Deeper than primes

[jsfisher]

Well you are wrong, not-A is not necessarily the complement of A (and I am not talking about Intuitionistic logic).

So you admit the contradiction is intentional. Very convenient for your ideas. All it takes is a single contradiction, than everything, even gibberish, follows.

 

[doronshadmi]

So you admit the contradiction is intentional. Very convenient for your ideas. All it takes is a single contradiction, than everything, even gibberish, follows.

No. You show that by your "nothing more, nothing less" reasoinig does not able to get the "more,less" reasoning, where "nothing more, nothing less" reasoinig is nothing but a single and particuler case of it.

You still do not get the fact that I am talking about the ontological level of logic that enables the very existence of propositions and logical connectives.

 

[jsfisher]

You still do not get the fact that I am talking about the ontological level of logic that enables the very existence of propositions and logical connectives.

You have done nothing to demonstrate you understand the term, ontological. You have a long history of misusing simple terminology, so why should this be any different.

That aside, you are still dodging the basic fact you are founding things on a contradiction. You aver not-A is independent of A. Such things are possible only in Wonderland.

 

[The Man]

Well it looks like were have entered a new Doronophrase phase. Our ‘local only’, ‘serial’ and ‘non-ontological’ ‘thinking’ is now “nothing more, nothing less” and “closed entropic” ‘reasoning’. Too bad Doron does not make an effort to actually understanding the words he uses as opposed to just using them to label the thinking of others.

 

[Little 10 Toes]

Read This: http://en.wikipedia.org/wiki/Cantor%27s_paradox

What you originally said, what I replied to, and what you responded to are three different things.

You orginally said:

Again,

By the standard notion a proper class is a collection that logically cannot be or it is too big in order to be considered as a set.

" Logically can't be " or "Too big" means that it is impossible to define such a collection in terms of set.

Please show me in your original message where you talked about Cantor's Paradox. I never brought it up.

Cantor's Paradox only talks about there is no greatest cardinal number. It does not talk about "a collection that logically cannot be or it is too big in order to be considered as a set". It also deflates your idea that "the full set is definable and proper classes are avoided, simply because only the full set is an actual non-finite". It doesn't matter if you have a finite, an empty, or an infinite set.


Please define the following terms:

• "the magnitude of existence of its members"
• Emptiness
• Intermediate
• Fullness

 

[doronshadmi]

Well it looks like were have entered a new Doronophrase phase. Our ‘local only’, ‘serial’ and ‘non-ontological’ ‘thinking’ is now “nothing more, nothing less” and “closed entropic” ‘reasoning’. Too bad Doron does not make an effort to actually understanding the words he uses as opposed to just using them to label the thinking of others.

You have done nothing to demonstrate you understand the term, ontological. You have a long history of misusing simple terminology, so why should this be any different.

That aside, you are still dodging the basic fact you are founding things on a contradiction. You aver not-A is independent of A. Such things are possible only in Wonderland.

Let us demonstrate your failure to get the ontological basis of Logic.

Let us demonstrate the failure to get the ontological basis of Logic by using the law of contradiction A AND not-A. A represents Emptiness. By the standard reasoning not-A is not-Emptiness where only Emptiness (only A) is considered. In that case Emptiness AND not-Emptiness is a contradiction because Emptiness cannot be empty AND non-empty.

By using an ontological view, not Emptiness has another level of existence, which is not Emptiness. If Emptiness is less, then not-Emptiness is more, so exactly as less AND more define the intermediate level of existence which is more than less AND less than more, so Emptiness AND not-Emptiness define the intermediate level of existence that is more than Emptiness and less than not-Emptiness.

Some claims " "more or less" are not crisp things so less AND more maybe define an intermediate existence which is more than less AND less than more, but it is impossible with a crisp state of existence like emptiness, we cannot define an intermediate state of existence between emptiness AND non-emptiness ".

