Sorry for getting back to this sort of late in the game. I guess I should have been more precise with terminology. I think a good explanation has already been given. You near missed with your description from my post, but didn't hit it dead on.
Perhaps an example applying both approaches to the same problem would help.
Let's take geology.
Faith uses deductive reasoning by starting with some initial premises, in this case that all geology can be explained by statements within the Bible regarding geological events. He also describes scientists as if they had an initial premise, which is that God does not exist and the Bible is counterfactual and so evidence must be explained so as NOT to coincide with Biblical literature.
Using this both sides set out to "explain the evidence" based on the stories they started with as an assumed truth. Problems with evidence must be explained away by adding elements not within the premise, that will help keep the premise intact.
Thus radiocarbon dating must simply not be accurate because "something happened" to decay rates, and the assumption they could be constant must be wrong as they would lead to evidence that does not fit with the Biblical text. In a similar fashion he appears to be saying that scientists see this decay and adopted an element (uniformitarianism) to help their original premise along.
Inductive reasoning would work differently. While one may be motivated by the Bible to go seek the truth about the world, how is by not assuming a premise. One gathers the evidence by observing strata of rock (orientation, size, composition), and how rock can be formed, and then creating a model or premise of how the layers might have been formed.
One might argue that uniformitarianism is a premise, but that is more of a practical tool than an outright premise. It can be abandoned if there is sufficient evidence that a disconformity in process can happen. Further, it cannot decide in advance what the rest of the model looks like. One cannot get the earth is not 6K years old simply by using an assumption of uniformitarianism.
And as I said that is more or less a practical tool. Without it there is no making models to be tested beyond our immediate temporal or even spatial proximity.
Okay so in this case what scientists did was inductive, by looking at rocks and processes of rock formation to form a model of how geology works on a large scale. This leads to an ability to create models of how the world's geological layers were formed and what kind of timescale it must have taken.
This model may be used in a slightly deductive manner for routine, or initial descriptions for new evidence. The difference being if there is a problem. Some may try and invent explanations to preserve the overall model, but it is not sacrosanct and need not be preserved. Good examples of overthrowing original model elements in geology is the eventual acceptance of catastrophic mechanisms as well as continental drift.
Further, in other scientific fields inductive reasoning has created models of how things work in that field. For example atoms, nuclear material, and ultimately radioactive decay. This was pursued separate from theories of geology.
As it turns out that model allowed for testing of assumptions regarding geology when one notes that radioactive material exists within rock. They run tests using the model of decay for radioactive elements, to check the model of age determination of strata in geology, and it is found to match.
That was not scientists running around looking for some kind of test that would come up with a number that matches a prediction. It was a happenstance result of another field's model, that we could test the geological model and did so and it turned out as would be predicted. Thus the model continues.
Hope this helps.
holmes
"...what a fool believes he sees, no wise man has the power to reason away.."(D. Bros)
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