You should be aware of something about me personally related to that... I'm incredibly patient. Don't ever feel you have to reply to me "timely"... in fact, I would prefer you took your time, and got about any actually important stuff in your life (including just enjoying it, which I consider important).

Reply whenever you're ready, not when you feel you're "supposed" to, because I'm not holding you to any time frames.

>1/2^c + 1/2^c + 1/2^c to k terms. There are the same number of terms in each series. — EnPassant

Okay, I think I got it (incidentally, c=k here, right?), but the same objection applies. You still can't apply theorem 1, because you still can't name an x for which you have an infinite number of terms of the value 1/x such that 0<1/x<1. Every x you name is finite; therefore, every term in your sequence is finite. You don't have an infinite number of 1/x for any 0<1/x<1, so you can't apply Theorem 1.

Or think of it this way. Note that every time you add a term, you change all of the terms. We go from 1/2, to 1/4+1/4, to 1/8+1/8+1/8, and so on. But note also that we can actually sum these partial terms too... 1/2=1/2, 1/4+1/4=1/2, 1/8+1/8+1/8=3/8, and so on.

The general form here is:
$\displaystyle\sum_{i=1}^{k}{\frac{1}{2^k}} = \frac{k}{2^k}$
But when you generalize this, you're talking about what that form becomes, so you really mean:
$\displaystyle\lim_{k\to\infty}{\sum_{i=1}^{k}{\frac{1}{2^k}}} = \lim_{k\to\infty}{\frac{k}{2^k}}$
But your theorem 1 just says:
$\displaystyle\lim_{\to\infty}{\sum_{i=1}^{k}{\frac{1}{x}}}=\infty$ where $0\lt\frac{1}{x}\lt1$
...so doesn't apply.

I'm not up to speed on binary. I don't think you understand what I'm saying. — EnPassant

I'm going to take a stab at your confusion then. Here is the full form of the inequality:
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 > 1024+1024+1024+1024+1024+1024+1024+1024+1024+1024

There are ten terms here. The sum on the left as it turns out is 1023/1024. The sum on the right is 10/1024. 1023/1024 > 10/1024, as you said.

I can't write the full form of 1024 terms without basically flooding the channel... 1024 terms itself is large enough, but the value of 2^1024 itself is huge:
179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216

But we can write the sums in power notation. The sum of 1024 terms of 1/2+1/4+...+1/2^1024 = ((2^1024)-1)/2^1024. That is less than 1 (just barely... by 1 divided by that huge number above, but less is less). But 1024*(1/1024) is equal to 1. So:
1/2+1/4+1/8+...+1/2^1023+1/2^1024 < 1024+1024+...+1024
...because:
((2^1024)-1)/2^1024 < 1

I don't think you understand what I'm saying. — EnPassant

Of course you don't, because you keep replying to me. But that's not what the problem is. The problem is that you don't understand what you're saying.

Now you have an infinite sum of positive quantities > 0 and that's infinite. — EnPassant

Dubious. Your argument was based on this theorem:

Theorem 1
Define 1/x such that 0 < 1/x < 1. If 1/x is summed to itself infinitely often, the sum is infinity. — EnPassant

There is no such term 1/x that is added to itself infinitely often in 1/2+1/4+1/8+...; nor is there a "squeeze term" such that in that sequence there are terms >=1/x added to themselves infinitely often. For this reason you cannot apply Theorem 1. If you disagree, name the number; but I already gave you a generic refutation... for any number you name, I can tell you how many finite terms there are in the sequence >=1/x, and you cannot name a positive number such that there are an infinite number. Theorem 1 requires something that's not there... therefore, you cannot apply it.

Now let the number of terms run to infinity and the sum on RHS is infinite. — EnPassant

You keep handwaving through the same argument's flaw.

You have an inequality that's true for term 10:
0.1111111111b > 1024+1024+1024+1024+1024+1024+1024+1024+1024+1024

That's all fine and dandy. But it doesn't hold at term 1024:
0.11111111......111b ≯ 1024+1024+1024+1024+1024+1024+1024....1024
(with 1024 1-bits on the left, and 1024 1024-terms on the right).

In fact, at that term:
0.11111111......111b < 1024+1024+1024+1024+1024+1024+1024....1024
...and after that term, you're adding values less than 2^-1024 on the left, which is << 1/1024... but for each such term, you're adding 1/1024 on the right.

So that it works at term 10 is irrelevant, because the inequality fails at term 1024 and for all terms after it. You can't go from 10 into infinity without passing 1024.

What is 1/2c added to itself infinitely? — EnPassant

Your latex is garbled... let me generalize and math this for you. For any positive integral x, no matter how large:
$\displaystyle\sum_{i=1}^{x}{2^i} \lt \sum_{i=1}^{x}{x} = 1$
...intuitively, you can see this by "argument from binary". The left sum is always:
0.111...11 with x 1-bits. That's always less than 1.

...and for each y>x:
$\displaystyle 2^y \lt 1/x$

It doesn't matter. An infinite sum of equal infinitesimals must be infinite. — EnPassant

There is no infinite sum of equals on the left side. For any positive x, no matter how small, there are only a finite number of terms greater than x in that infinite sum. Quick proof...
1. Pick your x.
2. Write 1/x in binary
3. Count the digits; call the number of digits plus one n.
4. 2^n is greater than your 1/x.
5. 2^-n is less than your x.
6. All terms after the nth term are less than 2^-n.
(eta: corrections)

The sum of terms 1/x is infinity if 1/x > 0. — EnPassant

What are you talking about?