This argument is wrong because we are using the crisp complement of Emptiness, which is Fullness. So the result of Emptiness AND Fullness is an intermediate level of existence, which is not totally empty AND not totally full. Furthermore, by using the intermediate level of existence as a researchable level, one defines Non-locality and Locality as the signatures of the extreme limits as they appear under the intermediate state of existence. For example: Emptiness is too weak for direct research, where Fullness is too strong for direct research. The intermediate result between Emptiness and Fullness is used to research them indirectly (to find their signature), as follows:

[ ] is a domain that exists at the intermediate level, where [ ] is used to distinguish between in_the_domain, out_the_domain binary states.

empty in [ ] NOR empty out [ ] is a non-local signature of Emptiness w.r.t the domain.

full in [_]_ AND full out [_]_ is a non-local signature of Fullness w.r.t the domain.

empty in [ ]_ XOR full out [ ]_ is a local signature of Emptiness w.r.t the domain.

full in [_] XOR empty out [_] is a local signature of Fullness w.r.t the domain.

By ignoring the difference between Emptiness and Fullness [ ],[_]_ (NOR with AND is NXOR) are reduced to Non-locality, and [ ]_,[_] (XOR with XOR is XOR) are reduced to Locality (we get NXOR\XOR Logic). OM's NXOR\XOR Logic cannot be understood by the standard view of Logic.

So as you see jsfisher AND The Man (jsfisher AND The Man is not a contradiction, because A=jsfisher=The Man="nothing more, nothing less" closed entropic reasoning of A AND A) OM is a new framework that cannot be understood from your "nothing more, nothing less" reasoning, because by your A AND A reasoning you deal only with A (you cannot get the ontological basis of A AND not-A) and as a result A AND not-A is indeed a contradiction by the "nothing more, nothing less" reasoning. But this is your limited closed entropic reasoning, which is definitely NOT OM's reasoning.

 

[jsfisher]

...<snip>...

Still trying to duck the issue I see. You are incapable of addressing the contradiction from your insistence that A and not-A are independent, so instead you continue to obscure things with other contradictions and inconsistencies, generously salted with insult.

Say hello to the Red Queen for us, if you wouldn't mind.

 

[doronshadmi]

You are incapable of addressing the contradiction from your insistence that A and not-A are independent

Please explicitly show this contradiction, and please do it in details.

 

[jsfisher]

Please explicitly show this contradiction, and please do it in details.

You are kidding, right? It was in the very post you quoted. Or did you mean any of your other, numerous contradictions?

 

[zooterkin]

Well you are wrong, not-A is not necessarily the complement of A.

What is it, then?

 

[doronshadmi]

You are kidding, right? It was in the very post you quoted. Or did you mean any of your other, numerous contradictions?

Let us say that I don't get the contradiction.

Since you get the contradiction you can also explicitly show it in detailes by using the post I quoted.

So, please explain it to the people of this forum.

 

[doronshadmi]

What is it, then?

If A is black and not-A is red, then not-A is not the complement of A.

As you see, not-A is not necessarily the complement of A.

I go further than that.

By using the ontological viewpoint of A;not-A I explicitly show how a researchable mathematical universe is exactly the result of complement concepts like Emptiness (A) and Fullness (not-A).

 

[Little 10 Toes]

Let us demonstrate your failure to get the ontological basis of Logic.

So as you see jsfisher AND The Man (jsfisher AND The Man is not a contradiction, because A=jsfisher=The Man="nothing more, nothing less" closed entropic reasoning of A AND A) OM is a new framework that cannot be understood from your "nothing more, nothing less" reasoning, because by your A AND A reasoning you deal only with A (you cannot get the ontological basis of A AND not-A) and as a result A AND not-A is indeed a contradiction by the "nothing more, nothing less" reasoning. But this is your limited closed entropic reasoning, which is definitely NOT OM's reasoning.

Sorry that you don't understand that the phrase "jsfisher AND The Man" does not mean "jsfisher=The Man". I've never taken a logic course or any math/programming classes and even I know that jsfisher does not equal The Man. I also know that The Man does not equal jsfisher.

