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Indon comments on The Dilemma: Science or Bayes? - Less Wrong
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You have it backwards. Evidence is the only thing that counts. Logic is a tool to make new models, not to test them. Except in mathematics, where there is no way to test things experimentally.
Your claim leads me back to my earlier statement.
Because as Kindly notes, this happens. Mathematicians do sometimes reach for mere necessary-but-not-sufficient evidence for their claims, rather than proof. But obviously, they don't do so when proof is more accessible - and usually, because of the subject matter mathematicians work with, it is.
There is a difference between checking the internal consistency of a simulation and gathering evidence. Scientists who use simulation calibrate the simulation with empirical measurements, and they generally are running the simulation to make predictions that have to be tested against yet more empirical measurement.
Mathematicians are just running a simulation in a vacuum. Its a very different thing.
What is an example of something a scientist can prove with 'just logic'?
I wasn't comparing scientists running a simulation with mathematicians running a simulation. I was comparing scientists collecting evidence that might disprove their theories with mathematicians running a simulation - because such a simulation collects data that might disprove their conjectures.
We'll need to agree on a subject who is a scientist and not a mathematician. The easiest example for me would be to use a computer scientist, but you may argue that whenever a computer scientist uses logic they're actually functioning as a mathematician, in which case the dispute comes down to 'what's a mathematician'.
In the event you don't dispute, I'd note that a lot of computer science has involved logic regarding, for instance, the nature of computation.
In the event you do dispute the status of a computer science as science, then we still have an example of scientists performing mathematics when possible, and really physicists do that too (the quantum formulas that don't mean anything are a fine example, I think). So, to go back to my original point, it's not like an accusation of non-elegance has to come from nowhere; those physicists are undeniably practicing math, and elegance is important there.