At the 1024th term on the left, we're adding 1024 terms... in binary point, 0.1, 0.01, 0.001, ... , 0.00...001 (with 1 in the 2^-1024th place). That sum is 0.111...11 (with 1024 1's).

At the 1024th term on the right, we're adding 1024 terms, each of which is 1/1024... that is by definition of multiplication equal to 1024*(1/1024), which is 1024/1024=1.

After the 1024th term, we're adding numbers on the left much smaller than 1/1024; in fact, they're smaller than 1/2^1024. And on the right, for each of these, we're just adding 1/1024.

1/2 + 1/4 + 1/8+....+1/1024 > 1/1024 + 1/1024 + 1/1024+....+1/1024 — EnPassant

So that's 10 terms. What happens at the 1024th term?

Your left sum is 0.111....11 with 1024 1 bits in binary. Your right sum is 1. Is 0.111...11 with 1024 1-bits greater than 1?

I'm saying if there are the same number of terms in each. Now increase x indefinitely with the same number of terms top and bottom. — EnPassant

...and you'll find the inequality always breaks down for some number of terms, and all terms after that. In fact, you can cheat... whatever positive integral x you specify, it will break down at the xth term.

1/2 + 1/4 + 1/8+....1/x > 1/x + 1/x + 1/x+...+1/x — EnPassant

dubious. Take x=10^9. I happen to know off the top of my head the left hand side goes below 1/10^9 at term 30 (because I work with computers). So in binary, the sum on the left is 0.111...11 with 30 1's. Take that sum and divide it by 1/10^9, you get a finite number... call that number's ceiling y. At term y, the sum on the right equals the sum of the left before term 30, and you're just adding smaller and smaller terms on the left. In fact, by the time you reach term 10^9 on the right, the right sum becomes 1; and the left sum by that term is simply 0.111...11 with 10^9 1's in binary, which is less than 1. After that, every term you add is going to be less than 10^9 on the left, and equal to 10^9 on the right.

the whole infinity of them - are positive and > 0. Right? — EnPassant

That's insufficient to use your theorem, as I explained in my previous reply.

What I'm saying is very simple. Suppose you had a kind of God calculator that would print out the actual addition of 9/10 + 9/100... what would that be 1 or infinity? That's what I mean by the actual sum. — EnPassant

Here's what I read is going on. You want to talk about an "actual sum" in a meaningful sense, outside of the provided definition. You intuit that it means something, but I'm not convinced it actually does.

To convince me, however, you metaphorically appeal to the God calculator, and sprinkle in "actual" as adjectives. But that's not convincing for me. I read both the metaphor and the adjective as just reifying.

God didn't give us addition on tablets; we invented it. The "base" definition of addition works recursively down to base cases, so that's fine for finite numbers of terms. But you cannot reduce an infinite recursion down to base cases. So there's no a priori definition of infinite sums.

To show how quirky infinite sums are consider the following (this is not meant to answer anything, it is just to illustrate how strange things become at infinity) — EnPassant

Theorem 1
Define 1/x such that 0 < 1/x < 1. If 1/x is summed to itself infinitely often, the sum is infinity. — EnPassant

It could be infinity; but it doesn't have to be infinity. You have to define what you mean by infinite sums first before you even get to say this sum is infinity. But let's grant that theorem; it works at least for one definition:

From this we conclude that any positive quantity added infinitely sums to infinity — EnPassant

...then this still does not follow. There are infinite sequences of terms in the range (0,1) such that for any such term x, there's only a finite number of terms greater than or equal to that x. In fact, 9/10, 9/100, 9/1000, ... is such a sequence. So even if you're going to try to apply some variant of a squeeze theorem to prove that this sum is infinite, you just can't do it... because there is no term in this series for which you're adding it or any larger number an infinite number of times.

But I am talking about an actual sum. — EnPassant

I realize that, but there's no "actual sum" to speak of outside of this definition. In principle I could give an intuitive argument for why .999...=1 using the idea that each digit in the decimal is dialing in on the "address" of the number it refers to. In such an argument I could say that if you have an infinite number of 9's after the string .999, then the resulting string dials in on the address of 1 itself. But in using this argument and applying it to a repeated decimal, I would in effect be using the limit definition.

What makes me suspicious is the paradoxes that exist at infinity. — EnPassant

I understand that as well... but analogously, divergent infinite sums can't use the definition above; only convergent ones. But that's precisely why we would apply this definition to infinite sums for convergent infinite sums (and in certain cases we can apply a definition to divergent sums, but with different definitions).

But I think in the bigger picture this thing boils away, because in the state of affairs that we're in, the "actual sum" for a convergent infinite sum has been defined, by this definition. In essence, the infinite sized string .999... is like a word, and we have assigned a formulaic definition for all words matching this pattern, including that one... and by that definition, .999...=1. We could say then that the address .999... has been assigned in such a way that the number assigned to it is 1.

Or phrased another way, I'm not sure you can actually say what it is you're disagreeing with meaningfully. To do so you would have to reify .999...'s definition without using the provided one, and claim that whatever reified thing you came up with "has a problem". But what problem? If the problem is it hasn't been defined, then it's a bit vacuous. If the problem is we don't know what it is, then you're presuming it has a meaning... in what sense does it have a meaning? What meaning did you assign to it? That's the problem I'm raising here... you cannot talk about this reified "actual sum" unless you can talk about it, and I'm not sure you've convinced me there's a thing to talk about.

