Traffic laws are a made-up game too. — fishfry

Uh, no, laws are not games. What kind of game do you get penalized for not playing?

But the word "contradiction" in mathematics has the meaning that I said: "A and not A" is not provable for any A. — Mephist

But I haven't yet accepted your mathematical rules. I am judging them as to whether or not they ought to be accepted. So I can only judge "contradiction" according to what it means in English.

What you call "contradiction", the impossibility to identify the terms of the language with physical objects, is not considered as a problem in mathematics: it's simply ignored. — Mephist

"Contradiction" has nothing to do with identifying things with physical objects, it relates to how words are defined. So for example, if "set" is defined as something having extension, and "empty set" is defined as a set having no extension, then there is contradiction here. "Empty set" breaks the rules expressed in the definition of "set", and therefore cannot be a set.

The rules of deduction (used in proofs) should not depend in any way on the meaning (or correspondence to real physical objects) of the words. — Mephist

"Meaning" is not necessarily dependent on correspondence with physical objects, it might be derived from relations within a conceptual structure. That's why I outlined two distinct types of "consistency", consistency within a particular structure, and "consistency" in how that structure relates to outside principles. Notice there is no necessity for correspondence with physical objects. But when correspondence with physical objects (what some call "truth") is one of those outside principles, then the conceptual structure might be judged in relation to this principle.

So, you say that this is all wrong, because you are allowed to create axioms that don't have any correspondence to reality. — Mephist

That's not what I'm saying is wrong. What's bad is if there is contradicting axioms, like in my example above. Suppose people are creating axioms, and the axioms are not necessarily corresponding with reality. There's no inherent problem with that. Now suppose a problem in application of the axioms appears, possibly because the axioms don't correspond with reality, perhaps some sort of paradox appears or something when people try to apply the axioms. So the people creating axioms decide that if they change this axiom, or create another axiom, the problem can be avoided. But maybe they don't realize that the new axiom contradicts another axiom, or if they do, they might still be inclined to accept it because it makes that particular problem go away. However, I think the contradictory axioms are bound to create other problems further down the road.

I just don’t understand how his actions can be misconstrued as “wrong-doing”. — NOS4A2

When your perspective is whatever is good for Trump is the correct thing, as yours is, it's easy to understand this statement. And since Trump is the saviour of the people, the second coming of Christ Himself, we might have to agree with you NOS4A2.

Were you like this when you learned to play chess? "This is the knight." "But no it's not REALLY a knight. Real knights don't make moves like that, they slay dragons and rescue damsels. I refuse to accept the rules of your game till you tell me what they mean outside of the game." — fishfry

That's not quite right. I learned how the game was played, then decided I didn't want to play it. The fact that it was a game, and the rules referred to nothing "real" probably made me think of it as a waste of time.

You have to prove that assuming those axioms leads to a contradiction. — Mephist

It's not a matter of whether or not the axioms lead to contradiction, it's a matter of whether or not the axioms themselves are contradictory. I demonstrated precisely this, that the axioms are contradictory, with the "empty set". If you've forgotten already, go back and take another look at those posts. Sure, there was some mention that the contradiction might potentially be avoided by introducing exceptions to the rules. But exceptions to the rule just serve to disguise and hide the contradiction in the rules, behind sophisticated complexities. They do not resolve it.

You have to use the rules of logic to produce a sentence of the form "A and not A" (I am not sure if "true" and "false" are terms of first order logic, maybe I made a mistake before saying that you
have to derive "false"). — Mephist

This is where you are wrong Mephist, and I can't seem to get this through your head. You cannot use the rules of the logic without first accepting the axioms. The axioms state the rules. You must agree to play by the rules in order to use the logic. If the axioms themselves are contradictory, then you accept those contradictions, when you proceed to use the logic. Therefore you cannot prove that there is something unacceptable about the axioms, i.e. that they are contradictory, through the use of the logical system, because by accepting the axioms you consent that there is nothing unacceptable about them, i.e. they are not contradictory.

Use of contradictory axioms may lead to absurdities like paradoxes, but a paradox does not prove that any axioms are contradictory, the appearance of paradox could be caused by something else. So when a paradox appears one might go back to the axioms, and determine whether or not there is a contradiction, using principles outside the logical system, the principles in which the system's axioms are based. The axioms are the rules of the logical system and they may just lead to an unsolvable paradox within the system. We do not necessarily know the cause of the paradox though, and sometimes analysis of the paradox cannot lead us to its cause. That's why it's a "paradox". if the paradox is caused by a problem with the axioms, then to solve the problem requires going outside the logical system to determine how the axioms are founded, the relations between them, interpretations of them, etc., and removing inconsistencies.

To take fishfry's example of the chess game, imagine contradictory rules in the game. This could lead to unsolvable problems within the game. From within the game, the problems cannot be solved because the rules leading to the problem are set. However, because the premise of my example is that their are contradictory rules, it appears obvious that the problems are caused by contradictory premises, as contradictory premises can cause problems. So you might think that if there are contradictory rules in any game, the problems they cause would demonstrate clearly, the very contradiction which exists in the rules. But this is not the case, because an equivalent problem might arise as a matter of a difference in interpretation. The "paradox" within the game, by the very nature of a "paradox" doesn't necessarily reveal the source of the problem. And although the rules of the game might include rules of interpretations, those rules of interpretation cannot have rules of interpretation, ad infinitum. Therefore contradiction, and other problems in the rules, or axioms, can only be determined and resolved by reference to principles outside the system composed of those rules, because they might equally be problems of interpretation.

The interpretation of the terms as sets (and then the meaning of the sentences) is a different issue.
You can argue that the terms that ZFC calls "sets" are not exactly correspondent to what we "intuitively" think to be sets, and a lot of people (even mathematicians) have this kind of objections to ZFC. But this is not about the consistency of the theory; this is about it's "meaning". — Mephist

Now perhaps you are starting to grasp what I am arguing. I am arguing the "meaning". Contradiction within the meaning of a theory's axioms is clearly a matter of inconsistency. We might have two distinct senses of "inconsistency" here though, whether the proceedings in a logical system are consistent with the axioms, and whether the axioms themselves are consistent. I am arguing the latter.

So you might hand me the rules of a game, and ask me to play. If I look over the rules and see that there is blatant contradiction in the rules, as in set theory, or even that the rules are open to contrary interpretations, or there are holes, possible situations not covered, I might tell you that I have no desire to play your game. And, I might proceed to show you what I see as blatant contradiction, the empty set. You might accept this and say ok, don't play then. You might also claim that this is only a matter of interpretation, and attempt to work out a satisfactory interpretation with me. But your insistence, that I join the game, even when I see a glaring problem in the rules, and then we try to work out this problem with the rules only after we develop a problem within the play of the game, is completely unreasonable.

Radiometers, a/k/a light mills. — tim wood

These are physical objects effected by light, so this is not much different from a demonstration of the photoelectric effect, which shows how supposed particles are effected by electromagnetic waves. It does not provide the evidence required to show that the light itself exists in any form other than waves.

The view to which I refer (positing no preferred moment in time) was probably not something Aristotle was aware of. The argument you outline assumes the opposite point of view (yours) and argues for a distinction between past, present, and future. I have little against the argument, but it is irrelevant to proving its assumption, that there is a present moment. — noAxioms

We seem to be talking about different things here. I have been consistently talking about a distinction between past and future, which we call "the present". You have been consistently talking about a "present moment". If what you call the present "moment" is the same thing as what I call the present, then it is impossible to make the "positing of no preferred moment" consistent with my perspective, which necessitates a "preferred moment", as the division between past and future. Perhaps we could compromise on our differences if we allow that the present (as the division between past and future), is not a dimensionless division as a "moment". I am willing to accept that the present, as the division between past and future, does not exists as a dimensionless divide, but as a period of "time", during which the past is changing to the future. This requires two dimensions of "time", and makes the present not a "preferred moment", but a "preferred time". Will you agree to this, and release your use of "preferred moment", and "present moment", for "preferred time", and "present time"?

So we're back to unproven conjecture. You need a proof that does not proceed right up from an assumption that a present moment exists, as both you and Aristotle do. — noAxioms

So, you have misunderstood my argument. I have not argued for a "present moment". I argue that there is undeniable empirical evidence for a distinction between past and future. That is what Aristotle demonstrated by showing that the law of excluded middle is applicable to past events, but is not applicable to future events. So we have a difference between actual events (past) and possible events (future). This difference, between past and future, necessitates the conclusion that something, a boundary or division, separates the two, and this is what we call the present. I did not say, nor did I mean to imply, that the present exists as a "moment".

