Logic, Meta-logic, Infra-logic, and the Seven Sacred I Wannas

Before circling back to The Philosophy of Being, I read something this morning that parallels Gödel's bottom-line insight into his own theorems, that

there are forms of Reason that bypass reason, and yet are perfectly reasonable and comprehensible. 

(Warren, https://www.thecatholicthing.org/2021/08/13/what-does-god-say/?utm_source=The+Catholic+Thing+Daily&utm_campaign=8d2a82a351-EMAIL_CAMPAIGN_2018_12_07_01_02_COPY_01&utm_medium=email&utm_term=0_769a14e16a-8d2a82a351-244304881.)

It seems that a lot of folks conclude the precise opposite: that the theorems imply that we are forever confined to our own formal systems, with no possibility of knowing the "truth." Well, Gödel may have been crazy but he wasn't stupid: he knew there are truths that are surely true despite being unprovable. 

Which brings to mind a wisecrack by Schuon to the effect that things aren't true because they are logical but logical because true; in other words, truth is a priori, and logic is just an indirect means of demonstrating it. But it is hardly the only possible demonstration, for (among other reasons) some of the most important truths are self-evident.  

This is why we begin with doubt, or skepticism, or the senses, but we do not end there, for the intellect is ordered to reality, not to ignorance. Nevertheless, the majority of readers well understand how modern philosophy so easily degenerates 

into an existentialism in which logic is no more than a blind, unreal activity, and which can rightly be described as an “esoterism of stupidity.” When unintelligence -- “worldly” intelligence -- joins with passion to prostitute logic, it is impossible to escape a mental Satanism which destroys the very basis of intelligence and truth.

Thus we see how modern philosophies -- which are at least wrong -- culminate in a contemporary postmodern insanity that isn't even wrong. 

Which is again why it is so fruitless to argue with postmodern progressives. For them, truth and reality are entirely beside the point. We understand them (insofar as it is possible to understand absurdity) while they never stop proving that they have no idea what we're talking about.

The craziness is pervasive here where I live in Blue Heaven, right down to our local weekly rag, the Agoura Acorn. Check out this doozy from a couple days ago: "We cannot employ colorblind ideology in a society that is far from it." Which is like saying "we cannot incarcerate murderers in a society with so many murders." 

Which they also believe, come to think of it. Which only demonstrates how

logic can either operate in accordance with an intellection or on the contrary put itself at the disposal of an error, so that philosophy can become the vehicle of just about anything (ibid.).

Yes, anything -- for if you believe men can get pregnant and give birth, there is nothing you can't believe. Likewise, if you believe math is racist or that reading standards discriminate against Africans, you're waaaaaay out there where the Buses of Reason don't run.  

Not only does man have direct contact with truth, but this is because the very substance of the intellect is truth (i.e., the image of God yada yada). However, 

when man has no “visionary” -- as opposed to discursive -- knowledge of Being, and when he thinks only with his brain instead of “seeing” with the “heart,” all his logic will be useless to him, since he starts from an initial blindness....

The fact that the philosophic mode of thought is centered on logic and not directly on intuition [falsely] implies that intuition is left at the mercy of logic’s needs (ibid.).

Back to the essay by Warren. Which I haven't actually read yet -- only the first sentence. So, wait a moment while I finish it, and with any luck it will confirm the celestial hunchwork outlined above.

Okay, this is way over the line. What's with the unchecked aggression? THE SUPREME COURT HAS ROUNDLY REJECTED PRIOR RESTRAINT!  

A jackhammer, or a buzz saw, or an electric guitar, can make a noise, but not music. Indeed, the development of "rock music," and further degeneration beyond punk, represents something different again: I would rather not give it a name.

