The mechanisms are mysterious... — Enrique

No, they are not. — SophistiCat

Sophisticat is in complete denial of the reality of human ignorance. 'There's nothing unknown out there, we already know it all.'

OK, welcome to the club. Have you read the thread?

194. With the word "certain" we express complete conviction, the total absence of doubt, and thereby we seek to convince other people. That is subjective certainty. But when is something objectively certain? When a mistake is not possible. But what kind of possibility is that? Mustn't mistake be logically excluded? — On Certainty

Following a rule allows one to be judged by others as correct. It obviously does not provide what is necessary for certainty of the subjective type. And it cannot provide what is necessary for certainty of the objective type because the possibility of mistake can only be excluded if we know that the person is following the specific rules, which are applicable in the particular set of circumstances. To exclude the possibility of mistake requires not only that one follows a rule, but that the rule being followed is the rule which will exclude the possibility of mistake.

Some suggest that we add in Purgatory as a means to solve the binary afterlife debate, leaving our options as Hell, Purgatory, and Heaven. This is still immoral and there is a division among very similar people who will receive eternal damnation in Hell and people who will make it to Purgatory, eventually making it into Heaven. Even if it takes several years to get into Heaven, it is still more satisfactory than eternal damnation in Hell. I believe adding in Purgatory is also an issue for the division between those going to Purgatory and those going to Heaven. Although they will all eventually make it into Heaven, it seems immoral that very similar people will either have to work for their place in Heaven whereas some will receive eternal salvation without the effort of Purgatory. — Bridget Eagles

I don't see why Purgatory doesn't solve the problem. The time spent in Purgatory varies according to the individual. Two similar people will spend a similar time in Purgatory, but not the same time. Therefore the problem, which is the issue of small differences between people (if there even is such a thing to begin with), corresponding to large differences in reward/punishment, is avoided. The reward/punishment scale allows for each individual to receive one's just desert.

So calculating according to a rule is enough. Even if it is legitimate to ask if the rule itself is reliable, we shouldn't expect by doing so to find another, higher level, transcendent rule. In the end it is in the very following of the rule that one attains correctness and reliability. — jamalrob

This is not conducive to certainty though. One could look at contradictory rules, and correctness could be obtained by following either one. Now all that person would have is uncertainty as to which rule to follow. Calculating according to a rule may be sufficient for correctness but it's not sufficient for certainty.

I just don't understand the insult culture around here. Over the past couple of years I've had to take extended breaks from this forum because someone started piling on personal insults at me over technical matters on which they happened to be flat out wrong. Not because I can't snap back; but because I'm perfectly capable of snapping back, and that's not what I'm here for. I'd suggest to members that whenever they throw an insult in lieu of a fact, perhaps they should consider whether they've got any facts. — fishfry

Fishfry, you appear to be very sensitive. From my experience, if someone points out to you, your misguided way, you take it as an insult. This is philosophy, so you ought to learn to take this as an attack on the ideology which has guided you, rather than an attack on your person.

An unstable system will change - that's what being unstable is. — Banno

A system is necessarily stable. That's what being a system is, a whole with temporal extension, and to exist as a whole requires stability in the relations of the parts. That is a balance. A "system" is an ideal, a model by which we judge the relations between things.

The fact that we can describe the degree to which the balance is not perfect (eternal temporal extension) in terms of instability does not mean that the balance is not there. Balance is implied by the descriptive term "system" and "unstable" refers to the imperfections of that balance.. .

Key take-away is the hold was put on the Ukraine aid because of the “the President's concern... — NOS4A2

Says it all.

Trump has been making deals for half a century so I suspect you have little clue what you’re talking about. — NOS4A2

The Trump deal. Take the money. Let the company go bankrupt. Creditors don't get paid because the money's been taken.

Your views here suite "Mathematics for science", while some mathematicians might insist on "Mathematics for Mathematics". — Zuhair

I find that hard to imagine, Mathematics for Mathematics. What would this consist of, people studying and producing mathematical principles just for the sake of doing that, and none of them actually doing anything with the mathematics? So people create mathematics, they study to understand mathematics, and they never apply the mathematics. That's a very odd thought. But in the university I went to, Mathematics was in the Arts department. I think it was studied as a useful art though.

I agree with the duality policy. The real issue is how to judge when a mathematician is going a stray? I mean as far as possible contribution to knowledge is concerned (i.e. application). I think a real foundation of mathematics must help direct mathematicians towards producing more beneficial mathematical theories. But how to judge this? I think this is a very important question? We need a foundation for applicable mathematics! But I'm almost very sure that a lot of mathematicians, possibly the most, wouldn't care the hell for that, they'll view it as too restrictive, and favor diving deep into the world of logically obedient rule following scenarios, no matter how wildly far their imaginative worlds are from reality. Sometimes I think this is like the dualism of religion and state in secular states. Let the mathematicians dive deep into the imaginary platonic world they like, and let science work with its strict observance to reality moto. The important matter is not to confuse both. We only need to coordinate both at applications! — Zuhair

Well you're right, mathematics as an art provides a freedom which is appealing to many. One can demonstrate all sorts of very beautiful things just by applying mathematics to mathematics. That is actually the beauty of mathematics, its very nature is incredibly beautiful. But suppose we can separate math for math's sake, creating beauty in mathematics, from applied math, which is math for some other purpose. The pure art of mathematical beauty would just be there to look at and think about, and the artists would have to warn people against trying to apply that math (some mathemagicians could put some real freaky tricks in there which are thought to be incredibly beautiful). The other mathematicians, creating mathematics for a purpose, would have to be disciplined so as to reign in that freedom, and keep things directed toward the proper goal. I think the two have already been confused as eloquence is becoming more and more of an important part of theories.

The real problem is even if it is false, still the logically obedient strict rule-following themes it negotiates can prove to be extremely useful, even if in part. The real problem is that we'll never know at which stage it will "run out its course"? Possibly one day foundations for 'applicable' mathematics would issue, having clear cut edge between what is beneficial and what is not?! Perhaps by then this platonic dream would vanish! perhaps?! but I don't really know where such a thing would start? or even if it could start really? Until such alternative is found, we'd better keep the current dualist stance. — Zuhair

It may not be that difficult. To begin with, any application in which the infinite is approached, in any way, is an application where the false premise of Platonism is causing a problem. The mathematician can devise all sorts of different ways to deal with the occurrence of the infinite, but these just disguise the problem. The very nature of infinite, and the nature of application (being practise), makes it impossible that the infinite could be encountered in any application. The mathematician might say 'we have to be able to apply the infinite, it's part of mathematics', but really all that the infinite is, is a thing of beauty, a beauty which is negated by any misguided attempt to apply it.

Yes, I think there is an intermediate position. Mathematics is producing rule following obedient fictional objects and scenarios. However, those happen to have applications in the real world. I suspect that the matter is not accidental. There is seemingly some common grounds between imagination and the real world. Some rules about arithmetic works fine when applied to real objects, and it really succeeded in increasing our understanding of the real world around us. On the other hand obviously there are rules that are not applicable to the real world like having infinitely many numbers, etc... I think logically obedient rule following imaginative scenarios do have some common grounds with reality. — Zuhair

I agree that correspondence with the real world is not accidental, and these principles are adopted for usefulness. But I don't think that any non-useful rules would be accepted. The reason why there is infinitely many numbers is so that we can count anything. It doesn't matter what the world might consist of, we will still, in principle be able to count it because we have infinitely many numbers.

I think we ought to consider a difference between corresponding with the real world, and being useful in the world. The two are clearly not the same. Mathematical rules I believe, are produced to be useful. This means that they do not necessarily correspond with reality, nor do they even have "some common grounds" with reality, they simply interact with reality by means of us using them. Perhaps this process, the activity of interaction, may be called a common ground, but we have to be careful to recognize that although it "grounds" the mathematical rules, it doesn't ground the real world. So for example some people say that the laws of physics describe the foundation for existence in the universe, but this is not really the case. The rules of physics are how we apprehend existence, in the universe, but we may be missing a whole lot, and therefore the rules of physics don't really describe the foundation for existence in the universe.

This is TRUE of many mathematical disciplines. For example a lot of set theory stuff is so imaginary that it might not even find any application at all. However, no one can really tell. Even imaginary numbers turned to have applications, even non-Euclidean Geometry turned to have applications. The problem is that we don't know really what our reality adheres to, or even what discourse about obviously imaginary objects could be useful in applications about the real world. — Zuhair

The problem with usefulness, and pragmatism in general, is that many things can be useful, in many situations. If you need to pound in a nail, you can pick up a rock and hit the nail, instead of using a hammer. So speculators may think up wildly imaginary theories, and people applying the mathematics will pick up what is available, and put it to use. Therefore we need some standards of efficiency, or something like that, by which to judge usefulness. This is complex. We need clearly defined goals, which in itself is difficult because our own goals are often not clear to us. Then we need the means for judging whether the goals are adequately being achieved.

