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For some reason it's fashionable to bash philosophical implications of Gödel's Theorem(s). Not only is the internet filled with articles like this, there is at

For some reason it's fashionable to bash philosophical implications of Gödel's Theorem(s). Not only is the internet filled with articles like this, there is at least one book dedicated to bashing on philosophical implications of the theorem, the one by Torkel Franzen (whose most notable work is that book). I find this sort of allergic reaction to be interesting in its own right. Yes, there are pseudointellectuals who abuse the theorem, but they're just that, pseudointellectuals, and academics usually don't engage with pseudointellectuals. I suppose the situation is similar with Aaronson's despair at the layperson's misunderstanding of quantum computers, but so far as I can tell Godel's theorem is virtually unknown among the masses, in any case much, much less known than quantum mechanics. So it's interesting why academics feel the need to have this sort of allergic reaction - in the case of quantum mechanics it's more understandable. So the more interesting because Godel, the man himself, was preoccupied with philosophical implications of his theorem. This is the man who "proved" God's existence with modal logic, the man who spent decades after publishing his most famous theorems in a dusty study writing philosophical (and extremely rigorous) implications of his theorems that hardly anyone read, the man who eventually starved to death because he thought - his philosophy led him to believe - he was being poisoned. In fact, Godel's theorem ought to be used more, not less, in philosophy. Some, like me, believe it has profound implications to moral philosophy. See: https://arxiv.org/abs/1805.08347 https://arxiv.org/abs/1805.08347 But this is a frustrating position to be in for someone like me, because philosophers don't understand Godel's theorem, and mathematicians/computer scientists don't care for philosophy. Instead they spend their time writing pieces like this that justify them for not caring about philosophy. It's pretty lame.

