Deeper than primes

[doronshadmi]

(Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.)

The axiom of minima:
Emptiness is that has no predecessor.

The axiom of maxima:
Fullness is that has no successor.

(Only Emptiness does not have a predecessor in the absolute sense.

Only Fullness does not have a successor in the absolute sense.

The next axioms are at the level of the existence of collections, which is > Emptiness AND < Fullness, where > or < are the order of exitence w.r.t Emptiness or Fullness.)

The axiom of existence:
Any existing thing has a predecessor.

(y and x are place holders for an intermediate state of existence between Emptiness and Fullness.)

The axiom of infinite collection:
If x exists then y>x exists.

(I do not assume numbers, I explicitly use numbers as measurements of the intermediate levels of existence between Emptiness and Fullness.

Simultaneity does not need any further definition in order to clearly be understood, exactly as step-by-step (the opposite of Simultaneity) does not need any further definition in order to clearly be understood.)

The axiom of Locality:
y, such that x = 1 to ∞ and ((y≥0)<x), is simultaneously at most at one location w.r.t all x.

The axiom of Non-Locality:
y, such that x = 0 to ∞ and x < y, is simultaneously at least at two locations w.r.t all x.

 

[doronshadmi]

Before you attempt to correct your axioms or alternatively try to tell me that I'm wrong, let's take a different approach. It's already been explained to you that ZFC is strong enough to deduce the negation of your central result known as the "Axiom of the Continuum". ZFC states some very obvious and intuitive things about the notion of a collection. Tell us, in detail, which ZFC axioms are wrong and why.

I will do it tommorow.

 

[jsfisher]

(Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.)

So, doronetics only works for well ordered collections. How limiting.

The axiom of minima:
Emptiness is that has no predecessor.

The axiom of maxima:
Fullness is that has no successor.

Neither of these are axioms.

(Only Emptiness does not have a predecessor in the absolute sense.

Only Fullness does not have a successor in the absolute sense.

The next axioms are at the level of the existence of collections, which is > Emptiness AND < Fullness, where > or < are the order of exitence w.r.t Emptiness or Fullness.)

No, they are not. You'd need to add extra words to the pseudo-axioms to create those sorts of restrictions.

The axiom of existence:
Any existing thing has a predecessor.

As I stated before, this establishes that emptiness is not an existing thing.

Oh, and look, the banned universal quantification again.

(y and x are place holders for an intermediate state of existence between Emptiness and Fullness.)

The axiom of infinite collection:
If x exists then y>x exists.

Great, but will you ever bother to assert that at least one thing exists? So far all you have done is explicit deny the existence of emptiness, and by this pseudo-axiom, you have now denied the existence of fullness, too.

(I do not assume numbers, I explicitly use numbers as measurements of the intermediate levels of existence between Emptiness and Fullness.

You cannot have it both ways, Doron. If they aren't already part of Doronetics before you introduce these pseudo-axioms, then you cannot use them in these pseudo-axioms.

Since you now deny numbers are assumed, and since you didn't bother to define location and location with respect to something, the remainder of your post is therefore gibberish.

 

[HatRack]

Doron, there are multiple problems with your axioms still. This list is certainly not comprehensive.

1. The first two "axioms" are not axioms at all, they are definitions.
2. You never assert the existence of anything, leaving your theory rather empty.
3. Your third axiom denies the existence of something you went out of your way to define.
4. The biggest problems lie with your last two axioms. If you wish to use numbers and infinity, you must assume the Peano Axioms + elementary set theory, which makes your theory inconsistent right off the bat. Otherwise, you must introduce numbers axiomatically.

I'm beginning to think you don't understand what mathematical rigor means. Okay that's a lie actually, I've thought that well before I even created a forum account here.

And jsfisher made a great point. You are using universal quantification in one of your axioms, the very thing you said was invalid several pages back to try and claim that 1/2 + 1/4 + 1/8 + ... = 1 was wrong. You and epix need to sit down together and read an elementary calculus text, at the very least, before criticizing the foundations of mathematics.

 

[laca]

In other words, you can't get Emptiness, Fullness, and the intermediate existence of collections between Emptiness and Fullness.

No, doron. You define emptiness and fullness but in the next two "axioms" you assert that they do not exist (taking into account your definition of successor). You call that useful in what way?

 

[laca]

How poor understanding about order (at its most general aspect) you have.

Forgive me for having a much clearer concept of what predecessor and successor generally mean than you. How is giving a new meaning for an otherwise generally accepted term useful? Why don't you just use the accepted terms?

 

[laca]

0 is a predecessor for pi and pi is a successor for 0.

No, 0 is less than pi and pi is greater than 0. Those are the terms you're looking for. Successor and predecessor have other meanings. Since the meaning you're trying to convey has a generally accepted term for it, I suggest you stick to it to avoid further confusion.

 

[laca]

Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.

Only Emptiness does not have a predecessor in the absolute sense.

Only Fullness does not have a successor in the absolute sense.

Your notion is still closed under the concept of Collection, which is an intermediate state of existence between Emptiness and Fullness.

WHAT?! Where has HatRack talked about anything but the general purpose of axioms? What does that have to do with collections? Do you even read people's posts before replying or just glance at it and decide on a stock gibberish reply?

 

[laca]

y and x are place holders for an intermediate state of existence between Emptiness and Fullness.

How does something exist between two nonexistent things? Your axioms forbid the existence of both emptiness and fullness. Methinks you need to revise your "axioms".

 

[doronshadmi]

How does something exist between two nonexistent things? Your axioms forbid the existence of both emptiness and fullness.