The problem is that if we take Quines-Putnam indispensability argument, then even those non-spatio-temporal features of mathematical object might need to be accepted as part of reality, even though not a physical concrete kind of reality, but some kind of reality there!? The mathematician usually do not bother with these philosophical ground. All of what he cares for is the analytic consequences of his assumption, which for clarity and simplicity they are usually stipulated outside of the confines of space or time or both, or within the confines of some imaginary world that has its own space and time characteristics, as well as its own part-whole relationship with respect to eternity issues in it. Most mathematicians work primarily in a Platonic world! Philosophy comes later! — Zuhair

I agree with this, and I am completely on board with you here. Maybe, as philosophers, we can analyze this separation between the Platonic world of mathematicians, and the real world which we live in. The difficult thing here is to understand how there can be such a separation in the first place. Let's say that the separation was created, it was manufactured, produced by dualist principles. Like the example above, with infinitely many numbers, the goal was to enable us. To measure the world, we need a measurement system which transcends the world, it must be capable of measuring anything possible in the world. As you say, we don't know what's in the world before we measure it, so we must have a system capable of measuring anything. Therefore the measurement system is based in the assumption of infinite possibility, whereas the real world consists of limited possibilities.

Do you agree that this is the basis of that dualist separation between the real world and the Platonic world? The human mind apprehends the world as consisting of numerous possibilities. In order for it to understand each, every, and any possibility, the mind assigns to itself, the capacity to understand infinite possibilities. But that assignment is wrong, because the human mind is restricted by the real world, being a part of the human body, and so its capacity to understand is really restricted. So the human mind has created this dualist premise, and all these dualist principles, in an attempt to give itself the capacity to understand anything, and everything, when in reality it doesn't have that capacity. That Platonism is self-deception. It was far a good cause, but when it runs its course and we see that it is impossible for it to give us what it was designed to give us, we need to get rid of it.

Meaningful disagreement, by my lights, is the sort of disagreement you have with someone while understanding the words they say. So we do not share the same belief. But I understand the statement the belief is about — Moliere

Thank you for clarifying that. So your point is that there is no disagreement concerning the meaning of the words, the disagreement is about something else, some other "belief". So how do you construe the disagreement itself as being meaningful?

You had attributed "meaningful" to "disagreement" in "meaningful disagreement", which I thought was incorrect. Now I see that what you really meant was that there is meaning, and agreement in the understanding of the words, yet disagreement concerning something else, some belief other than the belief in what the words mean.

How do you think that this belief exists as something other than the belief in the meaning of the words? Suppose we pass judgement of true or false, or some such thing, on the meaning of the words which we understand. If we disagree on this judgement, as we often do, how can this disagreement be meaningful?

Now here's the point. Your so-called background of agreement, upon which you apprehend a "meaningful disagreement", is simply the meaning of the words, itself. But this is not the background at all, it is the foreground, the surface, the shallows. The true background is the principles we hold (beliefs) by which we make judgements of true or false. The meaning, and all these agreements and conventions are the foreground, while in the background lie these judgements of true or false, where disagreement is abundant. Disagreement is abundant because such judgements are often based in intuitions, attitudes, feelings, and emotions, rather than rational logic. This is why the background is a background of disagreement, and agreement is conjured up in the foreground, by conscious minds. But the conscious mind is just the tip of the iceberg, and we often cannot even say why we believe some things and not others, because those principles often extend deep into the subconscious. So the background is full of disagreement.

If you allow that disagreement can be meaningful, you open the abyss of meaning without agreement. This is how we defend ourselves against the nonsense of Platonism, by showing that meaning emerges with agreement, and is not the property of some eternal objects. But then the background from which meaning emerges must be something other than agreement.

The point now, is do we simply say as I do, that this "other than agreement" is disagreement, or do we try to argue like Banno and some others, that it is actually some form of agreement? We might be best off to place it in a category distinct from agreement/disagreement, but how would we keep ourselves from getting lost then?

y the way do relativity theory speak about rules about the mathematical objects used to write its laws with? Aren't those mathematical objects a part of the theory? I don't think relativity theory assumes that numbers for example have a mass, or that they move with a speed less than light, etc.. Those mathematical objects are fixed, eternal, unchangeable. It's the physical objects that the rules of relativity theory applies to. I don't think that the mathematical objects and rules that it uses has anything to do with relativity theory. Imagine that number 1 for example will rut with time? That's crazy! Isn't it. — Zuhair

Objects existing in relationship to each other are objects existing in relationship to each other. If physics uses contradictory premises concerning objects existing in relationship to each other (the premises of relativity, and the axioms of mathematics being contradictory) then there is a problem.

It is irrational for you to claim that the "fixed, eternal, unchangeable" objects of mathematics are not subject to the laws of physics, unless you were to produce principles to support a dualist ontology. In that case, we'd have two distinct types of objects, and we'd have to start all over with our discussion of what constitutes an "object", starting with two distinct "objects". If we do not adhere to true principles, derived from the real existence of objects, we might as well allow that the construction of mathematical objects (being imaginary) does not need to adhere to any principles at all. What's the point in even assuming parts, and loose or tight relations at all, when it would be much easier to have eternal objects which have no parts whatsoever? Then the collections of such objects (sets) are not objects at all, but imaginary collections.

It seems to me like you want some half ass sort of compromised system for the existence of "mathematical objects" where you adhere to the principles of physical objects (loose and tight connections) to an extent, but when the principles of physical objects contradict the principles of eternal objects, which you desire to assume for the sake of simplicity, you are ready to throw these principles out the window in order to cling to the false facility of Platonism..

We use possibly fictional objects to display the mathematical rules with, because this is the most evident way in which it can be presented. Most of these rules, as well as the objects manipulated are non-spatio-temporal. But I think we can have pseudo-spatio-temporal objects representing mathematical worlds, thus in some sense approximating the real world. But I think also that nothing of the rule physical world law about physical objects would be applicable to these realms either. — Zuhair

The problem is, that mathematicians are manufacturing, creating, objects. These objects might be completely fictional, imaginary, and not intended to represent the real world at all. Or, in application, these objects might be intended to produce a representation of the real world. We need to decide which is the case. Are we using mathematics to model the real world, or are we using mathematics to create fictional, imaginary worlds? What good is the wishy washy position of saying that these objects are "in some sense approximating the real world"? Then those who want to use mathematics to model the real world will be dissatisfied, and those who want a fantastic, purely fictional mathematics will also be dissatisfied.

Of course collections would have different meaning across all applications, but they will have consistent meaning within the same application. Like how number 1 can have different meaning across applications — Zuhair

Then it would be impossible to create a reasonable hierarchy like you were talking about, if the meaning of tight and loose could vary.

I find your idea that an object cannot have parts unless its subject to temporal separability as un-supported. Especially under imaginary grounds. — Zuhair

Of course we can imagine things which would violate that proposed law, but the whole point is to exclude from our principles, things which are physically impossible. If we allow mathematical principles to include imaginary things which are physically impossible, and we apply mathematics within physics which employs inductive conclusions that exclude such things as impossible, then we will be employing contradictory premises in the very same application, as I described.

Relativity theory denies the possibility of eternal unchanging relations between parts (absolute rest). But if mathematical principles allow for eternal unchanging relations, then we have contradictory premises. To resolve this problem we cannot change our description of the physical world without loosing accuracy. So we must change these mathematical principles to provide consistency. That it would be difficult to make such changes, or that the existing principles are supported by simplicity, is no excuse.

I'd say even if that platonic realm is FALSE (i.e.doesn't exist), still, the logical-mathematical rules displayed in them are not necessarily false. And they can hold of some real scenarios, and so can possibly find applications, and that what really matters! — Zuhair

Sure, such mathematical rules would be applicable, and in the vast majority of cases they would give us very accurate conclusions. That is because the vast majority of cases don't deal with things like eternal objects, and infinity is never approached. And, when eternal objects are approached (fundamental particles for example), we can be fully aware of the faults within the principles, and take the conclusions with a grain of salt. However, as these faulty principles become more accepted, and work their way deeper and deeper into the hierarchical structure of the mathematical axioms, their application becomes more commonplace. At this time, they are subsumed by other principles, and we could loose track of when they are actually being applied, and not notice the mistakes which they produce.

They are not names of relations. Naming of relations is a different subject, and I've never attempted to speak about it in any of my prior comments. I've been always speaking about naming collections, and so speaking about naming objects, and not relations. — Zuhair

The point is that your description of the distinction between "loose" and "tight" does not provide us with an indication as to what these terms really mean. The reality is that the parts of a collection are either loose or tight depending on what type of relation they have with each other. Therefore there are all sorts of different types of sets, which may be named dependent on the relations between the parts. We cannot just classify loose and tight sets, just like we cannot just class soft and hard physical objects, there are all sorts of different type of objects which we name, like 'cars' and "houses". The naming of a set, as it is supposed to be the naming of an object ought not be any different. The name ought to indicate to us what type of an object that particular set is, by indicating something about the relations of its parts, or its use, or something like that. W#hen someone says "house", or "car", it brings to mind a specified type of object, the same ought to be the case when sets are named.

