BrunoStar,
Theory may be disproved by counterexample. Faith is not. For a theory to withstand the rigorous tests of scientific method - that is an accomplishment.
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Well Gödel's incompleteness theorem leaves us with a unsettling conclusion. It is all ultimately based on faith.
I think you are misinterpreting the connotations that Goedel's incompleteness theorem has on the scientific method.
First of all, the incompleteness theorem has nothing to do with the fact that all logical systems must be based on assumptions which are not provable within the system. That is a fundamental rule of logic. My previous post (which you did not respond to) addresses why this does not constitute "taking it on faith". I'll repeat the important point here.
Even the fundamental principles of science are based on solid supporting evidence. Sure, they cannot be logically proven to be valid. No statement about reality can be logically proven to be true. All that means is that there is no such thing as absolute knowledge.
The axioms of science cannot be logically proven. Nothing about reality can be logically proven. But like any scientific theory, those axioms are not taken on faith. They are accepted only because they have substantial reliable supporting evidence.
That said, what Goedel's incompleteness theorem tells us is that it is possible to construct statements within a formal logical framework, whose truth value cannot be derived from the axioms of that framework. An example is the question of whether there are infinite cardinalities between aleph-null (the cardinality of the set of natural numbers), and c (the cardinality of the set of real numbers). The answer to this question cannot be derived from the axioms of arithmetic.
What this means for science is that no matter how much we know, there will always be we can ask whose answers cannot be logically derived from what we already know. I fail to see how this has anything to do with faith. In fact, to take an answer to any of those questions on faith, would be very unscientific. There are many questions which can be asked about the physical World, whose answers cannot be logically derived from what we already know. That is one of the reasons why we do scientific research. It would, of course, be nonsensical to simply pick a possible answer, and then accept it on faith, rather than attempting to empirically verify it.
Dr. Stupid