Define "less than", "considered thing", and "absolute sense". "have" technically needs to be defined too since this is clearly not standard set theory, but I'll accept it as a primitive notion.
Deeper than primes
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Define "less than", "considered thing", and "absolute sense". "have" technically needs to be defined too since this is clearly not standard set theory, but I'll accept it as a primitive notion.
[latex]$$\sqrt{2} = \left \{ x \in Q : x^2 < 2 \lor x < 0\right \}$$[/latex]
Doron, your complete misunderstanding as to what this mathematical statement means is... I simply have no words.
doronshadmi
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On the contrary, you are using too many words and notations, until you do not understand the notions at the basis of them.
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doronshadmi
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An example of "less than" and "absolute sense":
-1 is less than 1 in the relative sense.
Emptiness is less than -1, 1 and 0 in the absolute sense.
"considered thing" is any abstract or non-abstract discussed subject.
"have" means that some abstract or non-abstract discussed subject is determined by a given property.
I never thought I'd see Doron Shadmi, the author of posts such as this one (http://www.internationalskeptics.com/forums/showthread.php?postid=4083359), accuse someone else of using too many words and notations.
Alright I'll take "have" and "considered thing" as primitive notions. But I will not accept "less than" and "absolute sense" as primitive notions. And I did not ask for examples of them, I asked for definitions. Please define the two terms "less than" and "absolute sense".
doronshadmi
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I never thought I'd see Doron Shadmi, the author of posts such as this one (http://www.internationalskeptics.com/forums/showthread.php?postid=4083359), accuse someone else of using too many words and notations.
These are particular examples on new notions that are not compressed yet into a compact representation of these notions.
On the contrary, your already agreed compact representation of your community, fails to formally define a framework, where any member of a set is also a set, and {} is a simple example of this failure.
Genreally HatRack, you are unable to discuss about a given subject, if it not first formalized. By this behavior you miss the understanding of the notions before they are formally addressed.
How long have you been working on this "subject" of Doronetics again, and you still don't have it formalized?
doronshadmi
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Hilbert did not define "point" and "line", when he re-wrote Euclid's axioms.
Furthermore he did not provide any example of what "point" or "line" are in order to
Leave these concepts the be relatively be changed under some context-dependent axiomatic framework.
On the contrary I explicitly gave you examples of "less than" and "absolute sense":
-1 is less than 1 in the relative sense.
Emptiness is less than -1, 1 and 0 in the absolute sense.
These examples are cross-contests, and therefore are fundamentally different than Hilberts context-dependent treatment of concepts like "line" and "point".
If you try to follow after Hilberts context-dependent treatment, you are going to fail to understand my cross-contexts treatment of concepts like "less than" and "absolute sense".
Furthermore he did not provide any example of what "point" or "line" are in order to
Leave these concepts the be relatively be changed under some context-dependent axiomatic framework.
On the contrary I explicitly gave you examples of "less than" and "absolute sense":
-1 is less than 1 in the relative sense.
Emptiness is less than -1, 1 and 0 in the absolute sense.
These examples are cross-contests, and therefore are fundamentally different than Hilberts context-dependent treatment of concepts like "line" and "point".
If you try to follow after Hilberts context-dependent treatment, you are going to fail to understand my cross-contexts treatment of concepts like "less than" and "absolute sense".
That's fine with me that point and line are undefined. The intuitive meaning of those concepts in synthetic geometry is obvious to even small children. You, however, have an entire slew of undefined terms, whose meanings seem to shift around from post to post. Add that to the fact that you're using numbers without ever having defined them in your framework.
Set theory accomplishes a great many things quite well, and uses a single undefined term (set). You seem to be one of the only people in the world who has a problem with it. Furthermore, you've yet to demonstrate a single advantage of Doronetics over set theory. In fact, all we've seen so far is disadvantages (we lose the ability to take derivatives and integrals).
doronshadmi
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HatRack, the concept of "formalization" is one of the discussed subjects here.
You automatically understand "formalization" as deductive-only and context-dependent framework.
I disagree with this automatic notion, so it takes time to re-establish new notions of the very concept of "formalization", and it is done at the philosophical level which is a meta level of discussion about the mathematical science and its current formal techniques.
You and your friends do not do any step out of your already agreed box of deductive-only and context-dependent framework, in order to re-examine it from the philosophical level, and as a result there cannot be any communication between us.
EDIT: Once again, this is a philosophical forum. If you don't wish or simply can't re-examine Mathematics from a philosophical level, then simply say it loud and clear, I'll continue to deal with this subject at the philosophical level (at least at this stage), but then you and me do not have any meaningful thing to discuss about.
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No Doron. You are masquerading your nonsense under the guise of philosophy. Make no mistake, it's painfully obvious to everyone who posts here that you are a crank who is in desperate need of attention for his "theories". That's fine, you get your attention, we get our laughs. And picking out all of the blunders and ignorance in your arguments makes me all the better at mathematics in the process. It's a symbiotic relationship.