I'll give it a name -- indeed, I'll give it seven names, the seven sacred I Wannas of Joey Ramone:

I Just Wanna Have Something To Do

I Wanna Be Your Boyfriend

I Don't Wanna Grow Up

I Wanna Live

I Wanna Be Sedated

I Wanna be Well 

and of course

Now I Wanna Sniff Some Glue

Warren is out of his element. True, God is the guest of silence. But not only silence. For while it is true that 99% of everything is garbage, this applies equally to the electric guitar as it does to theology, art, literature, blogjammin', whatever.

My only point -- Gödel's point, rather -- is this, and we'll have to put off The Philosophy of Being until the next post:

even in our most technical, rule-bound thinking -- that is, mathematics -- we are engaging in truth-discovering processes that can't be reduced to the mechanical procedures programmed into computers....  

Gödel's theorems don't demonstrate the limits of the human mind, but rather the limits of computational models of the human mind (basically, models that reduce all thinking to rule-following). They don't leave us stranded in postmodern uncertainty but rather negate a particular reductive theory of the mind (Rebecca Goldstein).

That's all I wanted to say. FINISHING MY COFFEE now. 

Logic, Meta-logic, Infra-logic, and the Seven Sacred I Wannas

Before circling back to The Philosophy of Being, I read something this morning that parallels Gödel's bottom-line insight into his own theorems, that

there are forms of Reason that bypass reason, and yet are perfectly reasonable and comprehensible. 

(Warren, https://www.thecatholicthing.org/2021/08/13/what-does-god-say/?utm_source=The+Catholic+Thing+Daily&utm_campaign=8d2a82a351-EMAIL_CAMPAIGN_2018_12_07_01_02_COPY_01&utm_medium=email&utm_term=0_769a14e16a-8d2a82a351-244304881.)

It seems that a lot of folks conclude the precise opposite: that the theorems imply that we are forever confined to our own formal systems, with no possibility of knowing the "truth." Well, Gödel may have been crazy but he wasn't stupid: he knew there are truths that are surely true despite being unprovable. 

Which brings to mind a wisecrack by Schuon to the effect that things aren't true because they are logical but logical because true; in other words, truth is a priori, and logic is just an indirect means of demonstrating it. But it is hardly the only possible demonstration, for (among other reasons) some of the most important truths are self-evident.  

This is why we begin with doubt, or skepticism, or the senses, but we do not end there, for the intellect is ordered to reality, not to ignorance. Nevertheless, the majority of readers well understand how modern philosophy so easily degenerates 

into an existentialism in which logic is no more than a blind, unreal activity, and which can rightly be described as an “esoterism of stupidity.” When unintelligence -- “worldly” intelligence -- joins with passion to prostitute logic, it is impossible to escape a mental Satanism which destroys the very basis of intelligence and truth.

Thus we see how modern philosophies -- which are at least wrong -- culminate in a contemporary postmodern insanity that isn't even wrong. 

Which is again why it is so fruitless to argue with postmodern progressives. For them, truth and reality are entirely beside the point. We understand them (insofar as it is possible to understand absurdity) while they never stop proving that they have no idea what we're talking about.

The craziness is pervasive here where I live in Blue Heaven, right down to our local weekly rag, the Agoura Acorn. Check out this doozy from a couple days ago: "We cannot employ colorblind ideology in a society that is far from it." Which is like saying "we cannot incarcerate murderers in a society with so many murders." 

Which they also believe, come to think of it. Which only demonstrates how

logic can either operate in accordance with an intellection or on the contrary put itself at the disposal of an error, so that philosophy can become the vehicle of just about anything (ibid.).

Yes, anything -- for if you believe men can get pregnant and give birth, there is nothing you can't believe. Likewise, if you believe math is racist or that reading standards discriminate against Africans, you're waaaaaay out there where the Buses of Reason don't run.  

Not only does man have direct contact with truth, but this is because the very substance of the intellect is truth (i.e., the image of God yada yada). However, 

when man has no “visionary” -- as opposed to discursive -- knowledge of Being, and when he thinks only with his brain instead of “seeing” with the “heart,” all his logic will be useless to him, since he starts from an initial blindness....

