Mathematics ends in meaninglessness: 6 reasons

#1
Mathematics ends in meaninglessness: 6 reasons
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Mathematics ends in meaninglessness: 6 reasons

1) an integer = a non-integer
2) 1+1=1
3) ZFC ends in contradiction: Axiom of separations bans itself-thus mathematics is inconsistent
4) Mathematicians dont know what a number is -without be impredicative
5)Mathematics is just a bunch of meaningless symbols connected by rules: Formalism-to avoid the pitfalls of Carroll’s Paradox
6) a 1 by 1 root 2 triangle is an impossibility
 
#2
Hey M, great post!

My suspicion here is that Psychologist Dean is committing what is called an Appeal to Plenitude.

The Appeal to Plenitude/Boundary Condition/Semantics
Afford me the miracle of a plea into infinity, and I can prove anything, or render anything absurd.
Bounce your critical logic off of a boundary condition and it will come back in a completely different form.
Love, art, music, consciousness therefore are absurd because I cannot reconcile them with my lexicon discipline.

1) 1 = .99999999... This is true by the nature of mathematical lexicon. But a lexicon is only our artifice approximating the nature of reality. However an infinite number of 9's is what is called 'plenitude' (or possibly a 'boundary condition', depending upon one's philosophy).

Any logical predicate which allows me to appeal into infinity (or boundary condition) as the basis of my argument, is unsound as a line of reasoning. It is pseudo-theory, because I can prove literally anything if you allow me to use infinity as my alternative resource.

2) 1 number + 1 number = 1 number This is called equivocation. Again psychologist Dean is ascribing natural equivalent to our approximating lexicon. Just because I cannot describe love, does not mean that it is absurd and therefore does not exist. The world around us is not enslaved to our (useful but not complete) lexicon.

3) Zermelo–Fraenkel set theory contradicts itself (by excluding urelements) Again, by making plea into urelements (elements of sets that are not themselves sets - which includes itself - which is plenitude) as a logical critical path, one has to appeal to plenitude in order to take a philosophical-only set and ascribe to it a literal (and therefore a very useful-as-equivocal) meaning as a Wittgenstein logical object.

To Wittgenstein, infinity is not a logical object. [Note: https://plato.stanford.edu/entries/wittgenstein-atomism/]
Of the seven schools of objective philosophy - Empiricism Logicism Formalism Intuitionism Naturalism Nominalism Structuralism - only one (possibly) regards infinity as a logical object - which could then be employed in a critical path syllogism such as the ZFS contradiction.
4) Mathematics is not the language of the universe The absurdity of the nature of a boundary condition - absolutely valid. A lexicon cannot comprehensively describe a boundary condition - and furthermore, cannot approach an element which exists outside that boundary condition - nor distinguish the two. This is part of the prison in which we reside. :) Don't drop your soap in the shower.

5) Mathematics is a lexicon - and a lexicon is never complete. Valid, but since this critique applies to literally EVERYTHING in our realm, it is what is called in philosophy a pseudo-argument. Our very existence is absurd, and given an appeal to plenitude, I can prove right now, by lexicon and procedure, that neither you nor I exist. This is not useful however.

6) The SQRT(2) = 1.41421356... is infinite as an identifiable set, yet the boundary of the triangle represented by it is a discrete and finite measure. Again, this is citing the mismatch between lexicon and utility (known as semantics). Math is a lexicon, it is not a comprehensive descriptive. Our universe is discretely bounded by what is called a Planck Interval. Everything is discretely bounded. Math is unbounded appeal to plenitude, i.e. math - reality is discrete and never fully continuous.

Literally every single principle, with the exception of possibly consciousness - will suffer the 'fallacy of meaninglessness' which Mr. Dean has cited here.

All Mr. Dean has done here is to Touch the Sky (plenitude, boundary, absurdity of lexicon) - and to touch that boundary 6 times.

“For the World is Hollow and I have Touched the Sky” was one of my favorite Star Trek episodes (although by this time well into syndication), not only from the perspective that Dr. McCoy got it on with some hott alien chick, but also because this issue was touched. In the plot, a man crawls to the end of the ‘sky’ and touches it, only to find it a tactile boundary, a dome of deception – the sense of which drove him to an insanity of just desserts for violating the strictures of the ‘god’ which ruled their planet and forbade such arrogance – as asking questions.
 
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#3
However, one must note that the principle of semantics and boundary, although providing for analogue between Maths and Love, is indeed an inversion when compared logically... In Maths, the lexicon principles (laws) themselves exist in a Suprareality - with its imprecise application here, whereas with Love, it exists (its laws??) in a Suprareality and its imprecise lexicon exists here in our reality.