The reason we call for formalization is because your informal, "philosophical" arguments make no sense to any of us at all. Yet, you refuse to adopt a level of formalism that would allow us to carefully examine this "theory" of yours. So, that leaves us with the possibility that maybe you do have some good ideas, but you are just terrible at communication. There are two things however, from a purely philosophical perspective, that indicate this is not the case:
- You have not demonstrated a single application of your "theory" to anything useful. Again and again, you claim that your "theory" bridges the gap between logic and ethics and will lead to a better world. However, we have yet to hear a single, specific application of what this "theory" could do that traditional mathematics and science cannot. Considering you've been working on this "theory" for 20+ years now as you claim, it looks pretty pathetic that there is not one single project that you've carried out which demonstrates its usefulness.
- You do not understand traditional mathematics, the very thing you claim which is wrong. Consistently, you have demonstrated that you do not comprehend the precise definitions behind many fundamental concepts which you bring up in your arguments again and again (circular reasoning, cardinality, first-order logic, limits of sequences, construction of the reals, diagonal argument). In order for anyone to give your "theories" any chance, you have to establish some credibility by showing that you understand traditional mathematics and can thus correctly characterize any problems with it. But, since you have not demonstrated any credibility, that leaves us with the conclusion that you are simply too cognitively deficient to understand mathematics, and that you use your "theories" as a way of feeling better about yourself because you don't like to think of yourself as a dunce.
Finally, instead of actually accepting that you've been bested when you've been completely backed into a corner, you make up more false claims to cover your previous false claims, or use the
icon and claim that others are not open-minded enough to accept your claims.doronshadmi
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I disagree with you, small children get a line as an indivisible object which exists simultaneously in AND out of a given domain like a circle, for example.
The context-dependent step-by-step deductive only approach of your community can't comprehend it.
Set theory accomplishes a great many things quite well, [/QUOTE]
Please define the member of {} as set.
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doronshadmi
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No Doron. You are masquerading your nonsense under the guise of philosophy. Make no mistake, it's painfully obvious to everyone who posts here that you are a crank who is in desperate need of attention for his "theories". That's fine, you get your attention, we get our laughs. And picking out all of the blunders and ignorance in your arguments makes me all the better at mathematics in the process. It's a symbiotic relationship.
The reason we call for formalization is because your informal, "philosophical" arguments make no sense to any of us at all. Yet, you refuse to adopt a level of formalism that would allow us to carefully examine this "theory" of yours. So, that leaves us with the possibility that maybe you do have some good ideas, but you are just terrible at communication. There are two things however, from a purely philosophical perspective, that indicate this is not the case:
- You have not demonstrated a single application of your "theory" to anything useful. Again and again, you claim that your "theory" bridges the gap between logic and ethics and will lead to a better world. However, we have yet to hear a single, specific application of what this "theory" could do that traditional mathematics and science cannot. Considering you've been working on this "theory" for 20+ years now as you claim, it looks pretty pathetic that there is not one single project that you've carried out which demonstrates its usefulness.
- You do not understand traditional mathematics, the very thing you claim which is wrong. Consistently, you have demonstrated that you do not comprehend the precise definitions behind many fundamental concepts which you bring up in your arguments again and again (circular reasoning, cardinality, first-order logic, limits of sequences, construction of the reals, diagonal argument). In order for anyone to give your "theories" any chance, you have to establish some credibility by showing that you understand traditional mathematics and can thus correctly characterize any problems with it. But, since you have not demonstrated any credibility, that leaves us with the conclusion that you are simply too cognitively deficient to understand mathematics, and that you use your "theories" as a way of feeling better about yourself because you don't like to think of yourself as a dunce.
Finally, instead of actually accepting that you've been bested when you've been completely backed into a corner, you make up more false claims to cover your previous false claims, or use the
This is nothing but another attempt to cover your inability to complehend http://www.internationalskeptics.com/forums/showpost.php?p=6667634&postcount=13318 , http://www.internationalskeptics.com/forums/showpost.php?p=6686934&postcount=13448 and http://www.internationalskeptics.com/forums/showpost.php?p=6692863&postcount=13479.
Your pathetic
airs its limited view all along our discussion.For example, you are unable to demonstrate how exactly the member of {} is a set.
If you can't do that, then your set's only framework does not have any rigorous formal foundation.
There is even no reason to laugh about pathetic limited thinker like you, maybe at best mercy fits in your case.
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I'll tell you what, let's get a sample group of small children, and WITHOUT feeding them any of your nonsense beforehand, we'll show each one a line and have them answer the question "Are there any gaps or holes in this line?". But you wouldn't agree to that study, would you? You know full well that not even small children, who have no exposure to Doronetics, would agree that there are gaps in the line.
doronshadmi
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There are no page or holes along a line exactly becuse a line exists even no sub-objects exist along it.
This property the fact that its size > 0 , gives it the ability to be in AND out of a given domain.
Again your collection-only notion fails you.
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Your patheticFinally, instead of actually accepting that you've been bested when you've been completely backed into a corner, you make up more false claims to cover your previous false claims, or use the
Proof that Doron doesn't actually read people's posts.
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Do you agree that any line segment can be measured with a ruler?
doronshadmi
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of his own state of mind.doronshadmi
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Do you agree that a line segment exists in AND out of a given domain (a circle, for example) even if it is not measured with a ruler?
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