When a set say set x names some collection C, then we call each "element" of C (i.e. each singular part of C) as a "member" of x. In some sense membership would copy element-hood but transfer it to an object external to the collection, that is to the name of the collection. But you need not confuse "membership" as a name for "element-hood", No! That is not the case. Membership is not a name, it is a relation, so it is not an object. — Zuhair

So this is a basic type of set. The set "C" has "members", "elements", that is what is specified of this type of set. Notice that there is no specification as to the relationship between members, the relations might be either loose or tight. Would you agree that the so-called "empty set", and the set with only one member, are different types of sets from the set which has members. We could have a set "A", which is empty, and a set "B" which has one member, and then the names A, B, C, would each specify a different type of set, therefore the name would be useful. We could then proceed to look at the different types of relations between members and have all sorts of subcategories of type C, but A and B would be distinguished as completely different.

Now through membership relation and sets (i.e., names of collections), one can easily define a hierarchy of sets. And that build-up proves to be an extremely useful tool in our understanding of many mathematical entities. And the witness to that is SET THEORY. In particular ZFC set theory (Zermelo-Frankel set theory with Choice), which proves to be very powerful in understanding mathematical entities and rules, through the iterative buildup of a hierarchy of sets. — Zuhair

Unless your hierarchy is built on real principles of distinguishing real difference between types of sets, that hierarchy will be arbitrary and misleading. Therefore the hierarchy is not built on the names themselves, but the type of set which the name identifies. We cannot make up relations between named sets, without first having a complete grasp of the relations between the members of the sets themselves, which gives us an understanding of the type of set, because such relations would be completely imaginary. Understanding the relations between the members, gives an understanding of the type of set, and understanding the type of set will allow us to proceed toward establishing relations between the types of sets. ZFC proceeds without a proper understanding of the types of sets, to produce imaginary relations between imaginary types.

Of course for the development of set theory, all of our units are un-breakable over time, and they don't change their tight connections with time, so they are remotely different from natural objects which rut over time or combine with other objects to build bigger units, etc... Here in the platonic mathematical imaginary world, all individuals (units) have non-changeable tight connections over time. So they are as you said "eternal". Then we can freely form collections of them using the descriptive tool, and with the help of the naming relation, we can speak of a hierarchy of them, which helps us encode almost all of mathematical entities in it. Thus serving as a FOUNDATION for MATHEMATICs. — Zuhair

As I said, the Platonic eternal, unchangeable object must be considered as imaginary, impossible, and must be excluded as not real, until its reality may be demonstrated. Therefore to base a set theory in this assumption is to start from a false, unjustified premise.

I'm speaking within the confines of a mathematical realm, some platonic realm in which time doesn't cause any change to connection relations. So what is actually separate is always separate, so separable is separate, and so temporal x spatial connection is immaterial in this realm. We only have spatial connection and separation. That said we need to revert again to loose versus tight connections. — Zuhair

But this is unreal, impossible, therefore I deny an such "speaking" as irrelevant, because you are speaking illogically, of the impossible as if it were possible.

My account entails that the existence of connections between parts of an entity is what qualifies that entity to be an object. So having loose connection is fairly enough for that quest. You don't need tight connections between parts of an entity to qualify it for being an object! NO! loose connection can do the job, so an entity in which loose connections between its singular parts exist, is perfectly qualified of being an "object. However, you need tight connections to form units (singulars) but units are just special kinds of "objects", so an entity that has tight connections over its parts and it itself doesn't have that kind of connection to external objects, that would qualify it to be a unit object. But objects need not be units. They can be totalities of loosely connected units, or what I call as "collections". So as such collections qualifies for being "objects". I hope this resolves the confusion. — Zuhair

But this is total nonsense. In the "platonic realm", all objects are eternal, so the distinction of loose and tight means nothing because one cannot be more susceptible to corruption than the other. And "loose and "tight" cannot refer to spatial relations because eternal objects are non-spatial. Therefore your specified relations are completely illogical, there is nothing to justify "tight" or "loose".

Ok, I agree it would be eternal since its not actually breakable. But why it can have no parts? Any object is itself a part of itself. — Zuhair

Again, this is illogical nonsense which has been accepted into set theory, the idea that a thing can be a part of itself. The adoption of that idea into set theory is representative of the breakdown in logic of set theory. "Part" means 'some but not all of', and "whole" means 'all of'. If we redefine "part" such that 'all of' may be 'part of', then we loose the essence of the distinction between part and whole, rendering a corrupted ontology.

The eternal thing cannot change, that's what defines its being as eternal. But if a thing is composed of parts, then the parts must exist in relations to each other. Sense observations demonstrate to us that all relations are changing (relativity). Therefore it is impossible that an eternal thing is composed of parts.

Even if we have an object that is eternally not breakable, still it can have many parts connected by tight connection in a manner that renders it a unit, it doesn't mean it doesn't have proper parts, it only means its no breakable to them, but it can have them always as parts of it. — Zuhair

As I've shown, your distinction of "tight" and "loose" amounts to meaningless nonsense. If the relations between an object's parts are so tight that these relations cannot change with an eternity of passing time, the claim that there are parts in relation to each other, rather than one changeless entity without parts, is unjustified. If the relationship between two so-called "parts" of an object cannot change, then the claim that they are "parts" is not justified. That is one object, a whole without parts.

In real life having eternal objects is itself faulty. — Zuhair

Exactly, therefore we must establish proper principles to distinguish between imaginary eternal objects, and real objects. An eternal object, by nature of what it means to be eternal, cannot consist of parts. This presents a problem to set theory. A set, by its nature consists of parts. Therefore those who work with "set theory" must resist the contradictory notion of treating sets as if they are eternal objects.

Now if we work in an imaginary space in which time has no effect, i.e. doesn't change connection relations of objects to each other, still it is imaginable for those objects to have parts, so having parts is not a function of temporal separability as you hold. Not only that, still without time we can fathom of having objects that are composed of units that are loosely connected to each other. So we can have collections having many elements. — Zuhair

Now, don't you see this as illogical? There is no such thing as a space in which time has no effect. that's like assuming absolute rest, which relativity theory has ruled out as impossible. So if we adopt this premise as a basis for "set theory", we are working from a premise which inherently contradicts relativity theory. If one were to apply this "set theory" in physics, all sorts of confused conclusions would follow from that application of contradictory premises.

Of course in a mathematical realm in which time is not operable, like "most" of mathematical contexts, then all unit objects in that realm are true units. — Zuhair

However, as I've shown, it is illogical to speak of "relations" in a realm where time is not operable. Relations must be justified. If the relation is spatial, it cannot be free from time. If you propose a type of relation which is not spatial, such a proposition needs to be substantiated, justified.

The problem is that this would add additional features to the picture, namely temporarily, which is not all that desirable in a mathematical realm. For the purpose of defining sets, we can simply hold the dichotomy of loose and tight connection as primitive concepts without relation to time. Our aim is largely descriptive. Since set theory serves as a foundation for mathematics then the particularities of what decides the "units" of a certain mathematical discipline is stuff related to the particularities of that discipline itself, so in Geometry units would be "points", in arithmetic units would be "numbers", in set theory units would be "sets", etc.... Here we are only concerned in introduced a general descriptive framework that can be applicable to diverse mathematical disciplines, and possibility even non-mathematical spheres of knowledge as well! For example the idea of having a "true unit" in time, might be useful in understanding the ontology of time and space? — Zuhair

The glaring problem here is that mathematics is fundamentally a tool which is used to understand the relations between objects, from the most fundamental, "order". In the mathematical realm, change to relations is as you say, not "desirable". However, change to relations is reality. So if mathematics assumes changeless relations, because this is desirable, but changeless relations are not real, then there will be a problem in the application of mathematics.

So we need to look directly at this fundamental idea of changeless relations, and determine whether we can make sense of it. I suggest that there is a type of relation, which is demonstrated by the existence of time itself, which may be changeless. This is "order". We can assume an "order" which is given by time itself, a changeless order which is the passing of time. However, we need to make this consistent with relativity theory.

I haven't got any questions for Mr. Pigliucci at this time, but I have some suggestions which may be useful to help facilitate the success of this project. They are as follows.

1. Allow Mr. Pigliucci to choose which questions (members) to address, directly from this thread.
2. Start with one topic, and create a parallel thread to allow other members to discuss the discussion. The parallel thread will help Mr. Pigliucci to get acquainted with the way that other members relate to his ideas, as the parallel discussions develop.
3. Leave this thread open to receive new topic suggestions at any time, and allow Mr. Pigliucci to choose new topics (members) to engage with, at will.

I would like to see a log running interaction, with numerous members joining the discussion with Mr. Pigliucci. Thank you very much for the efforts of all involved in this project.

Well I do agree that having a common description imply some material connection, but that connection is not the connection that imply inseparability. You can call these connections "loose" connections, as opposed to "tight" connection which is what causes continuity (inseparability), so if object K has tight connection to object L then they are in continuity, i.e. they are not separate, ie. they are in contact; while if object K has loose connection to object L then they are separate. — Zuhair

We agree to an extent, but you seem to have some ambiguity. Material connection is what makes parts into an object, and when its an object, you say that the parts cannot exist as separate objects. Yet now you say that material connection does not imply "inseparability". I would agree with this if we clarify by distinguishing between actually separate, and separable.