modzu 8y ago
seeing a comment like this downvoted to the bottom.. i just.. miss the old HN
- modzu 8y ago
  let the downvotes begin, rain them upon thee! am not looked to get myself banned but the parent comment is as outright an original, authentic, relevant comment you will find here. yet there it is, too light grey to read. serious question: what is going on?
  - pulisse 8y ago
    > the parent comment is as outright an original, authentic, relevant comment you will find here The comment casts a lot of aspersions on academics but doesn't actually justify any of it.
    - zzzzzzzza 8y ago
      so, tone policing. I'm not an academic but from my limited interaction with philosophy subreddits (r/philosophy, r/askphilosophy), which seem to an outsider to have an academic bent, there is 0 interest in the intersection of cs and philosophy/ethics; so from my outsider perspective he doesn't even seem entirely meritless in his tone.
      - pulisse 8y ago
        I'm not complaining about the tone of his criticisms. I'm complaining about the absence of any justification of them.
        deleted 8y ago
        [deleted]
- Kinnard 8y ago
  It's a good comment. I down voted because I do see the reason for the allergic reaction. Perhaps the diction could be improved but I think what the piece points out is a dastardly trap as you're just upon grasping (whatever can be grasped of) Gödel's Wonder. I speak as a layman.
  - jeromebaek 8y ago
    If there's nothing to be grasped in "Gödel's Wonder", why do you think the man himself, who, we can reasonably conjecture, understood his theorems more than anybody else, spent the remainder of his life "grasping" at what his theorems meant? I find it much more reasonable to conclude that there was, and is, in fact something significant to be grasped, and thinkpieces like this simply want to declare that there's nothing to be grasped.
    - Kinnard 8y ago
      I meant by people like me :)
    - throwawaymath 8y ago
      Brilliant mathematicians and computer scientists are capable of making mistakes. Atiyah was a titan of his field, but in the twilight of his life he published a superfluous, incoherent "proof” of Riemann. It was so deeply flawed that not a single well known mathematician has commented on it publicly out of respect for the man - the most you can find is a MathOverflow discussion picking apart specific claims. We aren’t flying too close to the Sun if we dare to question their conjectures, even those regarding their previous work. In consideration of this point and the available evidence, I remain deeply unconvinced there is a unrealized, grand philosophical insight to be derived from whatever Gödel’s later, more obscure work had to say about the incompleteness theorems. Likewise Fermat was probably the foremost authority on his most famous conjecture during his life; but the common consensus is that he did not, in fact, have a “truly marvelous proof” of the FLT which he couldn’t fit in the margins. Everyone thinks silly things from time to time, their prior work notwithstanding. I’m inclined to believe Gödel either wasn’t as invested in the philosophical implications of his earlier work as you believe. Or perhaps he was, but I really doubt he actually arrived at a novel, rigorous result from it. Occam’s Razor suggests we would know if he had.
pulisse 8y ago
> philosophers don't understand Godel's theorem Philosophy was the disciplinary home of formal logic until the latter part of the 20th century (meaning, research in formal logic largely took place in philosophy), and Anglophone philosophy departments are still full of people who are extremely competent at formal logic. I mean, look at the figures discussed in TFA: Boolos, Jeffrey, Hintikka, Quine, Smullyan, and Nagel were all philosophers. Are you really insinuating that Quine didn't know what he was talking about when discussing logic?
- jeromebaek 8y ago
  Obviously I'm not talking about people like Quine; if that's your definition of "philosopher", Gödel himself would be a philosopher. You make good points, but altogether my issue is that, at the current moment, few anglophone philosophers have more than a casual grasp of Gödel's theorem. How do I know that? I was in graduate school for philosophy, then dropped out, partly because philosophers who seriously engage in, e.g. both moral philosophy and computability theory are far and few between.
  - pulisse 8y ago
    > philosophers who seriously engage in, e.g. both moral philosophy and computability theory are far and few between That's a quite a bit weaker of a claim than "philosophers don't understand Gödel's theorem". To back that up you need to point to some philosophers who (a) discuss Gödel's theorem in such a way that (b) they demonstrate their lack of understanding. As it is you're just claiming that one particular subfield of philosophy doesn't have much overlap with another. How is that an indictment of the field? There are few computer scientists working at the intersection of quantum computing and database theory. There are few physicists working at the intersection of biophysics and string theory. It's not a meaningful criticism unless there's reason to think that there is something in the intersection that practitioners are culpable for overlooking, and you haven't provided any such reason.
    - jeromebaek 8y ago
      I think the reason is shallow thinkpieces like this :)
jonahx 8y ago
This should not be getting downvoted, no matter how much you disagree with its claims. It is articulate, well-written, contains novel (for me, anyway) biographical information about Godel, and is respectful enough even its critiques.
v_x_zebert 8y ago
I personally believe we live within a historiographical paradigm that blindspots large fundamental parts of intellectual history because it has been deemed to be too "philosophical" or "religious" unfortunately therefore ignoring the undercurrents or foundations of math and science which are very much "alchemical", "esoteric", "spiritual" or straight up weird. Today's list based interfacing with the internet, the nature of bite sized information surfing, the resulting fuzzy attention, and the property-based worldview makes it very difficult to transcend this paradigm of mechanical / single-threaded cognition without crossing some pretty deep and frightening oceans so to speak. Most importantly _every one_ of the great forefathers of thought were entangled in philosophical and mystical thinking which were not _only_ "silly magical endeavours" only worthy of X century but actually central to their worldview and absolutely central to the development of "how the western world is" today. Also most of them were polymaths, and so much more intelligent and broad scoped than what we give them credit for. That we see pop cultural icons like Neil Degrasse Tyson tweet that Philosophy is not a real science and is basically "stupid" is telling and a monumental crime against the history of "thought" in my eyes. Anyway I highly recommend the very scientific and very well made podcast the "Secret History Of Western Esotericism" for a deep dive into the genealogy of all of western thought that shakes things up a bit while giving a nice broad overview of philosophy from before the greeks until today : https://shwep.net https://shwep.net As a huge history/philosophy/math buff myself I think the world is in serious need of new historical paradigm that acknowledges that the borders between what we call Math/Philosophy/Science/Religion/Language is way more fluid than what we currently have written in our history books, and that such a reconnection to