## Bell's Theorem

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" **2 " means raised to the second power (i.e. squared). So " **3 " means raised to the third power, etc. This is standard scientific notation.

I've never seen "**" used as a symbol for the powers functions. I think the standard is "^", e.g. 5^2 = 25. In my experience, computer programs will accept that as input.
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there are programming languages where ** means exponentiation. It's not as common as ^ but it's not unheard of either.

My mobile keyboard has exponent numbers. 2² = 4
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Hah - I'm showing my age. We used that in Fortran programming. It's somewhat obsolete now but can still see it used occasionally. E.g. here you'll have to scroll down a bit to see this:

"Exponents are given with a double asterisk, such as "3**2" (three to the second power). "

Note to self: use ^ in the future to represent exponentiation. :roll:
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Hah - I'm showing my age.

Hah - I took Fortran during my freshman year in college in 1970. Timesharing and paper tape on a state-of-the-art mainframe.
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You came in later. I had to use punch cards - but graduated to paper tape.
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2² = 4
I don't know how to do that on my keyboard, but now that you've shown the way I can cut & paste from your example. :clap:

BTW that was paper from Einstein about his thoughts on aether was very cool - thanks for that.

And now we wait to see what mu will come up with next.
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What math? It's a philosophical problem, one which mathematics has not resolved. Look, there's a point in time, when a body at rest becomes a body accelerating. The body changes from being at rest, to being in motion at some point in time. Since the rate of increase of velocity (acceleration) is expressed as over a period of time, at this point in time, when the body changes from being at rest to being in motion, the rate of increase must be infinite because it's a number expressed over zero, x/0.

Regardless of philosophical issues, we can in fact experimentally verify, to some reasonable degree of precision, that bowling balls and pool balls both accelerate toward the ground when dropped. If you have philosophical problems with the concept of acceleration, you should separate that from your ability to look at that evidence and see what does, in fact, happen

Yes of course, such objects accelerate. They must, in order to get from zero velocity to having some velocity. The problem is that we as human beings, do not have a very accurate understanding of acceleration. Our mathematical representation of it is very problematic. Read the following: https://en.wikipedia.org/wiki/The_Analyst

Notice that the article says that Berkeley's criticism of Newton was resolved with the concept of "limits". But this really doesn't solve the problem of acceleration because it places zero as a boundary, limit, which is never obtained. So the principle utilized is that there is no point in time when the object changes from being at rest to being in motion, because an infinite amount of time would pass before the boundary is crossed. So the crossing of that boundary, between rest and motion is never actually obtained by the mathematical representation.

It is this same proposition, which makes calculus logically rigorous, which also leads to the uncertainty principle, by allowing this "infinite" into the mathematical representation, and having boundaries within the modeling which cannot be crossed. You determine the momentum (motion) or you determine the position (rest), whichever one you choose to make an accurate representation of, the other approaches the boundary (infinite uncertainty).

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Why don't you try answering his question?

I could not answer EricH's question because the presumptions which the question was based on were false. He said "I think you would agree that that is a true statement". I could not agree that it was a true statement, for the reasons I gave. He cited a measurement, and I explained that there is a measurement problem which did not allow me to agree that his measurement was "true". Then EricH tried to say that such a complex measurement was just an observation, which it clearly is not. That makes two false presumptions. What kind of inquiry is that, asking a loaded question with two false presumptions. That's like asking me 'did you stop beating wife, again?'.

Now flannel jesus gave me a better example of "an observation". Flannel said that heavy balls when dropped, accelerate toward the ground. I agree that they "must accelerate", because they go from being held to being in motion. But this is not an observation, it's more like a conclusion of logic. I do not notice the ball accelerating when I drop it, but I conclude that it must accelerate, because it goes from zero to having some velocity.

Now EricH's question concerned the relationship between "truth" and "understanding". EricH asked if I could agree to the truth of something without any understanding of what I was agreeing to the truth of. I'm sure many people could agree to the truth of something without any understanding of it, if this agreeing is done on faith, like the way that some religious people agree to the truth of God for example. But I am not prone to such agreements, I want to understand first, before I agree.

Regardless, this is irrelevant to the point I was making. I said "truth" implies understanding. But for someone to say "I agree that this is true", and for it to actually be true, are two different things. So "I agree that X is true" does not imply understanding in the way that truth itself implies understanding.
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Our mathematical representation of it is very problematic. Read the following: https://en.wikipedia.org/wiki/The_Analyst
In 1966, Abraham Robinson introduced Non-standard Analysis, which provided a rigorous foundation for working with infinitely small quantities. This provided another way of putting calculus on a mathematically rigorous foundation, the way it was done before the (ε, δ)-definition of limit had been fully developed.