As I said, the argument isn't particularly invalid, but it assumes your premises right up front. Aristotle can be forgiven because to my awareness the alternate position would not be proposed for around 14 centuries. — noAxioms

The premise, therefore, is that there is a substantial difference between past and future. I insist that it is undeniable, because it influences every aspect of our life, and all the things that we do. it is a basic principle underlying all science, inductive reasoning, and prediction.

I assume this premise, right up front, because I believe it is so fundamental, and undeniably true. If you have any reasons whatsoever, why this premise might not be true, then as I've requested of you, put these reasons forward. But to say that I should arbitrarily dismiss what is so obviously true, so that you can propose what is obviously false, is just nonsense. Sure you might call it a "bias", but this is the bias which allows me to distinguish science from science fiction, and I will not dismiss it just so that science fiction may pose as science.

Pretty much yes. To be a little more precise, if you assume a preferred frame, then there is an objective before/after/simultaneous relationship between any two events. If you assume neither a preferred moment nor a preferred frame (mainstream view), then there is a relationship of before/after/ambiguous between any two events (the 'ambiguous' meaning the relation is frame dependent). No event is in 'the past' or 'the future'. Thus any references to such properties in any demonstration of inconsistency of this view would be begging a different set of assumptions. — noAxioms

This is the precise point of our disagreement then. I believe that it is undeniably true that there is an "objective" past and future. This is the fundamental constraint which the "objective" universe imposes on any, and all living beings. The proof of this fundamental truth is supported by all aspects of life, including death, and all observations of the "objective" universe, induction, prediction, and the scientific method. To convince me to release this undeniable truth, so that you might propose something contrary to this, requires that you present me with at least one piece of evidence against it. You have given me nothing. You simply insist that I ought to drop my bias.

If A is before B, then B would be in the future of A and A would be in the past of B. This illustrates the usage of the terms as relations instead of properties. — noAxioms

Defining "past" and "future" in a different way doesn't give me what I requested, it just dodges the issue.

Argument here is hopeless. Is there a real, live physicist who will enter the discussion and untangle this mess? — jgill

You see, a "field" must have real, substantial, material existence, as the "thing" which has energy and momentum. Yet a field is modeled as the property of a vacuum, an electromagnetic field in a vacuum. Don't expect a physicist to sort this out for you, they are the ones who created the mess, and they are satisfied to simply live with it (shut up and calculate). That's why, when you search on the internet for whether a field is a real physical object or not, you'll get conflicting accounts, from different physicists. Some, such as Feynman, recognize and understand that the principles of Faraday's and Maxwell's ontological representations of electromagnetic fields, have remained essentially unchanged and valid, despite the introduction of Einstein's relativity theory. Others, adhering strictly to the principles of relativity will argue that a field cannot have ontological status as a medium, or ether. The problem is that not only are the ontologically real representations of the field valid representations, they are necessary, as the only way to adequately model electromagnetic activity. This is decisive evidence against those who insist that the field cannot be a substantial, or material medium, an "ether", proving them to be wrong. But physicists who argue metaphysics are usually careful in what they say, so as not to cast a negative light on their discipline. To untangle an apparently "hopeless" mess requires first to recognize it as a mess. The hopelessness is an apparition of the refusal to recognize it as a mess. So don't get your hopes up until the skeleton is pulled out of the closet.

Whatever you do, don't tell Metaphysician Undercover. This information upsets him terribly. — fishfry

Jesus Christ! You would ruin my fucking day by bringing my attention to a number which is irrational, wouldn't ya? Don't try to lead me to the river, because you know I won't follow you.



PI is another very good example of an irrational ratio. What I think, is that the existence of these irrational ratios indicates that our method of representing spatial existence, with distinct dimensions, is fundamentally flawed.

Consider that a straight line, representing one dimension, is fundamentally incompatible with a curved line, representing two dimensions. So for example, take a line segment which exists between two supposed points. That line is straight, one dimensional. Now let's bring in a second dimension, and produce a curved line segment in relation to the straight line segment. We need to produce some sort of divergence from the straight line, and we might represent this as an angle of x degrees. The problem, is that no matter how hard we try, the angle produces two straight lines related to each other by an angle, it does not produce a curved line. There is no real relationship between a curved line and a straight line, they are incommensurable.

So the circle, arc, or curved line, is a two-dimensional representation which is fundamentally incompatible with the two-dimensional representation which is straight lines at angles to each other. Another example of this problem is the point of tangent. But the irrational nature of the square, which Pythagoras had so much trouble with, indicates that straight lines relative to points, with angles, is a less accurate representation of two-dimensional space than is the non-straight line.

However, we actually use points, angles, and vectors, so I believe we need to validate such principles, which are not validated by the empirical evidence of actual spatial existence. The root of the problem is the non-dimensional point. It does not represent any real space. If we want to allow the point to have compatibility with spatial representation, we can give it "space", make it an infinitesimal point or something like that. But this creates all sorts of problems. What is the infinitesimal point's size, it's shape, and how is it related to other infinitesimal points (straight line relations wouldn't make sense)? So this approach is not practical, and it really does not resolve the problem, which is how supposed points are related to each other. We still have to produce the method for relating these infinitesimal points to one another, which is the real problem.

Therefore we ought to return to the non-dimensional points, and find the empirical evidence required to validate them. The empirical evidence is that it works. Non-dimensional points are highly useful. The problem is that we do not understand the type of existence that they have, so we do not understand how they are related to each other. Making the point a dimensional infinitesimal creates problems, as does drawing straight lines at angles create problems. So it's back to the drawing board. Until we understand the nature of the non-dimensional point, we cannot develop the principles to model the medium which exists between these points.

The next major advancement came during the Age of Enlightenment with the development of the calculus by Newton and Leibniz - but there were notable mathematicians even during those intervening years: Fibonacci, Fermat, etc... — Marlon

You seem to have left out what is arguably the most important factor, the Copernican Revolution.

NO. "false" and "true" in first order logic (the logic used in ZFC) are purely SYNTACTICAL expressions. They are determined ONLY by the logic of the system. That's the way it works! — Mephist

The problem though, is that I am talking about judging those premises or axioms which establish those definitions of "true" and "false". If I am to judge them, I must judge them in relation to something else, something outside the system If you are asking me to accept the precepts of the system without judging them, then you are being unreasonable. That's the way it works! We're grown adults, we have free choice to judge these things. It's completely unreasonable for you to say that I must accept the system's axioms in order to judge the system's axioms, when acceptance is dependent on judgement, and acceptance precludes the possibility of fair judgement. A conclusion cannot be incompatible with the premise, so if I accept the axioms, it is literally impossible for me to produce a judgement against them. Therefore you are being completely unreasonable.

In a formal logic system TERMS DON'T NEED TO BE DEFINED. That's why it is called "formal" logic. — Mephist

Logical systems use symbols. A symbol which represents nothing is contradictory nonsense, just like the empty set. So you're just spewing more contradictory nonsense in an effort to justify your earlier contradictory nonsense.

The proof of the theorem shows that a model always exists (if no contradiction is derivable) because it can be built using the strings of symbols of the formal language itself!
Probably that's the part that you strongly disagree with. But if you want to criticize the proof of Godel's completeness theorem, you should at least read it! That's what I meant by "looking at the paintings" before. — Mephist

Yes, that's what I strongly disagree with. Strings of symbols without definitions is nonsense. A symbol which represents nothing is not a symbol. If you are merely talking about a set of rules by which symbols are related to each other, then there is no reason why we can't discuss these rules in plain English. I think that your refusal to discuss this in plain English is evidence that you know that there is deception within the system. So, either you discuss these rules in plain English or I level the accusation that you're attempting to hide deception behind your language.

I don't see how your art analogy works for you. An individual can glance at a painting, and find it ugly without analyzing it, just by apprehending a few prominent features of it. Likewise, we can hear a piece of music, and right away form a dislike for it based on some fundamental aspect of it. Why would you insist that the person must make a thorough analysis, attempting to empathize with the artist's intent, wasting one's time, and even torturing oneself, to justify one's dislike for the piece? When the person can point to a few fundamental, and prominent features, and explain why these features make such an effort unappealing and unwarranted, why not simply accept that, rather than insisting that the person cannot make such a judgement. If fundamental and obvious aspects of the art are unappealing, why insist that the critic must analyze all the finer aspects before making a judgement of dislike?