I find your distinction between loose and tight connections to be very fuzzy, and I think we can replace it with the more substantial distinction between temporal continuity and spatial continuity. Suppose for example, that the apple exists as a collection of molecules. There is a tight connection between the molecules, and an even tighter connection between the atoms, and this spatial continuity indicates that these parts are not actually separate. Yet the molecules, and atoms are in principle separable, and this is a function of the temporal continuity of the object. The parts are not separate spatially, yet they are separable temporally.

So we need to distinguish temporal continuity from spatial continuity. If the parts are inseparable in the sense of temporal continuity, then the object is eternal, and it would appear contradictory to even talk about the object as being composed of parts. Such an object is the fundamental, or base "unit". It can have no parts because that would imply that the unit is separable in time. The spatial extension of such an object is dubious.

From experience, it appears like spatial extension implies parts which are separable. It's difficult if not impossible to conceive of a object that occupies space, which is not divisible into parts. If you think about this, you will probably be able to conclude that the actual unity, which is an object with spatial continuity, is really an illusory "unity" due to temporal separability. The spatial continuity which we observe really hides the underlying temporal separability, The parts of the spatial object which are connected through a spatial continuity, may appear to have a loose or tight spatial connection, but the true strength of that continuity will only be understood through an understanding of the temporal separability. Since the temporal aspect is what hands the parts of the object separability, the nature of time is better understood through the terms of discontinuity. Therefore we end up with spatial continuity which is an illusion, and temporal discontinuity which describes the reality of the object in terms of separability. The reality of the eternal object (true temporal continuity) is dubious, as synonymous with the object that has no spatial extension.

But this is not enough. You need representatives, or actually NAMEs, you can also call them tokens, or labels, those would be singular objects (units) that we arbitrarily assign to each collection, but provided that the assignment works along unique lines, I mean each collection is assigned only one name, and each name only names one collection. So although the choice of which object would name a collection is arbitrary, but once done naming of other collections cannot use that name, so the naming function is not totally arbitrary. Of course this is not Ontologically innocent, it involves adding unrelated material into the picture!

But why names? why should we assign an external object that is singular to act as a name to a collection that may have multiple elements, so why represent a multiplicity by a singular object? With external naming, there is no clear intimacy between the name and what is named, the assignment is arbitrary for that particular aspect. And this is what actually happens with naming generally, its artificial, for example the names used in language are all arbitrary, there is no special connection between the string of letters "horse" and the animal group it is used to represent. So that's the question: why we should bring an external object that doesn't bear a necessary relationship to a collection and make it act as a name, actually a "representative" for that collection? — Zuhair

OK, I'm with you here. I apprehend a name as an object, which is a representative of something else, as described. And I wonder why there is a need to bring names into the picture. The type of object which a name is, I think is a tool, and this tool has the purpose of understanding. It's the tool we use for understanding.

The answer is to develop a hierarchical account about collections! This cannot be done in an efficient manner without the use of singular names. The idea is that through this artificially made unique naming process, we can define a new relation, called "membership", that act to copy the relation of element-hood in collections but raises this relation to the name of the collection, and since names are singular objects so they can be elements of collections (while collections when they are non-singular objects cannot be elements of collections, so we can't have a hierarchy of collections in collections using directly the "element-hood" relation!!!), so all elements of a collection wold be "members" of the name of that collection. The "name" of a collection, is what we call as "set" in set theory. So for example the set of objects k,l, denoted by {k,l}, is actually the name given to the collection whose only elements are k,l. so k,l would be "members" of that set, i.e. they bear the membership relation to the NAME of that collection, which is the set itself. Through this copying process of elements to members, one can speak of a hierarchy of sets that are members of sets and so on.... And so indirectly speak of collections of collection of...This would give the powerful mainframe needed to interpret almost all of mathematics. — Zuhair

This I find to be very confused and I am unable to follow. I agree that we may use names to develop a hierarchical account, that is part of understanding, but where I find confusion is in your failure to recognize the distinction between naming an object, and naming a relation. These are two distinct uses of a name, like the difference between noun and verb.

So if we name "membership", what that name actually refers to is the relationship implied by "membership". Now we must guard against deception. We can name membership when no reasonable relationship has been identified. Therefore there is no point to naming "membership", unless to deceive. The relationship ought to be named directly, without the medium "membership". Furthermore, what follows from this, is that this "name", which is the name of the collection, but actually represents membership in the collection, which in itself represents a relation, is an even further layer of representation. So we have three levels of representation now, the name represents the collection, the collection represents membership, and membership represents a relationship. Plato warned us against such multi levels of representation, calling them "narrative". Any hierarchy produced in this manner would be extremely unreliable, as we ought to refer directly to "the good" to produce a hierarchy. Names are tools used for understanding, so the good here is understanding. Multi levels of representation are conducive to confusion rather than understanding.

Now you might be suspicious, and actually object, to such a buildup. Since its pivotal rule is built up through an intermediary that involves some arbitrariness, which is the choice of a name per particular collection of course. So its like building a big building that involves multiple big junks of tightly connected material put on top each other using light joining material, so the the whole buildup is bound to fail! — Zuhair

Exactly! A name is an object with extremely unreliable temporal continuity so we ought not construct structures using names. And, since it is required to produce a multi level representation to make the name into a building material, this makes the structure even more unreliable.

So we needs NAMES, to do the intermediary role in developing a hierarchy of sets of sets of..,etc.. It is the simplest way to do it! And this proves to be very powerful logically speaking, that almost all of mathematics can be encoded in it. — Zuhair

But there is no need for a hierarchy of sets, that is a faulty premise. What is needed is to understand the relationships between things, that is the good which we might put the tools (names) to use toward. The hierarch is produced naturally by understanding the nature of continuity, and the strength of relationships. So we begin with some fundamental determinations concerning the nature of continuity; for example what is prescribed above concerning spatial and temporal existence, and we proceed to name relationships according to their strength, producing a hierarchy of relations. There is no need for a hierarchy of sets.

No this is wrong. A collection can exist and be apprehended without having any representative, or even if it has a representative, the apprehension of the collection need not depend on it. Having representatives is and ADDITIONAL feature. — Zuhair

I don't see how this could be true. There is nothing to validate the collection as a "collection" without a representative. In both your examples, the lawyer and the tribe, the collection cannot be apprehended as a true collection without the representative. The representative is the thing which tells you things about the collection such that you might apprehend it as a collection. Without the representative, you might apprehend any group of objects as a collection, or not as a collection, with nothing to tell you whether it truly is a collection of not. If you move to predicates to validate the existence of the collection, rather than a representative, then you move to my system. But then we must work top down instead of bottom up. And, what would be the point to having a representative if you could apprehend the collection without a representative?

What I'm trying to achieve is a hierarchical buildup like bringing separate bricks, define a collection of them, assign some brick (external to them) to act as a representative of them, actually just a label of the collection of those bricks, now there are other representative bricks representing other collections of bricks, now put those representative bricks into collections and also assign other bricks as representative of those collections, and so on... going up. Each brick is a unit, but a collection of separate bricks is not a unit. It is something like this envisioning that I want to construct. — Zuhair

But this is not how we understand collections ontologically. We proceed toward understanding them by determining what they have in common, not by looking at a representative. So it seems to me like this idea of representatives is a step in the wrong direction.

However representatives of collections are essential for developing a hierarchical account about collections, i.e. when we want to speak about collections of collections of collections, etc... — Zuhair

It appears to me, like creating a hierarchical account through representatives would be prone to arbitrariness and error. Any hierarchy needs to be created through reference to real relationships between objects, not reference to representatives.

It seems from your accounts that you call a totality of unconnected parts as a random totality... — Zuhair

I would say that this is not even a totality. A totality must be the completion of a defined collection. if the parts are "unconnected' then they cannot be a defined collection.

To me a definable collection of separate unit objects, is itself an object, and it is not a random object because there is a strict "descriptive" rule that joins its separate unit parts. — Zuhair

So how could "unconnected parts" make a collection, or a totality?

and it is not a random object because there is a strict "descriptive" rule that joins its separate unit parts. However that descriptive joining of its unit parts should NOT be understood as a kind of "connection" between its unit parts that renders them inseparable, otherwise those would seize to be units, the unit parts still remain "separated" since there is no material (or if you like call it substance) that joins them together, so they remain separate apart, even though they are descriptively linked in some manner. — Zuhair

Here's the issue which you do not quite seem to grasp. If there is a "descriptive rule" which joins parts, then those parts have a real commonality, which joins them and renders them inseparable in reality. For example, two apples have a single descriptive rule, and they also have a common background, they came from a tree, and they have a common origin. This makes them part of that whole, which is understood through the common origin. We can also say the same thing about two oxygen atoms they have a common source. Being descriptively linked implies a material connection. So I don't think it's correct to make the separation which you want to.

