If the homogeneous state fluctuated between black and white for example then you could create a clock based purely on that even though there are technically no moving parts and no geometry. — Umonsarmon

You could only make a clock by referring to such fluctuations, if the fluctuations were temporally consistent. But your premises provide nothing to cause such consistency..

EXAMPLES? — Zuhair

You want examples of why conclusions drawn from false premises are unsound? Come on. Try this. The full moon is ten miles away. I can walk ten miles in four hours. Therefore I can walk to the full moon in four hours.

Non-standard analysis lives within a mathematical model that, to the best of my knowledge, is consistent. — John Gill

Consistency does not mean that the premises are true, that's the problem. A system with complete consistency, applying false premises will still give unsound conclusions.

It assumes (axioms) the existence of infinitesimals and infinity with symbols representing them and rules for manipulating these symbols. Can you determine the "truth" or "falsity" of these axioms? (no fair resorting to "manifest") — John Gill

Yes, we can make those judgements. We have to look at what the symbols represent, and make judgements on the reality of that If the symbols are supposed to represent objects, we can apply the law of identity, as proposed by Aristotle in his battle against sophism. We discussed this to considerable extent already in the thread. For instance, in the case of "2+2=4", I argued that if each 2 represents an object, then each 2 must represent an object which is distinct from the object represented by the other 2, or else there would be no equality with the object represented by 4.

This is the fundamental principle of counting. 1 represents an object. We add to that another object, represented by 1 (1+1), and we now have counted 2 objects. In order for there to be 2 objects in that count, each 1 must represent a different object. And, we can proceed indefinitely, to count numerous objects in this way, so long as we recognize that each time we add 1 to the count, it must represent an object distinct, and different from the objects already counted. If we count the same object over again, the count is invalidated, like in the case of the person who counts money folded over in one's fist, so that the same bills are counted twice..

Conviction of a crime implies that the criminal will be duly punished. The end, punishment, follows from the means, conviction. So it's not erosive to the justice system, to put people on trial for the purpose of punishing the criminals.

There are people, myself included, who see the Impeachment process being used as a tool to remove an elected President. — Brett

Isn't that what the impeachment process is there for, to remove an elected president? If so, then using it for this purpose is not an erosion of norms, it is just a normal procedure. It would only be an erosion, if the process was being used to convict the president of crimes he did not commit. Do you believe president Trump committed no crimes? If not, then why complain about the impeachment? ..

I never admitted that they are not sound. They are indeed sound of what they are describing in the platonic sense. And if platonic sense proves to be indispensable for discovering our reality, by then this would prove it to be sound. So the question of soundness of those axioms and its relation to application is still unsettled. — Zuhair

I thought we agreed that Platonic objects are not true objects. We assume these objects for some purpose or utility, but they do not have any real existence as objects. So if we create premises which describe Platonic objects as objects, when they really are not objects, but fictional objects, then these premises are false and therefore unsound.

But if they were unsound as you claim, then they must bear wrong theorems, i.e. we need to see MANY arithmetical consequences of those theories that violate true arithmetic. — Zuhair

This is not the case. "True arithmetic" is arithmetic as defined by the accepted axioms. So if unsound axioms are accepted into "true arithmetic", then we might see no such consequences if there is consistency between the unsound axioms. And of course, there is consistency in the unsound premises of Platonic objects. The undesirable consequences only become apparent in application, because the premises concerning the nature of an object are inconsistent with what an object really is. You can see these undesirable consequences in the particles of particle physics.

All I can say is that practicing mathematicians usually avoid these discussions unless they are in these sub-disciplines. — John Gill

Zuhair actually appears to be quite knowledgeable about mathematics and its axioms.

Don't yout think it is a sort of problem, that mathematicians would avoid discussions concerning the truth or falsity of their axioms? Think about other disciplines, a physician for example. Do you think a physician would be comfortable applying principles of medicine without any concern for whether the principles are true or not.

Now the purpose of this thread is to show that in order to account for this current existence, there is necessarily a duality in it. This isn’t to say that there cannot be existence without a duality, but that in this existence there is a duality, that it is impossible that it is all united as one, impossible that there is no fundamental separation in it. — leo

Well, I think the next move, after assuming "there is existence" would be to ask how we know there is existence. This will give us some idea of what is meant here by "existence". I think that we can go two ways here. We can refer to our senses, outside ourselves, and say that we sense things moving all around us, and this confirms "existence", or we can turn to the inside, like Descartes, looking at the passage of thoughts in the mind, and say that this confirms "existence".