And it is equally clear that, short as the article is, you did not understand any of the rest of it either. "Berkeley did not dispute the results of calculus; he acknowledged the results were true. The thrust of his criticism was that Calculus was not more logically rigorous than religion. Berkeley concluded that the certainty of mathematics is no greater than the certainty of religion." Berkeley was writing as a Christian apologist.

Any claim of yours, then, of any problem with the maths in question here, whether mathematical, philosophical, or metaphysical, is ignorant, stupid, self-serving, and that you used it to evade a fair question on your inconsistent usages of "truth," I call vicious.

These:
Yes, that's what I said, truth means corresponding with reality, therefore I'm using "truth" in the sense of correspondence theory.
"Truth" implies an understanding of what is going on, which takes us beyond the ability to predict.

These are incompatible. Reconcile them!
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Yes of course, such objects accelerate. They must, in order to get from zero velocity to having some velocity. The problem is that we as human beings, do not have a very accurate understanding of acceleration. Our mathematical representation of it is very problematic. Read the following: https://en.wikipedia.org/wiki/The_Analyst

Notice that the article says that Berkeley's criticism of Newton was resolved with the concept of "limits". But this really doesn't solve the problem of acceleration because it places zero as a boundary, limit, which is never obtained. So the principle utilized is that there is no point in time when the object changes from being at rest to being in motion, because an infinite amount of time would pass before the boundary is crossed. So the crossing of that boundary, between rest and motion is never actually obtained by the mathematical representation.

All of that is very intriguing but also entirely beside the point.
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In 1966, Abraham Robinson introduced Non-standard Analysis, which provided a rigorous foundation for working with infinitely small quantities. This provided another way of putting calculus on a mathematically rigorous foundation, the way it was done before the (ε, δ)-definition of limit had been fully developed.

I already told you the problem with the "rigorous" solutions. They are not real solutions because they allow "infinite" which is fundamentally unintelligible, as indefinite, into the mathematical representations. So any mathematical model employed, using these axioms which are designed to produce a "rigorous foundation" will have indefiniteness, which is a form of unintelligibility, built into it.

This is the problem with "formalism" (https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics)) in general. In its attempt to exclude the problems involved with applying the ideal (mathematical principles) to the material (physical) world, complete with accidents which appear as indefiniteness, formalism allows the indefiniteness (unintelligibility) to inhere within the formal (logical) structure itself. The result is that the source of unintelligibility (which inevitably arises in application), is impossible to isolate and identify.

If you do not understand this, then so be it. I will not try to explain, because I've done so numerous times on this forum, and I've come to respect that those who do not understand this are in that position because they deny the issue, and refuse to accept it as a real problem. They perceive that mathematics is very useful, and cannot apprehend the possibility that it could have problems. So it's generally a misunderstanding which is supported by a closed mind, and I am incapable of influencing people like you to open your minds.

And it is equally clear that, short as the article is, you did not understand any of the rest of it either. "Berkeley did not dispute the results of calculus; he acknowledged the results were true. The thrust of his criticism was that Calculus was not more logically rigorous than religion. Berkeley concluded that the certainty of mathematics is no greater than the certainty of religion." Berkeley was writing as a Christian apologist.

Yes, what I tried to explain is that the type of "truth" that Berkeley is talking about here is a faith based truth. It is "truth" in the sense of coherence theory. If there is coherency within the logical system it produces truth. This is why I as well, do not dispute the usefulness of things like relativity theory, and calculus. The problem is with the "false", in the sense of correspondence theory, principles which the "free-thinkers" in Berkeley's words, employed. The "free-thinkers" we can understand as the pure mathematicians who dream up mathematical axioms. The problem is that there is no requirement that any mathematical axioms be "true" in the sense of correspondence. And if the axioms prove to be useful they are accepted, and used, regardless of truthfulness (correspondence). Now we all know that the soundness of any logical argument relies on the soundness of the premises (mathematical axioms in this case), so if you prefer, we can replace "truth" with "sound", and analyze how sound the supposed "rigorous" logic is.