However my account is different totality from your account. You refuse to admit a collection of "unconnected parts" being an object, to you there should be a kind of necessary relationship between the parts of an entity for it to be an object. — Zuhair

Actually, I'm looking for compromise, by allowing that a descriptive rule implies a material connection.

That's why you call any try to describe a collection of unrelated objects, as an object, as being magical, since it brings to existence something out of nothing, to you it is some kind of fuzzy entity that doesn't qualify of being an object. — Zuhair

The fuzziness is now due to the inability to determine the material connections through the descriptive rules. The descriptive rule indicates that there is a material connection. But we cannot get to the material connection through the descriptive rule, and that's why the representative idea is faulty. We cannot get to the real connections which constitute the real existence of the object, through the description. We need to determine the real relationships.

The only sticking point I have found here is with folk - Metaphysician Undercover, for one - who cannot see that Davidson is talking about our beliefs as a whole, and so focus on the very small number of beliefs about which we disagree. OF course, these are the ones we find most interesting and hence that we spend the most time on. — Banno

I haven't followed the thread, but I'll comment on this. The point I make, and I believe this is consistent with Wittgenstein when he says that a concept is fundamentally unbounded, is that the background is lacking in agreement. Disagreement (unboundedness), is the background for all beliefs. Agreement is something which we must create through effort. We draw a boundary for a particular purpose, and others may accept, or agree to that boundary.

In the process whereby a person learns a language, as a child, such agreements are being created, and these were not existent in the child's natural state prior to this learning. The child learns boundaries. We might say that the child has an agreeable attitude, and therefore accepts the voice of authority, but the agreements are not there. An agreeable attitude is not itself an agreement. Yet the child has the capacity to learn the language without supporting the language acquisition on pre-existing agreement.

So I think that what Moliere refers to above, as "taking truth as fundamental", or "accepting as true", is more like submission to authority. Then the learning process is not a process based in fundamental agreements, it's based in submission, which implies that disagreement is what is fundamental, and the disagreement is overcome through the child's will to submit to the authorities.

In fact the further point he makes later is something I've stated a few times before -- that (meaningful) disagreement takes place on a background of agreement. — Moliere

So the point here is that the true background is one of disagreement, from which agreement is created. You misrepresent "disagreement" here by talking about meaningful disagreement. Meaning and agreement are closely tied, such that meaning is implicit within agreement, agreement is inherently meaningful. Disagreement, as the opposite, is therefore fundamentally meaningless. Meaningful disagreement is an oxymoron.

But the point, going back to partial untranslatability, has more to do with how charity is not an option, but is forced upon us. — Moliere

This gets to the point of why disagreement, and the consequent submission to the authorities, are fundamental. But I wouldn't go to the point of saying that charity is not an option, and is forced on us, I would say that we willfully submit to the authorities because to choose any other option would be completely irrational. And this submission is "accepting as true".

I cannot agree more! Of course, and that's what I was saying. But you totally misread what I was writing. I think because of you "apparently" not having experience with the topic of Mereo-topology.

What I'm saying is a little bit complicated. Seeing your comments, I realize that you completely mis-understood me. But I do concede that what I wrote was too compact. — Zuhair

Sorry for the misunderstanding, I'll try to stay on track.

Lets come to what I meant by "UNIT", I mean by that an individual. For example an apple is a unit, while the collection of two separate apples is not a unit. Now I envision a unit as an object that is not the whole of two separate objects, that is at the same time separate form other objects. This has something to do with separateness and contact. So a single apple has any two parts of it connected by a part of the apple, so it is in continuity, there is no breach to its material. — Zuhair

I tend to think that this is not a very good representation of what an object, or "unit" really is. It isn't based on an accurate description of the relationship between parts and wholes. A "unit" for you is something with existence separate from other units, yet its parts do not have such separate existence. In reality though, there is vagueness in what constitutes "separate". Due to this vagueness, there may be discrepancy in judgements as to what is the unit, and what is a part of a unit, depending on one's perspective. For example, the apple is really a part of the tree. Its generation, existence and subsistence is dependent on the tree, such that as soon as it gains "separate" existence it starts to degenerate. Also, consider a "unit" like the earth. You might think of it as "separate" from the sun, but really it only exists as a part of the solar system. Then the solar system only exists as a part of the galaxy, and so on. And if we look the other way, we are faced with the question of why this composition of molecules which is "the apple" is properly "the unit", and not the molecules themselves. After the apple separates from the tree, the molecules of the apple separate from each other in the process of degeneration. That is why I think your determination of what constitutes an object or "unit" is rather arbitrary, and dependent on one's perspective.

So a single apple has any two parts of it connected by a part of the apple, so it is in continuity, there is no breach to its material. While the collection of some two separate apples is not like that, you have one apple being a part of that collection and the other apple also being a part of that collection but you have a breach of material between them, i.e. the two apples are separate, i.e. not in contact with each other and no part of that collection is in contact with these two parts, such collections are NOT units, they are collections of separate units. — Zuhair

Now your description of a "collection" doesn't seem to provide principles to distinguish between an artificial collection and a natural collection. So for example you do not distinguish between a collection of apples in a bag, placed there artificially, and a collection of apples hanging on a tree. The tree might be an object, a unit, and the collection of apples exist as parts of that unit, but they could also be rearranged as parts of an artificial collection.

So a single apple has any two parts of it connected by a part of the apple, so it is in continuity, there is no breach to its material. — Zuhair

So this appears to be the critical question, what constitutes a "breach to its material"? The apples hanging on the tree clearly have no breach of material and are therefore part of the tree, but that's a simple example. Is there a breach of material between the earth and the sun, when the two are connected by things like gravity and light?

On the other hand, an artificial collection might very well be connected by something. Apples in a plastic bag are "connected". Apples of the same variety are "connected". Furthermore, when we manufacture things like cars for example, we connect parts together to produce a unit. So the distinction between artificial and natural, though it serves as an example, is not even a good distinction itself.

The issue here seems to be what constitutes a "material" connection. You would say that having a material connection to something else negates the status of being a "unit", making the thing a "part" of a unit instead. If we switch to Aristotelian terms we'd replace "material" with "substance". In his "Categories", "substance" in the truest and primary sense, is defined as that which is neither predicable of, nor present in, a subject. Notice that this produces a more rigorous restriction than your "material" connection. Not only do we have "present in" as a restriction, but also "predicable of". So for example, if X is predicable of Y, X cannot be given the status of substance, and cannot therefore be a unit or object. This would extend your category of material connection to include predication as representing a material connection.

I believe that the goal here is not to produce the artificial/natural distinction mentioned above, but to distinguish between substantial and non-substantial, or material and non-material collections. Consider my criticism of your last post accusing you of a "random collection of elements" which you flatly denied, accusing me of misunderstanding. If a collection is truly random, the so-called "parts" of that collection are actually units, there is nothing substantial connecting them, and the collection itself cannot be an object or unit. Therefore the "parts" of that collection are not properly "parts". But if the parts are connected for any valid reason, this must qualify as a substantial, or a material connection. Then the whole of the collection is a valid object or unit, and the parts cannot be understood as independent objects.

I define "collection" as a totality of units, of course that totality itself may be a unit (in the case the collection has only one unit part of it), or might not be a unit (like a collection of multiple units: like of two apples, 10 cats, etc...). I need to stress here that "being a unit" or not, has nothing to do with the collection being definable or not, even if it is definable after some predicate still the collection if it contains many units, still it is NOT a unit. Being a unit depends on the continuity of the material in the collection, and not on definability issues or the alike. — Zuhair

According to what I've explained above, I dismiss your criteria of "the continuity of the material", as being too vague, and replace it with the Aristotelian concept of substance. Therefore any valid "collection" is itself an object or unit, the parts having a substantial relation to one another, demonstrating the existence of a "whole". The parts are therefore not independent units. Having something in common for example, cannot be taken as merely coincidental, and must be understood as indicating that the parts are not independent objects, but parts of a whole.

The only collection that is at the same time a unit, is the singular collection, i.e. the collection having one element, i.e. has one unit part. Otherwise collections having multiple elements whether definable or not, are always not units. — Zuhair

I foresee an issue with this concept of a "singular collection". I'm afraid it might be somewhat contradictory like the empty set, or simply purposeless. Let's say that every object is unique, as per the law of identity. Any individual thing which we come across could therefore be a singular collection. However, it is pointless to make such a collection, because the reason for making a collection is to acknowledge relationships between things. So we could only place a thing in the category of "singular collection" if and only if there could be no relations between that thing and anything else. Having a relation would make it a part of a collection negating the status of "singular collection". Perhaps we could keep the category of "singular collection", but it would most likely remain an empty category. It's not an empty set though, but an empty category, because under my categorization a valid set (reasonable relations) constitutes an object.

