I don't deny that two plus two equals four.
I only assert the obvious, that "2+2", which represents an operation of addition, does not represent the same thing as "4", — Metaphysician Undercover
.. or of anything/whatever, hence the utility of a calculator.
Say, a set of my left ear, that soccer match, the Moon, and the experience of vanilla taste I had the other day when eating icecream, comes to 4 in quantity; kind of trivial to count. — jorndoe
You're now confusing quantity, predication, measurement, ...
Say, a set of you and I comes to a quantity of 2, |{you,I}|=2|{you,I}|=2; kind of trivial to count.
Say, where ϕϕ = is human (predicate), it so happens that ϕ(you)∧ϕ(I)ϕ(you)∧ϕ(I), I assume.
You're making a wicked mess of things. :confused: — jorndoe
If ““2+2”...does not represent the same thing as “4””, then in what sense are they equal? — Luke
We cannot count apples and oranges unless we say that an apple is equal to an orange. It is only by assigning equality to distinct things that we are able to count them One apple is equal to an orange, and then we count them, 1,2. So apprehending different things as having an equal value allows us to count them, 1,2,3,4.... — Metaphysician Undercover
To me, your use of [ standard notation that does away with confusion ] is what is making a "wicked mess". — Metaphysician Undercover
I am not sure I follow the argument from Fourier series to saying that "therefore the Planck scale is ontic." — fishfry
(A4) If something is epistemically random, the uncertainty associated with that randomness can be arbitrarily reduced by sufficient sampling. — fdrake
And why does "2 apples + 2 apples" "not represent the same thing" as "4 apples"? — Luke
Start over? — jorndoe
(A4) If something is epistemically random, the uncertainty associated with that randomness can be arbitrarily reduced by sufficient sampling. — fdrake
Quite obviously,"2 apples + 2 apples" signifies two distinct groups of two apples, and the "+" represents an operation of putting the two groups of two apples together into one group. — Metaphysician Undercover
There is no such two distinct groups of two, nor the operation of addition signified by "4 apples". — Metaphysician Undercover
So you agree that the group resulting from this operation of addition is “4 apples”? That is, you agree that “2 apples + 2 apples” = “4 apples”? — Luke
It is obviously signified by the equation “2 apples + 2 apples = 4 apples”. Both sides of the equation are equal in value or quantity. They “represent the same thing” in terms of value or quantity, which is the point of the mathematical equation. I’m not sure what point you are trying to make instead. — Luke
This is only assuming that all of the relevant data is being sampled. — SophistiCat
On the other hand, if you were sampling digits of pi, for example, then unless you already knew what you were sampling, you would never see that it is non-random from your sample, even if you were getting every digit with perfect accuracy. And if you knew what you were sampling, then the question would not arise. — SophistiCat
Yees. I am assuming the things accurately described as random are random. Do any of the interpretations you referenced remove the distribution from the theory? — fdrake
I quite don't understand the relevance of this. Can you elaborate? Are you saying that the real world might have a hidden number that removes all the randomness associated with quantum variables? — fdrake
Well, I have a mostly pop-sci "knowledge" of QM, my college physics being too rusty to be of much use, but as far as I know the "pilot wave" of Bohmian mechanics would make measurements deterministic - except, of course, being hidden, it is not part of the measurement. And MWI says that the full wavefunction evolution is deterministic (as the Schrodinger equation shows), but we can only measure one of its eigenvalues at a time, since our subjective state in which the measurement outcome is recorded doesn't encompass the full quantum state. If you perform successive measurements on identically prepared systems, the branching wavefunction will leave a trail of random results in each individual branch, even though across all of the branches every set of measurement outcomes will be the same. — SophistiCat
I am saying that if it did, we wouldn't know it just from this one sampling. We might guess that it looks suspiciously like the digits of pi, for example (if we were lucky to sample from the already calculated range), but such numerology is perilous — SophistiCat
Your point is simply that "2+2" and "4" are written differently or use different symbols. Or, as I said earlier, they are different expressions of the same value, or different ways of expressing the same value. Very profound :roll: — Luke
By the way, in case I didn't make this clear last time, I consider "different expressions of the same value" to be ambiguous nonsense, and "different ways of expressing the same value" does very little to clarify what you could possibly mean. Do you even know what "value" means? It refers to the desirability of a thing, or what a thing is worth. How do you apprehend "2+2", or "4", as an expression of what a thing is worth? — Metaphysician Undercover
It is only by assigning equality to distinct things that we are able to count them One apple is equal to an orange, and then we count them, 1,2. So apprehending different things as having an equal value allows us to count them, 1,2,3,4.... — Metaphysician Undercover
That's because we qualified value with "quantitative" value. — Metaphysician Undercover
AFAIK the Schrodinger equation's time evolution is deterministic, but that doesn't make the states deterministic. The states are samples from probability distributions (generalisations of probability distributions I guess? I vaguely recall that they break a few rules). It might be that someone can declare some aspect of the randomness "unphysical" and salvage a global determinism (if only we had (blah) we'd determine the output states!). I don't really know enough about it. — fdrake
I'm reading this as a claim that there's some source that determines the observed quantum states deterministically, it's simply that we don't (or cannot) know the behaviour of the source? Analogously, Pi's digits pass tests for statistical randomness, but they're determined given a way to arbitrarily accurately evaluate Pi. — fdrake
"We calculated the value of the national carbon footprint for last year to so-and-so."
"I greatly value a cold beer on a hot summer night." — jorndoe
Yes, because our discussion was in the context of mathematics. Or do you think that mathematics is all about monetary value (i.e. desirability/worth)? Don’t be daft. — Luke
If it is true that "4" expresses a value, then "2+2" does not express a value. — Metaphysician Undercover
Do you see that if "4" is an example of an expression of value, then in "2+2" there are two distinct values expressed, "2" and "2" whereas only one value "4" is expressed with "4"? — Metaphysician Undercover
The use of "value" in the first statement is extremely ambiguous because it is not related (grounded) to anything. — Metaphysician Undercover
2+2=4. You said that you don't deny this equation. How can "2+2" and "4" be equal if "2+2" does not express a value (i.e. a quantity, number, amount)? — Luke
Really? And yet you understood it fine? And well enough that you could, say, go look up annual carbon footprints and such...? (I could start listing examples ... maybe another day) — jorndoe
So, "2+2" does not represent a value, it represents two distinct values related with "+", and we say that this is equal to the value of "4". — Metaphysician Undercover
If you cannot see the difference between representing the value "one dollar", (which is represented as $!), and representing something equal to a dollar ("four quarters", or "ten dimes"), then I think you've got a problem. — Metaphysician Undercover
I really can't say I understood it at all. I have absolutely no idea what "the value of a national carbon footprint" is. Examples would not help. As I said, you need a scale of some sort. — Metaphysician Undercover
Feel free to explain the difference between "representing the value one dollar" and "representing something equal to a dollar" to anyone who cares to listen. — Luke
Do you understand the difference between saying "4 objects", and specifying a specific configuration of four objects? A specified configuration is not the same thing as the more general "4 objects". This is the type of difference I am talking about here. In both cases, "2 apples + 2 apples", and "4 apples", we are saying something about four apples, but "2 apples + 2 apples" says something more specific than the more general "4 apples". So we cannot say that the two phrases represent the same thing. — Metaphysician Undercover
You can't be serious.
"Based on those samples we calculated an average value of so-and-so."
My young nephew and niece understand what's meant in the English language. If you can't, then you're missing something. — jorndoe
Something equal to a dollar is "ten dimes", or "four quarters" — Metaphysician Undercover
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