Perhaps I should have said that Energy is what Mass is composed of. Mass is also a property of Matter. So again, what substance is Matter or Mass made of? — Gnomon

You can't really say 'what substance is', or 'what matter is', because if you could describe it you would be talking about its properties, not substance itself. Substance is what has properties, so you can't really describe it by referring to what properties it has.

Matter is now known to be composed of Energy, but what is energy made of? Nobody knows, so the essence of energy is undefined. — Gnomon

Energy is defined as the capacity to do work. Energy is not what matter is composed of, it is a property of moving objects.

So Philosophy is becoming relevant again for understanding the real world. — Gnomon

Yes, philosophy is relevant, as necessary to avoid misunderstanding, like above.

And in visual psychology, it should not be regarded as an error if a test subject reports that he saw 5+7 as 13. It simply means that visual phenomena are not a good model of ordinary arithmetic and vice versa. — sime

I think my eye doctor would prescribe glasses if I saw 5+7 as 13.

There was also a 90-100% chance it would hit Florida. No hurricane there either. — NOS4A2

The map shows the probability of tropical storm force winds, which Florida did receive. I believe Florida also receive some hurricane force winds as well as a large storm surge.

I took philosophy in university in the eighties, started as a general arts student. My first year philosophy professor called me to his office, and was very critical of the questions I was asking in class, but said that he was quite impressed that I had actually read the required readings, while the vast majority of his first year students never do. He recommended that I continue in philosophy.

Yes, actually, because you can see the data yourself with your own two eyes. — NOS4A2

Hmm, a 5 -20% probability of tropical storm force winds in the extreme south east corner of Alabama, no hurricane there. No wonder it wasn't included in the forecast.

It is a thing. It’s a non-scandal perpetrated by the press in the US. It’s quite shameful. — NOS4A2

The problem is that when the president issues a warning, you'd expect people to take heed. But if the president is always crying wolf, just to watch people get excited, then there's a problem.

Computers, unlike typewriters, auto format, with some fonts having letters of differing sizes, and some fully justify the words on both margins. This causes the computer to reformat the spacing. It's not correcting grammar or punctuation. It's just formatting. — Hanover

That's bullshit. The computer doesn't automatically remove all double spaces because this reformatting is required to make the words fit within the margins. Come on Hanover, get real.

True, probable because the people that designed the editing software figured that an educated person would only leave double spaces by accident and that everything else they wrote was because that was what they wanted to say. — Sir2u

Those software designers were wrong then. Do you think that no one has corrected them on this yet, or do they persist in this practise just to exercise control over us peons, and continually display this mastery with incessant annoyance? Spell-check is bad enough, when you have to re-correct stuff after it acts, then the spell-check sneaks back in again to overrule you when you hit 'send'. But at least it's there for a good reason. This double space editing is only there to let you know that the programmers have control over how your composition (creative work) will appear in it's finished form.

On the other hand, Quine's naturalistic epistemology involves a conception of objects as posits that we introduce in our theories about the world. — Janus

When you have to posit the existence of something, whose existence is not justified by anything other than that it is needed to make a particular theory work, you can be sure that the theory is faulty. This is the case with the cosmological constant (post above). But the existence of objects is much more complicated than this because it is supported at a fundamental level, empirically. Individuating, and identifying objects is a fundamental object (goal) of sensation. So empirical experience itself, as sensation, is fundamentally guided by this 'posit', that there are objects.

This places that 'posit' (the existence of objects) as prior to sensation itself because sensation is guided toward recognizing objects.. But when we reflect on this we see that this original, or primitive posit, is not really a posit of the existence of objects, but of what is required for us to conceive of objects. This is evident in Kant, as what is required for the "possibility" of experience, and it is manifest in Aristotle as the concept of "matter". There is not a primitive positing of the existence of objects, but a preconditioning which establishes the attitude (belief?) which allows us to apprehend the world as consisting of objects.

So the process of understanding the existence of objects might be something like this. Objects are present to the conscious mind, so we are inclined to simply assume or 'posit' their existence. But when we reflect on this, we see that this assumption is not really justified, it is only supported as a precondition for sensation. And, we are warned by philosophers to be skeptical of sensation. With a healthy dose of skepticism, and analysis, we see that this precondition doesn't really exist as an assumption of the existence of objects, or a positing of objects, what it is is extremely complicated and difficult to understand, and that's why metaphysics is not simple.