In this case the subject was "fluxions" (https://en.wikipedia.org/wiki/Fluxion). According to the Wikipedia entry, this concept was central to the disagreement between Newton and Leibniz. If you have not studied this, principal disagreement between Newton and Leibniz concerned the relative importance of Newton's "momentum", as mass times velocity, and Leibniz' "vis viva" (https://en.wikipedia.org/wiki/Vis_viva) as mass times velocity squared. As it turned out, each is important in its own way, but Leibniz' principle needed be adapted by a coefficient of a half.

Any claim of yours, then, of any problem with the maths in question here, whether mathematical, philosophical, or metaphysical, is ignorant, stupid, self-serving, and that you used it to evade a fair question on your inconsistent usages of "truth," I call vicious.

Uh huh. As I explained, I avoid your questions because I apprehend them as rhetorical. Your questions are presented not for the purpose of finding a point of mutual agreement, from which we can proceed in a rational inquiry, but they are designed for the purpose of opening up a point of attack. And when I refuse to answer, you are reduced to ad hominem, like above, demonstrating that you are overwhelmed by emotional weakness.

These are incompatible. Reconcile them!

I do not see the incompatibility. To represent reality in the way of correspondence (truth), requires necessarily that one has some understanding of the reality being represented. Therefore "truth" in the sense of correspondence, implies understanding.
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Regardless, this is irrelevant to the point I was making. I said "truth" implies understanding. But for someone to say "I agree that this is true", and for it to actually be true, are two different things. So "I agree that X is true" does not imply understanding in the way that truth itself implies understanding.

I think it's incredibly feasible to agree to the truth of something without fully understanding it.

Someone may not understand motion, because intuitively they keep coming back to zenos paradox. But even if they don't understand it, they can agree that, for example, This car moved relative to me (or I moved relative to the car), or other such statements.

The same is true for the example given before about acceleration. You may not understand or even philosophically agree with certain aspects of acceleration mathematically, but without that understanding you can still acknowledge observations that say, "after dropping the bowling ball, it was going at about 9.8m/s downward after 1 second , and it was going about 19.6m/s downward after 2 seconds , and it was going about 29.4m/s downward after 3 seconds".

You don't need to understand acceleration to agree with some basic observable facts about how bowling balls fall.
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From MU's reference, which btw is worth a look if only for its inadequacy in almost all respects. But we'll try to do our best with it:
"According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they aren't "about" anything at all."

And MU from above:
I already told you the problem with the "rigorous" solutions. They are not real solutions because they allow "infinite" which is fundamentally unintelligible, as indefinite, into the mathematical representations. So any mathematical model employed, using these axioms which are designed to produce a "rigorous foundation" will have indefiniteness, which is a form of unintelligibility, built into it.
If there is coherency within the logical system it produces truth.

So, the solutions offered as such by mathematics are not solutions? What do you imagine mathematics and solutions to be? What do you mean by saying the "'infinite' is fundamentally unintelligible"? Why does it have to be "fundamentally" intelligible? What does "fundamentally" mean? What does "indefiniteness" mean? Do you mean to say there is no coherency within maths/logic and that no truth is produced by them?

I don't think you can answer these without encountering your own confusions. Especially if you think maths/logic is problematic but Christian apologetics are coherent and "produce truth."

My two-cent analysis is that you allow yourself to be careless in terminology, e.g., in how you use and understand "truth," and further that, in denying any notion of presuppositions in your thinking, fail to realize that some presuppositions are appropriate in some areas and not in others, thus using the wrong criteria in thinking, leading to wrong conclusions - leading to Zeno-esque like absurdities. In passing, division by zero is held to be undefined, and not equal to infinity, or indefinite in any way. A nice Youtube video on this here:

Or to go back to Bell's inequality, the underlying phenomenon - whatever that may be - is not an artifact of the description, but is instead a reality that is (as we encounter it). I'm a god-doesn't-play-dice kind of guy, so I suppose the description, while in itself true and accurate, is merely incomplete and the completion of which, if and when, may engender radical new understandings of how it all works.
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To represent reality in the way of correspondence (truth), requires necessarily that one has some understanding of the reality being represented. Therefore "truth" in the sense of correspondence, implies understanding.

Here is the plain language definition per wikipedia
"In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world."

Now you are introducing the notion of understanding into the mix - and it's not clear to me what you mean here. If by the word "understanding" you mean that a statement is grammatically and syntactically correct and expresses a thought/notion that could potentially be real? Then that is trivially correct.

"My friend John is 5 feet 11 inches tall (within the limits of accuracy of my measuring apparatus)" is a true statement.