The exercise is done simply to recognize that your favored 'proven' view is not proven fact at all, but merely conjecture. — noAxioms

No, you're wrong. It's not conjecture, it's proven. The truth of it has been demonstrated to me as true, through evidence and logic, therefore it is proven. Aristotle thoroughly explained this thousands of years ago. The fundamental principle is that there is "truth" and "falsity" with respect to past events, but these terms cannot be used with respect to future events. Because they have not yet occurred, future events have no existence and are indeterminate, they may or may not be. He proposed that we allow that the law of excluded middle does not apply to future events, because there is no truth or falsity in relation to them (being possible), yet it does apply for past events, having actually occurred.

What I believe, has not yet been proven to you, that is clear. But if you think it's only conjecture, on my part, or that the real, substantial difference between past and future hasn't been proven to me, then you need to demonstrate this to me, because from my perspective, it has been proven.. I'm sorry but that's just the way things are. You can't unprove what has already been proven to me, simply by asserting that it hasn't been proven. It has been proven, and now you need to demonstrate that what has been proven to me as true, is actually false if you have any desire to lead me in another direction..

This requires a demonstration, which you have not given me. To say, that your demonstration requires that I put aside all the evidence for what I already belief, (therefore the proof for what I believe), is nonsense, because this asking me to ignore evidence. You need to be able to make your demonstration in a way which respects, and accounts for the evidence which has already proven to me what I believe.

The alternate view does not describe a different experience, so there is no distinction. There is still past and future, but they're just relations between events, not actual states of events. — noAxioms

"Relations between events" does not produce a past and future, it produces a before and after. In reality, all events are necessarily in the past, because presumed future events have not yet occurred, and therefore have no existence. They are not actually events, but only possible events. Therefore all relations between events are necessarily relations of the past. To produce a "present", i.e. a distinction between past and future, requires that you provide and describe a relation between actual events (past), and possible events (future). This is not "just relations between events". Until you model this difference, your model has no past and future.

No. But I would believe what Feynman produced. All you've been saying is you believe there is a physical substance through which waves travel, even electromagnetic impulses. I think the "medium" to which you refer is a metaphysical medium. — jgill

Did you read what I wrote? Energy is a property of the "field", transmitted through the field. The field exerts a force on the particles. You do not see that the "field" is therefore a "substance"? Also, the field exists between the object which creates it, and the particles effected by it. Do you not see that the field is therefore a substance.

In the past, I too held the opinion that the field is a "metaphysical medium" purely theoretical. I thought that a "field" was simply a mathematical construct, until I read same material provided by Dr. Feynman, which demonstrated the need to conceive of the field as having real physical existence. To noAxioms, this is evidence that I will release my biases with the proper demonstration.

I haven't found yet where Feynman presents the argument that it is necessary to understand the electromagnetic field is a real physical object, it might have been an interview, or in a book he wrote. But read this page, where he clearly treats the field as an object, referring to "the energy in the field": https://www.feynmanlectures.caltech.edu/II_27.html.

I find particularly interesting, the section 27.5, "Examples of energy flow", where he describes how the energy flowing through an electrical wire is really moving through the field which surrounds the wire, rather than through the wire itself. He has already described how energy moves in a field, now he gets to the peculiarities of this fact. One of the ways he explains this is by describing a wire with resistance. The resistance causes the wire to heat up. The energy which is being released by the wire as heat, is actually flowing into the wire from the surrounding field, and being lost by the wire to the air as heat. This is counter-intuitive, but when we say 'energy is flowing down the wire' it is not actually flowing through the wire, the energy is moving through the field which surrounds the wire. Only the amount of energy lost by resistance actually enters the wire. Here's the conclusion of that section:

Perhaps it isn’t so terribly puzzling, though, when you remember that what we called a “static” magnet is really a circulating permanent current. In a permanent magnet the electrons are spinning permanently inside. So maybe a circulation of the energy outside isn’t so queer after all.
You no doubt begin to get the impression that the Poynting theory at least partially violates your intuition as to where energy is located in an electromagnetic field. You might believe that you must revamp all your intuitions, and, therefore have a lot of things to study here. But it seems really not necessary. You don’t need to feel that you will be in great trouble if you forget once in a while that the energy in a wire is flowing into the wire from the outside, rather than along the wire. It seems to be only rarely of value, when using the idea of energy conservation, to notice in detail what path the energy is taking. The circulation of energy around a magnet and a charge seems, in most circumstances, to be quite unimportant. It is not a vital detail, but it is clear that our ordinary intuitions are quite wrong.

Notice the reference to Poynting theory. Poynting provides the formula for work done by a field, assumed to be in a vacuum. Following this, at 27.6, Feynman goes on to talk about the momentum of the field. "Next we would like to talk about the momentum in the electromagnetic field. Just as the field has energy, it will have a certain momentum per unit volume."

Yes, I could write 1 on one chair, 2 on the next, 3 on the next etc., to count them. Then I'd have a direct correspondence. After all the chairs are marked, I'd know that there is six chairs, and I could subtract six from ten to see that I still need four more to have the desired ten.

When you say mathematics can correspond exactly to reality, what do you mean? — Qwex

As in my example, There are six chairs at the table. I need four more to have ten chairs at the table. If this is not an exact correspondence with the reality of that situation, what more is needed? What I want is ten chairs, that is the reality of the situation. Doesn't mathematics tell me exactly and precisely that I need four more chairs?

If you want to prove that ZFC is inconsistent you have to derive "false" using the rules of ZFC's logic. You can't do it using english language, as you are trying to do.
You can't be an art critic without looking at the paintings! — Mephist

You do recognize that "false" and "true" are assigned to the premises, not by what is determined by the logical system, (which is validity), don't you? Inconsistent, or contradictory premises, is not determined by the logic of the system.

I criticize the axioms according to how they are expressed in English. If the fundamental axioms could not be expressed in English, or other natural languages, they would be meaningless. Terms need to be defined.

If a piece of art has any meaning at all, it would be recognizable by someone other then the artist. So, you don't need to be an artist to be an art critic. The critic assesses the meaning.

You might argue that the axioms have a different meaning in mathematics from what is represented in the English expressions of them, just like the artist might argue that the critic doesn't understand the piece of art. But what type of meaning could this be, if when it is represented in English it is contradictory? Sure, an artist might represent a person as being happy and sad at the very same time, but such illogical nonsense ought to be excluded from a logical discipline such as mathematics.

Here is my solution to Zeno's paradox, things that happen in reality like motion do not exactly correspond to things in mathematics. — Michael Lee

If this were true, then mathematics could not give us truth. But it's not true, because mathematics can correspond exactly with reality. Consider that I have a table with some chairs. I can count the chairs and know that there is exactly six chairs there. If I want ten chairs, I can know that I need to get exactly four more. In some instances though, the mathematics is applied in a way which doesn't correspond exactly with reality, and this creates a problem like Zeno demonstrated. "Infinite division" does not correspond to reality, so this idea is itself a problem.

The force on particles (iron filings) is exerted by the magnet nearby. Changes within the field are described as EM waves which require no medium. It works just fine with the opposite assumptions, therefore the argument demonstrates nothing. — noAxioms

The problem here, as I've already explained, is that the field is the medium. "Changes within the field" means that the field is a real, changing thing. The field is not the iron filings, and it is not the magnet, it is the medium between them.

As for energy, your comment seems to equate force to energy, which is just wrong. It makes it sound like the field itself has energy, and if that energy was consumed by something, it would be gone, leaving the magnet with no field. Gravity is like that. There's no gravitational energy of an object or its field. Nobody quotes some number representing the gravitational energy of say the Earth or its gravitational field (which is neither an energy field nor a force field, but rather an acceleration field). — noAxioms

I do not equate force with energy. Notice the word "and" in "the field carries energy and exerts a force on particles". And the field does have energy, that's clear, it is a property of the field, that's how Feynman describes it. Changes in the field are waves, so that energy moves through the field as waves. Bringing iron filings into the field creates changes in the field, so there are waves. Bringing a few iron filings into the field does not drain the magnet of all its capacity to create a field, that idea doesn't make sense.

Feynman, as a physicist, is very good at tutorials, putting things into words which non-physicists can understand. The field exerts force on the particles through the means of the waves, which are property of the field. Notice that "force" is not equated with "energy", which is consistent with Newton's laws. In Newton's laws, a moving body has momentum, as described by the first law. "Force" refers to the momentum which is transferred from one body to another, as described by the second law.