The fact that the philosophic mode of thought is centered on logic and not directly on intuition [falsely] implies that intuition is left at the mercy of logic’s needs (ibid.).

Back to the essay by Warren. Which I haven't actually read yet -- only the first sentence. So, wait a moment while I finish it, and with any luck it will confirm the celestial hunchwork outlined above.

Okay, this is way over the line. What's with the unchecked aggression? THE SUPREME COURT HAS ROUNDLY REJECTED PRIOR RESTRAINT!  

A jackhammer, or a buzz saw, or an electric guitar, can make a noise, but not music. Indeed, the development of "rock music," and further degeneration beyond punk, represents something different again: I would rather not give it a name.

I'll give it a name -- indeed, I'll give it seven names, the seven sacred I Wannas of Joey Ramone:

I Just Wanna Have Something To Do

I Wanna Be Your Boyfriend

I Don't Wanna Grow Up

I Wanna Live

I Wanna Be Sedated

I Wanna be Well 

and of course

Now I Wanna Sniff Some Glue

Warren is out of his element. True, God is the guest of silence. But not only silence. For while it is true that 99% of everything is garbage, this applies equally to the electric guitar as it does to theology, art, literature, blogjammin', whatever.

My only point -- Gödel's point, rather -- is this, and we'll have to put off The Philosophy of Being until the next post:

even in our most technical, rule-bound thinking -- that is, mathematics -- we are engaging in truth-discovering processes that can't be reduced to the mechanical procedures programmed into computers....  

Gödel's theorems don't demonstrate the limits of the human mind, but rather the limits of computational models of the human mind (basically, models that reduce all thinking to rule-following). They don't leave us stranded in postmodern uncertainty but rather negate a particular reductive theory of the mind (Rebecca Goldstein).

That's all I wanted to say. FINISHING MY COFFEE now. 

Even Paranoids have Real Friends

Let's complete our Journey to the Edge of Reason before circling back to The Philosophy of Being -- bearing in mind that a comprehensive philosophy of being is a journey to the edge of reason and beyond. 

In other words, no philosophy that confines itself to the necessarily circular and ultimately tautologous domain of reason is going to be complete. Which is indeed Gödel's whole point. 

Now, not everyone gets the point, including -- or so we have been told by the wise-in-their-own-eyes -- many experts. One such expert is Douglas Hofstadter, who wrote a popular book called Gödel-Something-Something way back in the disco era. But unlike the Bee Gees, it hasn't aged well. 

Here is an extract from the previous post, followed by a comment that cuts my coondle to the quick:

--The mind is not a computer. Sure, a lot of experts talk about artificial intelligence, but this is only because they are genuinely stupid. Or at least ignorant of Gödel.

You do know that the leading popularizer of Gödel in recent times, Doug Hofstadter, is an AI researcher?

Yes, we are aware of the book. In fact, it's buried somewhere in our vast Closet of Unnecessary Books. To be sure, these books are not totally unnecessary, as I will eventually get around to inflicting them upon the local library for profoundly serious reasons of tax avoidance.

At any rate, Gödel was a persistent Platonist (not that there's anything wrong with it), certainly not any kind of materialist. As it pertains to the possibility of artificial intelligence, he concluded that that the theorems are "decidedly opposed to materialistic philosophy," and that our intuition is "a more magnificent thing than what any machine could duplicate" (Budiansky). And 

If the mind is not a machine, then the human spirit cannot be reduced to the mechanistic operation of the brain, with its finite collection of working parts consisting of neurons and their interconnections (ibid.) 

Conversely, according to the always-untrustworthy-so-who-really-knows? Prof. Wiki, Hofstadter argues that consciousness -- not just his, but ours too! -- is but

an emergent consequence of seething lower-level activity in the brain.... he draws an analogy between the social organization of a colony of ants and the mind seen as a coherent "colony" of neurons. 

