[Ophiucus]

However, when it comes to the big cahuna theories in science, the game is confidance due to repeated demonstrations, which is induction, not proof. For that matter, the use of deduction, in and of itself, is not proof. A proof involves quite a lot of rig-a-marole surrounding the formal construction of a system of axioms and predicates, and establishing a methodical tabular presentation of the connection between the fundamental predicates, acted upon by the axioms, to produce the proof of the hypothesis.

There's a couple problems with this.

One, you are applying an overly strict usage of deductive reasoning that seems to be coming from a mathematical perspective, Euclidean even, or an upper level logic course. This is not the more 'common' version that science uses. Perhaps this might help to illustrate. Deductive reasoning is using a theory to explain a specific occurrence such as the gravity example. It is using the known general idea to go to the specific. This is the explanatory method used in science and also to predict. The classic misuse being "All bald and middle aged men are mature - Bob in the office is bald and 45 - therefor Bob will be mature."

Two, your use of proof is not correct for the sciences. Again, you are using mathematical or college class logic proof. In science, repeated demonstration is proof. For example in my time as a researcher, I wanted to prove that drug A was able to inhibit the release of hormone X. I administered drug A to a rat and measured the level of hormone X. It went down. This is not proof that drug A caused the lowering of hormone X. I had to administer the drug to many groups of rats. Since each group showed a decrease each time, I had my proof that drug A inhibited the release of hormone X. When tying the action to a specific receptor, I had to administer a receptor inhibitor before administering the drug and repeatedly show that the inhibitor prevented the drop of hormone X. Again, the repeated observations were my proof. I published, another lab did the repeated observations and I had my validation.

In science, if A leads to B once. It means nothing. But if you repeatedly do A, predicting that B will occur, and B does occur. You have your proof. The experiment must be repeated enough times to show that it wasn't a singular occurrence or a fluke. Then your results must be reproducible. That is how research in science works.

The case of the drug, inductive reasoning was that drug A inhibits hormone B because it did so every time I tried it. Then deductive reasoning, drug A is of drug class WW, so every time I use a drug of class WW, hormone X will be inhibited. This was the next step. Use other drugs of that class predicting that they will inhibit hormone X. They did.

So, science uses both inductive to go from observation to general rule and then deductive to use the general rule to predict specifics.

[donh]

In science, if A leads to B once. It means nothing. But if you repeatedly do A, predicting that B will occur, and B does occur. You have your proof.

No, you do not. Not in a formal sense, or in a practical sense either. The myriad of observations, over 200 years, of the efficacy of Newtonian physics did not prevent it from being superceded in astro-physics by Einsteinian physics.

I had to administer the drug to many groups of rats. Since each group showed a decrease each time, I had my proof

You did not have a proof, except in the half-baked way lawyers use the word. You increased your confidence to a high level. You did not make the contention in question unassailable.

This is, I aver, a poor usage, under the circumstances of trying to explain science to creationists, who keep insisting that that the theory of evolution has not been proved. In that it has not.

The experiment must be repeated enough times to show that it wasn't a singular occurrence or a fluke. Then your results must be reproducible. That is how research in science works.

Indeed--without recourse to proof.