"My friend John is 5000 feet 11 inches tall (within the limits of accuracy of my measuring apparatus)" is a false statement.

But if by "understanding" you mean something more than our shared understanding of the plain language meaning of words, then this raises all sorts of questions - what do you mean by "understanding"? Can we ever fully understand anything at all? Warning! Warning! Infinite regress ahead!

That said, perhaps you are using a variation of the standard definition/usage of correspondence theory? That's fine - there is nothing wrong with this. If you go to Stanford the theory of correspondence comes in a bewildering variety of flavors - and maybe you are using one of these variations?

Regardless of all this, I refer you to flannel's last comment:
You don't need to understand acceleration to agree with some basic observable facts about how bowling balls fall.
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What math? It's a philosophical problem, one which mathematics has not resolved. Look, there's a point in time, when a body at rest becomes a body accelerating. The body changes from being at rest, to being in motion at some point in time. Since the rate of increase of velocity (acceleration) is expressed as over a period of time, at this point in time, when the body changes from being at rest to being in motion, the rate of increase must be infinite because it's a number expressed over zero, x/0.

That's what I'm asking you, "What math?"

You keep bringing up mathematical issues, such as infinity and division by zero, as if they are magic words meant to distract from your inability to explain why they are of relevance.

It's starting to appear as if you don't know how to apply math to the situation. (Not that there is anything wrong with that.)
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I think it's incredibly feasible to agree to the truth of something without fully understanding it.

Sure, but the condition was understanding, not "fully" understanding. And, I really do not understand what "fully understand" would mean, because sometimes when I think that I understood something it turns out that I really did not. So "fully understand" would be a difficult concept to understand..

The same is true for the example given before about acceleration. You may not understand or even philosophically agree with certain aspects of acceleration mathematically, but without that understanding you can still acknowledge observations that say, "after dropping the bowling ball, it was going at about 9.8m/s downward after 1 second , and it was going about 19.6m/s downward after 2 seconds , and it was going about 29.4m/s downward after 3 seconds".

No, that's the point, I would not agree to this. I would want to see the measuring technique, the justification for this claim, that "it was going at about 9.8m/s downward after 1 second", etc.. What I said, is that some others might accept this, as a matter of faith in some principles they hold, but I am not inclined to accept things on faith. And the point is that I do not believe that accepting somethin completely on faith is really a judgement of truth. I would say that faith provides a type of understanding, but not all types of understanding necessitate truth. I would argue that "truth" implies a special type of understanding

So if you told me that it was going " 9.8m/s downward after 1 second", and I said yeah, sure, I believe you, I would not consider that I've judged what you have said to be true, unless I have some understanding as to why you said that. If I believe that I understand why you said that, then I would say that I accept it as truth. If I have no understanding whatsoever, of why you said that, yet I still accept it, then I accept it for some reason other than believing that it is true. Many statements are accepted for reasons other than the belief that they are true.

So, the solutions offered as such by mathematics are not solutions? What do you imagine mathematics and solutions to be?

Mathematics may provide some solutions sometimes, but in respect to the problem being discussed, the problem of acceleration, mathematics does not provide a solution. What it does is provide a "work around",. It veils the problem so that it disappears in some situations, so long as the temporal duration is not too long or too short, but then it simply reappears in other situations. As I said, the problem now reappears as the uncertainty principle, so the mathematics has clearly not resolved the problem.

"In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world."

Now you are introducing the notion of understanding into the mix - and it's not clear to me what you mean here. If by the word "understanding" you mean that a statement is grammatically and syntactically correct and expresses a thought/notion that could potentially be real? Then that is trivially correct.

Let's consider the definition you provided, truth concerns how a statement relates to the world. Do you not agree, that in order to establish a relationship between a statement and the world, there are certain requirements such as 1) understanding the meaning of the statement, 2) understanding the world which the relationship is to be established with. Without these two types of understanding how could there possibly be a relationship between the statement (a bunch of letters), and a thing which is called "the world"?

But if by "understanding" you mean something more than our shared understanding of the plain language meaning of words, then this raises all sorts of questions - what do you mean by "understanding"? Can we ever fully understand anything at all? Warning! Warning! Infinite regress ahead!

