Re: In an RDBMS, what does "Data" mean?

From: Anthony W. Youngman <wol_at_thewolery.demon.co.uk>
Date: Sat, 22 May 2004 14:34:09 +0100
Message-ID: <MudUgqBRb1rAFwRe_at_thewolery.demon.co.uk>


In message <2Zzrc.91775$536.15752758_at_attbi_s03>, Marshall Spight <mspight_at_dnai.com> writes
>"Anthony W. Youngman" <wol_at_thewolery.demon.co.uk> wrote in message
>news:nJvuJSCZOSrAFwHb_at_thewolery.demon.co.uk...
>>
>> As for "why the hell not" - well we should be looking for theories that
>> ARE provable/falsifiable.
>
>How might one falsify arithmetic? If arithmetic was falsified, would
>that mean it wasn't useful anymore?
>
What an excellent question !!! Because if I answer it properly, it clearly explains the difference between mathematics and science. Thanks!

Arithmetic is part of mathematics. Therefor, it is NOT falsifiable. We merely prove it correct or incorrect. The best example is "reductio ad absurdam" - if from our starting point we end up with two mutually exclusive results then either our starting point or our logic must be wrong. Now what's this got to do with science?

Let's go from arithmetic to geometry. In three dimensions we have Euclidean geometry. We can prove it correct (or self-consistent - same thing). In four dimensions, we have special relativity, and again we can prove it correct. In two dimensions, we have planar, spherical, and toroidal geometry, and yet again, we can prove them correct.

NOW! Let's apply all three of our two-dimensional geometries to the surface of the earth. THIS is the "falsifiable" bit.

Let's use planar geometry to describe the little bit of the world we can see. I know a little bit of American geography, as do many others, so I'll use that. Let's say we're in Kansas. We know New York is 1500 miles east, and Dallas is 2000 miles south. So we predict the distance and direction from New York to Dallas. The reality is we are going to be well wrong - we've just falsified the assumption that the world is flat. Or, to put it another way, "planar geometry does not describe the world". Toroidal geometry will come up with a similar mess.

Spherical geometry, on the other hand will be pretty close. So either we've cocked up on our geometry or, as is actually the case, the earth is an approximate sphere not a perfect one. Newton mapped his mathematical "mass", "energy", "space" and "time" to the real-world equivalents, and came up with a load of predictions that mostly worked. So he concluded that his maths was wrong. If he'd concluded that reality wasn't quite as he envisaged it, he might well have beaten Einstein to the theory of relativity!

So no. Your question "how do we falsify arithmetic" is meaningless. But science is about falsifying theories *based* *on* arithmetic (and other branches of mathematics). Use the maths to make a prediction about the real world, and then prove (as in test) the theory by seeing if the prediction is true or false. And if the prediction is falsified by an exception, then you've just got an example of "the exception proves the theory is wrong".

And that's why I say Newtonian Mechanics is scientific - it is a mathematical theory that can be proved/falsified, while Relational Theory is unscientific because I can see no way - not even with a Gedanken thought experiment - of trying to falsify it.

Cheers,
Wol

-- 
Anthony W. Youngman - wol at thewolery dot demon dot co dot uk
HEX wondered how much he should tell the Wizards. He felt it would not be a
good idea to burden them with too much input. Hex always thought of his reports
as Lies-to-People.
The Science of Discworld : (c) Terry Pratchett 1999
Received on Sat May 22 2004 - 15:34:09 CEST

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