I take my definition of "number" from OED: "an arithmetical value representing a particular quantity and used in counting and making calculations". Notice specifically the criteria "particular quantity". This rules out the possibility that .999... is a number. — Metaphysician Undercover

As I've explained to fishfry already, that two things are equivalent does not mean that they are the same thing. — Metaphysician Undercover

I don't believe that ".999..." and "1" refer to the exact same thing. — Metaphysician Undercover

You're all over the place here. You have a definition of number that refers to a value (read the newer version of OED; cf to definition 1b of your revision). 1 and .999... being equivalent means they refer to the same value. And don't think I didn't catch that suddenly "refer to" changed to "are"; nevertheless, it's common language to use forms of "to be" to represent equivalence under equality. If .999... represents the same "particular quantity" that 1 does, they refer to the same value, which is what it means to say that they are the same thing.

Therefore what is on the left side of the "=" (which indicates equivalent) does not provide a definition of what is on the right side. It seems you do not know what a definition is. — Metaphysician Undercover

Your "therefore" is thwarted by the definition of a number. Equivalence under equality means that the left hand side has the same value as the right hand side. Your OED definition of number is that of a value. Therefore, equivalence in this context means referring to the same number, since it's the same value. And you're complaining about tomfoolery?

But isn't one of this pie a different quantity from one of that pie? — InPitzotl
No, why would you think that? — Metaphysician Undercover

...

As I explained to Banno, it's very clear that "1/9 of a pie" does not indicate a particular quantity of pie, because pies vary in size — Metaphysician Undercover

Because pies vary in size?

One of anything is the same quantity as one of anything else. — Metaphysician Undercover

Apparently not. One pie is the same as one pie even if they are different sizes, but one ninth of a pie is not the same as one ninth of a pie because they are different sizes. I know special pleading when I see it. Again, you're all over the place.

If your inability to accept this fact rules you out of this conversation then so be it. — Metaphysician Undercover

Uhm... but...:

Some quantities cannot be divided in certain ways. It is impossible. Three cannot be divided by nine, it is impossible. Nevertheless, mathemagicians are an odd sort, very crafty, wily like the fox, devising new illusions all the time. They like to demonstrate that they can do the impossible. Some people even believe that they actually do what is impossible. That is a problem. — Metaphysician Undercover

...yet:

So I'm asking you, who apparently does believe this, why does mathematics, as a single unified discipline, have these two distinct symbols to refer to the exact same thing. — Metaphysician Undercover

...and:

Until then, I'll believe what seems very evident to me at this time, that these two have distinctly different meanings. — Metaphysician Undercover

What conversation pray tell are you even talking about? How can .999... have a second meaning if .9 means 9/10 and 9/10 is allegedly a problem? And how come you can't be honest about what you're inviting me to do? The problem isn't that you're missing that conversation about why there are numbers that have two representations in the decimal system... the problem is that you don't believe decimals are possible because you have a quixotic quest against fractions, and yet you present to claim that you believe .999... has a meaning at all. I'm not the problem here, MU; I can easily have that conversation with someone who isn't so wrapped up in your fictional world of fraction-denial. I just can't have this conversation with you because you can't face the fact that there's a thing to discuss.

But again, it's irrelevant, because your two-names-means-two-things premise is still as dubious as it ever was.

There was no implicit assumption that the same thing ought not have the same name, but an implicit assumption that if the same thing does have two distinct names, there is a reason for it having two distinct names. — Metaphysician Undercover

So instead of arguing "there are two names for a thing therefore there are two things", which is a red herring, you're just arguing "there are two names for a thing and there's no reason for it having a second name therefore there are two things", which is just a red herring with weasel (obviously if a thing has two names, there's a reason it has two names... it was named twice; and obviously that doesn't count... so, the weasel is in what constitutes "a reason"). Adding a weasel to a red herring is still not an argument, though I suppose the weasel would love the snack.

I don't believe that ".999..." and "1" refer to the exact same thing. — Metaphysician Undercover

Okay.

Until then, I'll believe what seems very evident to me at this time, that these two have distinctly different meanings. — Metaphysician Undercover

But that would be silly because your premise that two names must refer to two things is a red herring. Also, it's a bit fishy:

A fraction is not a number. — Metaphysician Undercover

If you cannot agree that a fraction is a number, how are you even qualified to talk about the meaning of .999... in the first place?

So I'm asking you, who apparently does believe this, why does mathematics, as a single unified discipline, have these two distinct symbols to refer to the exact same thing. — Metaphysician Undercover

I detect some language loaded to the brim with irrelevancies.

If you could answer this for me, then you might help me to believe what you believe.

...why does this sound like the hook of a con to me? My "belief" isn't relevant here (except insofar as I'm part of the math community which, technically, I am, but it's just a tiny part)... the terms here are terms of art in the math community. As mentioned before, the math community defines and uses these terms. And the way they use it, .999...=1. The definitions therefore are matters of fact. If you have any issues, it's with the proofs. But you're not pointing those out... you're just rattling about nonsense of two names having to refer to two things... it's your core broken intuition, and just propping it up with loaded language isn't going to fix what's broken here.

If we can't agree that 1/9 of a pie is a particular quantity of pie, then we can't have the conversation you want. But it's irrelevant anyway.

