I've used Gödel's theorem in this way before, and you're right about the implication: if no logical system can demonstrate its own validity, then that means that no *epistemological* system can either. Søren Kierkegaard also said that the whole Creation can only look like a complete system from a God's-eye standpoint, and not from the perspective of any existing person actually within the system. That would be like a character within a novel trying to occupy the perspective of the author.
Wonderful writing! I began reading Gödel Escher Bach back in the early 90s based on the fact that I love Escher and Bach. Who was Gödel? Well, I found out I didn’t really understand much of what he was saying, but could latch on a bit by putting his theorems into context with Bach fugues and Escher eye magic. But I understand him a bit better on his own terms with this piece - thanks!
There is an eternal tension between the mystic and the monastic-ascetic that weaves its way through all your pieces.
Reason may reveal Paradox, but it cannot resolve it. That's for us to live out. I think this is the great hidden Truth of the Gospels - that we are called to the sense of creative freedom you describe, but we cannot be told about it explicitly, lest it not be free.
The System is there to catch those without eyes to see. Even it has a sense of Love.
Coincidentally I've been studying formal logic this past week, having been motivated by a desire to understand Godels Incompleteness Theorems. I've not gotten nearly far enough to do that, but if I might say, the gist I was getting from it is the same gist it seems you've gotten.
Also, fuck the material conditional. It's not the natural conditional. Just needed to get that out there for the nerds who've struggled to learn formal logic, like me, haha.
“The wind blows where it wishes, and you hear its sound, but you do not know where it comes from or where it goes. So it is with everyone who is born of the Spirit." John 3:8
Beautiful piece, thank you. Maybe this is why your writing is more popular than your podcast, because it is heartbreaking, edifying, and warming to the soul. Love the podcast, too, though.
I don't think, speak, or understand mathematical language. I barely understand =. * or / are vaguely understood. What is the advantage of saying ~ instead of approximately? I have never been able to find a translation for a math formula in English; they just "explain" a formula by other formulas. And I can never be sure that what they are actually saying by that, "You're just too stupid to understand." At least with Latin, Greek, or German, most of what was said will translate into English. If math can be translated into English, why don't or won't someone do it. It's like Catholic priests who only read to parishioners a few parts of the Vulgate in Latin, with no translation into the common language of their parishioners. They didn't want then to know what the Bible said, but only what the priests said it said. It's like they knew that they were misleading their flock; the did not want the flock ever to know that there lying to them.
I guess that what I'm saying is that I don't trust mathematicians. When they tell me that it's simply a variation on the Ptetlogronian formulation, they just made it up rather than tell me the truth, that they have no idea either, but that don't want me to know that.
I guess by the same token it could be said "you can tell when someone is deceiving you even if you cannot explain how or prove it." Doesn't mean every expert is full of shit, but it does mean that expertise is insufficient for good character.
Nobody does this kind of writing better than you... fantastic stuff. Thank you.
So kind! Thank you!
I've used Gödel's theorem in this way before, and you're right about the implication: if no logical system can demonstrate its own validity, then that means that no *epistemological* system can either. Søren Kierkegaard also said that the whole Creation can only look like a complete system from a God's-eye standpoint, and not from the perspective of any existing person actually within the system. That would be like a character within a novel trying to occupy the perspective of the author.
Kierkegaard was one of the greats.
Wonderful writing! I began reading Gödel Escher Bach back in the early 90s based on the fact that I love Escher and Bach. Who was Gödel? Well, I found out I didn’t really understand much of what he was saying, but could latch on a bit by putting his theorems into context with Bach fugues and Escher eye magic. But I understand him a bit better on his own terms with this piece - thanks!
Liked cause Bach mentioned.
There is an eternal tension between the mystic and the monastic-ascetic that weaves its way through all your pieces.
Reason may reveal Paradox, but it cannot resolve it. That's for us to live out. I think this is the great hidden Truth of the Gospels - that we are called to the sense of creative freedom you describe, but we cannot be told about it explicitly, lest it not be free.
The System is there to catch those without eyes to see. Even it has a sense of Love.
Gut gesagt!
Coincidentally I've been studying formal logic this past week, having been motivated by a desire to understand Godels Incompleteness Theorems. I've not gotten nearly far enough to do that, but if I might say, the gist I was getting from it is the same gist it seems you've gotten.
Also, fuck the material conditional. It's not the natural conditional. Just needed to get that out there for the nerds who've struggled to learn formal logic, like me, haha.
"Knowing isn’t the same as “being able to explain” and your relationship with God isn’t invalid just because you don’t know how to put it into words."
Exactly and thank you. I cannot, after weeks of intermittent trying, put into words what is the ineffable and indescribable.
Your source of inspiration to explain your thinking or point is exemplary.
Thank you!
Amen, thank you
“The wind blows where it wishes, and you hear its sound, but you do not know where it comes from or where it goes. So it is with everyone who is born of the Spirit." John 3:8
Beautiful piece, thank you. Maybe this is why your writing is more popular than your podcast, because it is heartbreaking, edifying, and warming to the soul. Love the podcast, too, though.
Thank you for the compliment Ryan!
I don't think, speak, or understand mathematical language. I barely understand =. * or / are vaguely understood. What is the advantage of saying ~ instead of approximately? I have never been able to find a translation for a math formula in English; they just "explain" a formula by other formulas. And I can never be sure that what they are actually saying by that, "You're just too stupid to understand." At least with Latin, Greek, or German, most of what was said will translate into English. If math can be translated into English, why don't or won't someone do it. It's like Catholic priests who only read to parishioners a few parts of the Vulgate in Latin, with no translation into the common language of their parishioners. They didn't want then to know what the Bible said, but only what the priests said it said. It's like they knew that they were misleading their flock; the did not want the flock ever to know that there lying to them.
I guess that what I'm saying is that I don't trust mathematicians. When they tell me that it's simply a variation on the Ptetlogronian formulation, they just made it up rather than tell me the truth, that they have no idea either, but that don't want me to know that.
I guess by the same token it could be said "you can tell when someone is deceiving you even if you cannot explain how or prove it." Doesn't mean every expert is full of shit, but it does mean that expertise is insufficient for good character.