I will depart from this thread, feeling on my side that I can't talk to someone who is claiming that 2 + 2 is something other than 4. And also feeling deep down that I must be missing something really profound, but I don't think it's something I'd want to get even if I could. — fishfry

I suppose the feeling is mutual. I really cannot believe that there is a rational human being who truly believes that 2+2 is the same thing as 4. Isn't this what we learn in basic math, first grade? You take two things, add to them another two things, and you have four things. Very good. But we can get four by adding three to one, or by subtracting two from six, and an infinite number of 'different' ways. So it is impossible that 2+2 is the same as 4, because there would be infinitely many different things which are the same as four. Does it make any sense to you, to believe that there is an infinite number of different things which are all the same? Or can you see that 2+2 is not the same as 8-4?

Einstein didn’t predict the expansion of the universe, or rather this theory made no such prediction. I think it was Hubble and Le Maître that discovered the expanding universe some years after Einstein published his general theory. — Wayfarer

That's right, Einstein wanted a static universe, and introduced the 'cosmological constant'. It was meant to counter the effects of gravity which Einstein thought should be making the universe contract. Friedman argued otherwise. The point is that this principle could not be held because observations of the universe, interpreted through the lens of general relativity, revealed an expanding universe, which is not what Einstein thought general relativity should predict.

Now it is understood that expansion is accelerating, so dark energy is posited to account for this. In reality, general relativity cannot predict anything concerning the expansion of the universe, it has no mechanism for dealing with this phenomenon. And that's why the issue is so confused, the phenomenon known as "the expansion of the universe" is completely inconsistent with general relativity. The appearance of "the expansion of the universe" (which is a completely confused concept) is produced because the universe is observed from the artificial perspective of general relativity, and this perspective is faulty, so confusion results. Here's a quote from the Wikipedia page on "cosmological constant":

According to quantum field theory (QFT) which underlies modern particle physics, empty space is defined by the vacuum state which is a collection of quantum fields. All these quantum fields exhibit fluctuations in their ground state (lowest energy density) arising from the zero-point energy present everywhere in space. These zero-point fluctuations should act as a contribution to the cosmological constant Λ, but when calculations are performed these fluctuations give rise to an enormous vacuum energy.[7] The discrepancy between theorized vacuum energy from QFT and observed vacuum energy from cosmology is a source of major contention, with the values predicted exceeding observation by some 120 orders of magnitude, a discrepancy that has been called "the worst theoretical prediction in the history of physics!".[8] This issue is called the cosmological constant problem and it is one of the greatest unsolved mysteries in science with many physicists believing that "the vacuum holds the key to a full understanding of nature".[9] — Wikipedia

the lounge is hidden from view because it makes the philosophers of the site look bad if it comes up on the front page.

You show your age it seems. — Hanover

It's not a question of which age group has a better method, it's a question of why does the computer take it upon itself to correct this non-mistake. My spell-check never corrects this. And, my spell-check shows me many errors which, if I post them will pass right through onto the posting. So there's all kinds of grammatical errors which are not corrected when I post, yet for some odd reason a double space after a period is corrected. Why? Is the double space such an evil thing that it is singled out as the one thing which needs to be corrected? And it can't even be said to be 'wrong' anyway, just something practised by a different age group.

It is in a forum, spaces count the same as any other character. That means that for every sentence there is an extra character. over several thousand sentences that adds up to a lot of extra space on the server drive and extra download time for the people viewing the thread. There are some people that have limited data mobile services so every byte counts. — Sir2u

OOKK, BBuutt II bbeett II ccoouulldd ddoouubbllee uupp aannyy cchhaarraacctteerr,, aanndd oonnllyy tthhee ssppaacceess wwoouulldd bbee eeddiitteedd..

Same for distance, which, as Einstein pointed out, is actually the same thing (i.e. spacetime.) — Wayfarer

But this is a mistaken perspective. The concept of "the expansion of the universe", which is a consequence of the Einsteinian perspective, gives us a sort of movement which is incompatible with "movement" within the theoretical framework, distances which are not distances. So the theoretical framework given by Einsteinian relativity must adapted, exceptions described, in order to account for this movement which is not movement according to the framework. This indicates that the proposed relationship between space and time, which is described by Einsteinian relativity, is deficient, it's incorrect.