On the off chance that someone else is curious, yes, there's a reason that the decimal system representation of numbers gives two names for the same numbers, and it's not unusual for various systems to do so. On the off chance MU replies to this with a rebuttal, it's irrelevant... your entire two names is two things argument is dubious, so there's literally nothing to argue against including this.

Half of this pie is a different quantity from half of that pie. — Metaphysician Undercover

But isn't one of this pie a different quantity from one of that pie?

So I still believe that concepts such as "real numbers" operate without an acting definition of "number", providing for all sorts of tomfoolery. — Metaphysician Undercover

We agree on seeing tomfoolery, we just disagree on where we see it.

Is this Meta's claim? — Banno

It looks to go beyond this. Not only is 0.111... not a number, but there's no such thing as squares, because dimensions are incommensurable (@tim wood asked the question I was thinking before I got to it... and that was his response). Circles aren't real, so maybe trigonometry is a lie. Looks to me like Meta's a strange sort of Pythagorean?

If that's the case, then why have two distinct representations for one and the same thing? — Metaphysician Undercover

What do you mean "If that's the case, then"? There seems to be an implicit assumption that every thing should have exactly one name. Who exactly is making that assumption? It's not me, and it can't be you... does it say "Metaphysician Undercover" on your birth certificate? (And isn't 1 also equal to the fractions 1/1, 2/2, 3/3, and so on anyway?)

Any reason whatsoever for there being two distinct representations for the same thing would do. What's it to you that there are two of them? Is there supposed to be an objection here?

They compute limits which are not the same as sums — EnPassant

Given that the sum is by definition the limit, then by definition it's the same. You keep tripping over this same point.

I'm aware of that. — EnPassant

Apparently not... see the underlined as evidence for your continued confusion of the same point. The sum is by definition the same as the limit.

But it has not been explicitly defined. — EnPassant

Right after the citation @Pfhorrest gave:

That is,
$\displaystyle\sum_{i=1}^{\infty}{a_i} = \lim_{n\to\infty}\sum_{i=1}^{n}{a_i}$. — wikipedia

That still begs the question what is an infinite sum if nobody has ever computed it? — EnPassant

That begs the question of what the heck you mean when you're talking about an infinite sum. Mathematicians regularly compute what they mean by it. It's the thing you're talking about that's nonsense, not the thing mathematicians are talking about.

You can't jump from the finite to the infinite and expect finite rules to apply. — EnPassant

Case in point... what are you talking about?

And it is questionable that it has been defined. — EnPassant

No, it's factual that it has been defined. Definitions aren't handed to us from an abstract guy giving out tablets in some Platonic/Pythagorean plane of existence. They're established by people... in this case, it's technical definitions given by mathematicians. They define it. You question that they define it, but that doesn't erase the fact that they, indeed, defined it.

All that has been rigorously defined is a limit. — EnPassant

The infinite sum itself has been defined to be the limit... by mathematicians... who are the both the speakers of and designers of the language of math.

An infinite sum is undefined because nobody has ever computed it. — EnPassant

An infinite sum is defined because the mathematics community defined it; same as "twelve" is defined because English speakers defined it.

tends to infinity — Wikipedia

...that's a term of art. It means to increase without bound. You're choking on mathematical language that you think represents some ideal thing that it just doesn't represent.

ETA: Quite honestly, this whole discussion of infinite sums reminds me a lot of the maths video from Look Around You:

Narrator - What's the largest number you can think of?
Girl - uhm... hundred thousand?
Man - nine hundred and ninety nine thousand
Older man - A million
Narrator - In actual fact it's neither of these. The largest number is about forty five billion, although mathematicians suspect there are even larger numbers

...if I'm to understand correctly, the quibble you have is about what the "actual" infinite sum "actually" adds up to. Ironically, your quibble includes the notion that infinity is not a number. So I have no idea what you're talking about. Mathematicians define infinite sums differently.

This doesn't exist, because there's no limit for the sequence 10, 100, 1000, ... (That is, the sequence {10^n}). — Andrey Stolyarov

It can be defined using 10-adics:
$\underset{n\to+\infty}{lim}{|10|^n_{10}}=0$

Numbers are symbols that are only useful and meaningful when applied to real world situations. — Harry Hindu

Is strong encryption a real world situation?

"The scientific community has no consensus on whether quantum indeterminacy is a thing or not" Brings up Schrödinger's cat. The act of observation changes the physical thing. — Becky

Your use of the word "physical" is ambiguous. The controversy is based on your favorite interpretation of quantum mechanics (see Sean Carroll's "The Most Embarrasing Graph in Modern Physics"). In QM there are two processes... the Schrodinger Equation and the Born Rule. The former is deterministic; the latter is where indeterminacy comes in. The second process is controversial; MWI, for example, just "rejects" it (it's still there, it's just emergent... it's an anthropic consequence rather than something real)... when Schrodinger opens the box, his wavefunction just entangles with its contents (measurement is entanglement in MWI), leading to a world where Schrodinger sees a living cat and a world where he sees a dead cat (and to MWI, the wavefunction itself is physical; I'm guessing you mean what I tend to call classical?) Keeping that and Sean Carroll's embarrasing graph in mind, see this table for an inventory of where various interpretations stand on quantum indeterminacy (the Deterministic column should do).

