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thomastwo wrote
Nope, I'm not limiting the scientific method to observation. With that red herring that you invented out of the way, perhaps you'll have a go at just answering the original question.
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It's not a red herring on my part. It's what you're attempting to do when you seek to divorce logic and mathematics from the process of scientific inquiry and discovery. Besides, I already answered your question and the answer was no, I do not think mathematics and logic, when they are disconnected from any practical applications, can stand on their own as methods for obtaining any additional knowledge about the natural universe. Perhaps, you can provide me with an example where you think they can? I'm open to a demonstration of this alleged phenomenon.
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thomastwo wrote
No, I'm not limiting the scientific method to "mere" observation. What I'm saying is that math and logic can stand on their own as methods of obtaining knowledge without the use of the scientific method.
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Then demonstrate it. Lay some logic on me that's not connected to anything and tell me what you learned.
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thomastwo wrote
So, to be clear (and I'm repeating your argument back to you in my own words) you think that 2 + 2 does not equal 4 in an abstract sense? 2 + 2 only equals 4 if we are talking about bananas or some physical object that can be verified. Correct?
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Your words differ a lot from my words. I actually asked you a question to which you have yet to respond: What is the value of knowing that 2 + 2 = 4 if you have no intention of ever connecting that knowledge to anything practical? How does it lead to additional knowledge if that's as far as you're going to take that information?
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thomastwo wrote
And a bonus question for you. Can the scientific method prove that 2 + 2 = 4? (Hint the answer is no. So how do we know that 2 +2 really does equal 4 if the scientific method is the only source of knowledge?)
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Are you forgetting that it is my contention that mathematics and logic are intrinsic parts of the scientific method? One couldn't possibly test an assumption without them, for instance.
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thomastwo wrote
I think you are confused with this answer. You said that empiricism was not the only way to acquire knowledge. So, I'm asking you what are the other ways?
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No. What I said was that the scientific method entails more than merely observing. I'm not divorcing mathematics and logic from that process; you are.