When a theory is supposed to describe the relationship between two things, and it comes up short, we can conclude that the theory is incorrect. But modern physics is trapped within the confines of this incorrect theory, and this is really what is behind the "observer problem". Physicists have assigned to the observer a perspective which is false. The physicist observes through the lens of 'spacetime', and doesn't understand how the deficiencies of the theory affect the observations. From this false perspective the observations are incomprehensible.

Edit: The software automatically edits out the extra space, so you'll have to use your imagination, or I can come over to your house and show you with a pen and paper. — Hanover

Why? I learned in school to leave a double space after a period. So I diligently do that. Now the computer always edits it out. Why? It's not like it's a huge waste of valuable space or anything.

The view I am coming around to is that 'nothing exists without a perspective'. — Wayfarer

I find that this is easy to understand when one considers the temporal perspective. If you imagine what the world, or the universe, would be like with no human beings, then there is nothing to establish the temporal perspective. So you can ask yourself, at what time, in the existence of the universe, are you thinking about. Now, you cannot tell yourself that you are thinking about now, the time when human beings would have been here, and the universe would be exactly the same at this time, as it is now, because the exercise is to remove the presence of human beings.

This leaves you with the entirety of the temporal extension of the universe from its beginning to end, with no means of choosing one particular time, at which time you could say that the universe would be like this or like that. And, since things are moving, there is no way to say this would be here, or that would be there, because we are considering all of time now, so everything would sort of be everywhere. Furthermore, If you wanted to imagine how things would be like at a particular point in time, you would need some way of determining what a particular point in time is. We experience time as passing, so how long of a period of time would a point in time be, a Planck length? a nanosecond? a second? a minute? an hour? a year?, a few billion years? It doesn't even make sense to talk about a particular point in time without the human perspective, because the point in time is a product of the human perspective

I walked through this in detail a few posts ago. In the Peano axioms they are both the number SSSS0. In ZF they are both the set {0, 1, 2, 3}. = { ∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}} }. — fishfry

This does not show me the principle of identity. Saying that two things are the same does not make them the same. It's a hollow assertion without a principle. And I don't see any reference to sameness in your reference.

We must be talking past each other in some way. I cannot conceive of anyone claiming 2 + 2 and 4 are not the same thing. — fishfry

I can't believe there is a person who does not see a difference between 2+2 and 4. The two are equivalent. And, as I explained equivalence would be meaningless, and equations useless, if there was not a difference between the left side of an equation and the right. The Wikipedia page on "equation provides an analogy. "An equation is analogous to a scale into which weights are placed." Do you see that the things on the two separate sides of a balance are not "the same"? They are said to have the same weight, but this does not make them the same thing.

So, in the case of ZFC, by what property are the two sets said to be "the same"? It's not the same weight, as in the scale analogy, nor is it the same numerical value, as is the case in the equation (what alcontali refers to as "number theory" above). What is the principle of sameness?

Perhaps you have a reference to support your point of view. — fishfry

If you have no idea of what equivalent means, or of how equations are used, then I don't think I can help you. If you are simply asserting 2+2 is the same as 4 without thinking about what you are saying, because it supports your metaphysics, then why don't you smarten up?

But you claim that 2 + 2 and 4 are not the same object in ZFC. And THAT is an area where I am not ignorant. You're just wrong. 2 + 2 and 4 represent the same set in ZFC. — fishfry

I fully acknowledge, that in ZFC 2+2 is "the same" as 4. I am not denying this. I am saying that it is wrong, because it violates the law of identity, without any justification. If one wants to establish a principle in violation of a fundamental law of logic like the law of identity, then that person ought to provide justification for the proposed principle. Without justification, use of that principle is mere sophistry.

Well, first there is the understanding that the "=" symbol pretty much never means "identical". — alcontali

Tell that to fishfry, who is arguing the opposite, that the left and right of the equation actually are the same.

You tell me how 2 + 2 is not 4. If it's not, what is it? — fishfry

Refer to alcontali's post above. Thanks al.