Notice specifically the criteria "particular quantity". This rules out the possibility that .999... is a number. — Metaphysician Undercover

Ah, I think I understand. This is a language barrier. In the language spoken by the mathematics community, .999... represents the same particular quantity that 1 does.

What matters to the present discussion is that .999... does not represent a number. Nor does .111... represent a number, and that's the problem with the op. — Metaphysician Undercover

What a silly thing to say. .999, eighteen, XVI, and .999... all represent numbers.

"How do you know it's infinity and not, say, an octillion?" -- InPitzotl
Because I know it is not any nameable number. — EnPassant

You answered only half of the question... the half about your knowing that it's not any nameable number. What about the other half... how do you know it's infinite?

ETA: Probably obsolete now... once you accept that it's infinite, we could then enumerate as statements the meaning of each finite decimal expansion, and agree that we have no such infinite statement; then we can define the infinite statement to mean the limit (after possibly a quibble that we're defining the finite expansion's meaning anyway).

I don't know because I don't know if 'how many' applies to infinity. — EnPassant

How do you know it's infinity and not, say, an octillion?

It is a conservative statement. — EnPassant

So if you want to be conservative, just say what you're talking about... "the number of counting numbers".

How many 9s are we talking about? — EnPassant

Well there's a 9 in place 1, a 9 in place 2, and 9 in place 3, and so on...

There's a 9 in place 20, a 9 in place 4 billion... apparently, there's a 9 in all places n where n is a number.

So, how many numbers are there?

So does this mean ...999.999... = 0?

But all 3 types are expected to pay off soon; so if you test them repeatedly and they don't pay off soon, then the theory has been falsified. — Samuel Lacrampe

Ah, but you're forgetting the "falsity indemnification clause":

Slot machines can change types, though, so it's best to be a bit careful. — InPitzotl

Also you can still dismantle one of each type to check the mechanism. — Samuel Lacrampe

...if you could. But, if you could, you still won't falsify the theory. You'd merely have more information as to what type of machine it is. In fact, such a thing would simply be being careful, which the theory tells you to do.

Also the theory concludes that you should play regardless of the type — Samuel Lacrampe

...it not so much concludes that you should as waffles; again, see indemnification clause.

Finally, even if a theory is empirically unfalsifiable, it can still be rationally rejected as unreasonable. That's why we have such principles as Parsimony (Occam's Razor). — Samuel Lacrampe

Of course it's unreasonable... that's the whole point of it! But the problem with the theory isn't its lack of parsimony. Strictly speaking, a machine will either pay off before, roughly at, or after the expected frequency of payoff. There's no simpler description of when the machine would pay off. The problem with the theory is that it's useless. It doesn't give us any real information or use... it doesn't let you predict anything, doesn't tell you what you don't already know. But you said the problem was that it doesn't appeal to PoSR, which in our current form is some foundational principle about what you believe based on whether causes cannot be greater than effects or what not.

For fun, I could revamp it as so (needs polishing but you get the overall idea):
Causally speaking, everything that is physical is either determined or random. Acts from agents with free will are neither determined nor random. Therefore agents with free will are not physical. — Samuel Lacrampe

Indeed, you can revamp it that way. So as I understand it, this form of argument goes roughly like this. Random things and deterministic things are physical, but free will being neither random nor deterministic is non-physical. We have free will. Therefore we have a non-physical component, which we shall call a soul. Is that the form of argument you wish to present?

I have already answered this general question here — Samuel Lacrampe

No, you haven't. You used the word greater and said "in terms of", but there's no real lemon test I can put to this. Like the slot machine theory, there's no actual prediction I can rule out based on PoSR. You tried this twice, remember, and actually managed to rule out things that increase in energy one of those two times? That's how bad this definition is. We need something useful... something that can either actually be used, or something to where when we find a counterexample we can say for sure, "oh, I'm sorry, PoSR must be false then". If we don't have that... if you don't stick your neck out here... we just have a slot machine theory... nothing more than a poetic way to describe whatever is post-hoc.

But the model output must still be empirically verifiable. — Samuel Lacrampe

Not.... really. At the theoretical phases it simply should be coherent; it helps if it's "aesthetic" in some way. At some point down the road hopefully it'll be verifiable somehow, but the guy making the theory can still publish papers on it and discuss it even if he has no idea how to verify it. How do we verify String Theory? We don't know yet; don't know if it can be verified. Still, working out what forms it can take is part of the theoretical physicists' jobs, if they're interested in such things. So whereas this:

"It is judged by the extent to which its predictions agree" — Samuel Lacrampe

...is true, it's not a requirement for outputting (discussing/publishing/debating/etc) theoretical physics... it's instead a requirement for acceptance of the theory.

Is it not empirically verifiable, at least in principle? — Samuel Lacrampe

We don't quite know yet.

Side note: I suspect the MWI came about due to our desire to satisfy the PoSR — Samuel Lacrampe

Again with the opining of things already on the internet. Hugh Everett discusses his motivations in the introduction to his paper "The Theory of the Universal Wavefunction". Basically, compared with prior theory, the Born Rule looked a bit odd, artificial, and anti-symmetric. Roughly, the cat is supposed to be in a superposition, but Schrodinger is supposed to be a classical observer. But if Schrodinger were in a bigger box he's supposed to be in superposition. The rule being applied here is parsimony... the Born Rule is redundant, arbitrary, and inconsistent, so throw it out.