the historical roots of philosophy would be like reattaching humanity's umbilical cord after trying to separate our selfs too early from both nature and history somewhere after the enlightenment. I have struggled a bit with what I would call "coding brain" which makes it harder for me to appreciate abstract poetry or the improvisational character of social relations after a whole day of deep coding or deep math. Think Julian Jaynes crazy theories, something to do with brainwaves or left and right halves. I really have no idea why you get as locked in as you do, it's probably an evolutionary mechanism so you don't go crazy, something that shamans, philosophers and mathematicians have in common. If you force yourself (which almost no one does) to read through great poetry for a whole day, your reality tunnel begins to change from box-like to more fluid synchronistic, associative etc. Then take it one step further and begin to read "difficult" philosophy like Heidegger, Deleuze, or Kant, - really contemplate what they are saying while you read slowly (even less people do this) - and I promise you a whole new world will open up. Also try to develop visual / spatial thinking like Euclid to Einstein also employed. New modes of thinking get unlocked to use a modern methaphor. Sounds a bit crazy, but anyway that's where philosophy, math, poetry and thinking in general get real interesting!
speedplane 8y ago
> For some reason it's fashionable to bash philosophical implications of Gödel's Theorem(s). Gödel's Theorem's have been around for decades, and have been incorporated into most modern philosophical thought. Maybe the "internet['s]" view is more skeptical, but that's largely a function of it being newer than most of the literature. Gödel's Theorem's, as well as other post-modernist positions are currently receiving a backlash, overdue and well justified IMHO, the fact that they mostly appear on the internet is more a function of timing that form.
GranularRecipe 8y ago
> ... starved to death because he thought - his philosophy led him to believe - he was being poisoned. Can you elaborate on how his philosophy led to his starvation?
duckerude 8y ago
> In fact, Godel's theorem ought to be used more, not less, in philosophy. Some, like me, believe it has profound implications to moral philosophy. See: https://arxiv.org/abs/1805.08347 https://arxiv.org/abs/1805.08347 I've only skimmed it, and I'm not very familiar with moral philosophy, but this seems bizarre. If I understand it correctly, your claim is: 1. Free will is uncomputability (undecidability) 2. A good action is a free action (and therefore uncomputable) 3. A bad action is an action that pretends an uncomputable system is computable, thereby denying agency and humanity I think 1. is suspect because people are not proper Turing machines. They have limited storage and limited running time. They are not currently practically computable, but it seems physically possible to simulate them. I don't think Gödel's theorem applies, although practical uncomputability might be a working substitute. If you predict that some person will take some action, that's almost always a prediction that they will take that action within the next ten seconds/hours/decades. Actually simulating them is impossible for various reasons, but Gödel's theorem isn't one of them. You can't prove whether an arbitrary program will halt, but you can prove whether an arbitrary program will halt within the next hundred thousand execution steps. 2. seems like a really bizarre way to define goodness. I think morality is subjective enough that you could define it like that, but I don't know why you'd want to. I think the conventional view is that free will is the requirement for both good and bad actions, not that free actions are by definition good. I think 3. might cover almost every thought we have about other people. Internal computable models of other people are how we operate, as far as I know. Again, you could define badness like that, but I don't see the point. > [page 8] Now the question paraphrases to: does there exist an algorithm for me to love my child? Of course not. So the distinction between [shallow benefits] and [deep] benefits is that: there is an algorithm to bring about [shallow benefits], whereas there is no algorithm to bring about [deep] benefits. Doesn't that conflict with the idea that we are Turing machines? If we are Turing machines, then everything we do is the output of some (possibly uncomputable) algorithm, including loving people. I don't think this engages with Gödel's theorem in a useful way, or even depends on it.
- ngcc_hk 8y ago
  Does these include any arithmetic statement? Any recursive self referral statement involved? If not, Godel theorem is irrelevant
jjcc 8y ago
I personally use a term of "Extended Gödel Theorem" to explain many non mathematical topics , some paradoxical phenomena in daily life, even politics. But what I really mean is "Godel Theorem Inspired Theorems" which have some parallel analogies with real mathematical Gödel Theorem to avoid dispute.
perfmode 8y ago
Godel, Wittgenstein, Buddha
fmap 8y ago
You may be right that it is common to dismiss arguments that invoke Gödel's theorem. I've been guilty of this myself. However, just like with quantum mechanics the reason is that there are just so many people who invoke Gödel's theorem without understanding it as a technical result. I'm not talking about "pseudointellectuals" in this case, unlike with quantum mechanics. I'm talking about actual working mathematicians who use oblique references to Gödel to, e.g., dismiss formal methods or constructive logic as worthless. This is extremely annoying, since Gödel's theorem's, as the article rightfully points out, are precise statements about formal systems. There's nothing mysterious about any of it. When someone invokes Gödel you can usually take it to mean "I don't want to engage with this topic further" and not as a serious argument. > This is the man who "proved" God's existence with modal logic, I'm pretty sure that was a joke. The final assumption he makes in this proof is logically equivalent to "god exists".
- jeromebaek 8y ago
  What final "assumption" are you referring to, a definition or an axiom?
  - fmap 8y ago
    I'm referring to the axiom that being godlike is a positive property. You can show that being godlike is a positive property iff god exists.
cttet 8y ago
In my view, Godel's theorem means a lot to philosophy of mathematics and can do no more than that. I have a simpler description of the theorem that includes the details: You can choose 3 out of the 4 things within a axiom system (You can think of it as a language): 1. Completeness: No expressible statement can be neither proved nor disproved. 2. Consistency: There is no statement such that both the statement and its negation are provable from the axioms. 3. The system must be able to describe natural number 4. The system must use formal methods. (The proofs are finitistic) For mathematicians nowadays, some of them have a natural Platonist mathematics view and take away 4. Some ultrafinilist like Edward Nelson, wants to take away 3. In practical cases we can take away 1, e.g. total functional language. Some philosophers just wants to take away 2 without justify all the other assumptions. In terms of moral philosophy, a much simpler alternative to derive the undecidability of nature, Chaos theory, can be used instead of assuming 1, 3, and 4. The case here, in my view, is much less interesting philosophical than the interpretations of quantum mechanics, where most physicists refuse to discuss.