Of course 2 + 2 is the same thing as 4. I cannot imagine the contrary nor what you might mean by that claim. — fishfry

Explain to me then, how this set '2+2', is the same thing as this set, '4'. They look very different to me, and also have a completely different meaning. By what principle do you say that they are the same?

But more importantly, they are the same set in ZFC. So it's not an example of your claim that ZFC allows two distinct things to be regarded as the same. — fishfry

Yes, that's exactly the point. ZFC says that they are "the same" set, when they are clearly not the same by any intelligent reading of the law of identity. Therefore ZFC must employ some other principle of identity in order to say that they are the same. Can you state ZFC's law of identity?

But you hold that 2 + 2 and 4 are not the same? How so? Without quotes around them they are not strings of symbols, they are the abstract concept they represent. And they represent the same abstract concept, namely the number 4. You deny this? I do confess to bafflement. — fishfry

This is absolutely false. The symbol 2 has a meaning, the symbol 4 has a meaning, and the symbol + has a meaning. Clearly 2+2 is not the same concept as 4. Otherwise there would be no point in writing the exact same concept in two different ways, and the symbol =, which is commonly used to express the relationship between these two different concepts, would be meaningless. Do you see that 4=4 would be a meaningless equation in mathematics? Therefore it is very evident that 2+2 is not the same concept as 4, and the = sign expresses a meaningful relationship between these two distinct concepts, a relationship which is quite different from the useless expression of 4=4. The usefulness of an equation is due to the fact that something different from what is expressed on the right side, is expressed on the left side

Here's the sort short irony:

"The number three is used in the Torah to mediate between two opposing or contradictory values. The third value mediates, reconciles, and connects the two. Three is the number of truth." — 3017amen

Having to deal with the number three is what messes up the Pythagorean scale, causing the occurrence of the comma. For example, If we start with "one" unit of frequency, a designated length of string or whatever, as the base unit, then we double to two units, this gives us the harmony of the octave. If we double again, we have four, as the next octave. Now three is excluded, but we want to fit it in, as the half way point of the octave, halfway between two and three, thinking that the halfway point ought to be harmonic. The halfway point of the first octave is one and a half (3:2), and of second octave it is 3.

The problem is that the first set of octaves produced, 1, 2, 4, 8, etc., is fundamentally incompatible with the second set which is produced at the halfway point, 11/2, 3, 6, etc. However, if we take the base unit, 1, and cut that in half to get 1/2, this is compatible. So we can always take a designated frequency, cut it in half and produce a perfect harmony of an octave. But we cannot take a designated octave and cut it in half, to find the midpoint, without producing dissonance.

You made the statement that ZFC allows two different things to be equal. I said I know of no such example and you have not backed up your claim or put it in any context that I can understand. You must be thinking of something, I'm just curious to know what. — fishfry

I was in discussion with alcontali, referring to what was said by alcontali:

S1 and S2 describe the same set. Therefore, S1 = S2. — alcontali

2 + 2 and 4 represent the exact same mathematical set. '2+ 2" and '4' are distinct strings of symbols. I don't know any mathematicians confused about this. And, as you agree, the discovery that these two strings of symbols represent the same set, is a nontrivial accomplishment of humanity and is meaningful. — fishfry

The point I made is that 2+2 is not the same as 4. So if set theory treats them as the same, it is in violation of the law of identity.

I really don't understand your remark that ZFC allows distinct things to be regarded as the same. Unless you mean colloquially, as in the integer 1 and the real number 1 being identified via a natural injection. — fishfry

'2+2' is clearly different from '4'. Each of those two expressions are composed of different symbols, having different meaning. Despite the fact that they are said to be equal, in no way are they the same. If ZFC allows that they are the same, as you say above, then ZFC allows two distinct things to be regarded as the same.

Since they are not the same according to the law of identity, by what principle of identity does ZFC claim that '2+2' is the same as '4'?