Emptiness is exactly total non-existence, and Fullness is exactly total existence.

Emptiness is strictly below the concept of Collection and Fullness is strictly above the concept of Collection. Since you get concepts only at the level of the concept of Collection, you can't comprehend Emptiness or Fullness.

As I stated before, this establishes that emptiness is not an existing thing.

It is trivially true that Emptiness is not an existing thing.

Oh, and look, the banned universal quantification again.

Worng, the collection of all existing things above Emptiness AND below Fullness, holds.

So far all you have done is explicit deny the existence of emptiness

I don't have to, Emptiness is total non-existence, and Fullness is total existence.

Collection (finite or infinite (countable or uncountable)) exists relatively to these totalities.

This is a novel approach about the abstract foundation of the Mathematical Science, which your "closed under Collections" approach simply can't comprehend.

You do not do the needed paradigm-shift beyond the concept of Collection, and as long as this paradigm-shift is not done, you can't get Organic Mathematics and its novel reasoning of the concept of Infinity, Collection, Number, Function, Logic, Analysis, Geometry, Operation, Continuum, Discreteness, Order, Cardinality, Distinction or any other fundamental concept of the Mathematical Science.

You'd need to add extra words to the pseudo-axioms to create those sorts of restrictions.

It is done for one purpose at this stage, to give you the needed notions in order to help you to do the paradigm-shift beyond the Collection-only notion.

After this paradigm-shift is done, we do not need the extra words.

By analogy, these extra words are like scaffolds that are removed after the paradigm-shift is done.

 

[doronshadmi]

So, doronetics only works for well ordered collections.

Not well-ordering is, for example, the open interval (0, 1) that does not contain a least element.

(0,1) exists also by OM, such that the least existing thing that is totally local (a point), and the least existing thing that is totally non-local (a line), are excluded.

 

[laca]

It is done for one purpose at this stage, to give you the needed notions in order to help you to do the paradigm-shift beyond the Collection-only notion.

After this paradigm-shift is done, we do not need the extra words.

By analogy, these extra words are like scaffolds that are removed after the paradigm-shift is done.

What you're asking is to believe you without any question. That's not going to happen, sorry. You will have to do the work. Maybe then you'll realize how deluded you are.

 

[zooterkin]

Emptiness is exactly total non-existence, and Fullness is exactly total existence.

Emptiness is strictly below the concept of Collection and Fullness is strictly above the concept of Collection. Since you get concepts only at the level of the concept of Collection, you can't comprehend Emptiness or Fullness.

There's only one person having problems distinguishing between the existence of emptiness and what it means.

You first defined 'emptiness', then precluded it from existing. You also have a problem with "existing things". If emptiness does not exist (it does not have a predecessor, so it is not an existing thing), then how does the first thing exist, since it too has no predecessor?

 

[doronshadmi]

What you're asking is to believe you without any question.

Not at all, on the contrary, I challenge you to get things beyond the concept of Collection.

Until know you are using the concept of Collection in order to understand Emptiness and Fullness, but these concepts are the totalities below and above that concept of Collection, where the concept of Collection exists relatively to these totalities.

In order to get the concept of Collection from the level of these totalities, a paradigm-shift of the concept of Existence has to be done in your mind.

Without it, there can't be any meaningful communication between us.

This paradigm-shift has nothing to do with the concept of Belief.

 

[jsfisher]

Not well-ordering is, for example, the open interval (0, 1) that does not contain a least element.

(0,1) exists also by OM, such that the least existing thing that is totally local (a point), and the least existing thing that is totally non-local (a line), are excluded.

Well, whether the set of real numbers in the open interval (0,1) is well-ordered would depend on the order relation, now wouldn't it? Are you assuming a particular order relation? (Of course you are. You have many, many hidden assumptions.)

And I see now you assume the real numbers, not just the integers, in doronetics., too

Let's see: You require the real numbers as background to your little pseudo-axiom set without any basis. You need universal quantification, but forbid its use by others. You offer simple word-substitution definitions (which aren't definitions in any constructive sense) while claiming they are axioms. And you require an unspecified ordering relation.

Just out of interest, Doron, how do you propose to order the points in a plane? Or the points on a circle? More hidden assumptions, I assume.

 

[doronshadmi]

There's only one person having problems distinguishing between the existence of emptiness and what it means.

You first defined 'emptiness', then precluded it from existing. You also have a problem with "existing things". If emptiness does not exist (it does not have a predecessor, so it is not an existing thing), then how does the first thing exist, since it too has no predecessor?

The first existing thing has a predecessor, which is the concept of Emptiness.

Only Emptiness does not have a concept that can be used as its predecessor, otherwise it not the concept of Emptiness.

Please try to upgrade your abstraction in order to get that.

 

[doronshadmi]

You need universal quantification, but forbid its use by others

You have missed http://www.internationalskeptics.com/forums/showpost.php?p=6595906&postcount=12635 .

 

[Elf Grinder 3000]

Doron, there are multiple problems with your axioms still. This list is certainly not comprehensive.

1. The first two "axioms" are not axioms at all, they are definitions.
   

What is the difference between an axiom and a definition?

 

[jsfisher]

You have missed http://www.internationalskeptics.com/forums/showpost.php?p=6595906&postcount=12635 .

No, I didn't miss your non-sequitur. You used universal quantification. If universal quantification is not allowed, don't use it.

 

[doronshadmi]

And you require an unspecified ordering relation.

At this fundamental level, all is needed is the essentials which enable order, which are exactly < or >. Without them no order (well or non-well) is defined.

You simply force a further resolution at this fundamental level, but then you are not at this fundamental level of the concept of Order anymore.