I do not know what you mean by "shared understanding". To me, "understanding" is something personal. I might understand you, and you might understanding me, but this does not mean that we have a shared understanding, because each of us has a different understanding.

here's what my OED has for "understanding", and I think we could pretty much choose any of these. 1 a) the ability to understand or think, intelligence. b) the power of apprehension; the power of abstract thought. 2) an individual's perception or judgement of a situation etc. 3) an agreement; a thing agreed upon, esp. informally. Note that "understand" is defined first as perceive the meaning of (words, a person, a language, etc.) and second, perceive the significance, explanation or cause of.

It's starting to appear as if you don't know how to apply math to the situation. (Not that there is anything wrong with that.)

I really do not believe that there is a way to successfully apply math to the situation. That's the point, it's a philosophical problem which math cannot resolve. math has its limits, and there are many problems which it cannot resolve.
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No, that's the point, I would not agree to this. I would want to see the measuring technique, the justification for this claim, that "it was going at about 9.8m/s downward after 1 second", etc.. What I said, is that some others might accept this, as a matter of faith in some principles they hold, but I am not inclined to accept things on faith.

What's all this talk about faith? You think people came up with the 9.8 number on faith?
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What's all this talk about faith? You think people came up with the 9.8 number on faith?

No, I don't think it was produced from faith. But if you told me the thing was going 9.8 metres per second after a second, and I had absolutely no understanding of how you came up with that number, but still I believed you, wouldn't this belief be based in nothing other than faith?
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why is that the scenario you invented, rather than a scenario where I show you the numbers and how I got them?
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metaphysician, please recall that this all started with us imaging a scenario where these measurements were done to your satisfaction. Now, whether you think they're actually capable of being done to your satisfaction is entirely different question from your ability to imagine a scenario where they were done to your satisfaction.

If it's inconceivable to you that these measurements could be done, by you or anyone else, to a satisfactory degree, then I would propose that you are immune to science.

I'm also genuinely quite amazed at the conspiratorial nature of your approach to acceleration due to gravity. Do you really not think there's sufficient evidence for it? Are the physicists of the last hundreds of years incompetent or just lying? How did we manage to make it to the moon, or send rovers to Mars, if we don't even grasp the very basics of gravity? I can't tell how sincere you are about all this.
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I really do not believe that there is a way to successfully apply math to the situation. That's the point, it's a philosophical problem which math cannot resolve. math has its limits, and there are many problems which it cannot resolve.

Except that it resolves it/them just fine. But we know you, MU - and these others don't although they're learning - that you do not agree even that 2+2=4. I asked you above just "what... you imagine mathematics and solutions to be? And of course you ignored the question. Mathematics, as used in the sciences at least, is the language used to try to describe with some rigor, precision, accuracy, and consistency what is happening in nature, and when done well, called a solution. That is, maths is not nature, nor nature math. Oh! Wait! I didn't mention philosophy! And that is because philosophy has nothing to do with it. To question or discount or disregard mathematics used as a tool on philosophical grounds is an absurdity. If the math stands on mathematical grounds, that's an end of it.

Btw, as you well know there are at least several mathematicians who post here, and a characteristic of their work is the effort to demonstrate and make clear their own arguments and points about their topic, to educate and contribute to a general clarity and understanding. You on the other hand pontificate without substance, demonstration, evidence, clarity, or proof. And while you claim to understand that this is a philosophy site, you consistently refuse any substantive reply to the question, "How do you know?" Ultimately you're a waste of time, and I would like you to stop it!
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Now, whether you think they're actually capable of being done to your satisfaction is entirely different question from your ability to imagine a scenario where they were done to your satisfaction.

I thought I explained this . The current state of "mathematics", the axioms and rules which are the current conventions, make it impossible that this could be done to my satisfaction. So I cannot imagine this scenario. You are asking me to imagine something which I am saying is impossible for me to imagine. For me to imagine this being done to my satisfaction would be to imagine it being done with something other than "mathematics".

This is very analogous to the issue with the aether in an inverse way. The nature, characteristics and properties, of "the aether" are dictated by definition, because we have no sense perception, empirical data of it. So, for the M-M experiment it was stipulated that the aether was a separate substance from the massive bodies, therefore the bodies would make a disturbance in the aether, a sort of wake. The experiments showed no such disturbance, therefore there is no "aether", as defined.

But what the experiment really indicates is that the dictated properties of the aether are incorrect. And of course this is consistent with empirical evidence, because we see that light and electromagnetism passing right through many bodies, therefore the aether must also exist within the bodies, and not be a separate substance.

