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A Logical Journey: From Gödel to Philosophy
Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy . A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.
432 pages, Hardcover
First published January 10, 1997
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Displaying 1 - 11 of 11 reviews
February 16, 2009
I picked this up specifically for the chapters on Platonism in mathematics and mental computabilism, but ended up making my way through the entire book (eventually). Even the chapters I thought I'd hate turned out to be surprisingly interesting. Wang knows Godel better than most, and presents both his own and Godel's ideas on a bunch of topics clearly and (of course!) logically. At certain points I wondered if I might be better off just skipping the middleman and going straight to Godel, but Wang's commentary was pretty bitchin' all around. I've certainly got no complaints.
October 3, 2020
Hao Wang visited with Godel [how does one insert umlauts?] extensively towards the end of Godel's life and collected his impressions in this book, which he wasn't able to bring to full completion before his own death. The result is a strange work in progress: Wang clearly admired Godel and wanted to share his vision of platonic essences and Leibnizian monads, but Godel was a strange dude, and Wang never quite found the way to fit the puzzle together, or even present the puzzle in a fully intentional way. The book circles around familiar themes, offers occasional sketches of this and that in Godel's biography, and a bit of Wang's own life, and expresses Wang's own heartfelt desire to see things systematically. But this all is accidental, I think, and not exactly the book Wang set out to write. It is fascinating in its own way, but also incomplete (hah!) and puzzling.
July 23, 2009
Wang's writeup of his conversations provides unparalleled access to G's voice in the living time of thought.
There are some odd moments of (apparently unnoticed) self-referentiality in the first lines of Wang's Preface. We want to say, I think, about all of these, that they represent ways of speaking that we eventually would like to modify under the torsion of what's spoken about here: diagonalization.
1. "my own ongoing pursuit of a comprehensive view of things" -> How the diagonal relates limitation and desire. (Cf. Lacan)
2. "G's notes... remain concealed behind his Gabelsberger shorthand" -> The signifier as transparency, opacity, and, at the diagonal, the third mode (opacity/hypertransparency) relative to meaning (to truth).
3. throughout: the practical issues of quotation, archive, object-language and metalanguage...
4. "...what I take to be the most reasonable of his views on the issues he studied, rather than an attempt to depict faithfully the body of his philosophical thought. His total thought, inevitably, like that of every great thinker, is difficult to bring into focus, if taken as a whole, and contains parts of varying degrees of clarity." -> the inexistence of the one-all, once again relative to the desire/project of understanding. (It's clearly not a matter of simply surrendering this desire. Lacan again, on the relation of castration to Love on the one hand, but also the imperative not to cede one's desire. I.e., you are not to cede it, which amounts to pre-empting the Real, or we might say, normalizing the event. Why does Lacan not see that Antigone fails at this, that she is even in bad faith here?
5. "I have tried hard to find an inclusive framework... " "By doing these things I have been led beyond the scope of the planned book and find it hard to locate a suitable boundary between what should be included and what should be excluded." -> Precisely! This difficulty regarding boundaries is on one hand just what the theorems indicate, but on the other, traumatically, even tragically, that which G's psychoses indicate an inability to integrate into ordinary language. The clear need for a psychoanalytic supplement to metalogical formalism. Once we see that need, we also see that 20th C. French thought has been preoccupied with exactly this: Sartre, Merleau-Ponty, Levinas, Derrida, Deleuze, Lacan, Badiou.
6. "At the same time, I began to sense that there are ways of looking at philosophy superior to what I had been accustomed to." -> Wesenschau.
7. "I had to decide more or less arbitrarily where and when this book was to stop." -> A halting problem, which sounds like a cheap pun, but isn't! (Disciples of Sokal should count to ten before speaking.)
8. "a fairly complete record of what Godel said in our discussions" -> How the fundamental metalogical duality runs through language taken as fact and norm, so that 'what was said' keeps on both extending and dividing between an ideal and a signifier. (Think Derrida and Badiou here.)
I'm not intending to take easy shots at Wang here, especially given the importance of the admission in #. I'm not claiming that we can stop speaking a first-order language, or that I could do substantially better than he does in it. To the contrary, this is just the point. The Preface is a helpful text in which to read the symptoms of the diagonal, because Wang's prose is clear and honest enough that it shows with great economy and elegance, even in the most mundane settings, the ambiguous limits of this inevitable language.