A set (as that term is used in set theory) is a unit object that represent a collection of units, like in how a lawyer represent a collection of many accused persons. Each accused person is a unit object (because its material is in continuity, and it itself is separate form other material) and the lawyer is also a unit object, so here you have an example of some Representation relation where a collection of unit objects (that is itself (i.e. the collection) not a unit since there are many accused person in that collection of our example) that is represented by a unit object (the lawyer). That was an example of EXTERNAL REPRESENTATION. On the other hand there is INTERNAL REPRESENTATION where a single unit in the collection can stand to represent the total collection, like for example when the HEAD of some tribe represents the whole of its tribe in some meeting of head of tribes. The head of a tribe is a unit part of that tribe, and yet it can represent the whole tribe. Any group (collection) of people can always chose one among them that can stand to represent the whole group. This is internal representation. — Zuhair

So this is where your system gets very confused, and mine becomes much more practical. In your example, why not simply say that the collection of people represented by the lawyer is itself an object? They all have X in common, so they have that valid relationship to one another, and therefore exist together as that mentioned object. There is no need to assign to a member of the group the task of representation, such as the person who represents the group, and hand the group real existence through that representation, the group already has real existence through the real experience which they share, which constitutes a real relationship. Such real relations make real objects. And, in the other example, the tribe has real existence as an object, due to the relations between members, it does not require a "head" of the tribe, or representative of the tribe, to give it real existence as a collection or object. Requiring that the collection has a representative creates all sorts of problems, beginning with the representative's real capacity to adequately represent the collection. See, under this system, the collection, as an object, can only be apprehended as an object, to the extent provided by the representative. But the representative is not the true object, and we are better off to look directly at the object to understand its true existence.

The usual set theory with well founded sets is a theory of external representation of collections of representatives of collections of representatives of..... It is about tiers of representation of collections.

The empty set can be ANY individual object. For example take any particular apple. This can serve as the empty set, since apples are not representatives of collections of representatives..

Now take some unit object that serves to represent the chosen apple above (the one we called the empty set). This must be different form that apple, because the apple is not a representative of anything, while that object is representing that apple itself. This latter object would act as the singleton set of the empty set, denoted by {{}}. Now you can take a third object that act as a representative of the collection of the apple (the empty set) and the object that represents that apple (the singleton of the empty set), now this representative object would be the set of the empty set and the singleton of the empty set, denoted by { {}, {{}} }. And so on.... — Zuhair

Yes, this complexity is exactly why your system is bound to failure. As I described above, any individual object may be used to create a "singular collection". But that is to assume that the individual has no relations to anything else, and this produces an empty set. To make the set meaningful, another object must represent the singular collection, but that negates the status of singular collection. So your whole set system is based in something meaningless, or even contradictory, the empty set, which is represented by the singular collection. It's like you're building your sets bottom up, when they need to be produced top down to have any substance. The set must be principled on the real existence of parts to a whole, as an object, and not based on a part which is meant to represent a whole.

One needs to be careful! Not every collection has a representative! Even some well definable collections might not have representatives. Although this largely depends on what is meant by "well definable". — Zuhair

This is evidence that your system is faulty. We need to recognize a collection as an entity itself, and not rely on a representative. A representative is often incapable of representing to us, the "thing" which is responsible for the real and valid existence of the collection. And this is proven by the fact that some valid collections have no representative.

All of those have their wholes, For any predicate that hold of apples there is a totality of all apples fulfilling that predicate. And those totalities would be different totalities if the apples constituting them are different. But I've just presented to you a particular case. There is nothing special about two here or three or any number. — Zuhair

Right, that's why I say you're a magician. You claim that you can point to any random objects, and say those objects make another object, a whole. Your claim here amounts to an assertion that you can state "the predicate" which pertains to these two apples, or three apples, or any other number of apples, but no other apples. In reality there is no such predicate, it is a hollow claim. Therefore you have no principles for what constitutes an object, only "if I say it's a whole, then it's a whole". A principled "whole" has a defined completion, not the hollow (and sometimes impossible) claim that it's possible to define the completion.

I like to present matters in a Mereo-topological manner. Now a unit is an object that is not a whole of two separate (not in contact) parts, and at the same time it is separate from any other object. A totality of unites is a collection. The smallest collection is a unit. An element of a collection is a unit part of that collection. So the unit collection is the sole element of itself. Multipleton collections are those that are constituted of many unites. So they are not the elements of themselves. — Zuhair

See, you are using "totality" as if any collection of things is a totality of things. Now "totality" is meaningless and redundant because any collection of things is, by your usage, automatically a totality of things. But to have a proper totality, which gives "totality" meaning, it is required that we name a type of thing, and sum the complete number of those named things. To say that any random number of things is a "totality" is nonsense, because it's not the total of anything, it's just a random collection.

Now you claim that any random collection of elements is a "unit", but you have no principle of unity to substantiate that assertion, only the hollow claim that there is such a predicate which unifies them while excluding others. In reality, the elements cannot be a unit unless they are united by something which produces a unity. To say that any random collection of elements is a unity is to utter nonsense. By what means are those elements united?

Do you not respect the fact, that "a collection" must be defined? And, to complete the specified collection, to produce a totality, or "whole", it is required that the entire collection be summed. To insist that my collection is 'definable', and demonstrably the totality or whole of that 'definable' collection, does not justify the claim that it is a totality or whole. The definition must be produced, and it must be demonstrated that there are no other elements which would fulfill the conditions of that definition in order to justify the claim that the collection is whole, a totality, complete.

Set theory can be explained as an imaginary try to REPRESENT stable collections of unites, by stable unites. So any two stable collections (i.e. their unites are unchangeable over time) would have distinct representative unites (whether those representative units are part of those collections or external to them) as long as they are not the same, and each collection is only represented by one unit. This theory of representation of collections by units, is the essence of Set theory. Of course the representative unites are ideal, i.e. unchangeable over time. Now while element-hood of collections are being unit parts of those collections, yet "membership" in a set is another matter. Membership in sets can be defined in two ways, l personally like the definition of them being elements of collections represented by the unit, i.e. every set is actually a unit object that represents a collection of unites, now those unites of the represented collection are the members of that set. — Zuhair

If I correctly understand what you are saying here, a "set" is a collection. As a "unit" the set is complete, a totality, or whole. The completion is determined, fixed, perhaps even "caused", by the definition, the predicate. The definition makes the unit definite, and that is complete.

Here is the issue which I see. In reality, it is only possible that the definition may produce a complete collection, in some cases it may be the case that a complete collection is impossible according to some definitions. Completion of the collection is really dependent on the quality of the definition. A good definition may produce a complete set, while a bad definition will produce a set which is impossible to complete. Notice your opening sentence in the paragraph above: "Set theory can be explained as an imaginary try to REPRESENT stable collections...". The operative word here being "try". So if we take a poorly defined set, and try to produce a completion, or whole, or if we assert that a poorly defined set has produced a complete whole, this is a mistake.

We start with the non representative unit, i.e. a unit object that do not represent any collection of unites, this would stand for the empty set. — Zuhair

I see this as a self-refuting, contradictory start. The empty set would be complete, whole, with no members. It requires a definition which nothing could fulfill, a definition of nothing. But it is the definition itself which produces the entity, the unit, so the empty set is at the same time a unit, and also nothing. In common terms, to try and produce the empty set is to try to produce something out of nothing. There is no such thing as the empty set, it is an impossibility, by way of contradiction.

Therefore I propose as the true start, the definition of a unit, what it means to be an object, complete, whole, a totality. We cannot start with an empty symbol because that creates infinite random possibilities for nonsense. We need to start with what the symbol is really supposed to represent, a set, which is an object, a unit, or whole. In this way we may restrict the use of the symbol, to eliminate vain attempts to produce an impossible whole.

Remember, the possibility of completion is directly dependent on the quality of the definition. Therefore we ought to restrict poor quality definitions which are not conducive to the possibility of completion. Such definitions may produce the illusion of completion when no such thing is possible, allowing for misleading, or deception. This can be done with a proper definition of what it means to be a unity, a whole, complete or totality.

So the empty set, as a starting point ought to be replaced with the set of one, a whole, an object, complete, whole and total in itself, by its very nature; so that the principal or primary set is consistent with itself, and not self-contradictory as the empty set is.

According to this view a set is always a unit, and that unit act to represent a collection of units. — Zuhair

One problem, the empty set cannot be a unit, as described above, that's self-contradictory. It's an object composed of nothing.

I just wanted to put you in the picture, that sets (as used in mathematics) are different from the collections I've spoken about. While the genre of collections is the same as the genre of their elements, sets on the other hand can be totally external to the collections they represent and can indeed be of a different nature. There is a lot of confusion between collections and sets, even in standard text-books of mathematics, and especially there is the confusion between element-hood of collections and membership in sets, that many mathematical textbooks on set theory introduce sets in terms of collections and set membership in terms of element-hood of collections, and this is a great confusion. Sets do not function as collections, no they function as unit representatives of collections, thereby enabling us to speak of a hierarchy of multiplicities within multiplicities and so on... So the set concept is a stronger concept than the collective concept. The former is representational and latter is mereological. — Zuhair

I would say that this confusion is actually produced by the convention of allowing for empty sets. By allowing for a set with no members we produce a separation between the set, and the members of the set. But no such separation is warranted. The set itself is the object, the elements comprise that object, and the object is created by the definition. The quality of the definition determines the definiteness or definitiveness of the object. A vague definition produces a vague object. So the set, and the elements or members, must be one and the same, in order that the set be the object composed of those elements, while the definition is what has separate existence. Therefore judgement lies in conformity between the definition and the elements, such that a poorly defined set makes a vague object, or in some (impossible or contradictory) cases not an object at all.