So in the case of "mathematics", above, the word refers to something very real, supported by much empirical data, and usage of axioms and rules. So we have a very real thing being referred to, which we can look at, and see the properties of. This reality dictates the definition of the thing, mathematics. I'll call it a tool. Now, I look at this tool, and say that it is simply incapable of doing the job to my satisfaction. The tool referred to by "mathematics" cannot do the job I want done, and so I need a different tool. Therefore, either we can alter this tool to make it useful to my task, or we can come up with a new tool to do the task.

In the case of "aether", the situation is inverted. We cannot see, or otherwise perceive what we are looking for. We know from logic that it is there, whether it best be represented as "aether" or as "field", or whatever term. Now if we adhere to the defining terms of aether, which stipulate that aether is a substance separate from the substance of bodies, then we can know that there is no aether. But this conclusion does not help is to solve the problem. We still need to identify the medium, and learn its properties. That there is no "aether" in this case does not mean there is no medium, it just means the defining features of the medium were wrong. Likewise, when I say "mathematics" is incapable of resolving a specific problem, I do not mean that the problem is irresolvable. I mean that the defining feature of mathematics make it so that mathematics cannot resolve the problem. Therefore we need to either change the defining features of mathematics (as in the case of aether), which in this case means actually changing the tool, or, we need to come up with another tool (with a different name), like in the case of "aether", we'd give the medium a different name. .

I'm also genuinely quite amazed at the conspiratorial nature of your approach to acceleration due to gravity. Do you really not think there's sufficient evidence for it? Are the physicists of the last hundreds of years incompetent or just lying? How did we manage to make it to the moon, or send rovers to Mars, if we don't even grasp the very basics of gravity? I can't tell how sincere you are about all this.

I believe that what you call "acceleration due to gravity" is not well understood by human beings. And, I explained that the fact that people have the capacity to predict motions of bodies does not imply that the true nature of those motions is well understood. So questions like "how did we manage to..." have little if any bearing on this issue. The capacity to do things does not imply that the doer understands what is being done; that is what Socrates demonstrated. In fact, Socrates demonstrated the very opposite, in no cases of people doing things, did the people adequately understand what they were doing.

But we know you, MU - and these others don't although they're learning - that you do not agree even that 2+2=4.

This is an intentional misrepresentation. I do believe 2+2=4, and I've told you this before. What I've argued against, and strongly do not believe is that "2+2" represents the very same thing as "4". So what I do not believe is that "=" means "is the same as" which is what is argued by many here at TPF.

Mathematics, as used in the sciences at least, is the language used to try to describe with some rigor, precision, accuracy, and consistency what is happening in nature, and when done well, called a solution

OK, we have here: "mathematics...is the language used to try to describe.. and when done well, called a solution". Notice your use of "try", and "a solution" only occurs when "done well". And, as I've described using English, one of very many languages used to describe what is happening in nature, there are aspects of nature (such as acceleration) which cannot be described by the current grammar of this language called "mathematics". So, as I've pointed out, when people use mathematics to try to describe these aspects of nature, their attempts fail, therefore this ought not be called "a solution".

Btw, as you well know there are at least several mathematicians who post here, and a characteristic of their work is the effort to demonstrate and make clear their own arguments and points about their topic, to educate and contribute to a general clarity and understanding. You on the other hand pontificate without substance, demonstration, evidence, clarity, or proof. And while you claim to understand that this is a philosophy site, you consistently refuse any substantive reply to the question, "How do you know?"

Some mathematicians really demonstrate that they do not know what is being done with mathematics. They insist on silly principles such as the one mentioned above, that "=" means "is the same as". This indicates that they really have a very deep misunderstanding of what an equation is and what is being done by mathematicians with the use of equations. This is exactly what Socrates demonstrated many years ago, that when people are doing things, they really cannot accurately describe what they are doing, and this means that they do not know what they are doing.

Ultimately you're a waste of time, and I would like you to stop it!

Why do you keep asking me questions if you want me to stop posting? Your use of language demonstrates a base irrationality.
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Can you give an example of a statement involving the mathematical measurement of some physical property of an object that you would consider to be a true statement - per the correspondence theory of truth?
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I thought I explained this . The current state of "mathematics", the axioms and rules which are the current conventions, make it impossible that this could be done to my satisfaction. So I cannot imagine this scenario. You are asking me to imagine something which I am saying is impossible for me to imagine. For me to imagine this being done to my satisfaction would be to imagine it being done with something other than "mathematics".

