On 02 Jan 2013, at 21:01, meekerdb wrote:

On 1/2/2013 10:34 AM, Evgenii Rudnyi wrote:
A nice quote from Galileo by John L. Heilbron that shows:

1) One could trace the falsifiability to Jesuits of Galileo's time.

2) It could be a link between falsifiability and theology.


p. 318 ‘However, false is not useless. The motion supposed by Copernicus can be employed in calculations,

The Copernican model was less accurate than the Ptolemaic one. It wasn't until Kepler and elliptical orbits that the heliocentric model became superior for celestial predictions.

Interesting.




and might even be useful to the faith if mathematicians emphasized their falsity along with their utility. Here Inchofer had in mind the minor truth later rediscovered by Karl Popper: “mathematicians [should] … work more and more toward trying to falsify theories rather than to defend them“.

This seems confused. Mathematicians prove theorems from axioms - they don't have theories that can be falsified.

That's not true. Most first theories of set, lambda term, combinator have been falsified. It took time for some. The NF theory of set might still be. The falsification is a proof of a contradiction in the theory.

A different example are the fertile conjecture. many results in number theory are proved from assuming the Riemann hypothesis, which might be falsified, even empirically (by finding a zero of the zeta function out of the critical line).

Likewise, many result in theoretical computer science remains on the assumption P = NP, and might be all falsified in the case someone prove P = NP.

Etc.

Bruno


At worst they may think a proof is valid when it's not. He must have been using "mathematician" carelessly to mean scientist.

Brent
I don't know if God exists, but it would be better for His reputation if He did not.
     --- Jules Renard


To this anticipation of modern epistemology Inchofer added a pinch of ancient wisdom, Urban’s Simple in the words of the Preacher: “no man can find out the work that
God maketh from beginning to end.”‘

Evgenii

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