In this case, the concept of momentum has been replaced by the more apt "energy". And, instead of being the property of a moving body, as momentum is, the energy is the property of the field. "Force" here refers to the energy transferred from the field to the particles. The field exerts force on the particles. This is consistent with Newton's use of "force" in reference to the transferral of momentum from one body to another, except energy is transferred rather than momentum.

There is an argument, that thinking is a conscious activity, and thoughts may come without conscious activity (as a dream for example), therefore thoughts do not require conscious activity. If this is the case, then the relationship between "thought" and "thinking", which makes thought the past tense of thinking, implying that a "thought" requires a prior "thinking", is an improperly constructed relationship.

What is at issue here is the fact that thinking requires subject matter, something which is thought about, and the subject matter is generally believed to be thoughts. But this makes thoughts prior to, as required for thinking, such that thoughts cannot be the product of thinking, in any absolute sense. The classical resolution to this problem is to assign to the subject matter of thinking, a different name, like "Idea". Now the Idea is prior to the act of thinking, as the required subject matter, and the implication that thinking is prior to thought, by definition, is avoided.

infinity is a number, but it has a characteristic that all real numbers do not possess. Namely, it is a number that is greater than any particular real number. — Michael Lee

If infinity is a number greater than any real number, then by definition it is not a real number. So what kind of number do you propose that infinity is? If it is a real number greater than any real number, that is contradictory. If it is some other sort of number, how would we establish a relationship between this other number system, and the real numbers?

So you really can't back up your statement. — jgill

I can back it up, because I've researched it before, but I'd have to go back and find the same material again. That's a lot of time and effort just for you, someone I don't know. So I gave you a simple summary. If you took a few minutes of time to read and understand that summary, and question me on the parts which you do not understand or wanted more detail, showing a bit of actual interest, I might be inspired to look up the material. But now it looks like you just want to waste my time. It appears like you would not believe what I produced anyway.

So, what part of "the field carries energy and exerts a force on particles, therefore it is a real existent thing" do you not understand, disagree with, or think does not back up my statement ? If it's just a matter that you do not like the way that I put the argument of a famous physicist into my own words, then you'd better look up the primary source yourself. However, since I've reproduced the essence of the argument in my own words, I believe that my statement has been backed up.

You are incapable of setting aside your biases — noAxioms

Fundamental facts, proven by hundreds of years of application of the scientific method, are what you call "biases". I am actually very capable of putting aside such biases, when they are demonstrated to contain contradictions and inconsistent premises. I was trained in philosophy, so I was taught to root out these problems, and dismiss my biases which are rooted in them.

That's why I have a very unconventional attitude, I've already researched, and rooted out many fundamental contradictions and inconsistencies within accepted conventions, and I've dismissed the biases that I formerly held, which are manifestations of these faulty conventions. So you misjudge me, I am actually very capable of setting aside my biases, but only when good reason is given to me. That's the real issue here, I require "good reason" before dismissing such conventions. Which you have not given me.

I'm talking about the existence of a present moment, which has little if anything to do with refraction. — noAxioms

If that passage refers to the present in time, then it's pure nonsense. No wonder I didn't recognize it as such. That there is a difference between future and past is easily proven. Past events are remembered, and future events are anticipated. Furthermore, past events cannot be changed while future events can be created, or avoided. Therefore there is a fundamental difference between past and future. That this difference cannot be measured is irrelevant to the proof We do not need to measure things to prove that they are different, we only need to describe the difference.

To say that this difference between future and past has not been proven is utterly ridiculous. Its's just a denial of the validity of inductive reasoning. That the past is fundamentally different from the future is the inductive principle known with the most certainty. How we cope with this fundamental difference forms the basis for all inductive reasoning, and predictive capabilities. It's no wonder you're such an avid science denier, when you deny the foundations of inductive reasoning and predictive capabilities.

No, they can appear and move with no activity of what you might consider to be the medium. That's why I brought it up. — noAxioms

You might debate where the "activity" actually is, but a medium is still essential, so it makes the example irrelevant as an example of a "wavelike" activity without a medium.

Wrinkles in fabric are not movement, so 'clearly' hasn't exactly been spelled out. — noAxioms

OK, a wave (gravity wave) which is not movement. You're back to contradiction.

Your refusal to understand the view isn't evidence that it is inconsistent. Read up on it and attack it intelligently. — noAxioms

The problem is you have not presented anything which makes sense. Present me with contradictions and it's intelligent for me to attack them. How can I understand something which is loaded with contradiction? Sure, you might suggest that I just ignore the contradictions and get on with the understanding, but I think that would be misunderstanding. Therefore we must iron out the wrinkles in your principles before any understanding is possible.

There you go. You admit that you cannot let go of at least this one particular bias long enough to comprehend a view that doesn't posit it. Yes, the view indeed becomes contradictory if this additional 'obvious' premise is made, but the fact is that there is a different set of premises that predict the same empirical experience and these premises deny the existence of the present moment. Hence the truth of that premise is not obvious. — noAxioms

Before I drop what is "obvious" to me, you need to demonstrate how it is that the obvious is not true. Telling me to drop the obvious just so that your premises will make sense, is just a matter of telling me to let go of what I know to be true so that falsity will make sense to me. Your approach is fruitless if you cannot demonstrate why the thing which is extremely obvious to me might be false.

Your argument here is deeply flawed. What is extremely obvious to me is that there is a difference between future and past. That is my empirical experience. This empirical experience requires a separation between future and past, in order to support the reality of this difference. Two distinct things require something which separates them That is a logical conclusion, and this separation we call "the present". Therefore, your claim that the same empirical experience may be produced without the present is absolutely false. The empirical experience is of the separation between future and past and this cannot be produced without the present.

If your claim is that a similar empirical experience could be produced without the present, as in "a simulation", then you ought to say this. But then why would you claim it's "the same empirical experience"? So if you have premises which can simulate my experience of a difference between future and past, without a present, and free of contradiction, then let's see them.

Only when your argument is in fact invalid. — noAxioms

But my argument isn't invalid, that's what I showed. You are attacking the truth of the premise, "light exists as a wave". Therefore you are attacking the soundness of my argument, not the validity.

On the contrary, there seems to be no measurement that can be made to distinguish between the premise being the case or not, which makes hundreds of years of nothing. They've tried too. I've seen many attempts, mostly logical, to disprove one view or the other. I've never seen a successful one. I even have my own argument, but it rests on premises that cannot be proven. — noAxioms

I went through this with you already, it's called "refraction". Refraction is a property of waves. Light gets refracted, therefore it is a wave. You might insist that hundreds of years of studying refraction amounts to "nothing", but I already know that you're a science denier. What I want to know is the reason for such denial. What's the point to your denial?

P2 might be true by definition. It depends on how a real wave is defined. But yes, the logic goes pretty much along the lines of what you say here. Known real waves do things that light doesn't, and light does things that known waves do not. That doesn't demonstrate that light is not a wave, but it does demonstrate that your premises are not necessarily true. — noAxioms

This argument, like your other, is deeply flawed. As I told you already, the reason why I know that light is a wave is refraction, like the rainbow. To disprove the necessity which I claim, you need to establish a separation between waves and refraction, such that refraction can happen to something which is not a wave. The problem though is that "refraction" is by definition a property of waves. Perhaps you might show me light which doesn't get refracted So to demonstrate that my premise is not necessarily true you need to show how the rainbow, and the behaviour of light through a prism is not really refraction, but something else, or show me light which doesn't get refracted. Otherwise, if light actual refracts, it is necessarily a wave, because refraction is something that only waves do.

As an example of something wavelike: Take interference patterns, which are formed by things other than waves. Moire patterns are a good example of this. The patterns move in apparent 'waves' without an obvious medium carrying the waves, as evidenced by the fact that there seems to be no limit to the speed at which they move. — noAxioms

I don't see how this is relevant. The patterns exist in a medium. If they simply look like waves, but are not actually waves, they are still an activity of the medium. So this is irrelevant to the possibility of an activity which looks like a wave, but is not in a medium.

