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Mathematician: know thyself
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David Petry
2018-02-12 18:07:13 UTC
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"Know thyself. People make themselves look ridiculous when they try to know obscure things before they know themselves"
-- Plato attributes this to Socrates


It's been over a quarter of a century now that I've been promoting an idea that I think is very important. It's revolutionary. Here's the idea:


We (mathematicians) can and should view mathematics as the language of science. Especially, we should use that as a guiding principle when reasoning about the foundations of mathematics.

Modern pure mathematics is deficient as a language of science. In particular, the subject we call the foundations of mathematics is missing two key ideas:

1) Falsifiability is the cornerstone of scientific reasoning, and it can and should be formalized and integrated into the logic of mathematics.

2) Reasoning under uncertainty. Scientific reasoning always takes uncertainty into consideration. So reasoning under uncertainty should be viewed as the foundational logic of mathematics.

The reason mathematicians rejects those two ideas is, evidently, because they cling to Cantor's theory of infinity, which is incompatible with those ideas.

When I studying mathematics in graduate school, I wanted to work in the field of the foundations of mathematics, and the idea I wanted to work on was to build a foundation for mathematics that is built upon those two ideas--falsifiability, and reasoning under uncertainty. My claim is that such a foundation for mathematics would serve as a foundation for artificial intelligence, and would be a major advance in that field.

I was surprised by the mathematicians' reaction to what I was proposing. Especially on the internet! Besides suggesting the idea is a crank idea, they sometimes would accuse me of believing I am channeling God, or other silly things like that.

It only recently occured to me that I should respond by pointing out exactly where my ideas are coming from. They come from self knowledge. That is, as intelligent beings, we can make progess in understanding ourselves. We can understand how we reason about what we call reality. And so my radical claim is that mathematics should be consistent with our understanding of ourselves, and especially, how we reason about reality. And Cantor's theory of infinity fails that criterion.
John Gabriel
2018-02-12 20:57:23 UTC
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Post by David Petry
"Know thyself. People make themselves look ridiculous when they try to know obscure things before they know themselves"
-- Plato attributes this to Socrates
We (mathematicians) can and should view mathematics as the language of science. Especially, we should use that as a guiding principle when reasoning about the foundations of mathematics.
1) Falsifiability is the cornerstone of scientific reasoning, and it can and should be formalized and integrated into the logic of mathematics.
2) Reasoning under uncertainty. Scientific reasoning always takes uncertainty into consideration. So reasoning under uncertainty should be viewed as the foundational logic of mathematics.
The reason mathematicians rejects those two ideas is, evidently, because they cling to Cantor's theory of infinity, which is incompatible with those ideas.
When I studying mathematics in graduate school, I wanted to work in the field of the foundations of mathematics, and the idea I wanted to work on was to build a foundation for mathematics that is built upon those two ideas--falsifiability, and reasoning under uncertainty. My claim is that such a foundation for mathematics would serve as a foundation for artificial intelligence, and would be a major advance in that field.
I was surprised by the mathematicians' reaction to what I was proposing. Especially on the internet! Besides suggesting the idea is a crank idea, they sometimes would accuse me of believing I am channeling God, or other silly things like that.
It only recently occured to me that I should respond by pointing out exactly where my ideas are coming from. They come from self knowledge. That is, as intelligent beings, we can make progess in understanding ourselves. We can understand how we reason about what we call reality. And so my radical claim is that mathematics should be consistent with our understanding of ourselves, and especially, how we reason about reality. And Cantor's theory of infinity fails that criterion.
Mathematics is about well-formed concepts or noumena. That is what one needs to understand. Also, sound mathematics exists independently of the human mind or any other.
Jens Stuckelberger
2018-02-12 22:13:36 UTC
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Post by David Petry
Modern pure mathematics is deficient as a language of science. In
particular, the subject we call the foundations of mathematics is
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Notice that, these days, some in the string theory camp have
expressed a willingness to dispose of this criterion.
Post by David Petry
2) Reasoning under uncertainty. Scientific reasoning always takes
uncertainty into consideration. So reasoning under uncertainty should be
viewed as the foundational logic of mathematics.
g***@gmail.com
2018-02-13 01:34:41 UTC
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Post by Jens Stuckelberger
Post by David Petry
Modern pure mathematics is deficient as a language of science. In
particular, the subject we call the foundations of mathematics is
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Notice that, these days, some in the string theory camp have
expressed a willingness to dispose of this criterion.
'True' and 'False' however CONCEPTUAL *decide* which propositions to accept