Furthermore, their assumed input could still truly be random, because there is no method available to distinguish between the output of unknown mental faculties and sheer randomness. — alcontali

I think we've been through this all before, you and I. I don't think that just because there is no method available, the input is out of reach. Methods come into existence, and evolve, so things which are reached by existing methods were at one time out of reach. Therefore it's reasonable to believe that a method could be developed to reach the things which presently cannot be reached. So if someone reaches a conclusion through a mental process which you consider to be by your standards, not rational, this does not mean that it is impossible to reach that conclusion through a rational process. It is possible that the required rational process could be developed.

Still, the uncanny sensation of recognition suggests that this link is not necessarily, completely out of scope for other, unknown mental faculties. — alcontali

Yes, my point is that it requires effort to distinguish the good from the bad, but these "unknown mental faculties" may be brought into the realm of the known.

Very good description. I see why you say that my description is confused. I see the importance of the problem in a slightly different way.

We produce perfect harmony with the octave, doubling the frequency. But every time the frequency is doubled, there are many frequencies, notes, in between. These in between notes must be determined, in order to scale the octave. This requires division of frequency. The Pythagorean method proceeds by using only divisions of half. Half way between one and two is one and a half. Half way between two and four is three, half way between four and eight is six. Notice, that the only division employed is the half, though the half is always taken three times, each time it produces another in between note to scale the octave. The half is always in harmony with the unit that it is half of (as an octave) and that is why the Pythagorean method of scaling the octave is considered to be more truly harmonic. That the Pythagorean method produces the Pythagorean comma is a problem which has not been resolved. Going to a less harmonic system of division, equal temperament, is not a real solution. It's a simple fix which lowers the quality.

It is the same situation as with a sequence generated by a Mersenne Twister. From the outside, it looks random. From the inside, we can see that you will always get the same sequence depending on the seed that you use. Is the sequence random? For outsiders, yes. For insiders, no. — alcontali

It's not arbitrary then, it just looks arbitrary, in appearance, but it really is not. That it is arbitrary is an illusion. Would you see mathematical axioms in the same way? They look arbitrary, but they really are not. What is required to get beyond the illusion of arbitrariness is to get inside of the head of the artist. This does not mean to literally get inside, but to learn how to think in the same way as the artist. Then you will no longer be an outsider who sees mathematical axioms as arbitrary.

That would almost amount to saying that an artist's design choices are exclusively rational, and could therefore even be expressed in formal language. My own take is that I do not believe that. I believe that artists make use of other mental faculties, that are not rationality, when making their design choices. I also do not believe that it is possible to express, even in natural language, the output of these other mental faculties. — alcontali

Well, that would depend on how you define "arbitrary". Use of mental faculties in one's decisions negates randomness. If such decisions are arbitrary, then how do you understand "arbitrary"?

Actually, I don't know if I quite got it right. I learned a lot (from jamalrob I think) on the old forum, and followed up study of some of the principles on my own, being a musician and composer who was always lost in the theory. I believe the basic issue is that division starts from an assumed unit, which is divided, while multiplication starts from an assumed multiplicity. So, despite the fact that we look at division as a simple inversion of multiplication, it is not, there is a fundamental inconsistency between the two. One presupposes a unit, while the other presupposes a multiplicity. Since a conclusion always follows the principles of the premises, an act of division will always produce a specified unit, while an act of multiplication will always produce a specified multiplicity.

I think that resolving the problem of the Pythagorean comma will produce the universal key (the key to the universe), because it requires a determination of the fundamental unit of time, and producing a scale based in something real rather than an arbitrary frequency. This is where the wave theory of modern physics is currently lost. I am obsessed

Arbitrary axioms are the hallmark of creativity! — alcontali

Well, I really don't agree, and I think you misunderstand creativity. Art is not a product of arbitrariness, there are reasons for what the artist does, purpose, so arbitrariness is not the hallmark of creativity.

I don't think that can really be true though. Math IS useful and meaningful because it takes human effort to determine whether two different representations of a thing are actually the same thing. Don't you agree? 2 + 2 = 4 is formally a tautology. But historically, it was a really big deal for humanity. Agree or no? — fishfry

Yes I agree, but the key is understanding the limitations of math. If some logician were to argue that '2+2' and '4' are both the very same thing, because they are equal, we'd have to correct that person, showing that these are symbols, and '2+2' clearly has a different meaning from '4'. But then we are at the position of needing to explain what it is that is signified by these symbols. If we take the Platonic route, we say that the numeral '2' represents the number 2, and we avoid the question of meaning altogether. There is now no problem of what '2' means, because '2' represents a mathematical object which is 2. But now we are totally lost, because we can have no idea what the number 2 is, it's just a mathematical object. We cannot turn to meaning, because then we might as well just go back to the symbol, the numeral '2', and ask what it means. At this point we cannot turn to Platonism and say it's a mathematical object, because we want to know what the symbol actually means, not just say that it stands for an object (the existence of which cannot be validated).