This seems like you're still overthinking it. You're focusing so much on abstract mathematics and not enough on concrete measurements. Galileo didn't discover acceleration due to gravity via abstract mathematics, he measured it. If you can't imagine measurements, then let me do the imagining for you. I don't believe it's particular challenging.

I've set up an apparatus to measure the distance a cube is falling over time - it's just a really tall building (let's say 100m), with a bunch of measurements marked up its height, and a high speed camera to track how far it has travelled at every moment. Such a setup is actually pretty sufficient to get a good idea of this problem.

So, we start out by asking, how fast was it falling approximately at 1s? We look at our high speed footage and we measure is position at 0.9s and 1.1s. We find the positions are 3.97 and 5.93 respectively (measured in meters from the starting point). So we find out that in that 0.2s time frame, it travelled about 1.96m, which means it was going about 9.8m/s.

Then we ask, how fast was it going at 2s? So we do the same thing as before, we find it's position at 1.9s (17.7m) and 2.1s (21.62m). We calculate how fast it was going approximately over those 0.2s and it turns out it was going 19.6m/s.

We do the same thing for 3s, measuring it's position at 2.9s and 3.1s to be 41.24m and 47.12m, giving it a velocity of 29.4m/s.

We do the same thing for 4s, measuring position at 3.9s and 4.1s to be 74.58 and 82.42m respectively, giving it a velocity of 39.2m/s.

So we get all our results together, and quickly notice that every time a second passes, the cube seems to be traveling 9.8m/s faster than it was traveling the previous second.

Why are these sorts of measurements, and this sort of experiment, unimaginable to you? Are they still unimaginable to you now?
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Notice your use of "try", and "a solution" only occurs when "done well". And, as I've described using English, one of very many languages used to describe what is happening in nature, there are aspects of nature (such as acceleration) which cannot be described by the current grammar of this language called "mathematics".

Of course it is. I remind you of a saying you're doubtless familiar with, "The map is not the territory." I infer you want the map to be just like the territory, and if and where it is not, you are dismissive. But you are dismissive of the map because it is not the territory, and that is an unseemly and unaccountable (on rational terms) error for someone like yourself. You use language like "cannot be described" when in fact that is exactly what is happening. As with the 2+2=4, you say that the 2+2 does not represent the same thing as 4, and of course it exactly represents the same thing as 4. Had you said they were themselves simply not the same thing, maybe - not a discussion interesting to me. But you say they do not represent, and of course that is exactly what they do.

We know from logic that it is there, whether it best be represented as "aether" or as "field", or whatever term.
And this you exactly do not know. You may suspect; the logic may be suggestive or it may point or provide clues, but not knowledge-of. Or, perhaps you will make explicitly clear how logic might have this power of constitution that you appear to suppose it has.

Why do you keep asking me questions if you want me to stop posting? Your use of language demonstrates a base irrationality.
I would like you to reflect a bit more on what you're posting, with respect to the subject matter; to be as exact with language as your views require, and to stop wasting time with nonsense.

This is exactly what Socrates demonstrated many years ago, that when people are doing things, they really cannot accurately describe what they are doing, and this means that they do not know what they are doing.

And I refute this thus: When they are doing something, are they doing that thing, or are they doing something else? If you had read a little more closely, you would have seen that Socrates did indeed find people who knew what they were doing, but not wise, because they, knowing something, thought that they knew more that they did, thus knowing something, but not wise. That is, the Oracle had told Socrates that he was the wisest, and Socrates had to discover that wisdom and knowledge are not the same thing.
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Can you give an example of a statement involving the mathematical measurement of some physical property of an object that you would consider to be a true statement - per the correspondence theory of truth?

No, that's what Ive been arguing, we really do not know the true physical properties of objects. I think that's what the experimentation with Bell's theorem, discussed earlier in this thread, indicated.

This seems like you're still overthinking it. You're focusing so much on abstract mathematics and not enough on concrete measurements. Galileo didn't discover acceleration due to gravity via abstract mathematics, he measured it. If you can't imagine measurements, then let me do the imagining for you. I don't believe it's particular challenging.

I think that this is a misrepresentation, and this is why were having difficulty coming to agreement here. We cannot directly measure acceleration, nor can we even directly measure velocity. Determinations of these require a multitude of measurements, with an application of mathematical principles, such as averaging. Because this process of averaging is a requirement for any determination of acceleration, these determinations are not properly called "measurements" but are better represented as logical conclusions, i.e. conclusions derived from the application of logical principles to some premises. The premises might be called measurements.