P -> a -> b -> ... -> Q
P -> x -> y -> ... -> ~Q

______________________________

~P
WM
2018-02-13 12:28:10 UTC
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Post by Jens Stuckelberger
Post by David Petry
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Notice that, these days, some in the string theory camp have
expressed a willingness to dispose of this criterion.
They have every reason and do no harm to science. The assumption that the sum of all natural numbers is -1/12 is so ridiculous that string theory based thereupon cannot be considered a science anyway.

Regards, WM
FromTheRafters
2018-02-13 14:52:41 UTC
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Post by WM
Post by Jens Stuckelberger
Post by David Petry
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Notice that, these days, some in the string theory camp have
expressed a willingness to dispose of this criterion.
They have every reason and do no harm to science. The assumption that the sum
of all natural numbers is -1/12 is so ridiculous that string theory based
thereupon cannot be considered a science anyway.
Regards, WM
Ha ha ha, you've outdone yourself.
John Gabriel
2018-02-13 16:27:07 UTC
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Post by WM
Post by Jens Stuckelberger
Post by David Petry
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Notice that, these days, some in the string theory camp have
expressed a willingness to dispose of this criterion.
They have every reason and do no harm to science. The assumption that the sum of all natural numbers is -1/12 is so ridiculous that string theory based thereupon cannot be considered a science anyway.
The sum -1/12 is obtained by some really absurd arithmetic which is no longer math but mythmatics.
Post by WM
Regards, WM
bassam king karzeddin
2018-02-13 17:13:38 UTC
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Post by John Gabriel
Post by WM
Post by Jens Stuckelberger
Post by David Petry
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Notice that, these days, some in the string theory camp have
expressed a willingness to dispose of this criterion.
They have every reason and do no harm to science. The assumption that the sum of all natural numbers is -1/12 is so ridiculous that string theory based thereupon cannot be considered a science anyway.
The sum -1/12 is obtained by some really absurd arithmetic which is no longer math but mythmatics.
They use simply Infinity, to produce such rubbish, where they still don't understand that if the art of playing with infinity produce such rubbish, then infinity must be fictional as it is indeed, so this proves strictly the fictionalization of infinity so easily, but because infinity was established as a religion in the sheep mathematics, they choose the nonsense rubbish results as a remaining choice, and shamelessly call it discoveries, and more shamefully and devilishly attach it to physics phenomena of capacitor in electric city, wonder!

But actually there is no problem with their smartness, since the so common mainstream professionalism cheap sheepish love all kinds of fictions, for many business purposes and others, which are the whole problems all the time, for sure