If we use A as a feature of some object (i.e. "round") then not-A would mean "not-round", but by your logic, you say that not-A would be "the color blue".

"Hey look over there at that round and not-round thing!"
"What thing? You mean this round thing?"
"No, the other round and not-round thing over there."
"This not-round thing?"
"Of course not silly, it's the round and not-round thing right in front of you."
"You mean this blue ball?!?"

Let us say that I don't get the contradiction.

Since you get the contradiction you can also explicitly show it in detailes.

So, please explain it to the people of this forum.

Done!

 

[doronshadmi]

Sorry that you don't understand that the phrase "jsfisher AND The Man" does not mean "jsfisher=The Man".

You did not get it.

I mean that they are using the same reasoning, which prevents form them to get OM's reasoning.


EDIT:

If we use A as a feature of some object (i.e. "round") then not-A would mean "not-round" ...

In the case of "round" AND "not-round" if you are talking about a property of the same object you get a contradiction, which also can be avoided if these proprties are in a superposition with each other, or A is "round" by one research and "not-round by another research. This is, by the way the ontological viewpoint of wavicle.

My main claim is this: Standard logic (where P AND not-P is a contradiction) is a limited and weak framework, that cannot be considered anymore as standard, and should be replaced by another standard, which is more comprehensive (where contradiction is not its main principle).

For example: "full in [_]_ AND full out [_]_ is a non-local signature of Fullness w.r.t the domain" cannot be understood in terms of P AND not-P (the contradiction of Standard Logic).

 

[The Man]

If A is black and not-A is red, then not-A is not the complement of A.

As you see, not-A is not necessarily the complement of A.

I go further than that.

By using the ontological viewpoint of A;not-A I explicitly show how a researchable mathematical universe is exactly the result of complement concepts like Emptiness (A) and Fullness (not-A).

Not ‘A’ or not ‘black’ would also be blue, green, white, yellow ect.. everything that is ‘not black’. By defining ‘A’ as ‘back’ you also define everything else as not ‘A’. We can ‘generalize’ (to correctly use one of Dorons’s favorite words) this consideration by defining what constitutes ‘black’. As far as reflected or emitted spectrums go black is simply the absence of any perceivable spectrum. Not black then becomes the presence of any perceivable spectrum. They are not ‘complements’ they are opposites. In the case of white which is the presence of all perceivable spectrums we could break that down by wavelength, 'A' being up to and including a certain wavelength and not 'A' being anything above that wavelength. In this case 'A' and not 'A' are not opposites but complements. In the first example no spectrum AND all spectrum is a contradiction as they are opposites. In the second example wavelengths lower then and including some cutoff AND wavelengths above that cutoff is not a contradiction but a complementation by resulting in all wavelengths. So it all depends on being very specific about what you are taking about Doron. In fact by asserting that you are not considering 'A' AND not 'A' as being complimentary means that you or considering them as opposites, thus a contradiction. It should also be noted that jsfisher’s point still holds, once you define 'A' you have defined not 'A', they are always mutually dependent whether you are considering them opposites or compliment parts of some whole.


ETA:
Let’s take another example a coin one side defined as ‘heads’ and the other as ‘tails’. A proper coin by that definition must have a ‘heads’ side AND a ‘tails’ side, that is not a contradiction but a complementation of that definition of the sides on a proper coin. For any one flip of the coin the result ‘heads’ AND ‘tails’ is a contradiction while ‘heads’ OR ‘tails’ is a tautology. So again Doron it comes down to being very specific in what you are talking about and using terminology in the applicable context.

 

[doronshadmi]

Not ‘A’ or not ‘black’ would also be blue, green, white, yellow ect.. everything that is ‘not black’. By defining ‘A’ as ‘back’ you also define everything else as not ‘A’. We can ‘generalize’ (to correctly use one of Dorons’s favorite words) this consideration by defining what constitutes ‘black’.