Notice that in each case there is some sort of movement or change involved in the characteristics of "the thing" which demonstrates existence to us. This implies the temporal nature of existence. However, when we recognize that these two ways of apprehending 'existence" are quite distinct, we find a need for a spatial boundary between the inside and the outside, and it is this understanding of the spatial nature of existence which produces the need for a duality. Perhaps if we adhere to simple temporal terms there will be no need to assume a duality.

Yes indeed, we cannot completely dismiss induction, we simply have to recognize that induction doesn’t necessarily yield conclusions of universal validity, but that it may help us get closer to such conclusions, and even if we have no proof of that we can keep faith in it and see where it leads, and we can see that it is a tool that helps us and that has helped us. — leo

Yes, I think this is a good point. Induction gives us "universality" in a restricted sense. It is restricted by our perspective. We want a true "universal validity", but we can only go so far as our limited capacities will allow us. So we produce generalities, universalities, but we have to guard ourselves against the inclination to conclude that they have true universal validity. On the other hand though, we need to respect the fact that we have nothing but our own experiences with which to judge any conclusions about "existence", so we must give some credence to these generalizations if we even want to start to understand. Remember, you are starting with "existence" which is the most general, so to completely exclude generalizations as unreliable, would be to exclude your own premise.

And indeed we can say that “there is existence” and that “existence changes”. However this doesn’t yet imply that existence is made of parts, because we haven’t proven that one thing cannot change. A thing made of parts necessarily changes eventually, but a thing not made of parts may change too. — leo

This is another principle I find questionable. How could a thing which is not made of parts, change? For a thing to change, at least one part must become something other than it was. How could this happen if the thing had no parts?

I'm trying to make some general categories by which we can classify things, and this is a distinction between spatial and temporal properties of a thing. Are parts necessarily defined spatially? Is the separation between one part and another, necessarily a spatial separation? Can we consider a temporal separation between parts?

Suppose a changing thing at one time fits one description, and at a later time fits another description. We say that it is throughout the entire time, always the same thing, but it is undergoing some changes. Now we have a period of time in which the thing is existing, and at each moment in that time period, it has a different description. Can we say that at each moment, what is described, is a part of "the object", which exists as the complete temporal extension? If so, then what constitutes the separation between these parts, allowing them to be distinct parts? Don't we generally conceive of such a temporal extension as a continuity of the object, without such separations? However, without such separations within the temporal extension of the object, it appears like change to the object would be impossible. Therefore we must conclude that there is separation between the temporal parts of the object.

And so what I want to prove, or rather what I believe can be proven, is that this existence is not one, that it is made of parts. And I believe you have brought an important piece of the puzzle by showing that a thing made of parts cannot remain unchanging forever, I believe that will be a key part of the proof. — leo

Actually, I think we can prove that both aspects of existence, spatial and temporal, are composed of parts. In the spatial sense, we have the separation which arises from the two ways of apprehending existence, from the inside and from the outside. This produces a spatially defined boundary between the inside of the object and the outside of the object. This implies that the "existence" being described here, has parts. Also, as I just described above the temporal aspect of the object must also consist of parts, with a separation between these parts. Therefore existence, in both its temporal aspect and spatial aspect, is composed of parts.

But we might still say that this is an illusion, that what we perceive to be separate parts are in fact the one existence perceived at different times. — leo

This is why we need to address the temporal extension of existence as well as the spatial extension of existence, in order to soundly prove that existence is composed of parts. If temporal extension is a continuity, then there is no division between existence at one moment and the next, and it might be argued that all of existence is just "one", perceived from different perspectives. But there is an easier way to refute this claim. That claim requires the "perspective" to be something separate from the existence being observed, and this necessitates a separation anyway. So, once we recognize the reality of the fact that existence must be composed of parts, we can move to understand how temporal extension could be composed of parts.

But something else than existence is non-existence, and what is non-existence if not nothingness? So if existence didn’t arise spontaneously, it must have been always there. — leo

What has happened, is that we have taken "existence" as a noun, a thing, in an attempt to describe that thing, what it means to exist. This means that we separate it from other things. So we cannot say that non-existence is nothing, because by distinguishing existence from other things we have allowed that non-existence is something..

