The book Stress Analysis of a Strapless Evening Gown had an essay titled, IIRC, On the Nature of Mathematical Proof. The only ones I remember were Proof by Blatant Assertion and Proof by Lack of Counterexample. I wonder if they had a Proof by Selective Data.
There's an old joke about an astronomer, a mathematician and an engineer trying to prove that all odd numbers are prime. (We have to take 1 as prime for the purposes of the joke.) The astronomer says, "1's prime: yes, all odd numbers are prime. The mathematician says, "1's prime, 3's prime, 5's prime, 7's prime: yes, by induction all odd numbers are prime." The engineer says: "1's prime, 3's prime, 5's prime, 7's prime, 9? 11's prime, 13's prime, 15? 17's prime, 19's prime: yes, all odd numbers are prime; 9 and 15 are experimental error."
[(myl) There's a crueler version of the joke, in which one of the participants says "1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, ..." The inattentive or arithmetically challenged participant can be the engineer, the physicist, or the mathematician, depending on your prejudices.]
Come on. This is totally legitimate way of thinking. The nature (or Nature) is awfully complicated and, unless you are trying to find a theory of everything, your particular theory will sometimes work and sometimes don't. Now, if you dreamed of some interesting situation, say that under certain conditions the evolution will go along the Lamarckian lines, why not to search for something that actually behaves like this.