It is not a generalization. All you did is to force A and not-A (that can be interpreted also as two arbitrary different things) to fit to your one A's reasoning.

ETA:
Let’s take another example a coin one side defined as ‘heads’ and the other as ‘tails’. A proper coin by that definition must have a ‘heads’ side AND a ‘tails’ side, that is not a contradiction but a complementation of that definition of the sides on a proper coin. For any one flip of the coin the result ‘heads’ AND ‘tails’ is a contradiction while ‘heads’ OR ‘tails’ is a tautology. So again Doron it comes down to being very specific in what you are talking about and using terminology in the applicable context.

Very good example The Man.

In The Man's example we deal with already existing and researched things, and avoid any ontological viewpoint of the fundamental terms that enable their existence.

Let us follow this limited viewpoint (where Ontology is avoided).

In this case, we have an existing thing, called coin that has two properties.

The properties (called ‘heads’ AND ‘tails’) are observed by flips. Each flip returns one and only one result out of two possible results.

OM calls the ability to return one and only one result out of n possible results, Locality.

Local result A AND not-A is indeed a contradiction, because Locals cannot be simultaneously in more than a one state (as The Man says: "For any one flip of the coin the result ‘heads’ AND ‘tails’ is a contradiction").

But this is not the one and only one way to get A AND not-A.

Alternative 1: A AND not-A is the superposition of the possible results of each flip, and by superposition A AND not-A is not a contradiction.

Since OM uses Distinction as its first-order property, alternative 1 holds at OM.

Alternative 2: The researched thing is non-local. In this case the coin's flip example has to be replaced by another one, for example Line's location.

If we draw a line segment on a particular location that is determined by a point, the line segment is on AND not-on the point, and there is no contradiction because on AND not-on is the very nature of Non-locality (represented by a line segment, in this case) exactly as the coin's flip represents Locality.

Since OM defines Non-locality as one of its building-blocks in addition to Locality, then, again, A AND not-A is not necessarily a contradiction at OM.

----------------------------------------------------------------------------------

Let us carefully research A by using an ontological viewpoint.

A's existence is the result of an interaction of two opposites.

For example, OM's researchable universe is the result of the complementation between Emptiness AND Fullness, where Emptiness is the opposite of Fullness and vice-versa.

The result, called A, is not totally empty AND not totally full, which enables the research.

At this non-total state (A) one defines the concept of collection, which its existence is stronger than Emptiness AND weaker than Fullness.

By using a collection as a research tool, one defines Emptiness as "that has no predecessor" (value 0) and Fullness as "that has no successor" (value ∞).

These values are the magnitudes of existence of the researched and they are taken indirectly by the intermediate level of existence of collection (the non-total state A). These values cannot be defined directly because Emptiness on its own is too weak and Fullness on its own is too strong.

At A one defines the researchable states of Locality AND Non-Locality, where Locality AND Non-locality are mutually independent of each other, and together they are used in order to define A's researchable universe.

At A's researchable universe, P AND not-P is necessarily a contradiction iff P is Local.

Jsffisher's and The Man's "nothing more, nothing less" reasoning must be local, because P is "nothing more AND nothing less" (nothing beyond P is researched and we get a closed entropic reasoning that is too weak in order to deal with Non-locality or Distinction as its first-order properties).

 

[jsfisher]

If A is black and not-A is red, then not-A is not the complement of A.

If A is black, then not-A isn't red. Try again.

On the other hand, if you really, really, meant something else entirely, like for example, B is an element of not-A, then that's different. Of course, that isn't what you said. What you said, like most things you have said, was an outright contradiction. Did you really mean to let A be something and let B be something different from A?

Well, ok, laying aside the gibberish, what's the point? Why can't B just be a free variable like A? What advantage was gained by puncturing the proper class of possibilities for B?

Moreover, and this is key, since now there are proper classes in your premises, you are in no position to conclude you avoided proper classes.