There are some odd moments of (apparently unnoticed) self-referentiality in the first lines of Wang's Preface. We want to say, I think, about all of these, that they represent ways of speaking that we eventually would like to modify under the torsion of what's spoken about here: diagonalization.
1. "my own ongoing pursuit of a comprehensive view of things" -> How the diagonal relates limitation and desire. (Cf. Lacan)
2. "G's notes... remain concealed behind his Gabelsberger shorthand" -> The signifier as transparency, opacity, and, at the diagonal, the third mode (opacity/hypertransparency) relative to meaning (to truth).
3. throughout: the practical issues of quotation, archive, object-language and metalanguage...
4. "...what I take to be the most reasonable of his views on the issues he studied, rather than an attempt to depict faithfully the body of his philosophical thought. His total thought, inevitably, like that of every great thinker, is difficult to bring into focus, if taken as a whole, and contains parts of varying degrees of clarity." -> the inexistence of the one-all, once again relative to the desire/project of understanding. (It's clearly not a matter of simply surrendering this desire. Lacan again, on the relation of castration to Love on the one hand, but also the imperative not to cede one's desire. I.e., you are not to cede it, which amounts to pre-empting the Real, or we might say, normalizing the event. Why does Lacan not see that Antigone fails at this, that she is even in bad faith here?
5. "I have tried hard to find an inclusive framework... " "By doing these things I have been led beyond the scope of the planned book and find it hard to locate a suitable boundary between what should be included and what should be excluded." -> Precisely! This difficulty regarding boundaries is on one hand just what the theorems indicate, but on the other, traumatically, even tragically, that which G's psychoses indicate an inability to integrate into ordinary language. The clear need for a psychoanalytic supplement to metalogical formalism. Once we see that need, we also see that 20th C. French thought has been preoccupied with exactly this: Sartre, Merleau-Ponty, Levinas, Derrida, Deleuze, Lacan, Badiou.
6. "At the same time, I began to sense that there are ways of looking at philosophy superior to what I had been accustomed to." -> Wesenschau.
7. "I had to decide more or less arbitrarily where and when this book was to stop." -> A halting problem, which sounds like a cheap pun, but isn't! (Disciples of Sokal should count to ten before speaking.)
8. "a fairly complete record of what Godel said in our discussions" -> How the fundamental metalogical duality runs through language taken as fact and norm, so that 'what was said' keeps on both extending and dividing between an ideal and a signifier. (Think Derrida and Badiou here.)
I'm not intending to take easy shots at Wang here, especially given the importance of the admission in #. I'm not claiming that we can stop speaking a first-order language, or that I could do substantially better than he does in it. To the contrary, this is just the point. The Preface is a helpful text in which to read the symptoms of the diagonal, because Wang's prose is clear and honest enough that it shows with great economy and elegance, even in the most mundane settings, the ambiguous limits of this inevitable language.
April 7, 2025
Probably one of the hardest philosophy books I have read up to this point. The density of content and information alone was challenging and my rudimentary understanding of continental philosophy didn't help either. Regardless I have come out the other side more understand of Kurt Gödel and his impact of Mathematics and philosophy as a whole. From the biographical chapters to the abstract thought chapters there was always some new or unique understanding that Wang brings us too while providing access to a truly comprehensive collection of Gödel's ideas and opinions found no where else. All in all I would recommend to anyone who is interested in Kurt Gödel, his work, logic, or mathematical philosophy in general. Be prepared to take lots of notes.
November 11, 2024
Me lo he leído para ver qué se decía sobre la concepción de Gödel acerca de la fenomenología y su programa para decidir todos los problemas mediante la adición de axiomas nuevos.
Me he encontrado con mucho más de lo que pedía. Wang logra generar un relato de ideas consistente e intrigante a partir de anotaciones y apuntes dispersos de sus comunicaciones con Gödel.
5/5 merecidísimo, quizás me lo vuelva a leer sin buscar constantemente conexiones con Husserl.
Me he encontrado con mucho más de lo que pedía. Wang logra generar un relato de ideas consistente e intrigante a partir de anotaciones y apuntes dispersos de sus comunicaciones con Gödel.
5/5 merecidísimo, quizás me lo vuelva a leer sin buscar constantemente conexiones con Husserl.
