Uploaded by GaryGeckDotCom on 22.03.2012

Transcript:

This is Gary Geck from Gary geck.com.

Welcome to part 22 of my 42 part video series revealing the Secret History. For parts 22

through 28 which stand on their own. I will be exploring the life and work of a man often

called the greatest logician since Aristotle. In this video, I will be exploring the mind

of Kurt Gödel… this will not be a mere biography, but a revelation to the world of

who he really was.

Kurt Gödel, who considered nearly all of modern thought-especially the analytic tradition

to be dehumanizing and backwards A man whose results continue to shock the

world A man who married his sweetheart, Adele, a

beautiful nightclub dancer A man Who believed in God and Platonism in

dramatic opposition to the zeitgeist.. Who proved the limitations of formal systems,

and yet believed that the mind could solve any problem

A man was obsessed with Snow white and fairy tales because they showed how meaningful the

world should be Dr. Gödel Who believed a vast conspiracy

to keep mankind stupid and empirical instead of knowing about the full power of conceptual

truth In fact, Gödel believed that this dark and

conspiratorial force had been operating secretly for centuries and was after him in the same

way they were after Leibniz

This is Kurt Gödel

Many of the shallower works on Gödel are dismissive of his work outside of logic the

grounds of his mental issues. There is no question that Gödel struggled with his demons,

but I feel that the real story is so much deeper and more interesting. I would like

to begin this story with a quote from page 13 of Kurt Gödel the Album which eloquently

puts such demons into context:

Gödel’s intellectual adventures exacted a high price. He repeatedly suffered from

severe psychological crises and break-downs and spent much time in sanatoriums. The director

of his Institute described him in an official letter as a genius with psycho-pathological

traits. Gödel was haunted by the fear of being poisoned and in the end he died from

his determination not to take up any food. In

the intervals between his crises, or ''states", as he called them, he could be funny, brilliant

and extremely stimulating. But in Gödel’s presence, his close friend Oskar Morgenstern

always felt the chill from another world. Gödel himself was well aware that many of

his opinions were not shared by the majority. He was an unadulterated Platonist; he was

intensely interested in theology (the real one, with proofs of God's existence); and

as a time-traveler he would probably have visited Leibniz first. In a list of his philosophical

principles, he notes: "First, the world is rational". This by itself sounds oddly out

of tune with his time. What Gödel had to live through was everything but rational,

even without his "states" and fears. As he told Hao Wang in one of their long interviews:

"I do not fit into this century". And yet he left his mark on it, maybe precisely because

he remained a stranger.

Despite these personal "states" Gödel’s few publications changed the world of mathematics,

logic and philosophy . And to this day, we are still struggling to understand what are

the implications of his work.

To call Kurt Gödel interesting is an understatement. One of Gödel’s closest friends at the Institute

for Advanced Studies at Princeton was Albert Einstein who said once told Morgenstern that

in the later years his own work didn’t mean much and "…that he came to the Institute

merely...to have the privilege of walking home with Gödel".

To get a better understanding, I would like to go back to Vienna of the mid to late 1920s.

Gödel began college at the University of Vienna in physics but quickly changed to philosophy

and mathematics. Gödel saw philosophy and mathematics as more fruitful enterprises than

physical science, to understand reality. To Gödel the universe extended well beyond one

available to the sense organs that science is so preoccupied with. In a platonic tradition,

Gödel included the world of ideas in his view of reality. In such a world, mathematics

and logic were not only tools to be applied, but tools of revelation when they are correct.

But Gödel was sharp and was meticulous, and never loose in his speculations which were

always held up to the highest rigor in his own mind. To him publishing an error or a

claim that was not obvious to the intuition would be an unbearable embarrassment. In Gödel

was the combination of perfectionism and powers of discrimination to the extreme on the one

hand and an open and expanded mind to the mystical on the other. A combination that

Garygeck.com has long argued is the perfect recipe for genius.

It is revealing that, according to Dr. Gerald Sachs in a lecture I will quote often in this

series, Gödel requested that the logic journals at Princeton be moved from the science wing

to the humanities wing.

A link to Dr. Sach’s lecture on Gödel which is the best I’ve ever heard is available

on garygeck.com in the podcast section.

It is remarkable that the young Gödel developed with such a platonic philosophical worldview.

