Dear Anna, What you say is too contrived to be true! Would you let your child to choose the road that leads to her being for example kidnapped, while ...
I didn't claim an absolute platonic approach to mathematics, definitely not. But it appears to me that once we get to think about some mathematical pr...
Honestly I think its both cases. Some structures were actually contemplated due to their own beauty in a platonic world, while others raised secondary...
I don't see where you differ with me. Mathematics can also speak of patterns that had not been yet observed! Because it tackle all possible structures...
Its nice to be informed of that. But my knowledge about those issues is damn sketchy. And so I have no say in such subjects. Thanks for your informati...
That's not what I've asked about in my last comment. I wanted to know how the "uncertainty principle" is the error of applying an unsound mathematical...
Oh! but that's cornerstone in Quantum mechanics, isn't it? I always hear about a lot of strange conclusions in quantum theory like all possible worlds...
I never admitted that they are not sound. They are indeed sound of what they are describing in the platonic sense. And if platonic sense proves to be ...
If you are working within a FINITE fragment of ZFC, then the result is always arithmetically SOUND (that if ZFC is consistent). It's a matter of techn...
No! not always, if the proof is carried in a FINITE fragment of ZFC, and the proved statement is an arithmetical statement, then this is already known...
I just want to give an example of a sentence that is highly related to the finite mathematics, that can find a solution in a system that speaks of inf...
It is not enough to point it as bad, with mathematics you must demonstrate an alternative system with superior utility, something that is better. Once...
I find myself in full agreement with what you said! However, I do think that imperfections would sooner or later show themselves, no matter how much u...
Yes, I would agree with that of course. But it need not be so really. The issue here is that if we have something useful, even if it is not the best, ...
I'll put this as a separate reply. Because it speaks about role 1 (see prior comments). Now role 1 is the real issue. Because role 2 is not fundamenta...
It is sound! because it is the pure conclusion of the original sound theory. I'm just using theory A as a facilitator and then I'm checking it again i...
*stronger* is a logical term. Theory A is stronger than theory B if and only if every statement provable in B is provable in A, but not every statemen...
Unfortunately you are not following what I'm saying. I'm speaking of two roles that a stronger theory (deductively speaking) can play. The FIRST role ...
It doesn't matter whether its makes sense in relation to the real physical world or not! The point is that it can serve as a strong reducer of proof l...
I read all of the above account of yours carefully. It is really nice. I should say that it added a lot to my knowledge. So Thank you for that. There ...
Hi Metaphysician Undercover! I also cannot understand what you've wrote. I think we are departing a part. My argument was a very simple argument. I wa...
This is indeed a very big subject. And what you've said is reputable. Indeed some imminent mathematicians took that stance, and even a much more aggre...
I'm not really sure of that? But as part of history of mathematics, mathematics prior to the 19th century were very cautious when speaking about the i...
Yes. Actually I find myself in total agreement with what you said in this particular last comment. Of course we are speaking about mathematics judging...
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 al...
Yes, I think there is an intermediate position. Mathematics is producing rule following obedient fictional objects and scenarios. However, those happe...
You can! The hierarchy would be more of a mold, a frame, that suites a generality purposes. Of course in the particular application the hierarchies wo...
You Can! if your aim was to FOUND (i.e., lay the basis for) matters with. We leave "tight" and "loose" like blanks to be filled with the relevant appl...
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. Perhaps you mea...
As attractive as it sounds, this proves to be extremely difficult. Experience along such lines are moot. Its hopeless. Without a hierarchy of sets, or...
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 ...
Actually from experience with mathematics. We do need a hierarchy of sets. The other alternatives are not so promising. I find temporal versus spatial...
Well I do agree that having a common description imply some material connection, but that connection is not the connection that imply inseparability. ...
My outcast is descriptive, while your's is largely etiologic! Collections can be fairly described and recognized up to identity without resorting to a...
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...
I never said that, nor did I claim it. Actually what I said refutes that! You didn't correctly understand what I was saying! I cannot agree more! Of c...
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 totalitie...
Not it doesn't. Because it doesn't meet the definition of ">", here is the definition: X > Y if and only if there is an injection from Y to X, but the...
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 (...
So in your sense if I bought two applies today, then I only have two objects, that is the apples themselves, there is no other object that is the tota...
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...
Hmmm.. I see the confusion here, OK, when I said a relationship between tribe(s), I only meant that each of its arguments is a tribe. That's all. It d...
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. To complicate the situation we may even ...
No! you are confusing matters. Notice my original statement: Notice the "if and only if", the above statement is a DEFINITION of "||". Notice that it ...
Yes, I'm refusing this. "AND" here is "logical conjunction", it specifically means a function from the truth value of each statement linked by "AND" t...
Not it is NOT justified! Because we are using the "AND" in the GENERAL case of definition of marriage between any tribes A,B (whether A, and B are the...
Honestly I failed to see the "equivocation" you are referring to. "S" represents the WHOLE tribe, it represent all 50 woman and 50 men, i.e. it repres...
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