How do you make the distinction between fields of science vs philosophy? — Samuel Lacrampe

I'm not sure distinct is the right word... how would you distinguish natural sciences from natural philosophy?

For me? Religious reasons. But this should not count for or against any of the arguments brought forth previously. — Samuel Lacrampe

That's not what I'm after.

Joe and Bob are part of an elite group of people with a particular superpower; a mental feat requiring great intelligence that sets them apart from the rest of humanity. Or, so they thought. A guru comes to Joe one day and, to his great surprise, demonstrates that he's wrong... in fact, as it turns out, generally all humans have this capability. Later, the same guru visits Bob, demonstrating the same thing. Joe becomes severely depressed... Joe has believed all his life that he was special, and the guru just proved him wrong. Bob, OTOH, gets really excited. He believed all his life that he was special but, as it turns out, the guru proved that all of humanity is special.

Let's forget religion for just a second, except for that part of it that says whatever it says about the soul. But suppose the guru comes and proves that we are, in fact, physical. Are you Joe in this story, or are you Bob? Are you going to say, oh gee, we're not special because we're nothing but stinking dead matter? Or will you say, wait, physical things are like us too? I never thought physical things could be so special?

I'm not interested in defusing you of your religion... just your preconceptions. What I am asking is what the soul actually does for you, that you think being physical kills... with a side question of, why does it kill it?

There's obvious there's more to us than a bunch of atoms — Eugen

To get a more meaningful answer, I think we need a more meaningful question. In pursuit of this, can you explain why it's obvious to you that there's more to us than a bunch of atoms?

nature has also an abstract part — Eugen

This seems to imply your picture of materialism rejects the abstract... is that the case and, if so, could you explain your impression of materialism?

I think the theory is false. ... You can also disprove it statistically by playing it a large amount of time, or better yet, dismantle it to know its mechanism. — Samuel Lacrampe

You forget that SMT says machines can change types. There's no way it can fail! Your empirical statistical test will simply count 100% success rates, since there's no failure scenario. SMT isn't just true... there's no way it can be false. Or to use the traditional term, it's unfalsifiable.

It seems to commit the Gambler's fallacy. — Samuel Lacrampe

And you seem to be committing a fallacy fallacy. SMT's unfalsifiable; that makes it useless. SMT is simply an illustration of an unfalsifiable useless theory. I have no idea why you're trying to challenge it; it's as if you have an allergy to the concept of an unfalsifiable/useless theory. But, okay. Let's make a bet. I'll bet you cannot name a single scenario where SMT fails.

That doesn't sound right. ... So even if there is randomness at the quantum scale, it fades away before reaching the classical scale. — Samuel Lacrampe

Have you never heard of TRNG's? How about Geiger Counters? Or interference patterns or breaking of them? Or challenge yourself at the most basic of levels... how do you think us classical level beings ever managed to develop a theory of quantum mechanics in the first place if quantum mechanical effects always fade before reaching our scale?

At the classical scale, we have the laws of physics, and they are called laws because they are universal. — Samuel Lacrampe

No, they're called laws because they summarize the data in predictable terms. Hooke's law, for example, is known not to be universal... it fails once your spring exceeds its elastic limit.

I started explaining "greater" here, then I forgot where we ended up. Do you have specific questions in mind? — Samuel Lacrampe

Yes. What does greater mean in terms of your new definition of sufficient? Forgetting I understand, but all of these posts are still here... just go back and review them.

I think "theoretical physics" is — Samuel Lacrampe

I don't get it. This is the year 2020, supposedly well into the information age... so instead of opining, why not just look things up?

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. — Wikipedia

Sorry, I can't let this one go. — Samuel Lacrampe

Sorry, but what is the point of this? MWI's you're-splitting-into-countless-versions-of-yourself-that-you-aren't-aware-of is actually part of a respectable theory. You're allegedly trying to make the point that science doesn't deal with the metaphysical, despite this counterexample, by brain-vatting and Tommy-Westphalling? Not even theoretical physicists treat Boltzmann brains and superdeterminism seriously.

What do you lose should a triangle have four sides — Samuel Lacrampe

Not analogous. We can both count to four, but you don't quite know what physical means. Let's back up. Why is it important to you that we have souls at all? What does not having a soul mean we cannot say, that having a soul means we could?

There's also the Unruh effect. In theory if you were able to suspend your thermometer over a black hole with an anchor, due to the Unruh effect, it will experience a temperature by means of being in an accelerating frame.

Time may seem discrete because we are unable to measure time duration below the Planck scale. — jgill

Not to voice agreement or disagreement, but one of the difficulties of Planck scale is that it's a precise scale... it's hard to square that against Lorentz transforms. If there's something discrete about time, it seems it should also be related to something discrete about space. (Then, there's also singularity concerns, such as what this scale's meaning is at horizons).

Change my mind — Unlimiter

A bit of a disclaimer speech... the degree to which a belief is warranted is equivalent to the strength of the justification of the belief. Justifications could possibly be a bit difficult; one's not always aware of why they believe what they believe. But that should the focus. Do you agree?

Besides that, I have a few questions. You are using terms "unconsciously acquired" and "consciously made"... can you give me a slightly more formal definition of these terms... something to where if I were to point to a type of knowledge acquisition, we can categorize it as one or the other? Would it be fair to say that your proposal is wrong if I can point to knowledge acquisition that is unconscious? Also, it's a bit strange to me to talk just of acquisition, especially in terms of consciousness. How would your proposal relate to knowledge retrieval? For example (and to point to the oddity), suppose I acquired knowledge of X, but every time I retrieve that knowledge it looks like Y... is there a sense in which we can say the knowledge acquired really is X, not Y... even though every time I retrieve it, it's Y not X?