Between 1926 and 1929 he often sat in on a group usually characterized by vehement hatred

towards metaphysics and speculative thinking. [Wittgenstein et al. pictured] Called the

“Vienna Circle” it was a group which was associated with the mathematics department

at the university of Vienna and often met in cafes. Among coffee and cigarettes, philosophical

polemics often raged, but Gödel, according to Karl Menger (1902-1985), usually sat quietly

listening and only making head gestures in agreement or disagreement with what was said.

Gödel’s 1929 doctoral dissertation showed his powerful genius early on. It contained

fundamental results in logic, specifically his Completeness Theorem which answered positively

a question that David Hilbert and Wilhelm Ackermann had posed in 1928 . I will go into

much more detail on completeness in a different video in this 42 part series, but briefly

Gödel proved that all valid first order logical expressions are provable, no small feat.

One consequence of the Completeness Theorem is that it made the connection between semantics

and syntax explicit, but we will get into this more later.

Shortly after Gödel was awarded his doctorate, he discovered what he is most famous for,

his two incompleteness theorems. Again, other videos in this series will go into much more

detail about incompleteness because it is so central to our main story.

It upset a lot of people. I knew someone who was there the night the news came to Göttingen.

Of course they couldn’t sleep. A lot of people were upset with what he was doing to

mathematics and they think he damaged mathematics but I think he made it more interesting ”

Gödel’s incompleteness theorems were not fully appreciated for a while. But eventually,

partly thanks to John Von Neumann, some of their implications became clear. Bertrand

Russell and Albert North Whitehead …..

But to this day, the full implications of the incompleteness phenomenon is debated.

Gödel eventually made his was to Set Theory and made important contributions to that field.

Remember that Set Theory played an important role in parts 1-7 of this series. Gödel in

a way carried on the work of Set Theory’s father: Georg Cantor, who, like Gödel had

deep platonic philosophical views of mathematics. In the previously mentioned lecture by Dr.

Sachs, it’s mentioned that one of Gödel’s favorite topics to discuss was the Absolute.

As I discussed in parts 1-7, in Cantorian Set Theory, the Absolute is the Set of all

Sets. It is the highest infinity, encompassing the many seemingly unbounded infinities of

other infinities. Cantor might have viewed it as the God Set. Naturally the concept of

the Absolute seems contradictory. But Cantor and Gödel seem to have accepted this as natural

quality of the Divine. In fact, a long tradition going back to the German Hermetic theologian,

Nicholas of Cusa viewed God as the coincidence of opposites. One example of the paradoxical

nature of the Absolute is that, when using common set-theoretical axioms, the Set of

everything must contain the set of all sets that are not a member of itself! Because of

these issues, Cantor classified the Absolute as an inconsistent set. He divided all sets

into those which were consistent and those which were inconsistent. While mathematicians

continued to deal exclusively with the consistent sets through the developments of mathematics

over the past century, it is interesting that Gödel was a rare type to be fascinated with

an inconsistent one especially an inconsistent Set that was more or less Cantor’s mathematical

understanding of God.

Let us listen again to a clip of Dr. Sacks lecture on this:

so there was this dinner at the IAS in Princeton, New Jersey, and I would sit next to him, Gödel,

and keep him out of trouble. On our other side, a close friend, Oskar Morgenstern. So

we spoke during the dinner and of course I was always eager to hear what he had to say

and he brought up the Absolute with a capital A. That is not a concept that 20th century

philosophers tend to bring up. So what was it to him? In my mind it was the class of

all sets, but I’m not sure maybe it was more to him. He seemed to be talking about

the class of all sets. And hence all mathematical objects…that’s worthy to be called the

Absolute. And he says um, he told me know you …he seemed to have this boyish enthusiasm….he

says you know language uh does not enable us to define the Absolute. If you have a formula

F(X)..uhh it can never happen that that Formula has exactly one X, that satisfies it, that

X being the Absolute that can happen because we know from reflection principle in Set Theory

if uhh if we have the formula F(X) and F(V) holds where V is the class of all Sets, then

F must hold for some set. In other words, anything you say about the class of all sets

which is true is also true for some particular set. And Hence you cannot define the absolute…and

his eyes lit up and he said isn’t that wonderful: we know something about the absolute just

by reason. He was filled with enthusiasm.”

