Deeper than primes

[doronshadmi]

Just like your ability to define your terms, your ability to be "very clear" on anything lacks even one demonstration.

I define my terms in http://www.internationalskeptics.com/forums/showpost.php?p=6667634&postcount=13318.

They are simply not your deductive-only terms.

 

[epix]

Actually, no, not quite. The second axiom can not be used to establish that X has a predecessor.

Why is it so?
Once you establish through the second axiom the existence of 'x' and 'y' respectively, the conclusion is that 'x' has a successor and 'y' has a predecessor. Even if the first axiom doesn't refer to 'y' but to 'x' as "thing", any implied reference to a predecessor made elsewhere concerns the first axiom, if the variables including "things" belong to N. That's why I referred to the "natural predecessor." The existence axiom establishes 'z < x' and the infinite collection axiom establishes 'x < y'. The axiom of transitivity is now looming on the horizon, but Euclid would never make the mistake to use two separate axioms so his... well, successors would be able to construct a "transitivity theorem." That's the way I see it.

But I think that propositional logic should decide the case. That would need some cooperation from Doron, coz I fully agree that Doron's statements left unattended lack the necessary rigor that would enable the usage of the tool. Doron handles x and y, not just x and y, so these variables may come from a set known only to him and the demons of advanced celestial philosophy.

 

[epix]

(Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.)

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

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

IF 'x' is a considered thing AND 'x<y', THEN 'y' is a successor of 'x'. (x and y belong to N)

Necessary implication: 'x' must be the predecessor of 'y' where 'y' is the new and additional existing thing. Therefore, any existing thing has a predecessor. So the axiom of existence is actually a theorem. Right, Doron?

 

[epix]

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

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

Both axioms define Emptiness: If any existing thing has a predecessor, then Emptiness is not an existing thing.

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

The above says that the level of the existence of collections is greater than Emptiness. How the heck can you compare anything with something that doesn't exist?

There is only one being known to the universe that could pull a trick like that. No, it's not God -- we are swimming in the lake of rationality. That being is rumoured to have risen from the stardust that accummulates near NGC 5134.

 

[zooterkin]

The Man, as long as your reasoning can't get a simple notion like an atom (an indivisible element) with size > 0, all you get from Organic Mathematics is contradiction and self-inconsistency.

Are you saying that the equivalent of points in Doronetics have a size? How big are they?

 

[epix]

Sice you have no Meta view of the considered subject, you are missing the following:

I wish to share with you some Meta view of the Mathematical Science, which does not follow after some basic agreed notions. Let us start by using Gottlob Frege's notion about X≠X. He defined number 0 as the amount of the objects of the class of all X≠X ( ( http://plato.stanford.edu/entries/frege/ ) )

0 is not equivalent to Nothing, because 0 is, after all something, called a number. But it does not mean that Emptiness or Nothing can't directly be used in order to do some Math. Let us follow this notion by re-examine, for example, the notion of the empty set:

(X=X) means: "X exists" or "X is true"

(X≠X) means: "X does not exist" or "X is false"

Wouldn't it be better to hang on common sense and stick with

(X=Y) means "true"

(X≠Y) means "false"

rather than hold X non-existent when it happens to be false? That's a philosophical utopia, coz some folks are lying all the time to cover for naughty things they like to do. Then there are people who just make unintentional mistakes. That was all apparent to Frege:

Even the sentences of Frege's mature logical system are complex terms; they are terms that denote truth-values. Frege distinguished two truth-values, The True and The False, which he took to be objects. The basic sentences of Frege's system are constructed using the expression ‘( ) = ( )’, which signifies a binary function that maps a pair of objects x and y to The True if x is identical to y and maps x and y to The False otherwise. A sentence such as ‘2² = 4’ therefore denotes the truth-value The True, while the sentence ‘2² = 6’ denotes The False.

 

[doronshadmi]

How the heck can you compare anything with something that doesn't exist?

Nothing is not "something that doesn't exist".

Nothing is that has no predecessor.

Something is that has a predecessor.

For example: the minimal existing thing, known as a point, has a predecessor called Nothing, where Nothing has no predecessor.

Necessary implication: 'x' must be the predecessor of 'y' where 'y' is the new and additional existing thing. Therefore, any existing thing has a predecessor. So the axiom of existence is actually a theorem. Right, Doron?

No, the axiom of existence defines the minimal term for any existing thing, which is: it has a predecessor, where one of the predecessors is "that has no predecessor", which is Nothing or Emptiness.

Both axioms define Emptiness: If any existing thing has a predecessor, then Emptiness is not an existing thing.

You are using "that has no predecessor" (Emptiness) and "that has a predecessor" (Existing) in order to conclude that "that has a predecessor" is not "that has no predecessor".

But in order to conclude such a thing you need the axiom of minima and the axiom of existence:

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

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

Without these axioms you can't conclude that "that has a predecessor" is not "that has no predecessor".

 

[doronshadmi]

Are you saying that the equivalent of points in Doronetics have a size? How big are they?

What

A point is an existing atom with size=0.

A line (or any other space > point) is an existing atom with size > 0.

 

[The Man]

The Man, as long as your reasoning can't get a simple notion like an atom (an indivisible element) with size > 0, all you get from Organic Mathematics is contradiction and self-inconsistency.

Doron as long as your "reasoning" can’t get that your "atom (an indivisible element)" is just your own self-imposed and unnecessary limitation, all you will assert with your “Organic Mathematics” are direct contradictions and self-inconsistency.


Oh, and how about answering the question I asked…

So Doron do you actually have a self-consistent and generally consistent criteria for your "at" such that your " B is at" "A" as well as your "A is at" "B" both use that same criteria and your "at AND not at" is that criteria AND its negation?