An illusion in this context is: the impression that when you do (did) something, you could just as well choose to do (have chosen to do) something else. — Lida Rose

Illusion is the wrong word. Illusion suggests a percept, and the notion of free will you're describing is not a percept. Feelings of control, feelings of agency behind an action, and feelings of authorship are percepts, but none of those are based on perceiving alternate futures.

I'm rearranging this for focus.

I think your point is that the PoSR is not the only principle needed to find truth? — Samuel Lacrampe

No; my point is that the PoSR is superfluous, not foundational, to science.

It doesn't mean they are false. — Samuel Lacrampe

The slot machine theory isn't false; it's vacuously true. That's why you can't use it to bet... it's useless. You will go flat broke using your slot machine theory before proving it untrue, because fundamentally it's irrefutable, because it doesn't actually say anything. It's a "facade" of a theory... it presents the illusion of meaning without actually having to mean something.

Mathematical claims demand sufficient explanations like any other claims. — Samuel Lacrampe

We require a mathematical conjecture be proven before we believe it is true. But there are mathematical conjectures that are true that we simply haven't proven yet; likewise, there are mathematical conjectures that are true but unprovable.

Analogously, we require inductive claims to be justified before they warrant belief. But there are propositions about the world that are true that have yet to be justified. And there's no guarantee that a true proposition about the world can be justified.

Whether QI deals with physical things or not is irrelevant, since my argument only applies to things in the non-quantum scale. — Samuel Lacrampe

This is special pleading though, and I'm not sure how your argument can survive it. If QI were a thing, then certain classes TRNG's are truly random, and they produce random effects on classical scales. The scale isn't the problem; the random mechanics is.

But you have an unfinished new definition of PoSR to work on anyway (didn't come up in the last post except by quick mention). PoSR is the principle that for all things there is a sufficient cause where sufficient refers to the fact that the cause cannot be "greater" than the effect, but we still have no functional definition of greater... and this is part of why I'm rearranging this post... because the more we try to resolve what PoSR is, the more it looks like slot machine theory.

Regarding the physical, I think it may be best to just back up and try to get a much better definition of the physical than you currently have... I think you're underestimating what it takes to explain what physical means:

That doesn't matter. So long as those variables have a location property, then they are physical. — Samuel Lacrampe

...it's not quite that easy. In quantum mechanics, and especially in context with Bell's Theorem, counterfactual definiteness itself is questionable. Related to this context, that means that particles in QM do not in fact have a well defined location. This can get more complicated with certain theoretical physics constructs such as the Holographic Principle.

Empirical sciences don't deal with metaphysics which is the science of reality. — Samuel Lacrampe

You can technically talk about empirical science, but the thing we talk about when we say science doesn't equate to empirical. Empirical refers only to that which we measure and observe... when we make measurements and observations, they become data. Theories are not data; they are speculative attempts to describe the reality that produces the data. Sure, you can test a theory empirically, but that's part of the problem with your definition... because you can also test a theory theoretically (non-empirically)... this is, for example, a large part of what theoretical physics does. It seems you want to describe the limits of science, but to do that properly in a proof, you cannot be lazy here.

Empirical sciences have no say with what is real and what is not. For example, everything we observe, including the stuff QI deals with, could be caused in reality by a "brain-in-a-vat" — Samuel Lacrampe

...we need not refer to 17th century thought experiments here. MWI posits that reality is a universal wavefunction, and classical physics is emergent. CI with real WFC posits that QM is just an odd calculation trick, possibly ontic somehow, but that classical physics is fundamental. Those describe different metaphysics. But here's the problem with your "easy" description of the physical... it's kind of an open question still whether science can or cannot distinguish these two metaphysically distinct theories. The way you phrase it, though, it's just "obvious" science can't do this. A more fair assessment is simply that there's no guarantee of what science could do here versus could not do... someone could always invent a clever trick to test something that we just didn't think of. All we really know is that if we use good science and manage to show e.g. that MWI is what reality is like, that we leave a trail of justification worthy to warrant belief.

The property of being non-physical is essential to the concept of the soul. — Samuel Lacrampe

Why? Because some religious leader or lexicographer dictated it? What do you lose should the soul be physical? What if, say, there were indeed a whole spiritual aspect to reality, but, it turned out, that this aspect was much more complex and rich than what the current batch of religions describe? What if spirituality followed principles and laws? And if we write those down side by side with the principles and laws we call "physical", how clear is it exactly whether some arbitrary new law we discover should go into the physical bucket or the spiritual one? What is it about the soul being non-physical that's so important to you?

Have a nice day — Lida Rose

Thank you, you too, and I mean that sincerely! Behind all these terminals, we're all just ordinary people.

But let's keep the idle chat down (and the sarcasm)... this forum has a purpose... it's a community of people with a shared interest. That's what we're all here for, and that's whose stage you're borrowing from our kind hosts.