modzu 8y ago

seeing a comment like this downvoted to the bottom.. i just.. miss the old HN

modzu 8y ago
let the downvotes begin, rain them upon thee! am not looked to get myself banned but the parent comment is as outright an original, authentic, relevant comment you will find here. yet there it is, too light grey to read. serious question: what is going on?
- pulisse 8y ago
  > the parent comment is as outright an original, authentic, relevant comment you will find here The comment casts a lot of aspersions on academics but doesn't actually justify any of it.
  - zzzzzzzza 8y ago
    so, tone policing. I'm not an academic but from my limited interaction with philosophy subreddits (r/philosophy, r/askphilosophy), which seem to an outsider to have an academic bent, there is 0 interest in the intersection of cs and philosophy/ethics; so from my outsider perspective he doesn't even seem entirely meritless in his tone.
    - pulisse 8y ago
      I'm not complaining about the tone of his criticisms. I'm complaining about the absence of any justification of them.
      - deleted 8y ago
        [deleted]
Kinnard 8y ago
It's a good comment. I down voted because I do see the reason for the allergic reaction. Perhaps the diction could be improved but I think what the piece points out is a dastardly trap as you're just upon grasping (whatever can be grasped of) Gödel's Wonder. I speak as a layman.
- jeromebaek 8y ago
  If there's nothing to be grasped in "Gödel's Wonder", why do you think the man himself, who, we can reasonably conjecture, understood his theorems more than anybody else, spent the remainder of his life "grasping" at what his theorems meant? I find it much more reasonable to conclude that there was, and is, in fact something significant to be grasped, and thinkpieces like this simply want to declare that there's nothing to be grasped.
  - Kinnard 8y ago
    I meant by people like me :)
  - throwawaymath 8y ago
    Brilliant mathematicians and computer scientists are capable of making mistakes. Atiyah was a titan of his field, but in the twilight of his life he published a superfluous, incoherent "proof” of Riemann. It was so deeply flawed that not a single well known mathematician has commented on it publicly out of respect for the man - the most you can find is a MathOverflow discussion picking apart specific claims. We aren’t flying too close to the Sun if we dare to question their conjectures, even those regarding their previous work. In consideration of this point and the available evidence, I remain deeply unconvinced there is a unrealized, grand philosophical insight to be derived from whatever Gödel’s later, more obscure work had to say about the incompleteness theorems. Likewise Fermat was probably the foremost authority on his most famous conjecture during his life; but the common consensus is that he did not, in fact, have a “truly marvelous proof” of the FLT which he couldn’t fit in the margins. Everyone thinks silly things from time to time, their prior work notwithstanding. I’m inclined to believe Gödel either wasn’t as invested in the philosophical implications of his earlier work as you believe. Or perhaps he was, but I really doubt he actually arrived at a novel, rigorous result from it. Occam’s Razor suggests we would know if he had.

pulisse 8y ago

> philosophers don't understand Godel's theorem Philosophy was the disciplinary home of formal logic until the latter part of the 20th century (meaning, research in formal logic largely took place in philosophy), and Anglophone philosophy departments are still full of people who are extremely competent at formal logic. I mean, look at the figures discussed in TFA: Boolos, Jeffrey, Hintikka, Quine, Smullyan, and Nagel were all philosophers. Are you really insinuating that Quine didn't know what he was talking about when discussing logic?