In particular, Hofstadter claims that our sense of having (or being) an "I" comes from the abstract pattern he terms a "strange loop", an abstract cousin of such concrete phenomena as audio and video feedback he has defined as "a level-crossing feedback loop". The prototypical example of a strange loop is the self-referential structure at the core of Gödel's incompleteness theorems. 

Now, his ant colony is undoubtedly bigger than mine, but that doesn't make it truer than mine. Hat size correlates with intelligence, but only in the range of r = .2 to .4. 

But let's not make an ontos out of an anthill. According to Gödel, "My theory is rationalistic, idealistic, optimistic, and theological." "It is," writes Budiansky, "committed to accessing the immaterial world of higher philosophical truths" -- truths which are again discovered, not invented, whether by us or by any conceivable number of tenured worker ants. 

Besides, ant is to queen as is many to one. And human image to divine likeness. Sort of. The point is, there's always a telovator to the top floor. 

"There are," wrote Gödel, "worlds and rational beings, who are of the other and higher kind"; these latter are "connected to other beings by analogy, not by composition."  

Moreover, "There is a scientific (exact) philosophy (and theology)" that "deals with the concepts of the highest abstractness."

Because even paranoids have real friends.  

Even Paranoids have Real Friends

Let's complete our Journey to the Edge of Reason before circling back to The Philosophy of Being -- bearing in mind that a comprehensive philosophy of being is a journey to the edge of reason and beyond. 

In other words, no philosophy that confines itself to the necessarily circular and ultimately tautologous domain of reason is going to be complete. Which is indeed Gödel's whole point. 

Now, not everyone gets the point, including -- or so we have been told by the wise-in-their-own-eyes -- many experts. One such expert is Douglas Hofstadter, who wrote a popular book called Gödel-Something-Something way back in the disco era. But unlike the Bee Gees, it hasn't aged well. 

Here is an extract from the previous post, followed by a comment that cuts my coondle to the quick:

--The mind is not a computer. Sure, a lot of experts talk about artificial intelligence, but this is only because they are genuinely stupid. Or at least ignorant of Gödel.

You do know that the leading popularizer of Gödel in recent times, Doug Hofstadter, is an AI researcher?

Yes, we are aware of the book. In fact, it's buried somewhere in our vast Closet of Unnecessary Books. To be sure, these books are not totally unnecessary, as I will eventually get around to inflicting them upon the local library for profoundly serious reasons of tax avoidance.

At any rate, Gödel was a persistent Platonist (not that there's anything wrong with it), certainly not any kind of materialist. As it pertains to the possibility of artificial intelligence, he concluded that that the theorems are "decidedly opposed to materialistic philosophy," and that our intuition is "a more magnificent thing than what any machine could duplicate" (Budiansky). And 

If the mind is not a machine, then the human spirit cannot be reduced to the mechanistic operation of the brain, with its finite collection of working parts consisting of neurons and their interconnections (ibid.) 

Conversely, according to the always-untrustworthy-so-who-really-knows? Prof. Wiki, Hofstadter argues that consciousness -- not just his, but ours too! -- is but

an emergent consequence of seething lower-level activity in the brain.... he draws an analogy between the social organization of a colony of ants and the mind seen as a coherent "colony" of neurons. 

In particular, Hofstadter claims that our sense of having (or being) an "I" comes from the abstract pattern he terms a "strange loop", an abstract cousin of such concrete phenomena as audio and video feedback he has defined as "a level-crossing feedback loop". The prototypical example of a strange loop is the self-referential structure at the core of Gödel's incompleteness theorems. 

Now, his ant colony is undoubtedly bigger than mine, but that doesn't make it truer than mine. Hat size correlates with intelligence, but only in the range of r = .2 to .4. 

But let's not make an ontos out of an anthill. According to Gödel, "My theory is rationalistic, idealistic, optimistic, and theological." "It is," writes Budiansky, "committed to accessing the immaterial world of higher philosophical truths" -- truths which are again discovered, not invented, whether by us or by any conceivable number of tenured worker ants. 

