitive certainty. Tautologies are true under all possible circumstances. But they don’t tell us anything about the world that we didn’t already know. Acquiring new knowledge about reality comes at the cost of fallibility.

Einstein: “As far as mathematical propositions refer to reality they are not certain, and as far as they are certain, they do not refer to reality. Mathematical theories about reality are always uncertain — if they are certain, they are not about reality.”

Also, even the state of art in mathematics is fallible.