Please continue on to part 23 of this video series on Kurt Gödel and check out all videos

at garygeck.com

Welcome to part 22 of my 42 part video series revealing the Secret History. For parts 22

through 28 which stand on their own. I will be exploring the life and work of a man often

called the greatest logician since Aristotle. In this video, I will be exploring the mind

of Kurt Gödel… this will not be a mere biography, but a revelation to the world of

who he really was.

Kurt Gödel, who considered nearly all of modern thought-especially the analytic tradition

to be dehumanizing and backwards A man whose results continue to shock the

world A man who married his sweetheart, Adele, a

beautiful nightclub dancer A man Who believed in God and Platonism in

dramatic opposition to the zeitgeist.. Who proved the limitations of formal systems,

and yet believed that the mind could solve any problem

A man was obsessed with Snow white and fairy tales because they showed how meaningful the

world should be Dr. Gödel Who believed a vast conspiracy

to keep mankind stupid and empirical instead of knowing about the full power of conceptual

truth In fact, Gödel believed that this dark and

conspiratorial force had been operating secretly for centuries and was after him in the same

way they were after Leibniz

This is Kurt Gödel

Many of the shallower works on Gödel are dismissive of his work outside of logic the

grounds of his mental issues. There is no question that Gödel struggled with his demons,

but I feel that the real story is so much deeper and more interesting. I would like

to begin this story with a quote from page 13 of Kurt Gödel the Album which eloquently

puts such demons into context:

Gödel’s intellectual adventures exacted a high price. He repeatedly suffered from

severe psychological crises and break-downs and spent much time in sanatoriums. The director

of his Institute described him in an official letter as a genius with psycho-pathological

traits. Gödel was haunted by the fear of being poisoned and in the end he died from

his determination not to take up any food. In

the intervals between his crises, or ''states", as he called them, he could be funny, brilliant

and extremely stimulating. But in Gödel’s presence, his close friend Oskar Morgenstern

always felt the chill from another world. Gödel himself was well aware that many of

his opinions were not shared by the majority. He was an unadulterated Platonist; he was

intensely interested in theology (the real one, with proofs of God's existence); and

as a time-traveler he would probably have visited Leibniz first. In a list of his philosophical

principles, he notes: "First, the world is rational". This by itself sounds oddly out

of tune with his time. What Gödel had to live through was everything but rational,

even without his "states" and fears. As he told Hao Wang in one of their long interviews:

"I do not fit into this century". And yet he left his mark on it, maybe precisely because

he remained a stranger.

Despite these personal "states" Gödel’s few publications changed the world of mathematics,

logic and philosophy . And to this day, we are still struggling to understand what are

the implications of his work.

To call Kurt Gödel interesting is an understatement. One of Gödel’s closest friends at the Institute

for Advanced Studies at Princeton was Albert Einstein who said once told Morgenstern that

in the later years his own work didn’t mean much and "…that he came to the Institute

merely...to have the privilege of walking home with Gödel".

To get a better understanding, I would like to go back to Vienna of the mid to late 1920s.

Gödel began college at the University of Vienna in physics but quickly changed to philosophy

and mathematics. Gödel saw philosophy and mathematics as more fruitful enterprises than

physical science, to understand reality. To Gödel the universe extended well beyond one

available to the sense organs that science is so preoccupied with. In a platonic tradition,

Gödel included the world of ideas in his view of reality. In such a world, mathematics

and logic were not only tools to be applied, but tools of revelation when they are correct.

But Gödel was sharp and was meticulous, and never loose in his speculations which were

always held up to the highest rigor in his own mind. To him publishing an error or a

claim that was not obvious to the intuition would be an unbearable embarrassment. In Gödel

was the combination of perfectionism and powers of discrimination to the extreme on the one

hand and an open and expanded mind to the mystical on the other. A combination that

Garygeck.com has long argued is the perfect recipe for genius.

It is revealing that, according to Dr. Gerald Sachs in a lecture I will quote often in this

series, Gödel requested that the logic journals at Princeton be moved from the science wing

to the humanities wing.

A link to Dr. Sach’s lecture on Gödel which is the best I’ve ever heard is available

on garygeck.com in the podcast section.

It is remarkable that the young Gödel developed with such a platonic philosophical worldview.

