@GaryGeckDotCom I often wish that Gödel was right, but I do not really see
any evidence to the idea that mathematics is anything but systems that
refer to themselves using the axioms set up within that system. But I do
see your point, and it would be very interesting if we could find a
foundation for mathematics that is what Gödel envisioned. However, I think
his ideas about the human mind and its abilities where a bit off, but very
interesting.
@astroboomboy I have not undertaken a study of minksy but if you can point
me to one select paper by minsky i will read it and comment. I don’t get
your reference as a result, but by ‘shortcuts’ do you mean like how we
humans (and machines also) never write the infinite 0s in front of a number
like we really should? I’d rather comment on a specific paper.
A version of this vid w/out musical soundtrack is now linked to from the
description above towards the top…or in the video itself as an
annotation…or just go to my videos channel.
Thank you very much for the visual contexts, and the musical contexts. I
don’t think I would have had the patience to parse the structure of Godel’s
arguments to fully appreciate what he was expressing; and yet I am such a
fan of his work. I have spent years trying to understand his theorems in
addition to understanding his seemingly surprising position against the
current Zeigeist.
@GaryGeckDotCom There are many who criticize the idea that the Turing
machine makes it impossible to create AI, and that the human mind has to be
more than a turing machine. You have probably read Minsky, but his critique
seems to be rather plausible, that even though turing machines can’t make
infinite strings there are shortcuts, and our mind uses such shortcuts to
do these things.
@GaryGeckDotCom I think we have to be careful in taking Gödels theorems
outside of mathematics and projecting them onto the real world. And it
actually may be so that there are infinite ways of looking at the universe,
and our minds are only capable of certain interpretations that are
approximations of the things in themselves (as Kant would put it). And as
Kant would also state, time and space are the conditions of our faculties,
not something “real” and so reality will always evade us somewhat
@GaryGeckDotCom Not really. Mathematics stands on its own, and has no
relations to philosophy other than having similarities to logic.
Mathematics, like logics, is a formal system based on certain
axioms/assumptions through which you can derive general or specific
knowledge about the formal system that you have constructed. I don’t think
one can say that philosophy is the foundation, but rather that you can
philosophize about anything, including math. Do you agree?
Dear Gary, these videos are inspirational. I look very much forward to the
coming episodes and once the series is complete, I hope you will put all
episodes out on DvD, It would be a must buy for me.
@astroboomboy As far as Gödel and the mind goes that is the big question.
We don’t know the answer. It’s useful to clarify the options we have. One
option is that humans think in a way that is consistent and complete and
and somehow gets around the incompleteness phenomena. Another possible
explanation is that all knowledge is complete and inconsistent and that all
knowledge is a giant contradiction when taken as a whole “God is the point
where all opposites coincide” -Cusa
@astroboomboy Turing machines have limitations. Because they enumerate, ALL
real nums are out of reach. It can enumerate any given real num though (ex.
pi). Turing machines can make infinite strings…they just can’t make all
infinite strings. Diagonalization demonstrates this intuitively. I see it
as very well defined in terms of combinatorics. Whether the mind is only a
universal Turing machine is an open question still so you can say it can be
or it can possibly not be the case too.
Great video, but sometimes the music interferes with understanding what you
are saying.
thank you so much for this.
28/42 Kurt Gödel: Modern Dev. of the Foundations Of Mathematics In Light Of
Philosophy (w/music)
23:20,
Hi, you’ve mispelled the names of Sartre, Foucault and Strauss
Mind blown! THX!
28/42 Kurt Gödel: Modern Dev. of the Foundations Of Mathematics In Light Of
Philosophy (w/music)
@GaryGeckDotCom I often wish that Gödel was right, but I do not really see
any evidence to the idea that mathematics is anything but systems that
refer to themselves using the axioms set up within that system. But I do
see your point, and it would be very interesting if we could find a
foundation for mathematics that is what Gödel envisioned. However, I think
his ideas about the human mind and its abilities where a bit off, but very
interesting.
@astroboomboy I have not undertaken a study of minksy but if you can point
me to one select paper by minsky i will read it and comment. I don’t get
your reference as a result, but by ‘shortcuts’ do you mean like how we
humans (and machines also) never write the infinite 0s in front of a number
like we really should? I’d rather comment on a specific paper.
The pompous music is a bit distracting. Otherwise… good stuff!
We need moar videos… MOAR!!! 🙂
retard
A version of this vid w/out musical soundtrack is now linked to from the
description above towards the top…or in the video itself as an
annotation…or just go to my videos channel.
Suddendly I can’t watch the video anymore on my iPad 🙁 Some time ago, it
still worked. Probably the settings have been changed accidentally !!!
Thank you very much for the visual contexts, and the musical contexts. I
don’t think I would have had the patience to parse the structure of Godel’s
arguments to fully appreciate what he was expressing; and yet I am such a
fan of his work. I have spent years trying to understand his theorems in
addition to understanding his seemingly surprising position against the
current Zeigeist.
Go to amazon and type in kurt godel.
@GaryGeckDotCom There are many who criticize the idea that the Turing
machine makes it impossible to create AI, and that the human mind has to be
more than a turing machine. You have probably read Minsky, but his critique
seems to be rather plausible, that even though turing machines can’t make
infinite strings there are shortcuts, and our mind uses such shortcuts to
do these things.
@GaryGeckDotCom I think we have to be careful in taking Gödels theorems
outside of mathematics and projecting them onto the real world. And it
actually may be so that there are infinite ways of looking at the universe,
and our minds are only capable of certain interpretations that are
approximations of the things in themselves (as Kant would put it). And as
Kant would also state, time and space are the conditions of our faculties,
not something “real” and so reality will always evade us somewhat
@Lewclan Hans Zimmer – Inception
Alain Badiou is a contemporary philosopher, whose main interests include
set theory, mathematics etc…
@GaryGeckDotCom Not really. Mathematics stands on its own, and has no
relations to philosophy other than having similarities to logic.
Mathematics, like logics, is a formal system based on certain
axioms/assumptions through which you can derive general or specific
knowledge about the formal system that you have constructed. I don’t think
one can say that philosophy is the foundation, but rather that you can
philosophize about anything, including math. Do you agree?
Dear Gary, these videos are inspirational. I look very much forward to the
coming episodes and once the series is complete, I hope you will put all
episodes out on DvD, It would be a must buy for me.
@astroboomboy As far as Gödel and the mind goes that is the big question.
We don’t know the answer. It’s useful to clarify the options we have. One
option is that humans think in a way that is consistent and complete and
and somehow gets around the incompleteness phenomena. Another possible
explanation is that all knowledge is complete and inconsistent and that all
knowledge is a giant contradiction when taken as a whole “God is the point
where all opposites coincide” -Cusa
Looking at math in a philosophical light … why?
@astroboomboy Turing machines have limitations. Because they enumerate, ALL
real nums are out of reach. It can enumerate any given real num though (ex.
pi). Turing machines can make infinite strings…they just can’t make all
infinite strings. Diagonalization demonstrates this intuitively. I see it
as very well defined in terms of combinatorics. Whether the mind is only a
universal Turing machine is an open question still so you can say it can be
or it can possibly not be the case too.