Ukraine has publicly stated they want good relations with both Republicans and Democrats. If they were to acknowledge the pressure, it would hurt them with Republicans. It would also look bad within Ukraine, implying they were letting themselves be used for US political purposes - a bad image for someone elected for being anti-corruption. — Relativist

It is in the best interest of the administration of Ukraine to remain silent on this issue, and the US has no judicial power over potential witnesses. I think NOS4A2 has made at least one unfounded claim about what the administrators of Ukraine have said. Such claims of silent witnesses making statements, would be made in an effort to support Trump in the eye of the American public. But he seems to have no American witnesses to support his apparent lies.

If the premise is accepted, then spacetime isn't something that things travel through. If not, there is no spacetime at all through which a thing can travel. — noAxioms

Then you clearly have inconsistency, contradiction, if you model gravity waves as wrinkles in the fabric of spacetime, and you maintain that things do not travel through spacetime. And if you say that nothing moves because spacetime is an eternal static block, then you're just continuing to support bad metaphysics by denying the obvious, motion. We cannot even validly discuss motion anymore because nothing moves according to this perspective. What's the point in discussing the motion of things when nothing moves according to your principles?

I know you have a consistent history of inability to understand that view, as again evidenced by your statement above. — noAxioms

That's right, I cannot understand principles which appear fundamentally contradictory, and the appearance of contradiction is only made to go away when the obvious is denied. That's why I cannot understand eternalism in general, it appears contradictory, as motion existing in a static block. The contradiction only goes away by denying the present, because the present is where motion occurs. This is what allows for the reality of the static block, a denial of the present. However, this is a denial of what is obvious, the division between future and past, which is the present, containing the occurrence of motion. When you deny the reality of the distinction between future and past, you deny the first. most obvious principle of reality, upon which we live our entire lives, basing all of our decisions, that difference between future and past.

We have no easy way of knowing which premises are true if they contradict each other but each lead to the same observations. — noAxioms

That's very correct, there is no "easy" way to determine the truth. But if we make the effort to analyze and understand fundamental principles, the truth may be revealed. If observations of the very same thing produce contradictory premises, then we must dig deeper to see the principles which support the description, how the description (premise) is derived. This is like 'he said/she said', why are you describing the same thing in a different way from me? So we have to respect as different, the purpose or intention, from which we are both arguing. In this case it is not an instance of one of us intentionally lying, but the "thing" which is being described is so broad, and we can pick and choose the aspects of that thing which we want to use in our respective descriptions. If our descriptions are actually contradictory, we can look to why I chose this aspect, and you chose that aspect, and this leads us to the metaphysics which we are each attempting to support. Then we need to analyze those metaphysical principles themselves, for soundness. If we find weakness in those principles, then we ought to investigate the descriptions which appear to support those principles, as potentially faulty descriptions.

My point was that your arguments are very often not valid. — noAxioms

You might say this, but you attack my premises, not my logic, so you are really demonstrating that you think my arguments are unsound. For example, here's my argument. P1. Light exists as waves. P2. Waves require a medium. C. Therefore there is a medium for light, "the ether". The logic is valid, but you consistently attacked the truth of my first premise. So you are attacking the soundness of my argument, not the validity of it. However, my first premise is well supported by hundreds of years of scientific experimentation, empirical evidence, so you haven't gotten very far with your attack.

Also, you or others, have made some attempt at creating ambiguity, and obscuring the separation between P1 and P2, by saying rather that light is "wavelike". This allows P2 to appear unsound, because there could be a "wavelike" thing which cannot be called a "wave" because it does not require a medium. The ambiguity as to the criteria of "wave" allows for something which we would normally call a wave, to actually not be a wave, only "wavelike", and therefore exist without a medium.

If you can actually follow the argument presented in that exchange, you see the opposite position is suggested. — noAxioms

You might suggest it, but it's not at all a sound argument. Your proposition, "Spactime is not something that anything can travel through", is not a sound premise. If things do not move in spacetime, then what do they move in? Why would you prejudice gravity, allowing that gravity moves spacetime, but other things do not move in spacetime? I don't understand how you could say that gravity moves spacetime (creating waves), yet things do not move in spacetime, when gravity moves things. Are things and spacetime completely distinct substances which have no effect on each other? That can't be because the gravity waves move things.

The soundness (validity if you will) of a logical argument has nothing to do with the premises chosen, but rather what conclusions are (and are not) drawn from those premises. — noAxioms

Do you understand the difference between soundness and validity? Valid logic might use false premises, in which case the conclusion would be unsound. A sound logical argument has both true premises and valid logic. So the soundness of a logical argument has a lot to do with the premises chosen, it requires not only valid logic, but also that the premises are true.

Please do. I am curious. :chin: — jgill

Without taking the time to research specifics, I can tell you the simple idea. An electromagnetic field is necessarily a real object (what I call substantial) because it exerts a force on particles (exemplified by iron filings). This is the energy of the field. Changes within the field are described as waves, and this is how energy moves from one place to another through the field, by means of waves.

However, physical existence doesn't necessarily mean a substance as medium. It just means it exists and interacts with the physical universe. But I could be wrong. Probability waves are a lot more abstract. — jgill

This might be a semantic issue, but having real physical existence necessarily implies "substance", as substance is what supports physical existence. The electromagnetic field exists between particles and is the means by which energy is transmitted from one particle to another, so I would say that it qualifies as a "medium". So, having physical existence, and existing as part of the physical universe means that the thing has substance. And, the thing in question, the electromagnetic field, fulfills the criteria to be called a medium.

He is just not allowed to do so for political gain, which is entirely unproven. — NOS4A2

Where did you hide all the witness testimony that he did?

[quote

So why do you believe Trump pressured Zelensky? Is there any evidence? — NOS4A2

There's a whole lot of testimony from many witnesses. I won't say eye-witness testimony, but ear-witness testimony, because the trial concerns words. When multiple witnesses say that you did what you claim not to have done, this is evidence that you are lying. Lying is consistent with Trump's past behaviour. Put two and two together, and who do you believe, the witnesses or the liar?

There are two “articles of impeachment”, or in other words, Trump is being accused of committing two “high-crimes and misdemeanours” according to the House. The two articles are “Abuse of Power” and “obstruction of Congress”, neither of which are crimes. — NOS4A2

Do you understand the meaning of "misdemeanour"? There's a reason why "misdemeanour" is included with "high crimes". That is so that it does not require "high crimes" for an impeachment.



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Not arbitrary. In all such cases, the speed of the waves is pretty much fixed (isotropic) only relative to the medium. — noAxioms

Right, this is one reason (amongst others) why, as I explained, objects must be conceived of as part (features) of the medium. Understanding the appearance of objects as a feature of the medium, (for instance, apparent electron "particles" as a feature of the electromagnetic field), we can develop the tools to understand the activity of the medium itself. If the speed of light waves is fixed relative to the medium, yet the medium is active in some other way, then we need to understand this other activity to comprehend things like redshift/blueshift.

Your're a crank probably mostly due to the lack of ability to formulate a sound logical argument, — noAxioms

When you deny science, and the truth of obvious premises, as you were doing, you cannot distinguish a sound argument from an unsound one.

Here's where we have differences:

Surely you're aware of the dual nature of light. — noAxioms

It is the photoelectric effect which dictates that light might be conceived of as particles, photons of energy. However, this conclusion is dependent on the conception of an electron as a particle. If an electron is not actually a particle, and not conceived of as a particle (a unit of energy might exist in some way other than as a particle), then there is no need to conceive of light in a particle form.

So, the difference is that my commitment, that light exists as a wave, is based in all sorts of empirical observations, and sound scientific principles developed over hundreds of years. Your commitment, that light exists as a particle is based in the empirically proven fact that energy can only be measured in discrete quanta. An electron exists as a known quantity of energy. The deficiency in your claim, is that it has not been proven that this quantum of energy, what's called "the electron", actually exists as a particle, rather than as a feature of an electromagnetic field. If an electron does not exist as a particle, and this energy is a feature of a field, then there is no basis to the claim that a photon exists as a particle. The quanta of energy is better described as a feature of a field, rather than as a particle.

I never used the word, but I see it coming up quite a bit now. — noAxioms

Sorry, I forgot it was Sophisticat who jumped in, and I got confused who was who and saying what: my apologies. Let me go back for a moment now, and readdress Sophisticat's concern.

Technically, a (physical) field is just a distribution of physical values in space - nothing less, nothing more. Why would some additional stuff smeared over space be required? — SophistiCat

There has to be "stuff smeared over space", to support the reality, or truth of the values. We can call it "substantiation". We could assign physical values all over space, randomly, but these would have no substance, no meaning because they're random. If the values are to represent something real, there must be "substance" which supports them. Do you agree that most physicists accept that an electromagnetic field is real substance? If the values assigned to an electromagnetic field represent what is believed to be a real substance, then the other fields ought to be understood in this way as well.