I'm still mulling over "bad habits" in math. Sloppiness; jumping over points in a proof assuming they are true; assuming a hypothesis and then proving it; muddling a proof so badly other mathematicians can't verify it; etc. Using infinity or infinitesimals are the least of our concerns. — John Gill

I would say that having axioms (premises) which instead of being based in the reality of the objects we are familiar with, are based in some imaginary assumptions about imaginary objects, is far worse than sloppiness. Untrue axioms have an effect reaching into many applications, whereas sloppiness is specific to the particular application. And, sloppiness can be caught and corrected through various means of verification, whereas it requires good metaphysics to determine the truth about axioms.

Name me ONE conclusion that ZFC proved about arithmetic that is not sound? — Zuhair

I don't need to name any, they are all unsound. We've discussed the fact that the axioms lack truth, in how they describe objects. The axioms are the premises, and soundness requires true premises. The premises are not true, therefore the conclusions are not sound. Are you using a different meaning for "sound"?

The truth is massively overrated. — Isaac

So you're one of them then. When the evidence points to the truth of something other than what you believe, you dismiss the truth as "massively overrated".

Note that when I say that “something exists” I’m not saying that “only one thing exists” but that “at least one thing exists”. So “at least two things exist” does not negate “at least one thing exists”, it is simply more precise, they are both true as long as we prove that at least two things exist. — leo

You can start with an assumption like this, but it is really necessary to clarify what you mean by "thing". We might remove the notion of "thing" altogether, and start with the assumption of existence. Then we say 'there is existence', and this is not to predicate existence of some thing, or something, it makes existence the thing, as the subject. In this way we remove, from the starting premise, the duality which necessarily follows, created when you see the necessity of a plurality of things. The essence of this duality is really derived from the need for a boundary which separates individual things. If there is a multiplicity of things, there is necessarily a separation between the individuals, and this separation, forming the boundary between one thing and another, is a different sort of substance from the things themselves, so we get a substance dualism. If a multiplicity of things are all made of the same substance, there must be a different substance which separates the individual things.

So we can avoid this necessary conclusion of dualism by starting from a slightly different perspective, saying there is existence, making existence a noun, the thing to be analyzed, instead of saying something exists, making existence a predicate. This allows us to defer the question of what is a "thing", until we have first determined what it means to exist.

There could be several things existing completely in isolation from one another, in which case there would be no relation between them. However I would agree that we couldn’t know of these things if they were completely isolated away, so regarding this existence I agree to think of existing things as being related in some way. — leo

This is the problem I refer to, in distinguishing a multitude of things from one single thing. If things are isolated from one another, then we must assume some sort of substance which isolates them. So whenever we conclude that there is a multiplicity of things, we need to assume that there is something else, other than these things, which acts to separate them. This is the case regardless of whether the separation is absolute, as in your example, or relative as in my example. In each case there must be something real which separates the thing, or else they are not really separate things.

I wouldn’t appeal to the theory of relativity in the argument since it is based on several unproven assumptions, and here we are trying to find what we can be certain of regardless of what we assume. We can’t appeal to scientific theories which are based on induction which is unproven itself, so we’re left considering existence in the now.

…

It could be that a thing composed of parts remains unchanging as long as it is not influenced by another thing, and that when it is influenced only parts of the thing changes. So I don’t agree that a thing composed of parts necessarily always changes. — leo

OK, this is the difficult question. We might start with "existence in the now", as you say, and this is what I request above, to consider "existence" itself without reference to things. The problem here is that we cannot dismiss induction, as you request. If we are to proceed with any sound premises we must derive the premises from experience. We cannot make up imaginary assumptions of what "existence in the now" is, which are not consistent with our experience, so we must produce premises derived from induction, in order to have sound principles.

What we can say about "existence in the now", is that things are changing, and we conclude that time is passing. To deny this would be to accept an unsound principle. Therefore, I read your second paragraph above, like this. A thing which is composed of parts necessarily is influenced by something else. That "something else", is whatever provides the separation between the parts, such that they can be called individual parts. So what we observe, as time passes, is that a thing's parts are always being influenced by something else, something other than the thing itself which is making the parts into a whole. The "something else" is making the parts into distinct individuals. And, unless there is an absolutely perfect balance between the force of the thing which makes the parts into a whole, and the force of the other thing which makes the parts into separate individuals, we cannot say that this thing is unchanging.