No that is not correct. If you show me three or more apples, the totality object would be some OTHER object. I just showed you two particular apples (those that I've bought today), and I asked you simply if by today when I bought them, do I have an object that is the whole of both of them, and I explained this object in terms of Part-whole relationship, an object such that each apple (that I bought today) is a part of it, and such that it doesn't have a part of it that is disjoint (doesn't share a common part) of both these apples. — Zuhair

By showing me the apples you are not showing me the "totality object". This you would show to me in your explanation of "part-whole relationship", etc.. That is why number as an object, if it is an object, is something other than the objects which you use to demonstrate its rationality. The proper demonstration is an explanation, and the apples are just props.

This object is the smallest object that has both of these apples as parts of. — Zuhair

So by the time you are talking about a number of apples, "number" is completely abstract, and you are applying that abstract idea back, onto the apples. The claimed object which is signified by "2" does not have any apples as a part of it, it is abstract. And you cannot demonstrate that object to me by showing me two apples, because such a demonstration can only be done through an explanation of what it means to be 2.

It is simply this object that I've asked you to tell me whether it exists or not. — Zuhair

That claimed object, the "totality object", is what I see no reason to believe exists. You made some claim about "part-whole" relationship, but I see no reason why two apples, ten apples, or a million apples is a "whole" anything. Therefore there is no "whole" to this object which you are describing, and your descriptive terms are misleading. You are assuming that two apples is a whole, without any reasons why two apples may be a whole, and why it doesn't take three, four, five, or the proper totality of all apples, to make a whole. Surely there are more apples than two, so by what principle do you apprehend two as a whole?

This is what Plato's theory of participation demonstrates to us. The "whole" is an Idea, the parts participate in the Idea. Now the existence of the Idea, as the whole which unifies the participants producing the object, must be supported or else the whole theory of participation falls apart. "One" is fundamentally a whole, that is its essence, a unified entity, but "one" is fundamentally different from "two" by the difference between a singularity and a multiplicity. So what principle will you introduce to support your assertion that "two" is a whole, just like "one"?

I see each apple as an individual object. The claim that an apple is an object is justified by sense perception of its existence separate from other things. If you show me two apples and assert that the two are one, then you need to supply a principle to justify this claim.

Let's say that the two apples are "the same", in the sense that both are apples. So we place them both in that category, the set of apples. Notice that "the same" here is not being used in a way which is consistent with the law of identity. The apples are not really "the same" in that sense, as they remain two distinct objects. Now, what is one is the category, or set we have created called "apples". The apples are not really unified to be one, they are judged as being members of one set, according to the principle (the Idea) whereby we class them both as apples. This is explained by Plato in his famous theory of participation. The distinct objects partake in the Idea. It is well explained in The Symposium.

But it is important to note the deficiency of the theory of participation which is developed in Plato's Parmenides, which some people argue leads to the refutation of Pythagorean/Platonic idealism by Aristotle. Let's say that the Idea, which is "the set of apples", provides the unity whereby the two apples are judged as one. It is the Idea itself, which is one object, not the two apples. The problem is that no matter how many apples partake in this Idea (the set of apples), the Idea as one object does not change. Apples may come and go from the set, as time passes, but despite this activity the set itself, as an object never changes. We see that the sense of "the same" here means that the Idea is unchanging over time, whereas "the same" in the law of identity allows that the same object may be changing as time passes.

This makes the "Idea", or "set", as an object, passive and unchanging, and therefore independent from, separate and distinct from, the objects identified through the law of identity, which are the members of the set. Through generation and corruption, identified objects which are members of a set, like apples, come into being and cease being, while the idea, or set itself is supposed to be unchanging.

So when you show me two apples and say that they are one object, you might as well show me three or four apples, a thousand, or a million apples, and each time you are showing me the exact same object, the set, or Idea of apples. That object is the Idea, the principle whereby you unify them as one. But that seems like nonsense, that showing me two apples, or four apples, or a million apples, is showing me the exact same object. Therefore it appears like we cannot properly refer to these "Ideas", or "sets", as objects, because we do not allow them to change when change is warranted by what is exhibited. Showing me two apples cannot be showing me the same object as showing me a hundred apples. Therefore either the two apples do not properly make an object, or we do not understand the way that this object, being the Idea or set, changes when members are added or subtracted from it.

In any sense, even the sense of a practising doctor, practise gives a person experience, making one stronger in one's capacity to carry out that exercise. Where I live a doctor must take part in a supervised form of practise, residency, prior to obtaining a license to practise. Only after this can a doctor establish a "practice".

The benefit of working without pay is experience and it is experience which gives one the power to carry out the task in a efficacious way. That is strength. Thrasymachus' subject is power, and Socrates is referring to how power is derived from practise.

But that is not in itself a reason to jump to the conclusion that premise one should be read as a description of physical things instead of as a metaphysical truth. — Walter B

Care to explain what you think is the difference between these two?

Suppose that I said that from nothing nothing comes, and then said just look around you, why should it mean that within the realm of immaterial things, some immaterial things may come from nothing? — Walter B

I cannot perceive any immaterial things by looking around me. So looking around me doesn't serve to give me any evidence to create any principles concerning immaterial things.

When I read it, it seems to be the equivalent of "nothing moves itself and this is corroborated by everyday experience so you shouldn't doubt what is so obviously self-evident." In fact, I read it as invoking a metaphysical principle, rather than as a description of the behavior of physical things. — Walter B

The "nothing moves itself" premise is a common starting point for numerous arguments concerning the nature of the immaterial, dating back to Plato. I believe it is supposed to be an inductive conclusion drawn from our sense observations of the material world. But that is no different from how you describe it as "corroborated by everyday experience". The movement of immaterial things is outside our field of "experience".

Yes, now that I think about it, the premise must only apply to material things. Premise one starts with "look around you". We cannot see immaterial things, so the premise is an inductive conclusion drawn from the observation of material things. Therefore it would not be applicable to immaterial things.

We don't know how immaterial things act as causes, only that they do. So we can't make any such assumption.

The way you are presenting the argument seems to suggest that premise 1 should only ably to physical things. — Walter B

No. I am saying that the soul might be moved by some other immaterial thing. You only approached an inconsistency with 1 by saying that the soul moves itself. If you allow that the soul moves the body, but the soul is itself moved by some other immaterial thing, you have no reason to reject 1.

I would have thought Thrasymachus' whole contention would rely on 'pay' and 'self interest' being the only true 'benefit' of the practice. — Yanni

Working makes one stronger, "practise makes perfect". So exercise, which is practise, builds strength; and strength is good. The benefit of practise is strength.

However, the reason I think that Plato's argument fails (as it was presented in Philosphy demystified) is because premise 1 seems to contradict the conclusion. If nothing moves itself, then a soul can't move itself. So the soul's movement must be the product of some other thing and so on. Even if it is accepted that whatever is moved, because of something else, is itself causally impotent and whatever is its own source of movement is causally potent, we are left wondering if premise 1 is compatible with the notion that some things are their own source of motion. If somethings are their own source of motion, then it seems that some things can move by itself and premise 1 is false. — Walter B

You need not conclude that 1 is false. The argument takes the observation that movements of the body (or the parts of the body which originate the motions of the body as a whole, in your reformulation) are not caused by motions of other bodies. So a soul is posited as the source of motion of the body.

Let's suppose that to be consistent with 1, a soul cannot move itself. Plato assumes intelligible objects, which are not material bodies, and these may be responsible for the movements of the soul. So I'd say that the argument is meant to open one's mind to the reality of the fact that the immaterial realm is causally active, and not meant to show that the soul moves itself.

You and sandman might as well complain about the rules of chess for not conforming to your metaphysical preferences. — Eee

I don't see how that's an adept analogy. Metaphysical principles are based in how one apprehends the nature of reality. Chess is a game which we can choose not to play if we don't like the rules, how does that relate to reality? Not even by killing oneself can one choose not to partake in reality.

To be a mathematician it suffices to prove things using 'the rules.' — Eee

If the rules do not conform to reality, then I'd have to ask you what are these proofs sufficient for? I'd say they're sufficient to produce unsound conclusions. What exactly would the mathemagician be proving, if one uses poorly formed rules? I'd say that the mathemagician would be proving that confusion follows from the use of poorly formed rules.

One can think of it as a game with symbols. — Eee

I don't like playing games, I'd rather be engaged in something meaningful.

So to me the idea that mathematicians are true believers is in general ridiculous, and, in my experience, most online anti-Cantorism is purveyed by those who seemingly can't even play the game agnostically. That would take work, serious interest, and not just self-inflating online conspiracy theory. — Eee

That's the point, why put serious effort, work, toward something which is just a game? I know that athletes do it. Sorry, but I'm not interested.

