Mojo
Mostly harmless
People who say they want to use "logic and philosophy" instead of the scientific method usually mean "making ◊◊◊◊ up". Kumar, for example, called it "thinking dynamically".
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Merged Is Scientism Really Justified?
- Thread starter Gubiosak
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Puppycow
Penultimate Amazing
Every real science incorporates both mathematics and logic. No real scientist claims that mathematics and logic are not an essential part of the foundation of their science. Any real scientist needs to be able to use both math and logic in his/her work. This idea of "Scientism" that you propose isn't something that scientists believe. There's an acronym called STEM which stands for Science, Technology, Engineering and Mathematics.
Other things that aren't science may not require either math or serious logic. I don't know whether Astrology uses any real math, or valid logic. Nor Tarot card reading. But any legitimate science (I can't think of any exception) will use math (and logic) for at least some aspect of it.
Mathematics - Wikipedia
Logic - Wikipedia
Physics is a prime example of a science that uses lots of advanced mathematics. But experiments are still needed to verify that the theories actually correspond to reality and can make accurate predictions.
And it requires evidence to validate those mathematical theories, to the classical example of Einstein: his maths seemed sound, but it was the evidence for its conclusions that pushed it forward, and to use a non-classical example: Dirac’s maths predicted antimatter but it required evidence to prove it did exist.
Gord_in_Toronto
Penultimate Amazing
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And sometimes the current answer is that we don't have a (current) answer. And maybe never will. But that;s OK too.
I see the concern about circularity. My question is precisely about whether some forms of knowledge require foundational justification outside empirical testing.
theprestige
Penultimate Amazing
That's a philosophical question. Everyone gets to come up with their own answer. What is your answer to the question? How would you go about setting up a foundational justification, in case it's needed.
Personally, I'm results-oriented. If it works, that's all the justification I need. "But how do you know it works?" I hear you ask. That's a philosophical question. We could go down that rabbit hole all day, challenging axiom after axiom and never getting anywhere useful. Boring stuff.
Is there a particular claim you can provide as an example? A claim you would like to try to elevate to the status of "true", but not through scientific means? Perhaps through logic alone, without observations or testing?
Another couple questions of mine, for you to answer. I hope you get to them soon.
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Mathematical truths are an example. The statement ‘there are infinitely many prime numbers’ is established by proof, not by empirical observation or testing. The question is whether calling this ‘science’ changes the distinction between deductive and empirical knowledge.
theprestige
Penultimate Amazing
We've already been over this. That's a question of taxonomy, of labels.
My taxonomy labels both deduction and empiricism as two species of science, because they both use the same observe, predict, test, observe toolset. Your taxonomy doesn't need to label them the same way. That doesn't matter at all, as to whether they use the same toolset.
The proving the statement "there are infinitely many prime numbers" uses the exact same tools as any other scientific proof:
- Observe the rules and emergent behaviors from those rules, in a given mathematical domain.
- Predict whether some behavior will emerge from those rules.
- Test whether this prediction holds true.
- Observe the results of the test.
Do you disagree? Do you think the Pythagorean Theorem came from some process other than observe, predict, test, observe?
No, mathematical proofs aren't empirical; testing billions of cases doesn't prove a theorem, as math requires logical deduction. Redefining empiricism to include pure logic dilutes the word's actual meaning.
theprestige
Penultimate Amazing
Okay then. There's your answer. There's more than one way of knowing things.
Is there anything else to consider, or have we reached the natural conclusion of your thread?
If mathematics and empirical science are both called science, what distinguishes a deductive proof from an empirical test?
JayUtah
Penultimate Amazing
And, as such, it tells you only something about mathematics. You can consider it knowledge in the sense that it's something you just realized follows inexorably from some other things you imagined.
You seem to be equivocating among different kinds of knowledge. Empirical science doesn't claim to be the only source of all kinds of knowledge. But to imagine that something besides evidence-driven investigation is as good as or better at acquiring the kinds of knowledge that allude to evidence and observation seems like yet another attempt on your part to make people feel bad for rejecting sketchy beliefs because they don't stand up to evidentiary discovery.
JayUtah
Penultimate Amazing
An empirical test still has an inductive leap. A mathematical proof can be deductively strong, but only because its premises are contrived.
theprestige
Penultimate Amazing
You just now described the distinction that matters to you. Why are you asking a question you've already answered to your own satisfaction?
Meanwhile, I've already explained that while I consider the two to be distinct in some ways, I still label them both as science because I see them as having one very important thing in common: The toolset they use to know things.
I've also already explained what that toolset is, and why I think both methods have that toolset in common.
You keep replying to me, but your replies keep ignoring my explanations, and asking the same questions over and over again. Even after you've already answered those questions yourself.
I understand your point, but my question is whether a shared general method is enough to erase the fundamental difference between deductive necessity and empirical evidence.
Distinguishing deductive necessity from empirical observation isn't a defense of 'sketchy beliefs'—it’s acknowledging that physical science itself requires mathematical logic to function.
Axioms aren't 'contrived'; they are the logical foundation that enables empirical science to make sense of its data.
JayUtah
Penultimate Amazing
I said it does in my first post. However you seem to be hung up on “necessary” versus “sufficient.”
JayUtah
Penultimate Amazing
I said premises, not axioms.
theprestige
Penultimate Amazing
No you don't.
If you understood my point, you'd understand that this question is meaningless.
My point is that the two things can be grouped together according to their fundamental similarity. Nothing about that erases, or requires erasing, the fundamental differences.
In fact, in some of my other posts, which you also mistakenly claimed to understand, I clearly recognized and upheld the fundamental differences between the two things, even while grouping them together according to a fundamental similarity.
So your question is meaningless. There's no need to justify an erasure that isn't happening, and that nobody wants to happen.
You know who else doesn't understand a point? Me. I don't understand your point at all. I keep asking you clarifying questions, so that I can understand your point, but you keep ignoring them.
Every time I do think I understand your point, you weasel away. You say your question is one thing, and then you answer your question. But when I point out that you've answered your question, you turn around and say your question is something else instead.
So I think maybe you don't want to understand my point, and you don't want me to understand yours.