Inductive. I have seen people put things in bags before and usually they are in there. That doesn't mean it will turn out the same way this time. But it's pretty likely.

What is your view of the claim "1 + 1 = 2"?

Also, what of Michelson-Morley?

(By the way, there's no "wrong' answer insofar as some believe that all knowledge is ultimately derived from experiences. I'm just exploring the consequences of holding such a viewpoint.)

An IOU worth $10,000 not to be cashed before 2080 for anyone who can prove that I don't have $10,000.

Mathematics is deductive. 1 + 1 will always be 2, we defined it like that.

Michelson-Morley is inductive. We had two hypothesis and did an experiment and got a result that indicated one of them was correct. But the entire reason science is supposed to be reproducible is for the inductive step.

What does it mean for you to say that a claim is "deductive" while simultaneously claiming "it was defined like that"?

Edit: In other words, what did you deduce "1+1=2" from? On what basis do you accept its truth?

You didn't answer the original question. So far, you're just reciting your inductive/deductive mantra.

I'm not sure I follow your question. Mathematics defines 1 + 1 = 2. Those are the rules arithmetic.

Whoops, I thought you were asking if I thought the experiment was an example of deduction or induction.

I believe that the Michelson–Morley experiment provided enough evidence to safely conclude relatively is a more accurate model of the universe than the ether hypothesis. That does not mean that the ether hypothesis is proven wrong, if you define 'proven wrong' as 100% certainty that ether does not exist.

Do you believe that the definition is arbitrary? And by that, I don't mean that we could also have a change of symbols such as "I + I = II," but rather that the idea of one-ness and two-ness (and three-ness) could somehow have ended up with us picking "1 + 1 = 3" and still thinking that this is a meaningful statement? Or is such a belief grounded in the physical world somehow, like an extension of putting bricks into bags?

Your understanding is anachronistic. The Michelson-Morley experiment was conducted in the late 1800s, but special relativity was not proposed until the early 1900s. That is, when the experiment was run, the question was not "Is special relativity or luminiferous ether a more viable explanation for the propagation of light?" So the conclusion that "relativity is a more accurate model" doesn't really follow in the way you suggest.

Which god? The Flying Spaghetti Monster? There no way anybody could ever disprove his noodley greatness, therefore he is the one true god!!!!!!!!!

Logic'd

I don't have a strong enough grasp of epistemology to answer this question.

Whoops, got my history confused. But my conclusion still stands. The experiment was enough evidence to marginalize ether hypothesis.

It's worth taking the time to think about it. If you want to draw a strong dichotomy between inductive reasoning and deductive reasoning as you've set up here, there are certain consequences that you would need to come to terms with.

Do you believe that the luminiferous ether can exist while not being detected by the MM experiment?

The difference that is relevant to this discussion is described in the first sentence of the wiki page:

".. is the process of reasoning from one or more general statements (premises) to reach a logically certain conclusion", which is in direct opposition to induction, by all definitions I have seen.


It is always possible the experiment doesn't tell us what we think it tells us.

It runs deeper than this. For example, if you hold that "1+1=2" is absolutely true and you hold that it is not possible to make absolute truth claims about the physical world, then how does "1+1=2" fit into your conception of the universe? Do you hold that the mental content is real in some sense (Platonism)? Do you believe that "1+1=2" is grounded in sensory experience of the physical world (much like an extension of putting bricks into bags)? If so, "1+1=2" needs to be doubted at the same level as your other sensory experiences and it does not make sense to draw a hard distinction between inductive and deductive logic (since both are premised in the physical world).

It's easy to make naive distinctions between the two categories, but the consequences of those beliefs as they fit into a larger framework of ideas is often quite intricate.

That doesn't answer the question. I think you're not answering the question because you are holding tightly to your inductive/deductive dichotomy rather than thinking more carefully about the experimental setup.