jeromebaek 8y ago
Obviously I'm not talking about people like Quine; if that's your definition of "philosopher", Gödel himself would be a philosopher. You make good points, but altogether my issue is that, at the current moment, few anglophone philosophers have more than a casual grasp of Gödel's theorem. How do I know that? I was in graduate school for philosophy, then dropped out, partly because philosophers who seriously engage in, e.g. both moral philosophy and computability theory are far and few between.
- pulisse 8y ago
  > philosophers who seriously engage in, e.g. both moral philosophy and computability theory are far and few between That's a quite a bit weaker of a claim than "philosophers don't understand Gödel's theorem". To back that up you need to point to some philosophers who (a) discuss Gödel's theorem in such a way that (b) they demonstrate their lack of understanding. As it is you're just claiming that one particular subfield of philosophy doesn't have much overlap with another. How is that an indictment of the field? There are few computer scientists working at the intersection of quantum computing and database theory. There are few physicists working at the intersection of biophysics and string theory. It's not a meaningful criticism unless there's reason to think that there is something in the intersection that practitioners are culpable for overlooking, and you haven't provided any such reason.
  - jeromebaek 8y ago
    I think the reason is shallow thinkpieces like this :)

jonahx 8y ago

This should not be getting downvoted, no matter how much you disagree with its claims. It is articulate, well-written, contains novel (for me, anyway) biographical information about Godel, and is respectful enough even its critiques.

v_x_zebert 8y ago

I personally believe we live within a historiographical paradigm that blindspots large fundamental parts of intellectual history because it has been deemed to be too "philosophical" or "religious" unfortunately therefore ignoring the undercurrents or foundations of math and science which are very much "alchemical", "esoteric", "spiritual" or straight up weird. Today's list based interfacing with the internet, the nature of bite sized information surfing, the resulting fuzzy attention, and the property-based worldview makes it very difficult to transcend this paradigm of mechanical / single-threaded cognition without crossing some pretty deep and frightening oceans so to speak. Most importantly _every one_ of the great forefathers of thought were entangled in philosophical and mystical thinking which were not _only_ "silly magical endeavours" only worthy of X century but actually central to their worldview and absolutely central to the development of "how the western world is" today. Also most of them were polymaths, and so much more intelligent and broad scoped than what we give them credit for. That we see pop cultural icons like Neil Degrasse Tyson tweet that Philosophy is not a real science and is basically "stupid" is telling and a monumental crime against the history of "thought" in my eyes. Anyway I highly recommend the very scientific and very well made podcast the "Secret History Of Western Esotericism" for a deep dive into the genealogy of all of western thought that shakes things up a bit while giving a nice broad overview of philosophy from before the greeks until today : https://shwep.net https://shwep.net As a huge history/philosophy/math buff myself I think the world is in serious need of new historical paradigm that acknowledges that the borders between what we call Math/Philosophy/Science/Religion/Language is way more fluid than what we currently have written in our history books, and that such a reconnection to the historical roots of philosophy would be like reattaching humanity's umbilical cord after trying to separate our selfs too early from both nature and history somewhere after the enlightenment. I have struggled a bit with what I would call "coding brain" which makes it harder for me to appreciate abstract poetry or the improvisational character of social relations after a whole day of deep coding or deep math. Think Julian Jaynes crazy theories, something to do with brainwaves or left and right halves. I really have no idea why you get as locked in as you do, it's probably an evolutionary mechanism so you don't go crazy, something that shamans, philosophers and mathematicians have in common. If you force yourself (which almost no one does) to read through great poetry for a whole day, your reality tunnel begins to change from box-like to more fluid synchronistic, associative etc. Then take it one step further and begin to read "difficult" philosophy like Heidegger, Deleuze, or Kant, - really contemplate what they are saying while you read slowly (even less people do this) - and I promise you a whole new world will open up. Also try to develop visual / spatial thinking like Euclid to Einstein also employed. New modes of thinking get unlocked to use a modern methaphor. Sounds a bit crazy, but anyway that's where philosophy, math, poetry and thinking in general get real interesting!

speedplane 8y ago

> For some reason it's fashionable to bash philosophical implications of Gödel's Theorem(s). Gödel's Theorem's have been around for decades, and have been incorporated into most modern philosophical thought. Maybe the "internet['s]" view is more skeptical, but that's largely a function of it being newer than most of the literature. Gödel's Theorem's, as well as other post-modernist positions are currently receiving a backlash, overdue and well justified IMHO, the fact that they mostly appear on the internet is more a function of timing that form.

