Moderation Questions
The last iteration of the moderation discussion thread was a complete disaster. Numerous attempts to keep it on topic fa
jfc why would I want to do that?
j/k
That's right, because (as yet) there's no mathematical proof, so it remains a scientific theory.
Mathematical conjecture, not scientific theory.
I think you are confusing different issues here. One is related to infinities and the fact that mathematics deals in infinities whereas reality does not. This is true. Mathematical theorems also do not fall into categories of falsifiable or not, they can either be proved from the axioms or they can't - otherwise you could make facile statements like "how do we know that all rig
I’m working with the definition given by Karl Popper, which requires you to be able to physically falsify it in order for it to count as falsifiable. That’s how he is able to explain the progress of science, by appealing to increases in technology expanding the limits of what is falsifiable. But something could be corroborated without being falsifiable.
Your pockets aces never being dealt example doesn’t work, because all it takes is for aces to get dealt once for it to be false. The other way is not the case, because it doesn’t matter how many times in a row aces are dealt, you will still have another hand you can deal.
This is all having to do with skeptical cases in induction raised by Hume. The classic example of this is the proposition “all swans are white”. It doesn’t matter how many white swans you see, it doesn’t provide a deductive basis for that universal, since all it takes is one black swans, which could always be the next swan you see.
I think you're stating this backwards. The Pythagorean Theorem is falsifiable, all it would take is one example that we could verify with a simple computation and it has been falsified. The strange belief that there is some a, b, and c out there that violates the Pythagorean Theorem despite the proof and all the examples of it holding is unfalsifiable. This actually matters
The Pythagorean theory is false outside of euclidean geometry. Non-euclidean geometry (which better maps on to the real world) shows that you can indeed have right triangles where the sides don’t follow the Pythagorean theory.
Math follows from axioms which are in principle not falsifiable, since they are taken as given. We found out that the axioms that the Pythagorean theory relies on don’t work in curved space.
Your pockets aces never being dealt example doesn’t work, because all it takes is for aces to get dealt once for it to be false. The other way is not the case, because it doesn’t matter how many times in a row aces are dealt, you will still have another hand you can deal.
I think we're talking about different propositions. You're talking about "all hands that will ever be dealt will be pocket aces" (potentially infinite) whereas I am talking about "it is possible for every hand you get dealt for the rest of your life to be pocket aces" (finite). This is an important distinction I feel. Once you start introducing infinities, you have a lot more than falsifiability to grapple with. There are branches of mathematics (inter alia, calculus, number theory, probability) that deal with different infinities in different contexts. But I feel that propositions involving infinite processes don't really come under the umbrella of scientific theories, as such processes are not possible in reality. Also, it's important to draw the distinction between "arbitrarily large but finite" and "infinite". These are very, very different things.
These are just my thoughts on the matter. I have no formal education in this topic so I am not stating any of it as incontrovertible fact.
Oh got it, yes, if we introduce an upper bound then we can say that it’s possible to falsify. But it would be better to introduce the upper bound on the amount of hands instead of the lifetime, because trivially we could just deal one hand of aces and then never get dealt another hand. I think we’re trying to say something about actually getting dealt a significant amount of aces in a row. Of course even if we said this, it wouldn’t in principle show that the infinite case could be falsified, because no matter what you set the upper bound to it will always be infinitely far away from infinity.
That's lottery odds. Well, to get dealt aces 3x in a row from a given starting hand obviously. To get a streak of 3x aces in a row across all hands dealt lifetime is much shorter.
Indeed. People win the lottery and get struck by lightning all the time.
I don’t think anyone has gotten struck by lightning while winning the lottery
When do you win the lottery? When the numbers are drawn? When you check your ticket? Or when you turn your ticket in?
That's long odds. Greater than 10,000,000 to 1 that your next three hands will be AA.
But as everyone noted, a great many very unlikely things happen every day.
That's long odds. Greater than 10,000,000 to 1 that your next three hands will be AA.
But as everyone noted, a great many very unlikely things happen every day.
I think I had AA 3x in a row a couple of times in the last month actually. Been playing a lot of PLO-5 :p
That's long odds. Greater than 10,000,000 to 1 that your next three hands will be AA.
But as everyone noted, a great many very unlikely things happen every day.
I think there could be some possibility that the shuffles were poor and thus increased the chances of getting dealt the same hand above what they would normally be.
Also, I know you're probably trying to be slick here, but this phrasing is somewhat disingenuous. Extremely unlikely events are uncommon by definition. It's just that while "you will win the lottery" is an extremely unlikely event, "someone will win the lottery" is not.
Also, I know you're probably trying to be slick here, but this phrasing is somewhat disingenuous. Extremely unlikely events are uncommon by definition. It's just that while "you will win the lottery is an extremely unlikely event", "someone will win the lottery" is not.