You just cannot speak without contradiction, can you?

 

[The Man]

It is not a generalization. All you did is to force A and not-A (that can be interpreted also as two arbitrary different things) to fit to your one A's reasoning.

“can be interpreted also as two arbitrary different things”, only by the ignorant.

Very good example The Man.

In The Man's example we deal with already existing and researched things, and avoid any ontological viewpoint of the fundamental terms that enable their existence.

Let us follow this limited viewpoint (where Ontology is avoided).

In this case, we have an existing thing, called coin that has two properties.

The properties (called ‘heads’ AND ‘tails’) are observed by flips. Each flip returns one and only one result out of two possible results.

OM calls the ability to return one and only one result out of n possible results, Locality.

Local result A AND not-A is indeed a contradiction, because Locals cannot be simultaneously in more than a one state (as The Man says: "For any one flip of the coin the result ‘heads’ AND ‘tails’ is a contradiction").

But this is not the one and only one way to get A AND not-A.

Alternative 1: A AND not-A is the superposition of the possible results of each flip, and by superposition A AND not-A is not a contradiction.

Since OM uses Distinction as its first-order property, alternative 1 holds at OM.

Alternative 2: The researched thing is non-local. In this case the coin's flip example has to be replaced by another one, for example Line's location.

If we draw a line segment on a particular location that is determined by a point, the line segment is on AND not-on the point, and there is no contradiction because on AND not-on is the very nature of Non-locality (represented by a line segment, in this case) exactly as the coin's flip represents Locality.

Since OM defines Non-locality as one of its building-blocks in addition to Locality, then, again, A AND not-A is not necessarily a contradiction at OM.

----------------------------------------------------------------------------------

Let us carefully research A by using an ontological viewpoint.

A's existence is the result of an interaction of two opposites.

For example, OM's researchable universe is the result of the complementation between Emptiness AND Fullness, where Emptiness is the opposite of Fullness and vice-versa.

The result, called A, is not totally empty AND not totally full, which enables the research.

At this non-total state (A) one defines the concept of collection, which its existence is stronger than Emptiness AND weaker than Fullness.

By using a collection as a research tool, one defines Emptiness as "that has no predecessor" (value 0) and Fullness as "that has no successor" (value ∞).

These values are the magnitudes of existence of the researched and they are taken indirectly by the intermediate level of existence of collection (the non-total state A). These values cannot be defined directly because Emptiness on its own is too weak and Fullness on its own is too strong.

At A one defines the researchable states of Locality AND Non-Locality, where Locality AND Non-locality are mutually independent of each other, and together they are used in order to define A's researchable universe.

At A's researchable universe, P AND not-P is necessarily a contradiction iff P is Local.

Jsffisher's and The Man's "nothing more, nothing less" reasoning must be local, because P is "nothing more AND nothing less" (nothing beyond P is researched and we get a closed entropic reasoning that is too weak in order to deal with Non-locality or Distinction as its first-order properties).

Well besides your normal misuse of terminology and word salad, I’ll just comment on a couple of key points. Superposition in mathematical terms is just a linear addition. You seem to continue to confuse the addition inference of ‘and’ with the logical conjunctive function of ‘AND’. The probability of getting ‘heads’ on any one flip is 50% as is the probability of getting ‘tails’. A superposition of these outcomes (50% + 50%) gives us a 100% probability that there will be an outcome of ‘heads’ or ‘tails’. Were this to be a ‘superposition’ of opposites as you claim your ‘emptiness’ and ‘fullness’ are the probability of one would be say 50% and the other -50%. The resulting superposition would be a 0% probability of one or the other of those outcomes. This type of event or outcome suppression is not unusual in quantum mechanics where the superposition of wave functions (or probability amplitudes) is a fundamental feature. The superposition of equal opposites results in 0 the superposition of all the complements that make up a whole (some of which could be opposing, equal or not) results in that whole. In fact if we do a superposition of your ‘measurement of existence’, 0 for your ‘emptiness’ and ∞ for your ‘fullness’, we get 0 + ∞ = ∞ or just your ‘fullness’.