I have little doubt that "1 + 1 = 2" started with observations of the physical world, but eventually axioms were made which separated the expression from reality. We can talk about that without any reference to the physical world deductively. We can create maths that don't have a (proven) correspondence with reality as well.

Please don't ascribe motivations to what I say.

I think it does answer your question, perhaps I was too vague though. I believe that the M-M experiment produces evidence that is in conflict with the ether hypothesis, which means that if the experiment is correct the ether hypothesis is false. However, that doesn't mean there isn't an error in the assumptions of the M-M experiment.

But on what basis can you "trust" the process of logical inference from these axioms? We know we can't "prove" the logical consistency of the system, so why do you think you can trust it in some absolute sense?

Sure. But now the question falls on the math itself. Why is math so trustworthy? What it is grounded in that makes it beyond doubt?

What do you mean by a "correct experiment"?

If we say that "luminiferous ether (the medium through which light travels) fills space" as a statement of a fundamental property of luminiferous ether and we find that "luminiferous ether" is not detectable anywhere on earth, in what sense can it be true that "luminiferous ether" exists?

Miley Cyrus and Justin Bieber still have careers. There is no God.

Pay me.

I'm not sure I follow your question. You seem to be stating the 'trustworthiness' of mathematics has to be earned. I'm saying that this is false. We define the meaning of the symbols in mathematics. We also have methods of showing if something is internally consistent (which we cannot do with everything). It is always trustworthy because we define it to be as such. I'd be glad to see a counter example of this though.

The application of mathematics to the natural world is quite different though. That would be an inductive reasoning (not mathematical induction), and that trustworthiness has to be earned.

Oh, but I am arguing something different. If you could have an ether detector that you can know with certainty never has a false negative then you would know ether cannot exist (at least where you tried to detect it). But you don't have a detector that is certain to have no false positives, so you cannot rule out that the ether exists. It is certainly marginalized to the point of not being worth researching, but that is distinct from knowledge of its lack of existence.

It has been proven that any logical system robust enough to incorporate basic arithmetic cannot be proven to be consistent.

I do not understand how we can "define" math to be trustworthy. I agree that it is, but just because I make a series of claims involving symbols (like "1+1=2") does not inherently suggest that the overall scheme that is being used can be fully trusted. In fact, on its own, I could claim that there's no particular reason to believe that math should be trusted. The trustworthiness of math follows from the fact that it faithfully represents elements of the physical universe. (And *then* the ideas are extended into an abstract framework, and so forth...)

For example, if it were the case that when we put one brick into a bag, and then a second brick into the bag, that the bag contained five bricks, I don't think we would believe that "1+1=2" is a meaningful statement, and should therefore be rejected as being math (in the same way we reject "1+1=5").

Trustworthiness in a purely mathematical context relies upon the trustworthiness of a base logic. Why should logic be trusted?

There are two lines of logic in play.

1) If ether existed, then we would see effect X. We don't see effect X, therefore the ether does not exist. -- Your challenge at this point is that there could be a problem with the detector for effect X. That's fine.

2) The ether hypothesis is incompatible with observation Y. Since we see Y, we know that ether does not exist. -- It's this second line of logic where I don't think your argument works. Moving to the present tense, we know that the existence of a medium through which light must travel is inconsistent with the observations of special relativity.

Since special relativity and ether are inconsistent theories, we know that they can't both be true. Does the fact that we are able to confirm the effects of special relativity inform us that the ether does not actually exist?

---

On a related note, can I claim that there are no elephants in my bedroom? (No, I'm not talking about stuffed animal elephants, or pictures of elephants, or anything like that. I mean the actual living creatures.)

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If OP's word is good he should at least settle for 80 cents on the dollar based on the above.

I wonder if this is the thread OP envisioned when he first posted it.

It's neat how God knows what all 7 billion ppl in the world are thinking at all times.

QED

i just wanted to give you guys something to endlessly argue about. haha.

Didn't really work out that way did it.

my point, exactly. lmao.