So, we start out by asking, how fast was it falling approximately at 1s? We look at our high speed footage and we measure is position at 0.9s and 1.1s. We find the positions are 3.97 and 5.93 respectively (measured in meters from the starting point). So we find out that in that 0.2s time frame, it travelled about 1.96m, which means it was going about 9.8m/s.

According to what I expalined above, you have taken two measurements, the position at .9s and the position at 1.1s, applied some logic, and concluded the object was moving at 9.8m/s in the duration. Of course, if the object was actually accelerating during this time period, this is not a true representation. If the object was accelerating, its velocity was different at .9s from what it was at 1.1s. But your method concludes that the object was going at the same speed for the entire .2s period, and this is contradictory to the premise that the object is accelerating. So it's very clear to me that this method of averaging does not give a true representation, regardless of assertions that it does.

So we get all our results together, and quickly notice that every time a second passes, the cube seems to be traveling 9.8m/s faster than it was traveling the previous second.

Why are these sorts of measurements, and this sort of experiment, unimaginable to you? Are they still unimaginable to you now?

Well, look what you have shown me. Between .9s and and 1.1s the object was moving at a constant speed. Then it accelerated between 1.1s and 1.9s. Then between 1.9s and 2.2s it moved at a constant speed again. And so on. How is this imaginable to you? It implies that the force (gravity) acted to accelerate the object over a period of time, then it quit acting on the object for a period of time (between .9s and 1,1s) when its velocity remained constant, then it acted again, then the force quit acting again, etc.. How is this imaginable to you? Why would the force stop and start acting in complete coincidence with the timing of your measurements, when the timing of your measurements is completely arbitrary?

But you are dismissive of the map because it is not the territory, and that is an unseemly and unaccountable (on rational terms) error for someone like yourself.

No, I am dismissive of the map because it is misleading, as I clearly explain above, in this post. And, a misleading map gets people lost.

As with the 2+2=4, you say that the 2+2 does not represent the same thing as 4, and of course it exactly represents the same thing as 4.

I disagree that "2+2" represents the exact same thing as "4", and you're very naive to believe this. I've explained why, elsewhere. If it did represent the exact same thing, equations would be completely useless. The left side of the "=" would necessarily represent the exact same thing as the right side, and the equation would do absolutely nothing for us. But of course, that's not how we use equations in practise, the left side always represents something different from the right side, and in working out why the two distinct things are equivalent we solve a problem.

And I refute this thus: When they are doing something, are they doing that thing, or are they doing something else? If you had read a little more closely, you would have seen that Socrates did indeed find people who knew what they were doing, but not wise, because they, knowing something, thought that they knew more that they did, thus knowing something, but not wise. That is, the Oracle had told Socrates that he was the wisest, and Socrates had to discover that wisdom and knowledge are not the same thing.

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And, a misleading map gets people lost.

Ah, the irony.

There are none so blind...
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you're still over thinking everything. Or you're just immune to science.

Well, look what you have shown me. Between .9s and and 1.1s the object was moving at a constant speed.
That's an assumption YOU made, not me. I said APPROXIMATE speed. I didn't say constant. I don't know why you would assume it's constant, the data doesn't say that.

If you insist on overthinking it, you should be very careful in your overthinking.
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Or you're just immune to science.

MU has as much as said that his mind is closed to the extent that he can keep it so:

I, am an impenetrable fortress. Nothing, I repeat nothing, from that "external world" can infiltrate my defenses, and move me. All which exists within my mind comes from the inside. Thus is my reality.

There is however, a sense in which ideas come to my mind from somewhere other than my mind. Since they cannot penetrate through my fortress, and enter from the external, and "ghostly phenomena" is silly talk, I conclude that they enter my mind through "inner space". And since the ideas which enter my mind through inner space seem to be very similar to the ideas which enter your mind through inner space, I can conclude that we are very well connected through inner space.
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I see. I suspected it was some situation like that, interesting that he just lays it out so explicitly.
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I said APPROXIMATE speed.

I think you've stated my case for me very well, flannel. "Approximate" with respect to a representation means near, or close to what is actually the case. This does not imply truth, but the contrary, it implies a lack, or deficiency of truth. So the fact of the matter is that we just do not have an accurate, precise, or truthful representation of what acceleration actually is. And that is exactly the deficiency which I've been claiming.

And here, thinks that this sort of approximation process provides for a "rigorous foundation". Rigorous: "strictly exact or accurate". I apprehend an implied contradiction between "approximate" and "rigorous".
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