Furthermore, we can refer to observation, and induction, to say that such an absolutely perfect balance does not exist. This is because we have no examples of a thing that is composed of parts which remains unchanging. So this idea, of a thing composed of parts which is unchanging, is an ideal, an absolute which represents nothing real. If we adopt it as a principle because it might be useful for comparison (as the basis for a scale or something), we must remember, and be careful not to accept it as a principle of what "existence in the now" means. This unchanging thing is an abstraction, removed from "the now"; the principles of "the now" we only know through induction.

It can be doubted, maybe existence came from nothing or maybe it was always there. From a limited point of view within existence we can’t say, and there is no point of view outside existence by definition. There is already something so we don’t see anything coming from nothing, even if something seems to come from nothing we can say that it came from something that exists but that we don’t see. But without seeing the whole of existence we don’t know, so it can’t be said to be a fundamental truth, it’s rather a working assumption. — leo

The principle, "existence could not come from nothing", does not mean that existence was always there. When we say that something came from something else, we mean that the something else is other than the named thing. So what is implied is that existence came from something other than existence. This principle, that "existence could not come from nothing", again, is an inductive principle. it is derived from our understanding of how things come into existence through change. I implore you not to dismiss inductive principles as unsound, because then you are left with nothing to base your principles on. You could make up any system of consistent and coherent imaginary principles and claim that your system is sound, because it is coherent and logically consistent, when really you have no means for verifying that system.

OK, might want to jettison calculus then . . .and all the technology we use as a result. — John Gill

The point is that "usefulness" as a principle to base judgement on, is misleading. The existence of "bad habits" demonstrates this fact.

What are you arguing, that scientists tend to believe bad metaphysics?

Science and metaphysics are distinct. Do you understand that? It appears like you are saying that most scientists have bad metaphysics. That's not surprising, as they are not trained in metaphysics.

Yeah, I took part in that. It was quite good in places, but I'm thinking here about the reasons why such a promising start seemed to fade out. The people involved didn't just stop posting, so it's not a matter of their having trouble setting the time aside. — Isaac

What happened is that we got to the difficult part. Not necessarily difficult to understand, but difficult to accept the reality of what was to be exposed. That's the problem with the approach that many here have to philosophy, they are not looking for the truth, rather they are looking for material to support what they already believe. So when articles of philosophy approach the truth, and it is not what these people already believe, they tend to turn away.

Understand now?

Do you think science can advance without speculation? — ovdtogt

No I don't think science can advance without speculation, but I don't think speculation is science, it's more like metaphysics.

Whatever number the field is assigned, as a value for energy, is irrelevant to the fact that the field which is assigned that value, must be something.

To assign to a thing zero energy, and then argue that because it has no energy it is nothing, is self-contradicting, because it is already premised that there is the thing which has no energy, as the premise of the thing which is assigned zero energy.

Right, it's speculation, not science.

I think you're confusing "scientific" with "scientism".

It is the scientific belief. — Metaphysician Undercover

That's false, there's nothing scientific about it at all. If it were scientific you could show me the process.

What is that 'nothing' then? Give us your hypothesis. — ovdtogt

As I said, it doesn't make sense to speak of that as nothing. And, it isn't bright scientists who speak of it as nothing, they speak in terms of fields, it's only you who wants to call this "nothing".

I was following the Scientific route. — ovdtogt

To say that life came from dead matter is not scientific at all, because it is not supported by any empirical evidence. It's just an illogical speculation.

If there are quantum fluctuations in a vacuum, then very clearly that vacuum is not "nothing".

I don't think it's possible to go from no life to life, that's what I've been saying. Therefore life must be first, and the fact that some people think that the universe went from no life to life simply indicates how little they know about the universe.

I don't think anything ever comes from nothing. Isn't that a fundamental truth?

Life didn't "come alive". That implies that there was a time when life was not alive, prior to coming alive, and that's contradictory.

And? — ovdtogt

It refutes your claim that life evolved out of dead matter.

So the second absolute truth is that there cannot be only a single thing that exists in this reality now, there is at least a fundamental duality, there are at least two things that exist. — leo

I think this second truth negates your first truth as contradictory to it. If there is a multiplicity of things existing then they exist in relations to each other, and these relations are changing, as the passing of time, and relativity theory, demonstrates to us. An existing "thing" therefore cannot be composed of parts, because the thing would be changing, always becoming something other than it is. The thing composed of parts does not "exist" because it is always something other than it is as time passes. So we must consider the particular "things" which make up the multiplicity, the elements which exist in relation to one another. Since they are all particulars, they cannot all be the same thing. Therefore we cannot refer to these as "something" which exists, they are things which exist, and we no longer have the first truth "something exists"..