This is a very strong argument (inductive inference) for 'something else' - It is the counter to Nihilism as Religion - which Nietzsche missed.

love and mathematics.png
 
#4
Wow - this is going seriously above my head, but since I am probably not the least mathematically aware person on this forum, I think it would be fantastic for many people if you could unpack some of this a bit more - with simple examples. I mean skimming the linked PDF, I find
Again most say the most certain of things is 1+1= 2
but 1 number + 1 number = 1 number 1 number (10) + 1 number (20) = 1 number (30) 1 chemical (na sodium) = 1 chemical (cl chloride ) = 1 chemical (nacl salt) thus maths ends in contradiction ie meaninglessness
That sounds trite on the face of it, but perhaps it was a clever way of saying something important - if you get it, please explain it in the simplest and most direct way possible!

I am reminded of Gödel's theorem, which seems to span the boundary between things I know about maths, and the infinity of things that I do not know. It says that given a set of axioms complex enough to describe integer arithmetic, there will be 'undecidable' statements that can't be proved true or false - so you can flip a coin to select one of two equally valid ways to extend mathematics by adding the problematic statement as an extra axiom, or by adding the negation of the statement as an axiom. The new, enlarged axiom set will have its own undecidable statements, so this process never terminates. (I hope I didn't garble that too much!).

David
 
#5
That sounds trite on the face of it, but perhaps it was a clever way of saying something important - if you get it, please explain it in the simplest and most direct way possible!
IMHO shot at it David, Re: the 1 number + 1 number = 1 number therefore a problem in maths.

Dean illuminates his apparent contradiction with an example thankfully (which is skin in the game, so I respect that)

The Australian leading erotic poet philosopher colin leslie dean points out 1+1=1
a. get a salt shaker pour out one heap of salt on the left
b. pour out one heap of salt on the right
- You have 1 and 1
c. now push the 2 heaps together (ie we add them together)
- now what have we we have one heap of salt in the middle
thus 1+1=1 thus a contradiction in maths thus maths ends in contradiction ie meaninglessness-
Dean here is equivocating between set theory and mathematics. The statement in blue is the magician's sleeve. The sleight-of-hand. They are not the same thing, even though they employ the same symbols. So this is technically an equivocation in philosophy. A 'Union of sets' and a 'reduction lexicon of 1 + 1' are not the same thing. A ∪ B not≅ X(A) + Y(B)

A union B is still a 'set of 2', when used in the context of 1 add 1 = 2.

A union B as an entity (logical object) however is a NEW set, not a reduced version (mathematical) of the old sets.

Mathematics is reductive, it does not on its own create new entities. Set theory is constructive, so it can and does.

 
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#6
IMHO shot at it David, Re: the 1 number + 1 number = 1 number therefore a problem in maths.

Dean illuminates his apparent contradiction with an example thankfully (which is skin in the game, so I respect that)

The Australian leading erotic poet philosopher colin leslie dean points out 1+1=1
a. get a salt shaker pour out one heap of salt on the left
b. pour out one heap of salt on the right
- You have 1 and 1
c. now push the 2 heaps together (ie we add them together)
- now what have we we have one heap of salt in the middle
thus 1+1=1 thus a contradiction in maths thus maths ends in contradiction ie meaninglessness-
Dean here is equivocating between set theory and mathematics. The statement in blue is the magician's sleeve. The sleight-of-hand. They are not the same thing, even though they employ the same symbols. So this is technically an equivocation in philosophy. A 'Union of sets' and a 'reduction lexicon of 1 + 1' are not the same thing. A ∪ B not≅ X(A) + Y(B)

A union B is still a 'set of 2', when used in the context of 1 add 1 = 2.

A union B as an entity (logical object) however is a NEW set, not a reduced version (mathematical) of the old sets.

Mathematics is reductive, it does not on its own create new entities. Set theory is constructive, so it can and does.

So does that muddle manifest itself in some significant real world cases?

David
 
#7
So does that muddle manifest itself in some significant real world cases?

David
Ehhhh... not that I am aware. :eek: When Dean laid it out - that was the first I had ever seen this formal fallacy committed.

And now that you bring it up David - I could actually document it as a formal fallacy, but I am not sure that I will ever encounter it again. LOL!!
 
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#8
So does that muddle manifest itself in some significant real world cases?

David
Actually, now that I think of it, it might - applied in the inverse to Dean's magician's sleeve above.

The Lottery Ticket Scam - two co-workers pool their money to buy 10 lottery tickets (a set of 1). Only one of the co-workers is assigned to journey to the Mighty Mart and obtain the lottery tickets. When he arrives back at the workplace, the other co-worker who stayed behind asks, 'How'd we do?' To which the ticket buying co-worker replies, "Fantastic, but unfortunately all your tickets lost." (1 = 5 + 5)

:D
 
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