Besides, ant is to queen as is many to one. And human image to divine likeness. Sort of. The point is, there's always a telovator to the top floor. 

"There are," wrote Gödel, "worlds and rational beings, who are of the other and higher kind"; these latter are "connected to other beings by analogy, not by composition."  

Moreover, "There is a scientific (exact) philosophy (and theology)" that "deals with the concepts of the highest abstractness."

Because even paranoids have real friends.  

My Kingdom of Logic is not of this World

Is it ironic that the 20th century's greatest logician went insane? 

Or would it be ironic if he hadn't gone insane? 

Either way, the 21st century would surely have pushed him over the edge. At least the previous century was characterized by a lot of wrong ideas. Now they're not even wrong.  

Which is one of the left's patented tirade secrets: their ideas provide no sane person with a coherent or consistent toehold in reality. Arguing with a progressive is like trying to play basketball without gravity: there's nothing stable to push off of. More generally, follow any leftist argument to its conclusion, and it ends in either absurdity or self-contradiction.

Example: why do black lives matter? Because all men are created equal! Okay, so all lives matter. RACIST! Or, here's a progressive conundrum: if you place "trans-women" in a female prison, how did the females get raped and impregnated. Although it sounds impossible, keep pondering. There is a correct answer!  

Anyway, over the weekend I read this new biography of Gödel, Journey to the Edge of Reason. I enjoyed it, although there's really only so much one can say about his personal life. You could say he lived a dual existence, one side dwelling in the purest realm of abstract logic, the other in a messy haze of concrete delusions. He was only 25 when he made his most important discoveries. Then he lost his mind. End of story, more or less.

After the age of 27 the mind came and went, but when he died in 1978 it was definitely gone. As was his body; indeed, he weighed just 65 pounds. Why? Well, he had a lot on his mind. In addition to longstanding fears of his food being poisoned, the Nazis were doing their best to have him declared mentally incompetent, and had already recently sent his brother to a concentration camp. Moreover,

people hated him, he was a terrible person, the doctors were all imposters, evil spirits had removed from his desk a letter about his unfinished essay on Carnap [I hate when that happens!], and his friend Abraham Wald had actually not died in a plane crash nearly thirty years earlier but had survived and was secretly living in the Soviet Union (Budiansky).

So, he had a lot on his plate. No wonder he couldn't clean it.

Now, I saw my share of paranoiacs over the years, but then I decided to stop watching MSNBC.

The Paranoid Mind. That subject could easily hijack the rest of this post, but I think I'll leave it alone. Suffice it to say, it is fruitless to argue with paranoid types, especially when they are intelligent, which they often are. They exhibit a kind of watertight hyper-logic that can always cherrypick sufficient factual trees to support the delusional forest. It's how the media discovered Trump was a Russian spy, or how our intelligence community found out Hunter's laptop was Russian disinformation.

I'm going to highlight a number of passages that arrested my attention for one reason or another. There's nothing complete or consistent about them. Or, perhaps there will be once we specify them; in other words, maybe we'll discern a pattern. 

Starting with the theorem(s), they represent "the most significant mathematical truth of the century," the "staggeringly brilliant and paradoxical proof" to the effect that -- wait for it -- "no formal mathematical system will ever capture every mathematical truth within its own bounds."

I'm no doubt missing something, because this strikes me as common sense, and I'm no logician, let alone brilliant, although I have been known to stagger.  But if you know what the soul is and the intellect does, obviously they transcend any mathematical or computational system. The mind is not a computer. Sure, a lot of experts talk about artificial intelligence, but this is only because they are genuinely stupid. Or at least ignorant of Gödel.

Speaking of which, although the theorems were published in the early 1930s, there was no popular book on the subject until the late 1950s. Then they were used by anyone and everyone to prove anything and everything (similar to how people take the Theory of Relativity to mean everything's relative, when it implies the opposite). Deepak no doubt uses Gödel to prove that our minds create reality. 

More generally, there are people who loved the implications and people who hated them, but both camps tended to misunderstand them.