Brute fact: living things die, dead things do not come alive.

No! not always, if the proof is carried in a FINITE fragment of ZFC, and the proved statement is an arithmetical statement, then this is already known to be SOUND, i.e. any finite fragment of ZFC (even though it speaks about infinite sets) if it proves an arithmetical statement, then that arithmetical statement is part of TRUE arithmetic, i.e. it conforms to a proof that only relies on finite objects. — Zuhair

From my perspective, ZFC has unsound axioms concerning the nature of objects, as we discussed earlier. Therefore any proof using ZFC is unsound.

Not only that! It is expected after knowing Wiley's proof of Fermat's Last Theorem (which he actually did it in a theory even stronger than ZFC! — Zuhair

But your use of "stronger theory", as you explained, really means a theory with less rigorous criteria for the soundness of its premises, and is therefore actually a weaker theory, less sound.

So a theory basically about the infinite did help us understand provability within a theory about the finite, a kind of a detour though it to simplify matters! — Zuhair

That a conclusion from a theory with unsound premises happens to be consistent, or "the same" as a conclusion from a theory with sound premises, might be completely coincidental. You seem to be forgetting about all the wasted time spent using that theory with unsound premises to create conclusions which are inconsistent with the sound theory, to focus on one conclusion which coincidentally happens to be consistent, in an attempt to justify use of the unsound theory.

So... Would it be possible, and desirable, to create a section/category for discussing actual papers or works of philosophy (or perhaps even papers on closely related topics)? — Isaac

Check the section called "Learning Centre".

As I said, that I use fingers and toes for certain purposes doesn't mean that this is the reason why I have them. You are confusing the purpose of the user with the purpose of the designer. I did not design my body, so how I use the parts of it does not reflect why those parts are there.

Looking at the way I use some parts of my body doesn't necessarily tell me why I have those parts.

How could nipples define us sexually when both men and women have nipples? I don't know why I have nipples, nor do I know why I have fingers or toes.

Why do you think a man has nipples? Why do you think a female has a small penis? Why do you think a man can grow breasts? Why do you think both men and woman have testosterone and estrogen hormones in their body? — ovdtogt

I don't see how that's relevant, you might as well be asking why males and females both have mouths and noses. If you want to start with something real, start with the y chromosome.

It is obvious you lack even the most basic knowledge of biology. Your ignorance is to vast to fathom. — ovdtogt

Show me a human body which is both male and female, and I will argue that it is neither. Let the vastness of my ignorance overwhelm you!

There isn't a third possibility here. — Wittgenstein

Yes there clearly is a third possibility, it's not a case of either Cantor is right, or the op is right, because both Cantor and the op might be wrong.

… like Sq root 2, which was discovered to be irrational by the Ancient Greeks, much to their consternation. — unenlightened

Actually I think it was Pythagoras who first proved that the square root of two is irrational. And I think it really frustrated him because it demonstrates that the geometrical figure, the square, cannot be a real figure, The two perpendicular sides of a square are incommensurable. This is similar to the problem with pi. It appears like there is an incommensurability between one dimension and another which makes two dimensional figures inherently irrational. It's very odd when you think about it because it casts doubt onto our understanding of spatial existence in terms of dimensions. It may well be that spatial existence would be better represented in another way.

Of course the possibility of mistake still exists, and if "resolution" requires removing that possibility, it would remain unresolved. But that's why I retained the option that both are wrong. However, broadening the mind to numerous options, presented from numerous different perspectives increases one's understanding of the subject, thereby lowering the probability of misunderstanding, even when there is no "resolution".. Therefore you are wrong to assert that doing this wouldn't tell you anything you didn't already know. The mistake is to assume that there is a "resolution" when there is not.

Relax, give the man some time.

Actually, there is a third possibility, as I said, and that is that both Cantor and the op are wrong. This raises the probability that the mathematicians are idiots to about 67 percent. The number of mathematicians involved is irrelevant, as herd mentality demonstrates. The number of people carrying out an action has no bearing on whether the action is correct.