We want to know what the president is thinking, whether he is right or wrong, silly ideas or not. — NOS4A2

Lies and deceit do not tell others what you are thinking. And if lies and deceit are what makes other politicians bad, Trump is clearly not any better. In fact he seems to lie and deceive even more that the average politician. He's taken politics to a new low.

Well you seem to refuse tribe as an object, well this is a deep point. Anyhow to me a tribe, a herd, a bunch, etc.. all of those are objects, and they are well specified objects as long as each individual member of them is a well specified entity. Anyhow I don't think I can discuss refusal of such clear kinds of objects. — Zuhair

Correct, under your definitions, I refuse a 'tribe" as an object. If we are to consider a "tribe" as an object, the relations between the members are essential to the existence of that object. Remove those relations and you have no object.

You seem to think that you can randomly point to a bunch of objects, say "abracadabra", and suddenly there is another object, which exists as the unity of those objects you have pointed to. Sorry, but that's not reality.

I guess you did not read the OP. — tim wood

I've read the op, but as I've said, I don't agree with your principles of categorization. I think your expressed principles display a lack of understanding of what it means to exist. That's why I suggested that we ought to clear up the issue of what it means to exist before we attempt any such categorization.

But this is all useless. Clearly you are unable to take part in the general point of the thread, and you have nothing to offer but that "which I am familiar with." — tim wood

How do you suppose that I could offer you something other than what I am familiar with?

I haven't yet been able to find "the general point of the thread". It appears like your intent is to define "exist" in some odd sort of way, and I can't understand why. Despite the fact that I've made some suggestions to help you to express yourself, you haven't been able to clarify at all, what you're trying to do. So I remain lost and confused. Now your argument has digressed to ad hominem premises drawn from my confused state. If you are completely disinterested in what I am familiar with, and your intent appears misleading to me, how can we find common ground?

I'm looking to ordinary language for guidance... — tim wood

No, you have clearly expressed that you are not looking to ordinary language for guidance. Your intent appears to be to offer guidance through an abnormal use of language, and this I class as misleading.

It doesn't indicate that those arguments must be distinct from each other.

...

A tribe is a well specified entity, it refers to the totality of specified individuals. — Zuhair

OK, since a "tribe" is meant to be an object, you are defining "object" with these principles. Accordingly, an object is a whole, composed of the totality of specified parts. And, there may be an overlap between the parts of one object and another, such that the parts of one object may also be the parts of another object.

Now, I suggest that you are missing a very important (essential) aspect of an "object" in your definition. For the existence of an object, it is necessary that the parts exist in specific relationships to one another. This is why your definition, and consequent "rule" is ambiguous, as I've said. An "object" is not a random collection of parts, in any random relations, but the parts must exist in a very specific way in relation to each other, in order to constitute an entity. Those relationships are essential to the existence of any object, such that when the specified relations cease to exist, the object ceases to exist, despite the fact that the totality of parts may continue to exist. In other words, "totality of specified individuals" is insufficient for "well specified entity", and your claim that "a tribe is a well specified entity" is absolutely false. It is this ambiguity (lack of definition) in the relationships between parts of your so-called "entity" which allows for your mathemagistic sophistry.

This is a well specified entity.

...

Clearly each tribe is a well defined entity... — Zuhair

As explained, this is absolutely false. Your entire argument above, relies on the truth of this false assertion, which you seem to think that if you repeat it enough it will magically become true.

Cantor was an illusionist, who fooled many people. That's it. — sandman

Very true, that's why I like to call people like Cantor mathemagicians.

Individual mathematicians may have metaphysical beliefs, but those beliefs don't play a role in proofs. — Eee

Yes, those metaphysical beliefs clearly do play a role in mathematical proofs because they are entrenched in the axioms, as foundational support for those axioms. And Cantor is a good example. What is at issue here is how we conceive of an "object".

S||S is a particular case of A||B; also C||D when C, D are disjoint tribes is also a particular case of A||B. — Zuhair

I'll grant you that as true. But the point is that there is ambiguity as to what "||" signifies. So, we must be careful not to equivocate.

This is like variation in particularities of objects fulfilling a predicate, for example the predicate "is a circle", now not all circles are really a like, they might vary in their size for example, in their colors, etc.., that doesn't affect them all being circles. No equivocation at all. — Zuhair

That's right, there need not be any equivocation if we respect the differences. The equivocation would only occur if we say that one circle is "the same" (as specified by the law of identity) as the other, on account of them each being a circle.

Similarly the relationship || between tribes has strict definition, and whenever that definition is met, then the relationship holds between the respective tribes, variations in particularities of individual actualization of that relationship are immaterial as immaterial is the size of the circle in meeting the definition of a circle. — Zuhair

That definition of "||" is not so strict as you seem to think. You describe it as "the relationship || between tribes", as if it is necessarily a relationship between a plurality of "tribes". Yet in the case of S||S it does not represent a relationship between tribes, but the internal relations of one tribe. Do you apprehend this difference? This is the difference between what is internal to an object (part of the object), and external to the object (not part of the object).

We name an object, "X" for example, and we can describe relationships between this object and other objects. Or, we can describe relationships internal to that object, as relations of the parts, but these relations are not relations between the object X and other objects. The former is properly relations of the object, the latter is relations of the parts (as objects themselves).

Now, you conflate these two with your definition. You say that if the parts of tribe A have a specified relation with the parts of tribe B, we can call that a relation between the objects named by A and B. This is not true though, there is no such relation between two objects "A" and "B" being described. There is only a group of parts (as objects themselves), with specified relations between these elements. This is very evident in the case of S||S. There is not two objects "S", with relations between those two objects, there are relations between elements and a rule which produces the claim of two objects named S with a relation between those two objects. It appears to me, like you may have some system for naming a particular group of parts by names such as "A", "B", and "S", but this assignment might be completely random, so we cannot say that these names refer to objects. They refer to groupings of elements, the elements themselves being objects

Therefore you have some random, or principled groupings of objects, and these groups of objects have received names, like "S". These groups are not objects, but artificial groups. You also have the members of the groups, which are the real objects that exist in certain relationships with each other. Your system for naming the groups as objects is ambiguous because it doesn't distinguish between internal relationships (relations between members of the group) and external relationships (relationships between a member of one group and a member of another group). Because of this failure, to distinguish the internal from the external, which is an essential aspect of an object, your groupings cannot be understood as objects. Very clearly in the case of S||S the two S's cannot be understood as signifying the same object with a relationship to itself. It really signifies that the objects which are the members of group S have the necessary relations with each other, to apply the rule, and say S||S.

The rule is ambiguous because it allows that internal relations between the members of a group are treated in the same way as relations between members of one group and members of another group. This annihilates, negates, or renders insignificant, the boundaries of the group, leaving the groupings as meaningless

The whole matter began when I wanted to coin a relation that can exist between something and itself other than the identity relation! So the relation || as I defined in the example can occur between a tribe and itself, and also can occur between distinct tribes, so its not the identity relation. As far as the "application" of relation ||, there is no equivocation at all.

So identity is not the ONLY relation that can occur between something and itself.

But

Identity is the ONLY relation that can ONLY occurs between something and itself. — Zuhair

Let's be specific with the terms here. I said that in the case of "4+4=8", if "4" is to represent an object, each of the two 4's must represent a distinct object. You gave S||S as an example of a case where each of the two S's represents the same object. Now I've demonstrated that "S" does not represent an object at all, but an artificial grouping, which cannot be apprehended as an object due to an inability to distinguish which elements are internal to (part of) the group, and which elements are external to (not part of) the group. The artificial grouping does not follow the rules of having a meaningful boundary, which is necessary for an object.

Now, it appears like an artificial grouping can be created which does not follow the rules of what "an object" is. The law of identity, what you call here "the identity relation", applies specifically to objects. If you can create an artificial group, which is not an object, it's quite clear that this artificial group might not follow the rules of what an object is. So your example really shows nothing, because your artificial group is not consistent with "object", therefore the identity relation is not applicable to your artificial group.

A man will face years in prison because he made mistakes during the process of an investigation of which there is no underlying crime. — NOS4A2

There are reasons why those mistakes, of lying and witness tampering were made. Those mistakes are only made when the person is already guilty.

I guess two confuses you, and three - don't forget four and the rest of them. And love justice and The American Way. Superman, unicorns, dragons, all of the English and French kings - they do not exist, do they. These have no existence? Maybe we should pause here: answer: do these exist, yes or no? — tim wood

No they do not exist. In the common usage of the word "exist", which I am familiar with, fictional things do not exist. Nor do love, justice, and other ideas exist. They are conceptual only, and therefore not existing things. Notice that love and justice refer to relations between things, while concepts and imaginary fictions are ways of thinking. None of these are themselves, things, and that's why we cannot class them as existents.

Is the problem "encounterable"? Let's consider that no one "encounters" anything at all, except mediately through perception and idea. And by that standard, unicorns and their like are more purely existent than any of the furniture of the "real" world, being pure idea undiluted by perception. You really are not making sense. Why is that? — tim wood

It's you who's really not making any sense here. I simply rejected "encounterability" as the defining feature of existent, for very good reason which I explained. I don't know what you're trying to say.