Between 1926 and 1929 he often sat in on a group usually characterized by vehement hatred

towards metaphysics and speculative thinking. [Wittgenstein et al. pictured] Called the

“Vienna Circle” it was a group which was associated with the mathematics department

at the university of Vienna and often met in cafes. Among coffee and cigarettes, philosophical

polemics often raged, but Gödel, according to Karl Menger (1902-1985), usually sat quietly

listening and only making head gestures in agreement or disagreement with what was said.

Gödel’s 1929 doctoral dissertation showed his powerful genius early on. It contained

fundamental results in logic, specifically his Completeness Theorem which answered positively

a question that David Hilbert and Wilhelm Ackermann had posed in 1928 . I will go into

much more detail on completeness in a different video in this 42 part series, but briefly

Gödel proved that all valid first order logical expressions are provable, no small feat.

One consequence of the Completeness Theorem is that it made the connection between semantics

and syntax explicit, but we will get into this more later.

Shortly after Gödel was awarded his doctorate, he discovered what he is most famous for,

his two incompleteness theorems. Again, other videos in this series will go into much more

detail about incompleteness because it is so central to our main story.

It upset a lot of people. I knew someone who was there the night the news came to Göttingen.

Of course they couldn’t sleep. A lot of people were upset with what he was doing to

mathematics and they think he damaged mathematics but I think he made it more interesting ”

Gödel’s incompleteness theorems were not fully appreciated for a while. But eventually,

partly thanks to John Von Neumann, some of their implications became clear. Bertrand

Russell and Albert North Whitehead …..

But to this day, the full implications of the incompleteness phenomenon is debated.

Gödel eventually made his was to Set Theory and made important contributions to that field.

Remember that Set Theory played an important role in parts 1-7 of this series. Gödel in

a way carried on the work of Set Theory’s father: Georg Cantor, who, like Gödel had

deep platonic philosophical views of mathematics. In the previously mentioned lecture by Dr.

Sachs, it’s mentioned that one of Gödel’s favorite topics to discuss was the Absolute.

As I discussed in parts 1-7, in Cantorian Set Theory, the Absolute is the Set of all

Sets. It is the highest infinity, encompassing the many seemingly unbounded infinities of

other infinities. Cantor might have viewed it as the God Set. Naturally the concept of

the Absolute seems contradictory. But Cantor and Gödel seem to have accepted this as natural

quality of the Divine. In fact, a long tradition going back to the German Hermetic theologian,

Nicholas of Cusa viewed God as the coincidence of opposites. One example of the paradoxical

nature of the Absolute is that, when using common set-theoretical axioms, the Set of

everything must contain the set of all sets that are not a member of itself! Because of

these issues, Cantor classified the Absolute as an inconsistent set. He divided all sets

into those which were consistent and those which were inconsistent. While mathematicians

continued to deal exclusively with the consistent sets through the developments of mathematics

over the past century, it is interesting that Gödel was a rare type to be fascinated with

an inconsistent one especially an inconsistent Set that was more or less Cantor’s mathematical

understanding of God.

Let us listen again to a clip of Dr. Sacks lecture on this:

so there was this dinner at the IAS in Princeton, New Jersey, and I would sit next to him, Gödel,

and keep him out of trouble. On our other side, a close friend, Oskar Morgenstern. So

we spoke during the dinner and of course I was always eager to hear what he had to say

and he brought up the Absolute with a capital A. That is not a concept that 20th century

philosophers tend to bring up. So what was it to him? In my mind it was the class of

all sets, but I’m not sure maybe it was more to him. He seemed to be talking about

the class of all sets. And hence all mathematical objects…that’s worthy to be called the

Absolute. And he says um, he told me know you …he seemed to have this boyish enthusiasm….he

says you know language uh does not enable us to define the Absolute. If you have a formula

F(X)..uhh it can never happen that that Formula has exactly one X, that satisfies it, that

X being the Absolute that can happen because we know from reflection principle in Set Theory

if uhh if we have the formula F(X) and F(V) holds where V is the class of all Sets, then

F must hold for some set. In other words, anything you say about the class of all sets

which is true is also true for some particular set. And Hence you cannot define the absolute…and

his eyes lit up and he said isn’t that wonderful: we know something about the absolute just

by reason. He was filled with enthusiasm.”

Please continue on to part 23 of this video series on Kurt Gödel and check out all videos

at garygeck.com