You are right: this isn't even cranky, this is just stupid. But I didn't say that only a crank could defend the idea that waves and fields require a medium: on the contrary, I was looking for an intelligent explanation. And I have found some some, such as McMullin's paper.

I acknowledge that historically, it made sense to think that way. Waves transmit influence, they cause action at a distance. It makes intuitive sense to think that matter is required to transmit action: you want to move something - you push it, poke it with a stick or throw a rock at it; even a monkey understands that much. Hume defined a cause in accordance with contemporary understanding as "an object precedent and contiguous to another." Of course, Newton's gravitational interaction violated this "law of causality" quite spectacularly, and indeed this issue vexed him and those who followed. — SophistiCat

Do you recognize the conclusion of the quoted passage, referring to the "ontological" basis of field theory? I believe that some physicists such as Feynman have produced very convincing arguments which demonstrate that electromagnetic fields must have real physical existence, i.e. substance. If you're not familiar with this, I could look it up for you

But like also throws crisp shadows given a small light source, and that is very much not quacking like a duck. — noAxioms

A crisp shadow is not inconsistent with a wave, as an object in a wave tank demonstrates. There is a crisp shadow created by the object. There is still some disturbance in the water behind the object due to different reflections and other activity, just like a shadow is not absolutely dark.

The conclusion you should draw from this is that the nature of light is not exactly like a classic wave in a medium with a known velocity, and thus isn't necessarily best expressed as a function of such a medium. No wave in an inertial medium throws hard shadows or is measured at a single point instead of spread-out, and all waves with known mediums behave differently in frames other than the one in which the medium is stationary, and thus drawing a conclusion of the existence of a medium is premature. — noAxioms

I don't see how this is relevant, sound waves are not "exactly the same as waves in a water. And light behaves differently in different mediums (passing through different objects), just like sound, and any other waves. That's how we know about refraction. Designations such as "inertial medium" are arbitrary because motion is relative. Whether the wave tank is on a train, or on the surface of the earth, or whether the wave is in a moving river, the medium is always moving in some fashion. That's why the medium for light is so hard to understand, it may be moving in so many ways that we do not even know about. So physicists posit numerous fields.

There also seem to be a lack of working model using such a medium, since I've seen no links to one, only hand-waving and assertions of how it would work if such a model was created. — noAxioms

I told you the logic. To say it's "hand-waving" is a continuity of your propensity for denial.

Gravity waves are probably the closest analogy. They are sort of modeled as waves in the 'fabric of spacetime'. That wording suggests a frame-independent medium of spacetime itself. If there was a necessity for some preferred frame, it would be called the 'fabric of space'. — noAxioms

OK, so you do recognize the need for a medium. That's good, so why do you keep denying it? That's all I'm trying to get to the bottom of. People like me will insist on the need for a medium, and people like you will deny this need, and speak of people like me as if we're "cranks". But when we get down to brass tacks, people like you suddenly admit that you've recognized the need for a medium all along. What I think is that people like you insist on defending some theories, or metaphysics which assert that there is no medium, but in reality you recognize that in practise we deal with these things as if there is a medium. So there is a huge inconsistency between what you preach (metaphysical theory), and what you practise. And if someone like me tries to point this out, you find the easiest response is denial and "crank".

This would not work with a 3D medium since it would change the properties of the waves in any frame that doesn't match the one in which the medium is not stationary. — noAxioms

Of course the medium is not stationary, that's what I've been trying to impress upon you all along, the "activity" of the medium. You didn't seem to like that term, but now you've simply replaced it with "not stationary". The broader term, "activity" is the better than the narrower "not-stationary", because we have no point of reference, no absolute rest, from which to establish "inertia". So imagine for example a container of water, which we designate as "stationary". Even within the individual particles, the molecules, there is activity, despite the water being "stationary". The assumption of "stationary" is arbitrary, and really quite false.

A set is a bottom-up conception, assembling a whole from discrete parts. True continuity is a top-down conception, such that the whole is more fundamental than the parts. — aletheist

Mephist draws on a top-down description of a set; the set as more fundamental than its elements, to explain topology. This is the only way that "empty set" makes sense, if the set is a top-down construction. So a set may be a bottom-up construction, but set theory employs sets as if they are actually top-down, by utilizing the empty set.

If you don't believe in sets, why go to the trouble of explaining why you don't believe in the empty set? I wonder if that shows that you haven't thought your idea through. Why bother to argue about the lack of elements, when you don't even believe in sets that are chock-full of elements? — fishfry

The problem with the "empty set", which I have described, is a demonstration of the reason why I don't believe in the existence of sets. So I take the trouble of explaining the problem with the empty set to justify why I do not believe in sets. A set is a Platonic Form, and it's nonsense to speak of the Form of nothing. Yet we use "zero", and "nothing" commonly. Therefore I do not believe in this type of Platonic realism because it doesn't give us an appropriate way to represent what "zero" means.

Nobody has claimed sets have "real" existence, whatever that is — fishfry

Sorry fishfry, but you stated quite clearly "if you believe in the existence of any set at all, and you accept the axiom schema of specification, then you must accept the mathematical existence of the empty set."

You're making up nonsense if you are asserting that there is some sort of existence which is not real existence. When I say "real existence", I mean existing, categorically, as distinguished from not existing. What is it, if it's not real existence, an illusion? Real existence is opposed to the illusion of existence. I'd call it deception, claiming that something exists when you know it's not real existence but an illusion. And it's completely nonsensical to claim that there is a type of existence "mathematical existence", which is not real existence. How would that work in set theory? You have a set of existing things, and you have a subset, "mathematical existence". Then you say that "mathematical existence" is somehow outside of the set of existence, because it's not a real existence.

I went through this with aletheist already. Altheist was trying to distinguish different types of existence corresponding to different subjects (fields of study), but refused to recognize that all of these are a member of a single, more general category of "existence" itself. So aletheist refused to recognize ontology as the study of existence in general, what all different sorts of existents have in common, and insisted on placing "mathematical existence" outside of, separate from 'ontological existence". But that is nothing other than an assertion that there is no such thing as ontology. Now you attempt the same move, by saying that mathematical existence is not real existence, you place it outside the field of ontology, which studies "being", "existence", rendering ontology useless by saying that there is a type of existence which cannot be studied by the field of study, ontology, which studies existence in general.

I could easily take you down the rabbit hole of your own words. Is an electron "real?" How about a quark? How about a string? How about a loop? And for that matter, how about a brick? Are there bricks? When we closely examine a brick we see a chemical compound made of molecules, which are made of atoms, which contain protons, neutrons, and electrons, which themselves are nothing more than probability waves smeared across the universe. — fishfry

We can look at these concepts, "electron", "quark", "string", "brick", and see if there are inconsistencies, contradictions, or other forms of fallacious logic, and if not we can say that the thing referenced most likely has some form of existence. So I'm not nihilist, I just believe that contradiction negates the possibility of existence, such that it is impossible that a contradictory thing exists. So things referred to have a probability of existing, until they are proven impossible, then that probability is removed.

Do you believe in the existence of bricks? Physics tells us that even bricks are nothing more than probability waves smeared across the universe. — fishfry

If you define "brick" in this way, as "possibility waves smeared across the universe" it probably doesn't have existence, because physics uses a lot of contradictory mathematics and inconsistent principles, as I am arguing here. But there are other ways that we can define "brick", and use the term, which do not involve logical inconsistencies, and so a "brick" in this sense would have a reasonable probability of existence.

Do you deny science along with math? — fishfry

Science which uses faulty math is obviously faulty, don't you think? The soundness of the conclusions is dependent on the soundness of the premises.

That's the problem, I don't believe in the existence of any set. That any set has real existence has not yet been demonstrated to me. And axioms which allow for the demonstrably contradictory "empty set" lead me away from believing that sets could be anything real.