BKK
Post by John Gabriel
Post by WM
Regards, WM
David Melik
2018-02-13 08:38:37 UTC
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Post by David Petry
"Know thyself. People make themselves look ridiculous when they try to
know obscure things before they know themselves"
-- Plato attributes this to Socrates
Okay, well Socrates got 'Know thyself' from one of the two maxims carved
int The Temple of Apollo at Delphi, i.e., originally written by an
ancient Apollinian priest(ess) or maybe one of 'The Seven Sages of
Greece' (whom stated larger text of /The Delphic Maxims/) even before
Pythagoras, whom said similar things (Plato being Pythagorean.)
Post by David Petry
Modern pure mathematics is deficient as a language of science. [...]
No; mathematics isn't deficient; it's the (only) ideal, perfect,
absolute, immutable, eternal truth, and everything else (not just
subjects, but aspects of existence/reality) is a 'subset.' A problem is
in fact new schools of thought since Platonism (and Aristotlean formal
reasoning/logic, recombined into Neopythagoreanism & Neoplatonism,
Leibnizianism, and Ante Rem Structuralism is similar) that are
degenerating away from its formal reasoning/logic & formal science
(mathematics, logic, etc.) and towards popular modern empiricist
materialist science (popular natural science.)
Post by David Petry
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Falsifiability isn't falsifiable; verifiability isn't verifiable (they're
only fairytale-type sensory-materialist storytelling emotionally liked by
people afraid of opposing intuitionist-rationalist logical/ideal/mental/
immaterial Platonic first principles.) They're popular axioms among
natural & social scientists nonetheless, but have no proper place in
philosophy & formal science, because non-demonstrated axioms are one of
the three bases for false reasoning (see ' Wikipedia:Munchausen's Trilemma
', MT.) Mathematics rests on ideas such as reason/logic & number theory,
tautologies/equations (tautologies being the basis not noticed for MT) &
geometry, proofs using those and demonstrated axioms (such as certain
visually-geometrically in Euclid, later perhaps analytically-
tautologically, but not naturalistic axioms which are part of methods for
'evidence,' which is subjective and categorically separate/distinct/
opposite from/than proof, which is only in mathematics, and is always
objective.)
Post by David Petry
I was surprised by the mathematicians' reaction to what I was proposing.
Especially on the internet! Besides suggesting the idea is a crank
idea, they sometimes would accuse me of believing I am channeling God,
or other silly things like that.
I'm not surprised by them (or you,) and wouldn't go so far as to say the
similar (unless becomes clear later, though 'God' is either nonexistent
or is mathematics) but empiricism is belief/faith opposed to reason/
logic. Belief/faith in senses in religion of empiricism (natural
science, Buddhism, etc.) and reason/logic is philosophy of rationalism (
Classical formal science, Platonism, aided by intuition, opposite
perception mode than senses.)
Post by David Petry
It only recently occured to me that I should respond by pointing out
exactly where my ideas are coming from. They come from self knowledge.
That is, as intelligent beings, we can make progess in understanding
ourselves. We can understand how we reason about what we call reality.
And so my radical claim is that mathematics should be consistent with
our understanding of ourselves, and especially, how we reason about
reality. And Cantor's theory of infinity fails that criterion.
Okay, well truth is always in context of coherently/objectively
reasonable/logical statements so that have truth value, thus can be
nothing but mathematical (or translated perfectly to English, as a good
math instructor is capable of in speech, even with polynomials like
saying ‘quantity’ before an exponent.)
David Petry
2018-02-14 00:43:26 UTC
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Post by David Melik
Post by David Petry
Modern pure mathematics is deficient as a language of science. [...]
No; mathematics isn't deficient;
What I mean is that when scientists apply mathematics, they must fall back on intuition, because (pure) mathematics doesn't provide them with all the conceptual tools they need. Hence, mathematics is deficient as a language for science.
Post by David Melik
it's the (only) ideal, perfect,
absolute, immutable, eternal truth, and everything else (not just
subjects, but aspects of existence/reality) is a 'subset.'
I guess if you insist that mathematics is an art form, then current pure mathematics could be described as "ideal, perfect, absolute, immutable, eternal truth" by true believers.

The idea I'm trying to prommote is that mathematics could serve as a foundation for artificial intelligence, but current pure mathematics is deficient for that purpose. We should formalize the ideas that applied mathematicians must fall back on intuition to apply, and integrate those intuitions into mathematics.
Post by David Melik
Post by David Petry
1) Falsifiability is the cornerstone of scientific reasoning, and it can
and should be formalized and integrated into the logic of mathematics.
Falsifiability isn't falsifiable;
I think you're missing the point. My claim is that when we examine our own thinking--i.e. how we reason about the real world--we find that falsifiability is part of that reasoning. And, so I claim, mathematics should be consistent with our understanding of how we think.
Post by David Melik
(see ' Wikipedia:Munchausen's Trilemma ', MT.)
OK, I'll look that up.

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