I seem to recall the old philosophical standby of the morning star and the evening star, which appear to be two different things but (upon astronomical research that took millennia) turn out to be the same thing, namely the planet Venus and not a star at all. — fishfry

OK, but this analogy assumes that there is a thing, an object which "morning star" refers to, and it turns out to be the same object that "evening star" refers to. We cannot do that here with mathematical objects, because as I described above, if the symbol refers to an object, then we deny that there is any real meaning. The symbol stands for a mathematical object, and this is the only meaning there is. The symbol stands for an object, and that's that. There is no meaning. This is pretty much the stance that alcontali takes, axiom s are arbitrary, so there is no such thing as the axiom's meaning, it's just an arbitrary thing.

If you reduce everything to the law of identity, you are saying those millennia of observation and theory and hard work by humans means nothing. I don't accept that. — fishfry

No, this is exactly the opposite to what I am arguing. When we adhere to the law of identity, then everything has an identity proper to itself, therefore its own meaning. This does not rob meaning from mathematics, it only establishes clear limits to the possibilities of mathematics, so that mathematicians will not believe themselves to have accomplished the impossible, like putting the infinite within a set.

Modern tuning of the twelve tone scale is usually "equal temperament", in which the octave is divided into twelve equal parts.The Pythagorean tuning of the 12 tone scale is called pure temperament, or just temperament, because the designated notes are derived from the 3:2 ratio which gives the perfect fifth, pure consonance. With the numerous octaves required to produce the twelve notes of the scale in the Pythagorean method, a slight gap opens up, called the Pythagorean comma. This creates a slight difference between the same note, played in a different key. So modern musicians have turned to equal temperament to avoid this problem, making modulations smooth.

Incidentally, the problem of the Pythagorean comma is a function of the relation between frequency and time. There is no starting point, no base unit or fundamental frequency. So divisions or multiplications may proceed infinitely. Therefore your harmonies are always determined by your starting point, which due to the nature of time cannot be well-defined. I believe it is this same inability to define perfect harmony, because there is no base unit, which produces the infamous uncertainty principle from the Fourier transform. You might say that the Pythagorean comma and the uncertainty principle are symptoms of the very same problem.

They probably worked it out by trial and error until they got something that sounded good to them. — Bitter Crank

Well, you cannot keep drilling holes in the same piece of wood, in the process of trial and error, because your instrument would be ruined. So measurement would be necessary, to ensure that the errors were not repeated, and the successes were maintained. I think therefore, that the holes in your 40,000 year old instrument were measured. Otherwise it wouldn't be an instrument at all, it would be a stick with random holes.

The axiom of extensionality depends on the law of identity, which is a principle of logic and not of set theory. A thing is equal to itself. Then we define two sets to be equal if they have "the same" elements, meaning that we can pair off their respective elements using the law of identity. — fishfry

By the law of identity, two distinct sets cannot be the same. If they actually are the same, then they are necessarily one, the same set. It's contradictory to say that two things are the same. If it is the same, it is only one. Being equal and being the same are very different because "equal" refers to a multitude while "same" according to the law of identity refers to one, and only one. If ZFC states that two equal things are the same, it clearly violates the law of identity, which necessitates that the appearance of two is an illusion, there is really just one (Leibniz principle). And we cannot talk about one being equal, because there is nothing for it to be equal with.

This is a fundamental problem with the so-called "objects" of mathematics. Distinct things are allowed to be the same object, contrary to the law of identity, through the means of a principle of equivalence. Mathematicians will defend the existence of these objects, as objects, through reference to a difference which doesn't make a difference. But strict adherence to the law of identity allows no such contradictory nonsense. If there is a difference between what "2+2" refers to, and what "4" refers to, then these cannot be the same object, despite the assertion that this is a difference which doesn't make a difference.