Suspect away, but just to remind you, it comes from my OP — Lida Rose

And that thing in your OP comes from your intuitions. You have libertarian intuitions; that is, you intuit PAP. But you're not the only one with intuitions; compatibilists have intuitions too. But there's an overall context implied by the fact that you're posting on a philosophy forum... I would think people actually interested in philosophy should be interested in analyzing and questioning their intuitions, especially if the intuitions are not universal.

where I said, "This means that praise and blame come out as pretty hollow concepts. As I mentioned, if you (A)cannot do other than what you did

But that means less than what you're making it out to mean. A rabbit (B)can go into my shed, but an adult blue whale (B)cannot go into my shed. I had lemonade last night, but I (C)could have had milk. (A), (B), and (C) all use different senses of the world could/can.

You're presenting a pet theory... that one (D)cannot be assigned praise/blame if one (A)cannot do other than what they do. But why (D)can't they? Why (D)can't someone be assigned praise/blame based on whether or not the (C)could have done otherwise as opposed to (A)could have?

I don't think your pet theory has weight; rather, I think your intuition's messed up.

why should you be praised or blamed for them?

If I choose with intention, because I chose with intention.

To do so is like blaming or praising a rock for where it lies. It had no "choice" in the matter."

The rock is not an agent; people are agents. People act with intention; rocks do not go to places due to intentions. People actually mean to do what they (intentionally) do; rocks do not. Those are significant and relevant differences. It's impossible to blame a rock for being where it is because the rock didn't "mean" to go there, but the same cannot be said of a person acting with intent. In fact, it's not even the actual act we tend to hold people responsible for... it is just the intent behind it. (This isn't always true, but in the ways relevant to praise/blame it's true enough for government work as they say).

That we (A)can't do other than what we will do is simply a consequence of the fact that there's only one reality, but we still in that reality are causes of the thing we intend. Determinism doesn't conflict with the fact that we act based on intentions; in fact, the suggestion that we act based on intentions is causal by nature.

In polite discourse the proper way to indicate one's disinterest in going down a whole other path of discussion is to let it be known. — Lida Rose

I'm not buying into that narrative. From start to end, this is a public forum, and when you reply someone it's like ringing their doorbell, especially with this setup. Also, you're not merely indicating your disinterest; you're advancing arguments. And this is not "a whole other path of discussion", it is the thing you're discussing... you're explicit here that you're interested in praise and blame in this previous reply.

I have an interest in forestalling any further discussion about compatilibism — Lida Rose

But your alleged interest does not compel me to share it. And your discussion about compatibilism is where the primary weakness of your argument against the ability to assign blame/praise lies. In theory we could talk about original causation as a third mechanic (besides determinism/randomness), but I think the biggest problem is your acceptance of PAP. It's reasonable to reject original causation until the burden is met demonstrating that it is indeed a possible mechanic, and whereas libertarians tend to demonstrate this by appealing to the fact that we have free will and that it's impossible without PAP, I don't see that as compelling... especially when PAP itself is suspect.

something that obviously hasn't worked because here you are still wanting to talk about it — Lida Rose

...of course it hasn't "worked"; I don't share your interest in forestalling discussions of why you're wrong, and your conveying that interest doesn't compel me to share it.

I think a serious consideration of compatibilism will reveal the flaws in your argument. I could possibly be in error here, but if I am, then I have a vested interest in correcting that error, which counters your vested interest in forestalling discussion of it.

So our interests conflict.

and me having to reiterate my :yawn: with it. — Lida Rose

...but that's the thing... you don't have to reiterate your disinterest in it. All you have to do is not reply. This is a public forum, not your email inbox. So others may be interested in the flaws of your arguments even if you aren't.

But be assured, this will be my last word about it to you. :smile: — Lida Rose

In this case, inaction speaks louder than words. But it's also irrelevant to me anyway. Disinterest is not a compelling argument.

Compatibilism is the wimp's "Yah-but" way of skirting around their acceptance of determinism, and I have absolutely no interest in their "apologetics." — Lida Rose

As a free will agnostic, I'm unconvinced by your ad hominem arguments and appeal to motive fallacies.

I personally find the whole free will debate a bit fishy, on all sides... people have been arguing this stuff for well over 2 millennia... certainly something's off. I find that incredibly interesting. But I find it a bit suspicious that this thread had "Praising A Rock" in the title, that you wrote a 1000+ word op on a philosophy forum complaining about free will, that compatibilism allows for assigning praise and blame in such a way that none of your points stick, and that you find no interest in it.

There is something to this 2+ millennia old idea of compatibilism... it's not a reaction to (at least the modern) determinism. Several people besides me have already pointed this out. Just in case you're interested (the proper way to show lack of interest is to not reply).

"Free will" is a manmade conventional name. It was invented solely as a means to exhonerate the God of Abraham from the existence of evil. That need cam and yet still comes as a result of a brilliantly worded argument against the God of Abraham. — creativesoul

This sounds like an anachronism; the concept of free will traces back to the ancient Greeks... who were not exactly God of Abraham types. As far as the name goes, we're talking BCE, so this conceptualization predates the English language. Mind you, a quick search does confirm that Augustine advanced this argument, but the proposal here still sounds out of order.

We made choices long before the need to exonerate the God of Abraham from the existence of evil. We make a choice each and every time we consider the options. The problem, of course, is that sometimes one is completely unaware of some of the options that are available to them. When those unknown options are the best, there is no ability to 'freely' choose what's best.

Feel me? — creativesoul

That makes sense to me; what we subjectively seem to do when we choose is limited to what we know and think, and doesn't get to "sniff out" the result.