July 17, 2019
Highlights:
1. Science/Math suggests world has underlying regularity and and is ordered.
Principle of sufficient reason: There are no "accidents"
2. There are still intentional paradox in "elementary" concepts like "proposition", "proof", "concept", and "set" (multiplicity/unity) that are, as Godel puts it, "far from trivial"
3. Very interesting remark on introspection versus collecting "data"
4. Weyl-Polya wager, "number", "set", "countability" being vague.
5. Remarks on ultra-finitism:
if 10^10 is inconsistent then there is no theoretical science.
Strictly speaking we only have clear proposition about physically given sets and then only about simple examples of them. If you give up idealization, then mathematics disappears. Consequently, Is is a subjective matter where you want to stop on the ladder of Idealization.
6. Refutation of materialism. To be material is to have a spatial position. Spatial contiguous objects represent one another. WE do not know what the objects are if we know merely that they are in space. We understand space only through the drive of objects in space; otherwise we have no idea what space is. [But if material objects and space are define by each other, materialism in this "spatial" sense is untenable.] For this reason, materialism was given up at the beginning of the century and "the study of structure" has taken its place. But the "study of structure" is a confession that we don't know what the things really are. Real materialism is nonsense.
Errors:
1. Though the passage of time is an illusion, "Concepts" divorced from their anthropological origins (how idea came about in life) leads to paradoxes (similar to Wittgenstein and word-use). Godel was a Platonist and believed concepts to exist independent of space-time, but origins of many concepts are traced back to activities in human life. Playing with concepts in vacuum of mind is interesting but not primary. Concepts must be understood with respect to how they originated and how they are used IN life.
2. With due respect, Godel (known to be a man-child, by many of his colleagues, whose life-line was his wife), seems to be gullible to bullshit like "psychiatry" and "psychology". He was aware that his "doctors" were making "mistakes in their calculations" but he was not aware of the CON/HUSTLE. (as do other scientists / see Smullyan)
3. Godel likes to draw drastic conclusion from low probability events. However, It would be surprising if Godel was not aware of the Law of Large numbers in probability which states that in the universe of events, low probability events happen with high frequency.
4. His protest of his "rights" to the "reich" shows little to no street smarts / autism. Since historical accounts are usually False (as Godel observes), his favoritism of austere practices of the Teutons versus the civilized Romans may not be based on fact, but a rather bias account. For example, the Teutons may not have been austere out of choice but necessity and did envy their Roman counterparts-- thus the invasions/wars. (common sense street instincts would confirm)
4. His will to "understand" / get to "see clearer" what is "fundamental", is a desire like any other desire folks have. It is a form of Will to Power (not worldly political power).
6. Regardless of whether the brain is connected to a spirit. Everyone's personal experience with exercise, food (chemistry), drug-use (chemistry), sleep-deprivation knows that the brain/mind is dependent on mechanistic properties.
5. His remarks about Husserl and religious-like statements are not further developed.
1. Science/Math suggests world has underlying regularity and and is ordered.
Principle of sufficient reason: There are no "accidents"
2. There are still intentional paradox in "elementary" concepts like "proposition", "proof", "concept", and "set" (multiplicity/unity) that are, as Godel puts it, "far from trivial"
3. Very interesting remark on introspection versus collecting "data"
4. Weyl-Polya wager, "number", "set", "countability" being vague.
5. Remarks on ultra-finitism:
if 10^10 is inconsistent then there is no theoretical science.
Strictly speaking we only have clear proposition about physically given sets and then only about simple examples of them. If you give up idealization, then mathematics disappears. Consequently, Is is a subjective matter where you want to stop on the ladder of Idealization.
6. Refutation of materialism. To be material is to have a spatial position. Spatial contiguous objects represent one another. WE do not know what the objects are if we know merely that they are in space. We understand space only through the drive of objects in space; otherwise we have no idea what space is. [But if material objects and space are define by each other, materialism in this "spatial" sense is untenable.] For this reason, materialism was given up at the beginning of the century and "the study of structure" has taken its place. But the "study of structure" is a confession that we don't know what the things really are. Real materialism is nonsense.
Errors:
1. Though the passage of time is an illusion, "Concepts" divorced from their anthropological origins (how idea came about in life) leads to paradoxes (similar to Wittgenstein and word-use). Godel was a Platonist and believed concepts to exist independent of space-time, but origins of many concepts are traced back to activities in human life. Playing with concepts in vacuum of mind is interesting but not primary. Concepts must be understood with respect to how they originated and how they are used IN life.
