Is Math/Science Absolute? | Better HN

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bediger40004y ago· 2 in thread

Math, maybe, despite your very valuable readings and insight. By "maybe I mean "inside some axiomatic system (like ZFC, or lambda calculus) math is absolute".

Science definitely isn't absolute. It's based on observation, hypothesis, experiment and verification. A new observation can be made at any time. Most theories have some things that don't fit, like Mercury's orbit didn't fit Newtonian mechanics. Right now we've got observations of galaxy-sized objects that don't quite fit Einsteinian Relativity. There's probably other things that we know that just don't fit. So, no absolutes there.

hegzploitOP4y ago

Thanks for your valuable insight, I'm yet to read more about these topics since I was just scratching off the surface and I find Mathematical Logic to be a very interesting area.

A lot of people have been recommending "Gödel, Escher, Bach" which I'll check out.

bediger40004y ago

You might want to also look at Raymond Smullyan's "Beginner's Guide to Mathematical Logic", and "Beginner's Further Guide". I got hung up at the first order logic section, and the Axiomatic Logic is tough, but he includes a lot of topics and how they interrelate.

    Kurt Gödel then showed that this was impossible
    and the number system needs to be inconsistent for it to
    be complete.

IMO this is favoring the wrong end of Gödel's argument: a "complete" number system sounds like something desirable, but it's equivalent to one where "1 = 0" is a true statement and literally anything can be proved.

The converse part is usually more important: given any consistent system of mathematical logic, it is always possible to produce a theorem in that system that the system cannot prove to be EITHER true or false.

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