I am concerned with the principles of the system, not any installed base, or legacy, these are irrelevant to the acceptability of the principles. I know that you believe axioms are completely arbitrary, making such things very relevant, so join the mob, if you like the "mob rules" philosophy.

That's all fine and dandy, but the instrument in question proceeded Pythagoras by maybe 40,000 years. What the 40,000 BCE people had discovered was a) pleasant sound could be made by blowing into a hollow bone and that b) holes in the bone, covered and uncovered, would change the sound. c) one could play the same sounds over and over. Not enough of the bone remains to know how the sound was initiated; an unknown amount of the bone tube has been lost--we can't know how long it was. — Bitter Crank

If the positioning of the holes was not random, it was measured. And it couldn't have been random or the sound wouldn't be musical. Don't you agree? The fundamental ratios, which Pythagoras laid our were very basic division, 1/2, 1/3, and 1/4. The 3:2 ratio is one and a half. I would expect that the people of 40,000 years ago knew how to divide lengths into halves, and into quarters, that was how harmonies were produced.

I believe Pythagoras developed the twelve tone scale, based on the 3:2 ratio which gives the prefect fifth. Though the designated intervals could be recognized by the human ear, he taught that they ought to be determined my mathematical ratios to maintain the pure tones. The Pythagoreans extended the mathematical principles of harmony to the entire cosmos such that each of the orbits of the planets were described as emitting different tones according to their orbits. He called it the harmony of the spheres, which is a similar concept to cosmic vibration.

However, their brains were pretty much like ours by the time the flute was made, so maybe... but we just don't know what kind of quantitative thinking they did. — Bitter Crank

Musical instrument makers think in terms of ratios, so there is necessarily measurement involved, to get the right notes.

Since when would a metaphysician think a thing as immaterial as theoretical moral philosophy have any kind of deterministic force incorporated in it, as a means of its justification? — Mww

That was your argument, that moral laws determine one's volition through the means of "moral constitution". I was merely pointing out the inconsistency in what you were saying, your self-contradiction.

Moral law is the source of the form of determinism you said you don’t see. The laws conform to the agent’s innate qualifications, and determine one’s moral constitution, that which the will uses to formulate its volitions. — Mww

First you say people can behave in opposition to moral law, then you said that moral law determines ones volitions. How can moral law be said to determine one's volitions if people can behave in opposition to moral laws?

The sentence "they both describe the same set and therefore they are extensional" is therefore in accordance with the axiomatic foundation of ZFC set theory. — alcontali

Right, but as I noted, this theory is deficient. The two sets are not the same set by any rigorous standard of "same", though they are "the same set" according to the deficient standard of ZFC set theory; the law of identity being the appropriate standard for "same", not ZFC theory. ZFC theory allows that two distinct things are the same, contrary to the law of identity. Since they are not the same, your argument, which requires that they are the same, to reach its conclusion, fails. Therefore they are not even equal.

You conclude that the two sets are equal based on the assumption that the two distinct descriptions describe "the same set". They do not describe the same set, by a rigorous standard of "same", therefore you cannot even conclude that the two sets are equal.

S1 and S2 describe the same set. Therefore, S1 = S2. — alcontali

That two things are equal does not mean that they are the same. This is a known deficiency of mathematics, equality cannot replicate identity. Anyone who argues that 2+2 is the same as 4 needs to learn the law of identity, and respect the difference between equality and identity. The two sets are not "the same" in the sense of "same" used in philosophy, they are "the same" in the sense of "same used by mathematicians (i.e. equal). In philosophy, an actual thing is not the same as a possible thing, and we have a law of identity to prevent this type of sophistry, employed by mathematicians who creep into philosophical discourse without the appropriate discipline.

Yes, now what about the way that mathematics links space and time, when will that be overturned?

Morality speaks to what is good, not what is right. What people commonly do that is not right is with respect to an objective want, called inclination, in opposition to cultural acceptance, thus not necessarily against moral disposition. What people much less commonly do that is not good is with respect to a subjective interest, called obligation, in opposition to moral law, which is very much so against moral disposition. — Mww

Now you leave "moral disposition" as meaningless.