Your notion about lines and points is also flawed, as usual. A point is either on a line or it is not and the line either includes that point or it does not. The phrase “the line segment is on AND not-on the point” is just your typical non specific nonsense. A line segment is not ‘on’ a point although the point might be on that line segment.

 

[doronshadmi]

A superposition of these outcomes (50% + 50%) gives us a 100% probability that there will be an outcome of ‘heads’ or ‘tails’.

For a contradiction we need 100% probability for A AND 100% probability for not-A, where A is Local.

Let us say that A is local (for example: the coin's flip example). Since each flip has 50% probability for A ('heads') AND 50% probability for not-A ('tails') under superposition, we do not have a contradiction under flip's superposition, because:

50% probability for A ('heads') AND 50% probability for not-A ('tails') = flip's superposition

Is NOT

100% probability for A ('heads') AND 100% probability for not-A ('tails') = flip's contradiction.

In other words, thank you The Man for helping to support my argument.

(by the way, 50% probability for A ('heads') AND -50% probability for not-A ('tails')(or vice versa) = no flip is tended to collapse to a 100% actual result of A ('heads') OR not-A ('tails') local result)

Were this to be a ‘superposition’ of opposites as you claim your ‘emptiness’ and ‘fullness’ are the probability of one would be say 50% and the other -50%.

No, the intermediate result that is not 100% empty AND not 100% full enables us to research, in the first place. You mix between the ontological foundations of the researchable (which are Emptiness and Fullness) and some existing researchable result, where a researchable result must be more than 100% empty AND less than 100% full, otherwise it is not researchable. The magnitude of existence of Emptiness (value 0) or Fullness (value ∞) can be defined only indirectly, by using, for example an existing tool like set, that its magnitude of existence is more than 100% Emptiness (more than 0) AND less than 100% Fullness (less than ∞).

In fact if we do a superposition of your ‘measurement of existence’, 0 for your ‘emptiness’ and ∞ for your ‘fullness’, we get 0 + ∞ = ∞ or just your ‘fullness’.

0 is not Emptiness and ∞ is not Fullness. The intermediate ontological result that is not 100% empty AND not 100% full enables us to indirectly research (by using a set) the magnitude of the existence of Emptiness (value 0) and the magnitude of the existence of Fullness (value ∞). Also ∞ (the magnitude of exitence of Fullness) is not ∞ (the magnitude of existence of a non-finite collection).

In other words The Man, you simply do not understand with what you deal here, and make a word salad out of it.

-------------------------------------------------------------------------------

Now, let us check what you have to say about the Line\point example.

Your notion about lines and points is also flawed, as usual. A point is either on a line or it is not and the line either includes that point or it does not. The phrase “the line segment is on AND not-on the point” is just your typical non specific nonsense. A line segment is not ‘on’ a point although the point might be on that line segment.

Here you trivially and artificially force the local view of Line\point interaction ("A point is either on a line or it is not and the line either includes that point or it does not.") and brutally ignore the non-local view of this interaction, which is (by basically using your example):

"A line is (on the point) AND (not the point) and it does not include the point, because it is an atom, exactly as the point is an atom (the line and the point ar not derived from each other).


In other words The Man, you simply do not understand with what you deal here, and make a word salad out of it.

-------------------------------------------------------------------------------


In general, you are a living proof of why standard reasoning is too weak in order to deal with OM's reasoning.

 

[doronshadmi]

Some correction of my previous post:

Instead of:

"A line is (on the point) AND (not the point) and it does not include the point, because it is an atom, exactly as the point is an atom (the line and the point ar not derived from each other).

it has to be:

"A line is (on the point) AND (not on the point) and it does not include the point, because it is an atom, exactly as the point is an atom (the line and the point ar not derived from each other)."