Oh yes, extremely disingenuous
IÂ’m working with the definition given by Karl Popper, which requires you to be able to physically falsify it in order for it to count as falsifiable. ThatÂ’s how he is able to explain the progress of science, by appealing to increases in technology expanding the limits of what is falsifiable. But something could be corroborated without being falsifiable.Your pockets aces never
Atomism was metaphysics for about 2,000 years because it wasn't conceivably falsifiable given the scientific knowledge of the time. The same would apply if Aristotle had proposed something like the general idea of spacetime. That's different from positions like materialism or idealism, which aren't falsifiable even in principle.
So it seems that anything we can't rule out as unfalsifiable in principle counts as a candidate for science.
The Pythagorean theory is false outside of euclidean geometry. Non-euclidean geometry (which better maps on to the real world) shows that you can indeed have right triangles where the sides don’t follow the Pythagorean theory.
The Pythagorean Theorem is always true when Euclids axioms, especially the 5th are valid.
Math follows from axioms which are in principle not falsifiable, since they are taken as given. We found out that the axioms that the Pythagorean theory relies on don’t work in curved space.
You just gave an example of an axiom that can be falsified. If Euclids parallel postulate doesn’t hold you get non Euclidean geometry which still makes sense.
Atomism was metaphysics for about 2,000 years because it wasn't conceivably falsifiable given the scientific knowledge of the time. The same would apply if Aristotle had proposed something like the general idea of spacetime. That's different from positions like materialism or idealism, which aren't falsifiable even in principle.So it seems that anything we can't rule out as unf
Falsifiability only means you have to be able to construct a hypothetical experiment which will disprove the proposition, not that you have to be able to carry out the experiment in practice. For example, the idea of parallel universes/many worlds is not falsifiable because there is not conceivable experiment you could carry out to contradict it. The idea of atomism was always falsifiable if you had a powerful enough microscope (figuratively speaking). These things are not the same.
That's long odds. Greater than 10,000,000 to 1 that your next three hands will be AA.
But as everyone noted, a great many very unlikely things happen every day.
I think that misses the point that the absence of extreme outliers like someone being dealt pocket aces every hand is exactly what we expect from a genuinely random process, and that consistency helps confirm the validity of our assumptions about randomness.
I think that misses the point that the absence of extreme outliers like someone being dealt pocket aces every hand is exactly what we expect from a genuinely random process, and that consistency helps confirm the validity of our assumptions about randomness.
You would need 15,000 earths' worth of people all getting dealt out hands at the same time to have a > 50% chance that one of them will hit a streak of 6x pocket aces from their first deal.
Falsifiability only means you have to be able to construct a hypothetical experiment which will disprove the proposition, not that you have to be able to carry out the experiment in practice. For example, the idea of parallel universes/many worlds is not falsifiable because there is not conceivable experiment you could carry out to contradict it. The idea of atomism was always
That bar seems too high. I can't imagine how the Greeks could have even conceived of a hypothetical experiment to falsify the existence of 'actual' atoms.
Not falsifiable: We live in a simulation.
Falsifiable: We live in a simulation with finite computational resources.
I'm not sure these lines between science and philosophy are all that clear.
There are claims that us being in a simulation is falsifiable and that it is proven we don't live in a simulation
"It has been suggested that the universe could be simulated. If such a simulation were possible, the simulated universe could itself give rise to life, which in turn might create its own simulation. This recursive possibility makes it seem highly unlikely that our universe is the original one, rather than a simulation nested within another simulation," says Dr. Faizal. "This idea was once thought to lie beyond the reach of scientific inquiry. However, our recent research has demonstrated that it can, in fact, be scientifically addressed."
The team's conclusion is clear and marks an important scientific achievement, says Dr. Faizal.
"Any simulation is inherently algorithmic—it must follow programmed rules," he says. "But since the fundamental level of reality is based on non-algorithmic understanding, the universe cannot be, and could never be, a simulation."
The simulation hypothesis was long considered untestable, relegated to philosophy and even science fiction, rather than science. This research brings it firmly into the domain of mathematics and physics, and provides a definitive answer.
That bar seems too high. I can't imagine how the Greeks could have even conceived of a hypothetical experiment to falsify the existence of 'actual' atoms.
I guess you could make the argument that no matter how powerful your magnifying device, if you don't see the atoms it's just because you need a more powerful device, so that avenue doesn't lead to falsifiability. But we inferred the existence of atoms through other experiments before we ever saw them with electron microscopes, so we know that we can identify them through means other than observing them directly; I don't know if these methods would produce a negative result in the event of non-existence of atoms though.
ETA: If you modify the proposition slightly to say that the atoms are no smaller than x size, it is falsifiable through direct observation via a sufficiently powerful microscope.