Dimensions are not necessarily ‘spatial’ representations, but are defined as aspects of reality, of which actuality only accounts for four, at best. So I’m not sure what you think dualism answers here, except to reduce reality to only two aspects, with no viable explanation for how they interact. What you refer to as ‘dimensionless’ reality is, for me, at least two non-spatial aspects of reality that extend beyond what you refer to as ‘actuality’. — Possibility

Right, the more we can reduce the need for a huge multitude of aspects of reality, in our descriptions, the less complicated and easier it is to understand. Dualism actually provides a comprehensive explanation of how the two aspects interact, so that assertion, that dualism has no viable explanation for how the two interact is just a monist straw man. You'll notice that Plato introduced a third factor with his "tripartite soul", to account for interaction. The third thing is not really a distinct aspect though, it is the mixing, or interacting of the two aspects, so "dualism" remains as the appropriate term.

So, for example what's the point to positing "at least two non-spatial aspects of reality"? If the spatial aspect of reality is described as three dimensional, this does not mean that there are three distinct aspects of spatial existence. it's just how we draw things, as three dimensional. We're much further along, in our efforts toward understanding if we simply look at spatial existence as one aspect of reality, and non-spatial as another.

The first aspect is possible awareness or existence, the second is relative distance or potential energy; the third is relative shape, action or chemical qualities; and the fourth is relative space, velocity, duration, complexity or sensory qualities. The fifth aspect of reality is the relative perception of value, significance or potentiality, including ‘qualia’ and conceptual relations. And the sixth aspect of reality is pure relation, meaning or possibility. — Possibility

See here for instance, why don't you combine #2 with #4? I see no reason to separate "relative distance" from "relative space". And, since #6 is "pure relation", why not class all the other "relatives", #2, #3, #4, and #5, in with #6. This simplifies things, leaving us with the possibility of awareness #1, and relations #6. Everything can be reduced to these two categories.

A closet is an enclosed space in which I hang my clothing.

One day I remove all the clothing from my closet.

Do I still have a closet?

Do I not in fact have a perfectly empty closet? — fishfry

How is that relevant? As Mephist said, a set is identified by its elements. That's the reason why an empty set makes no sense. Clearly a closet is not identified by its elements..

But I didn't say that only a crank could defend the idea that waves and fields require a medium: on the contrary, I was looking for an intelligent explanation. And I have found some some, such as McMullin's paper. — SophistiCat

I didn't say a field requires a medium, I said a field is a medium. It is the medium which substantiates the wave function, and therefore the existence of particles. That's what an electromagnetic field, for example, is, a medium..

I acknowledge that historically, it made sense to think that way. Waves transmit influence, they cause action at a distance. It makes intuitive sense to think that matter is required to transmit action: you want to move something - you push it, poke it with a stick or throw a rock at it; even a monkey understands that much. Hume defined a cause in accordance with contemporary understanding as "an object precedent and contiguous to another." Of course, Newton's gravitational interaction violated this "law of causality" quite spectacularly, and indeed this issue vexed him and those who followed. — SophistiCat

This is irrelevant, Newton's gravitation is not a wave. The issue here is whether a wave requires substance for its existence. It think it's very clear, and it ought to be clear to you as it is taught in basic physics, that a wave only occurs in a substance.

So no, Meta, it does not look and act like a wave. — noAxioms

Continuing with the denial of science I see. The activity of light is described by a wave-function. Where's your evidence that light does anything which is not wavelike?

To me it seems like a quaint prejudice to insist that anything that is wave-like requires a medium. Maybe there is something to the idea; I wish there were some non-cranks here who could explain this point of view. — SophistiCat

If you automatically designate as a "crank" anyone who expresses this idea, that if it looks like and acts like a wave, then it is a wave, and a wave by definition, requires a medium, you'll never find a non-crank who could explain this idea.

That the conventional wisdom is to completely ignore what is necessitated by logic, making those who respect the logic into "cranks" is a pathetic state of affairs.

I would like to hear this from a physicist. — jgill

We had a precious few physicists involved in discussions, but they seem to have vanished. The "cranks" (and I mean real crackpots) seem to frustrate them.

Natural numbers in set theory are defined as sets: the natural number N is a set that contains N elements. If there is no empty set, there is no zero, right? — Mephist

This is exactly why it is contradictory. If there is a set without any elements it is not a set at all. With zero elements the supposed set is non-existent. But if you propose that the number zero is itself an element, such that there can be a set with "zero" as an element, you are saying that there is a set which has an element "zero", but also has zero elements. That is contradictory.

Therefore if we adhere strictly to the method of definition provided, then within set theory, there ought to be no natural number "zero". The natural numbers are defined by the sets which have those elements. There is no such thing as a set which has no elements, this is contradictory, as a collection of things without any things. So zero is excluded as a natural number. by the precepts of set theory. As I explained already, this very same problem was exposed by Aristotle, in slightly different terms, so the Neo-Platonists established "One" as the fundamental Form. To place "zero" as the fundamental form, or "set", is to base the system in contradiction.

So, you say that zero is not like the other natural numbers (that are sets), but is only a symbol not well defined. I understand this, but then you say - in "the number 0", it means a point of division between positive and negative integers - but what are negative integers then? Aren't they just symbols? Following your reasoning, I would say that only positive natural numbers are real and all other kinds of numbers are just not well-defined symbols. OK, then how should they be defined correctly? I mean: it seems to be a little "restrictive" to throw away all mathematics except from positive natural numbers... — Mephist

The symbol has a different meaning depending on how it is used or defined. The natural numbers are used for counting objects. We name a type, apples or oranges etc., and count the number of that type. Since we can name a type and also have no object of that type, we can have zero of that type. "Zero" allows the named type to have meaning, when there is none of them, by allowing that we have the potential for a quantity of that named type, without actually having any of them now. This concept of zero, as the "potential" for objects of a specified type allows us also to count negatives of that type.

Do you see that if we make the number which is named by the symbol, an object itself, then we lose the capacity to use "zero" as the potential for a number of the named type of objects? Zero is itself the object which is named, so there is no such thing as none of those objects. The set of "0" already has an object so it cannot be an empty set.

Try looking at it this way. The natural numbers are used for counting objects. The "count", the number or quantity, is distinct from the objects themselves. "Five", as the quantity of apples on the table, is distinct from the actual objects on the table, it is not a property of the apples. It is only by apprehending the quantity as distinct from the objects, that we can use "zero" as a quantity (natural number). If the quantity of objects was not distinct from the objects, if it were a property of the objects, then there'd be no such thing as zero objects, because there'd be no objects to have that property, "zero". It is only by postulating that the quantity is something distinct from the specified objects that we have the capacity to say that there is zero of the specified type of object. Do you recognize that in set theory, the quantity itself, (as the natural number), is the specified object, therefore we have no capacity to talk about none of those objects? Mentioning that object, as the object talked about, necessitates that there is not zero of that object.

OK, I understand! NO EMPTY SET OF REAL THINGS EXISTS IN REALITY. I agree. But the problem remains: how can you define the other mathematical entities except from positive natural numbers? I think you have to allow the use of symbols that are NOT REAL THINGS if you want to do mathematics, don't you agree? — Mephist

It's not a matter of what exists in reality, it's a matter of what is contradictory in principle. To say " I am going to talk about this object, but this object is not really an object, because there is zero of them", is blatant contradiction. To bring this expression out of contradiction we must amend it. I might say for instance, "I am going to talk about a type of object, of which there are none", or I might say "I am going to talk about a quantity, and this quantity is zero". But if I make the category mistake of conflating these two options to say "I am going to talk about this quantity, zero, as an object itself, and assert that there is none of these objects", then I contradict myself.

In set theory a set is identified by it's elements, and extensionality is an axiom. — Mephist

Do you see that this proposition denies the possibility of an empty set? The empty set has no identity as a set, and therefore cannot be a set.

An analogous thing to "the class of all sets" is for example "the class of all groups" (in the sense of group theory). You don't describe groups by saying what a group is "made of", but only saying what are the properties of groups: how they relate to each other, and not what they are "made of".
The same is true for sets in topos theory: the theory describes how sets relate to each-other, and not what a set is "made of". — Mephist

So consider that we have a defined property. A "group" is all the members which have that property. We can establish relation between individual members of groups, based on the different groups that they are in. However, the properties are properties of the members, they are not "properties of groups", that would be a composition fallacy. So we cannot proceed toward establishing relations between groups this way, that would be a relation based in a fallacy. Suppose one property is "red", and the other is "hot", and we find that many red things are also hot things, it would be invalid to establish a relation between the property "red", and the property "hot", in this way.

See, "the set", or "group", is based in the defined property. To deal with "the group" as if it were a whole, an object, means that we are dealing with types, the defined property, a universal, rather than the individuals of the group. As an object, the universal, or type is a Platonic Form. A Form, as a universal, is completely different from a particular, an individual. The rules for relating universals to each other are completely different from the rules for relating individuals, because we relate individuals by determining their properties, but a universal is nothing other than a property already.