2. With due respect, Godel (known to be a man-child, by many of his colleagues, whose life-line was his wife), seems to be gullible to bullshit like "psychiatry" and "psychology". He was aware that his "doctors" were making "mistakes in their calculations" but he was not aware of the CON/HUSTLE. (as do other scientists / see Smullyan)
3. Godel likes to draw drastic conclusion from low probability events. However, It would be surprising if Godel was not aware of the Law of Large numbers in probability which states that in the universe of events, low probability events happen with high frequency.
4. His protest of his "rights" to the "reich" shows little to no street smarts / autism. Since historical accounts are usually False (as Godel observes), his favoritism of austere practices of the Teutons versus the civilized Romans may not be based on fact, but a rather bias account. For example, the Teutons may not have been austere out of choice but necessity and did envy their Roman counterparts-- thus the invasions/wars. (common sense street instincts would confirm)
4. His will to "understand" / get to "see clearer" what is "fundamental", is a desire like any other desire folks have. It is a form of Will to Power (not worldly political power).
6. Regardless of whether the brain is connected to a spirit. Everyone's personal experience with exercise, food (chemistry), drug-use (chemistry), sleep-deprivation knows that the brain/mind is dependent on mechanistic properties.
5. His remarks about Husserl and religious-like statements are not further developed.
This entire review has been hidden because of spoilers.
June 27, 2012
An extraordinarily detailed biography of Kurt Goedel's life and philosophical work. Hao Wang is perhaps the only person to engage Goedel on these questions in his lifetime, and thus the account he provides is invaluable to understanding the thoughts and beliefs one of the 20th century's brightest lights.
This is not easy reading, even though it doesn't spend much time on the incompleteness theorems, but this book reaches substantial depth on philosophical inquiry, fusing Goedel's views with some of Wang's own interpretations and ideas. The topics range from the more familiar realms of computation, logic and set theory, and out into the bizarre world of Platonism and monadology.
I can't suggest this book for the casual reader due to the hefty bite of philosophy (good portions of it were over my head), but for anyone interested in Goedel as a historical figure and thinker this is an invaluable resource.
This is not easy reading, even though it doesn't spend much time on the incompleteness theorems, but this book reaches substantial depth on philosophical inquiry, fusing Goedel's views with some of Wang's own interpretations and ideas. The topics range from the more familiar realms of computation, logic and set theory, and out into the bizarre world of Platonism and monadology.
I can't suggest this book for the casual reader due to the hefty bite of philosophy (good portions of it were over my head), but for anyone interested in Goedel as a historical figure and thinker this is an invaluable resource.
October 17, 2014
Wang provides unprecedented insight into Godel's life and philosophy. With that said, some of the later chapters on set theory and Monadology are very technical. I didn't understand many of the references to Kant, Husserl, and Leibniz.
I found it fascinating that Godel seemed to believe in God because his theorem implies that if the human mind is mechanical in nature, it cannot comprehend itself. I gathered that Godel was in the same boat as Einstein, in that he was transfixed on the idea of finding a general solution to metaphysics. Such a humble goal...
"Will is the opposite of reason." I've never looked at it that way, but many of Godel's notes were in an obscure shorthand of German. I'm more inclined to think that the translation is lacking.
I found it fascinating that Godel seemed to believe in God because his theorem implies that if the human mind is mechanical in nature, it cannot comprehend itself. I gathered that Godel was in the same boat as Einstein, in that he was transfixed on the idea of finding a general solution to metaphysics. Such a humble goal...
"Will is the opposite of reason." I've never looked at it that way, but many of Godel's notes were in an obscure shorthand of German. I'm more inclined to think that the translation is lacking.
December 11, 2021
The most coherent, exhaustive & intelligent book on Godel & his ideas. The difference to others books on Godel maybe that the material is written by a mathematician/logician/scientist/philosopher rather than fluff piece written by a journalist/non technical writer.
May 27, 2012
need more background, will be back to it later on in my life
May 3, 2014
Difficult to read through. I did not go cover to cover on this one. The book was not edited very well at all. Still there were some valuable insights for those interested in Kurt Godel.
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