Moral law is the source of the form of determinism you said you don’t see. The laws conform to the agent’s innate qualifications, and determine one’s moral constitution, that which the will uses to formulate its volitions. — Mww

This is not true, by what you've said above. People behave in opposition to moral law, so moral law cannot act as a determinist force.

All possible sentences you can say in English is a set. — alcontali

No it isn't. A set consists of objects, not possible objects.

But what do i have to do to make them one, tie the laces together - glue the soles together - crush them into a singularity? — unenlightened

That's quite simple, to make them one, you have to refer to them as one, and not as two. if you refer to them as two things, a pair, or any such thing, then you are talking about two distinct things. But if you refer to them as one, then you are talking about one thing. But you cannot talk about them as two things and one thing at the same time without contradicting yourself. So either "two" refers to one object, a mathematical object, in which case it does not mean two distinct things, or "two" refers to two distinct things. You can use the word either way, but you must be careful not to equivocate, so you can't use it both ways at the same time.

So don't do it. — unenlightened

The problem is with the people who want to make mathematics do the impossible, not with the people who point out that what the mathematicians are doing when they're tying to make mathematics do the impossible, is contradictory.

The concept of infinite set is abstract and very Platonic but not contradictory. — alcontali

It is contradictory, because a set is closed, complete, (as an object it is bounded, defined) whereas an infinity of anything is open, incomplete, unbounded and indefinite. I went through this in another thread recently, you weren't there.

C’mon, man, really? Nonsense? Look at what you wrote...river still flows according to the direction of the tide. If the tide is the major determinant factor, then the necessity resides in the tide, not the river, re: estuary. I can see one from my deck, complete with lobster boats. Navigational charts call it a river because shoreline proximity precludes calling it a bay, cove, inlet or sound. — Mww

So it's not a river you're talking about, it is an "estuary". Make up your mind, because my analogy did not refer to estuaries, it referred to rivers. Show me a definition of "river" which does not contain 'flow" or something synonymous. Then you might have an argument that some rivers don't flow.

Ahhh.....now we’re getting somewhere. There is a kind of determinism in play. Granting that a moral disposition is predicated on certain qualifications, whether innate genetically or instilled very early on from experience, then in order for proper moral agency to manifest, the agent must conform to whatever those qualifications happen to be. Hence, a form of determinism. It follows that the volitional determinations of the will must adhere to one’s moral disposition in accordance with his pre-established personal qualifications. Hence, a form of determinism. — Mww

I really don't see how this is a form of determinism. We can choose to go against our moral disposition. This is called doing what one knows is wrong, and people do it commonly. So one's moral disposition cannot act as a determinist force.

All well and good, peachy, have a nice day.......right up until the will is called upon to determine a proper moral volition in direct conflict with a vested interest of the agent called upon to act. Here, the will is not free to relieve the conflict at the expense of the agent’s moral constitution. To do so is the epitome of immorality, which manifests in the agent as “guilty conscience”, “dishonor”, ill-will” and the like. And NOT....oh jeez, can you believe people actually think so???......as farging court appearance!!!!! (Gaspsputterchoke) ‘S-ok, though; they can’t separate ethics from morality either, so what can you expect? — Mww

So this is where you're wrong. We often act against what our moral disposition dictates, and your appeal to "guilty conscience" does nothing to resolve this. A person may or may not feel a guilty conscience, but this is irrelevant to the fact that one is free to go against the dictates of one' moral disposition, and is evidence of this freedom.

but if you find no value in any of what’s been said, there’s no point in continuing, right? — Mww

I don't know, you seem to be arguing both sides of incompatible positions, as if they are compatible.

OK, you have two shoes. By what principle are these "two" things, one object? If they are a "pair" of shoes, this does not make them into an object, it is just another way of saying that they are two, a specialized form of "two". They are still not one object.

The first evidence of a musical instrument that was made to purpose is an ivory instrument with holes drilled at regular intervals. This instrument belong to 'modern man' and was made 45,000 years ago.
...
But the first applications of math were (as far as I know) applied to trade, which is very recent, 5,000 years ago, after the invention of writing. — Bitter Crank

Are you sure that the construction of that ancient musical instrument was not an application of mathematics, as is the case with the construction of all musical instruments today?