So here's an example of how we relate Forms or universals. In the Aristotelean way, the more general is "within" the less general, as an essential property, by definition. For example, "animal" is within "human being", as an essential property, like "polygon" is within "triangle", by definition. Further, "human being" is within "Socrates", Socrates being a specific human being. The particular, being the specific thing referred to, the individual human being who bears the name Socrates, is not within anything, and so is called primary substance. Do you see that it is possible for something to be within nothing (within no set), as the more general is always within the less general, so the most specific is not within anything, as primary substance? But that which is within nothing is still something. Now, at the other extreme is the most general, that which is within everything. Never is there the possibility of a set, or defined property which has nothing within it. So we might ask what it means for something to not be within a set, but it makes no sense to talk about a set which has nothing within it.

My view is that it is absurd to think that we are not aware of the present moment. — Bartricks

You ought to consider that if everything is in the past, as you describe in the op, then things we are aware of are only memories. However, this is clearly not the case, because we anticipate things of the future, and are aware of them, at the same time. Because of this anticipation, the future affects our awareness just as much as the past. Therefore our awareness is part past, memories, and part future, anticipation.

You might think that if our awareness is partly of the past, and partly of the future, the present remains an illusion. However, when we realize that there is a substantial difference between future and past, then we must recognize a real division between them, to justify that difference. This is the reality of the present. Awareness of the present is not an illusion, it's the apprehension of a real difference between future and past.

“Democrats are just trying to force anyone, with any remote connection to this issue, to testify without administration lawyers present, and that puts national security at risk and also creates risks for potential witnesses who may unknowingly divulge privileged or classified information,” White House spokesman Hogan Gidley said. — ZzzoneiroCosm

I see, it's a matter of "national security". I guess the president's allowed to do anything when national security is at risk.

None of those require a preferred frame for the fields. Any theory corresponding to the ether would need to. — noAxioms

This is not true. The preferred frame, what Leo called the "absolute inertial frame" could only be produced from an accurate understanding of the activity of the ether. The fact that we do not understand the nature of the ether inhibits our capacity to produce such a frame. So physicists have to construct numerous different fields to deal with the numerous different aspects of material existence.

All empirical evidence for real waves (like in water) have an obvious medium, and no real waves behave like that which the M-M experiment is measuring, so this is just your biases talking. — noAxioms

Electromagnetic waves behave just like other waves. That's why when we study the physics of waves, we learn the fundamental principles of wave motion by observing and studying visible waves in wave tanks, then we move on to vibrating strings, sounds, and light. The fundamental principles of all wave action are the same no matter what the medium is. Your claim that electromagnetic waves are somehow fundamentally different than other waves not only biases your perspective, but it puts you in the wrong.

Kind of by definition, yes. What jgill was questioning not that definition, but where you assert "Empirical evidence indicates that there are waves". That part does not hold up. — noAxioms

Remember, I mentioned the rainbow, and "refraction"? Refraction of light has been studied for hundreds of years. Here's how Wikipedia defines it: "refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium." You said maybe the rainbow isn't produced from refraction of waves. Your just denying hundreds of years of accepted science, and the empirical evidence which supports that science.

OK, so I have a question: does the number zero exist? Where's the difference between the number zero and the empty set? — Mephist

This is a symbol, "0", or "zero". As you seem to be fairly well educated in mathematics, you'll know that it means different things in different contexts. Despite your claim that mathematical languages are very "formal", there is significant ambiguity concerning the definition of "zero". Do you agree that when we refer to "zero" as an existing thing, a number, like in "the number 0", it means a point of division between positive and negative integers? How is this even remotely similar to what "the empty set" means?

Then I think you should like topos theory: in a topos the object that represents the empty set (the initial object) is not in general required to exist. You can assume it's existence, but it's not required by the definition of a topos. — Mephist

It's not "the object which represents the empty set" which I am concerned about, it is "the empty set" itself which bothers me. It is a self-contradicting concept. If a set is to be something, an object, then, as an object, it cannot be empty because then it would be nothing. You would have an object, a set, which is at the same time not an object because it's composed of nothing.

So there is a distinction to be made between the definition of the set, "the set of...", and the actual set, or group of those things. If there is none of those defined things, then there is no group, or set of those things, such a defined set is non-existent. There is none of the describe things and therefore no set of those things. There is a defined set, "the set of..." which refers to nothing, no things. It is not an empty set, it is a non-existent set. Only through the category mistake of making the defined set ("the set of..."), into the actual set, can you say that there is this set which is empty. So if we allow that there is this actual set, the set of nothing, then the set becomes something other than the collection of things which forms that set. And we'd have no way to identify any set because the set would not be identified by the things which make it up.

Any possibility in relation to a universe of zero dimension must come from beyond that ‘point’, necessitating a universe of at least one dimension, consisting of the possible point and its possible relation. — Possibility

This is not a necessary conclusion. There could be a dimensionless reality, actuality which validates the dimensionless possibilities which has relations not describable in terms of dimension. This is what dualism gives us, the basis for a dimensionless reality, the principles required to describe actual existence with principles not derived from spatial representations (dimension).

n the two-dimensional universe of atomic relations, however, it’s important to understand that quantum particles aren’t rotating around a nucleus in space, but are simply at a certain ‘distance’ in relation to that nucleus. — Possibility

These locations, and 'distances' are not actual distances, they are possible. So this dimensional (spatial) representation is inadequate because it cannot provide an actual spatial representation, only possible locations. For an actual representation we need to turn to the dimensionless actuality (granted to us by dualism) and determine the actuality which underlies the dimensional representation of possibilities.

The error we make in materialist interpretations is in assuming this ‘distance’ is spatial or at least quantifiable, simply because that’s how we tend to perceive it manifested in relation to the universe. It is better described as ‘perceived potential’. — Possibility

Yes, the monist materialism presents us with this problem; we cannot understand any reality in terms other than spatial. That is why we must accept the precepts granted by dualism, and move toward recognizing the actuality which exists on the other side of the "perceived potential", as a true non-spatial existence.

So if we continue in the same vein, a universe of five dimensions allows for distinction between four-dimensional relations, manifesting as detailed and significant experiences: information consisting of differentiated ‘objects’ or environmental conditions with velocity, duration, space or complexity as well as texture, taste, colour, scent and sound in relation to this ‘perceived potential’. — Possibility

This is a move in the wrong direction though. You have described the non-spatial, zero dimensional, then you move to represent this as a fifth dimension. How is that consistent? Instead of proposing that we represent the non-dimensional as it is described, as non-spatial, you apply a spatial principle "dimension", and try to represent it that way, as a fifth dimension.

Yes, but that's not mathematics! The distinction of which concepts are more "fundamental" is very useful to "understand" a theory, but it cannot be expressed as part of the theory. Mathematical theorems don't make a distinction between more important and less important concepts: if a concept is not needed, you shouldn't use it. If it's needed, you can't prove the theorems without it. — Mephist

The problem is that your demonstration, through this technique, produces a misunderstanding of the theory, rather than an understanding. So the criticism is of your technique. You describe topology through reference to set theory, but to understand set theory requires an understanding of extensionality. You demonstrate a misunderstanding of extensionality. The fundamental assumption that a set has extension negates the possibility of an empty set. Therefore your demonstration, which places the set as more fundamental than its elements, implying an empty set, is a demonstration of misunderstanding.

The axiom of extension dictates that a set's identity is established by its elements. Therefore a set without elements can have no identity as "a set", and is therefore not a set. Some set-theorists are wont to obscure this fact by saying that the empty set is unique, when in reality it is distinct from all other sets because it is not a set at all; it has no extension. As I explained, this problem was overcome thousands of years ago by making "One" the fundamental "unique set", as the term "unique" implies.

I'm afraid I share Metaphysician Undercover's misgivings about this remark. — fishfry

When you and I agree on something, that's really something to be afraid of; better move the hands on the doomsday clock. But I think the appearance of agreement is based in different principles, so there's really nothing to worry about.

Sure, but how's that relevant? What is at issue is the postulate that a set is more fundamental than its elements. That's plain English.

I see mathematical axioms expressed in plain English.

What is the medium through which probability waves in QM travel? — jgill

I believe that fields, like the electromagnetic field, are a real medium in particle physics.