GranularRecipe 8y ago

> ... starved to death because he thought - his philosophy led him to believe - he was being poisoned. Can you elaborate on how his philosophy led to his starvation?

duckerude 8y ago

> In fact, Godel's theorem ought to be used more, not less, in philosophy. Some, like me, believe it has profound implications to moral philosophy. See: https://arxiv.org/abs/1805.08347 https://arxiv.org/abs/1805.08347 I've only skimmed it, and I'm not very familiar with moral philosophy, but this seems bizarre. If I understand it correctly, your claim is: 1. Free will is uncomputability (undecidability) 2. A good action is a free action (and therefore uncomputable) 3. A bad action is an action that pretends an uncomputable system is computable, thereby denying agency and humanity I think 1. is suspect because people are not proper Turing machines. They have limited storage and limited running time. They are not currently practically computable, but it seems physically possible to simulate them. I don't think Gödel's theorem applies, although practical uncomputability might be a working substitute. If you predict that some person will take some action, that's almost always a prediction that they will take that action within the next ten seconds/hours/decades. Actually simulating them is impossible for various reasons, but Gödel's theorem isn't one of them. You can't prove whether an arbitrary program will halt, but you can prove whether an arbitrary program will halt within the next hundred thousand execution steps. 2. seems like a really bizarre way to define goodness. I think morality is subjective enough that you could define it like that, but I don't know why you'd want to. I think the conventional view is that free will is the requirement for both good and bad actions, not that free actions are by definition good. I think 3. might cover almost every thought we have about other people. Internal computable models of other people are how we operate, as far as I know. Again, you could define badness like that, but I don't see the point. > [page 8] Now the question paraphrases to: does there exist an algorithm for me to love my child? Of course not. So the distinction between [shallow benefits] and [deep] benefits is that: there is an algorithm to bring about [shallow benefits], whereas there is no algorithm to bring about [deep] benefits. Doesn't that conflict with the idea that we are Turing machines? If we are Turing machines, then everything we do is the output of some (possibly uncomputable) algorithm, including loving people. I don't think this engages with Gödel's theorem in a useful way, or even depends on it.

ngcc_hk 8y ago
Does these include any arithmetic statement? Any recursive self referral statement involved? If not, Godel theorem is irrelevant

jjcc 8y ago

I personally use a term of "Extended Gödel Theorem" to explain many non mathematical topics , some paradoxical phenomena in daily life, even politics. But what I really mean is "Godel Theorem Inspired Theorems" which have some parallel analogies with real mathematical Gödel Theorem to avoid dispute.

perfmode 8y ago

Godel, Wittgenstein, Buddha

fmap 8y ago

You may be right that it is common to dismiss arguments that invoke Gödel's theorem. I've been guilty of this myself. However, just like with quantum mechanics the reason is that there are just so many people who invoke Gödel's theorem without understanding it as a technical result. I'm not talking about "pseudointellectuals" in this case, unlike with quantum mechanics. I'm talking about actual working mathematicians who use oblique references to Gödel to, e.g., dismiss formal methods or constructive logic as worthless. This is extremely annoying, since Gödel's theorem's, as the article rightfully points out, are precise statements about formal systems. There's nothing mysterious about any of it. When someone invokes Gödel you can usually take it to mean "I don't want to engage with this topic further" and not as a serious argument. > This is the man who "proved" God's existence with modal logic, I'm pretty sure that was a joke. The final assumption he makes in this proof is logically equivalent to "god exists".

jeromebaek 8y ago
What final "assumption" are you referring to, a definition or an axiom?
- fmap 8y ago
  I'm referring to the axiom that being godlike is a positive property. You can show that being godlike is a positive property iff god exists.

cttet 8y ago

In my view, Godel's theorem means a lot to philosophy of mathematics and can do no more than that. I have a simpler description of the theorem that includes the details: You can choose 3 out of the 4 things within a axiom system (You can think of it as a language): 1. Completeness: No expressible statement can be neither proved nor disproved. 2. Consistency: There is no statement such that both the statement and its negation are provable from the axioms. 3. The system must be able to describe natural number 4. The system must use formal methods. (The proofs are finitistic) For mathematicians nowadays, some of them have a natural Platonist mathematics view and take away 4. Some ultrafinilist like Edward Nelson, wants to take away 3. In practical cases we can take away 1, e.g. total functional language. Some philosophers just wants to take away 2 without justify all the other assumptions. In terms of moral philosophy, a much simpler alternative to derive the undecidability of nature, Chaos theory, can be used instead of assuming 1, 3, and 4. The case here, in my view, is much less interesting philosophical than the interpretations of quantum mechanics, where most physicists refuse to discuss.