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Is a logical conclusion really substantially different than a prediction from scientific theory?

For example, you can say that the Pythagorean theorem, a^2+b^2=c^2, can be proven true. However, what is rarely stated is that it is true only for a particular set of assumptions, in this case, flat geometry. If you use a curved surface, then the theorem is no longer true.

Likewise, scientific theory presents us with what we know is true in a particular set of conditions (if it actually does rise to the level of a theory rather than a mere hypothesis). What's the difference between the set of conditions that a scientific theory is based on, and the set of conditions a "logical conclusion" is based on?

Thank you so much for sharing your insight! Indeed, you may wish to combine numbers 3 and 8 from my list into a single entry on yours with clarification (and of course, your own ranking of relative 'certainty'). js1138 saw a similar weakness in axioms on his list.

As for me, I'll leave the two separate because one is a prediction and the other self-verifies (albeit with reservations, such as your example in plane geometry).

You just posted a mouthful. Almost everything has something underlying that may not be recognized. Most recognize and have a detailed body of knowledge regarding God. Notice I said most. Some beliefs go beyond what is known as God and recognize a different reality.

Much of knowledge involves pigeonholing or classifying something. What is often missed is there may be unknown relationships or realities that renders the "known" knowledge bogus. The current classification may work but once the unknown becomes known, it's a different ballgame. I think humankind tends to act in a prejudiced way towards knowledge. If you're not prepared to jettison previous assumptions, you may always miss the forest for the trees. Prejudice is a natural human coping mechanism But it blinds us to other possibilities. Often the most knowledgeable about the current beliefs are the most prejudiced.

However, what is rarely stated is that it is true only for a particular set of assumptions, in this case, flat geometry.

You said it.

Scient-ism is that particular group that would keep the monopoly on certainty for its particular set of assumptions. But there are other dogmatists.

I'm glad you posted your response.

I think that the main difference between logical deduction and scientific theory is that logic is deductive whereas most conclusions or calculations from scientific theories are inductive in nature. For example, given the axioms of Euclidean geometry, it is deductively necessary that all right triangles will conform to the Pythagorean theorem. It is just as impossible to find a right triangle that varies from this theorem as it is to find a square circle. The concept of a right triangle in a Euclidean geometry that doesn't follow the Pythagorean theorem just doesn't make sense.

With regard to scientific theory, OTOH, an observation that contradicts the theory is at least sensible. That is, it is not impossible to find a counterexample to a theory; one just hasn't been found, which is why the theory is accepted. A good example would be the calculated force of gravity between two objects, as given by the theory of general relativity (or equivalently in most situations, Newton's law of gravity). According to theory, the calculation works no matter which two objects we use to measure the force of attraction. However, we haven't measured the attractive force between EVERY two pairs of objects in the universe. Logically, it is possible that if we somehow measure the attraction between two galaxies that are a couple billion light years away from us, that this will not adhere to the accepted scientific theory. This would have profound implications for our scientific understanding, but it is not impossible that our scientific understanding is incomplete or incorrect.

For example, you can say that the Pythagorean theorem, a^2+b^2=c^2, can be proven true. However, what is rarely stated is that it is true only for a particular set of assumptions, in this case, flat geometry. If you use a curved surface, then the theorem is no longer true.

Which reminds me of the classic:

3 is greater than 2
(except for unusually large values of 2)

Check your Jacobians, folks. . .

Cheers!

Full Disclosure: You Frech should check your Jacobins, too!