…keeping in mind of course your own self-imposed limitation of ‘indivisible elements’.

 

[The Man]

EDIT:

jsfisher, all you have to do is to get the way I use predecessor and successor in terms of existence.

Doron all you have to do is get that “predecessor and successor” are only aspects of ordering and that a successor is just a predecessor in reverse order.

Also why do you simply not consider negative "existence"? Is it just so you can claim your “Emptiness” has no “predecessor” in some particular ordering?

If you do that maybe, just maybe, you will be able to get out of your and get things like atoms with size > 0.

It’s your box Doron. The ‘indivisible atoms’ as well as the lack of negative values of “existence” are just your own self-imposed limitations.

You still try to get OM as a deductive-only framework.

You still don’t get your own self imposed limitations of your “OM” that you fantasize as some kind of “framework”.

 

[epix]

Are you saying that the equivalent of points in Doronetics have a size? How big are they?

As big as they go.

 

[epix]

Originally Posted by epix
How the heck can you compare anything with something that doesn't exist?

Nothing is not "something that doesn't exist".

I never mentioned the word "nothing." Now it's apparent that when you peruse math literature for inspiration, you see stuff in there that... well, actually doesn't exist in the text.

You are using "that has no predecessor" (Emptiness) and "that has a predecessor" (Existing) in order to conclude that "that has a predecessor" is not "that has no predecessor".

Eat your heart out, zooterkin. I think I caught a bigger fish than you did.

But in order to conclude such a thing you need the axiom of minima and the axiom of existence

I never made a bit of the twisted conclusion only you are capable of.

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

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

Without these axioms you can't conclude that "that has a predecessor" is not "that has no predecessor".

I never attempted any of the suggested conclusion. Things are less than simple:

1. Property axiom: Anything that thinks has brain. (logically identical to the Existence axiom)

2. Posession axiom: Doron has no brain. (logically identical to the Minima axiom)

3.(Conclusion): Doron doesn't think.

You can use Frege symbolism or stick with the current propositional logic symbolism to find out that the conclusion is true and so is the conclusion that Emptiness doesn't exist. And when it doesn't, its property is unknown and therefore not comparable to things that do exist. So your comparison was false.

 

[HatRack]

Try just try to get out of your because there is a universe beyond it, that is blocked by your deductive-only view.

Doron, you should think about becoming a 9/11 twoofer. Their "movement" could really use more people like you. The kind that denies science and logic in the interest of advancing their own warped agenda.

 

[doronshadmi]

Also why do you simply not consider negative "existence"?

Negative existence is a case of existence.

I an talking about predecessor and successor in terms of magnitude of existence, such that Emptiness has no predecessor and Fullness has no successor. Your limited notion gets predecessor and successor only at the level of existing collections of negative, positive, imaginary etc. ids.

It’s your box Doron. The ‘indivisible atoms’ as well as the lack of negative values of “existence” are just your own self-imposed limitations.

There are negative values of existence at the level of collections, as well as complex objects, which are the results of the linkage between indivisible atoms that are cross-contexts or under contexts.

 

[doronshadmi]

unnecessary limitation,

The unnecessary limitation is your inability to get cross-contexts elements, which are non-local and atomic by nature, otherwise they are closed under a given context.

So Doron do you actually have a self-consistent and generally consistent criteria for your "at" such that your " B is at" "A" as well as your "A is at" "B" both use that same criteria and your "at AND not at" is that criteria AND its negation?

No The Man, only a cross-contexts element is at AND not at a given context.

" B is at" "A" as well as "A is at" "B" is closed under a given context.

Once again your limited mind airs its view.

 

[doronshadmi]

I never mentioned the word "nothing"

And this is exactly the problem.

 

[doronshadmi]

Doron, you should think about becoming a 9/11 twoofer. Their "movement" could really use more people like you. The kind that denies science and logic in the interest of advancing their own warped agenda.

You are talking nonsense, deductive-only systems are trivial where real complexity gets on stage.

For example: http://en.wikipedia.org/wiki/Unreasonable_ineffectiveness_of_mathematics .

You belong to a community of anti-evolutionist persons, where "mutations" are not allowed among already agreed terms, so use your anti-scientist propaganda among your own community.

The community of pure mathematicians are like creationists, they do their best in order to ignore existence in order to live in their sterile platonic abstract fantasy universe, where they play like gods by define their isolated axiomatic sterile universes.

This is the way of the cowards that do not take any responsibility on the trivial physical applicative results (like mass destruction weapons, for example) of their sterile games that are blind to the complexity of real life, and like any blind force it can easily be used against its blind users.

HatRack your deductive-only reasoning is a pure poison of blind force.

 

[jsfisher]

You are talking nonsense, deductive-only systems are trivial where real complexity gets on stage.

For example: http://en.wikipedia.org/wiki/Unreasonable_ineffectiveness_of_mathematics .

So, are you just going to throw out the link, or is there something intelligent you can say to show you actually understand the issue being raised?

 

[doronshadmi]

EDIT:

So, are you just going to throw out the link, or is there something intelligent you can say to show you actually understand the issue being raised?

Gelfand ( http://en.wikipedia.org/wiki/I._M._Gelfand ) already said the "something intelligent".

There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology. ( http://en.wikipedia.org/wiki/Unreasonable_ineffectiveness_of_mathematics )

Mathematicians like you can't get it.

 

[jsfisher]

EDIT:



Gelfand ( http://en.wikipedia.org/wiki/I._M._Gelfand ) already said the "something intelligent".



Mathematicians like you can't get it.

You could have just said straight up you don't understand the issue. No reason for this aside.