Although Gödel was a member of the famous "Vienna Circle," he ended up placing intellectual dynamite under its absurdly pretentious and narrow-minded empiricism and positivism; although he mostly kept it to himself, he inclined to

the deeper conviction that there were truths to be found not just in the empirically perceivable, but perhaps more beautiful and enduring ones in the realm of abstract conceptions, where they awaited human discovery not through tangible perception, but by thought alone.

Okay, prove it!

The rest is history. Although his proofs still haven't managed to vanquish scientism, reductionism, materialism, Marxism, atheism, naturalism, humanism, evolutionism, et al. To be sure, they've been defeated, only they don't yet know it and don't want to know: matter over mind!

For Gödel, mathematics is not a human invention but a human discovery, a proposition that has literally infinite pansophical implications. "Mathematical objects and a priori truth were as real to him as anything the senses could perceive." Same. Well, maybe not the former, since I'm no math wiz. But a priori truths are as real to me as reality, since there is no reality without them.

Gödel regarded mathematics as "a search for truth, and more specifically a search for pre-existing truths that inhabited a reality separate from the human mind."

What?! A reality separate from the human mind? Yes, it's called reality for short. It's that thing that doesn't go away even when progressives refuse to acknowledge it.

Gödel once made a gag that "It's just as hard to be wrong about everything as it is to be right about everything."

St. Thomas would approve, for it is only possible for man to be right about anything because he cannot in principle be right about everything. The first follows from the second; ideologies that pretend to be right about everything (e.g., Marxism) are inevitably wrong about everything, or at least the most important things.

This post has gone on long enough. It's not complete, but I think it's pretty consistent.

My Kingdom of Logic is not of this World

Is it ironic that the 20th century's greatest logician went insane? 

Or would it be ironic if he hadn't gone insane? 

Either way, the 21st century would surely have pushed him over the edge. At least the previous century was characterized by a lot of wrong ideas. Now they're not even wrong.  

Which is one of the left's patented tirade secrets: their ideas provide no sane person with a coherent or consistent toehold in reality. Arguing with a progressive is like trying to play basketball without gravity: there's nothing stable to push off of. More generally, follow any leftist argument to its conclusion, and it ends in either absurdity or self-contradiction.

Example: why do black lives matter? Because all men are created equal! Okay, so all lives matter. RACIST! Or, here's a progressive conundrum: if you place "trans-women" in a female prison, how did the females get raped and impregnated. Although it sounds impossible, keep pondering. There is a correct answer!  

Anyway, over the weekend I read this new biography of Gödel, Journey to the Edge of Reason. I enjoyed it, although there's really only so much one can say about his personal life. You could say he lived a dual existence, one side dwelling in the purest realm of abstract logic, the other in a messy haze of concrete delusions. He was only 25 when he made his most important discoveries. Then he lost his mind. End of story, more or less.

After the age of 27 the mind came and went, but when he died in 1978 it was definitely gone. As was his body; indeed, he weighed just 65 pounds. Why? Well, he had a lot on his mind. In addition to longstanding fears of his food being poisoned, the Nazis were doing their best to have him declared mentally incompetent, and had already recently sent his brother to a concentration camp. Moreover,

people hated him, he was a terrible person, the doctors were all imposters, evil spirits had removed from his desk a letter about his unfinished essay on Carnap [I hate when that happens!], and his friend Abraham Wald had actually not died in a plane crash nearly thirty years earlier but had survived and was secretly living in the Soviet Union (Budiansky).

So, he had a lot on his plate. No wonder he couldn't clean it.

Now, I saw my share of paranoiacs over the years, but then I decided to stop watching MSNBC.

The Paranoid Mind. That subject could easily hijack the rest of this post, but I think I'll leave it alone. Suffice it to say, it is fruitless to argue with paranoid types, especially when they are intelligent, which they often are. They exhibit a kind of watertight hyper-logic that can always cherrypick sufficient factual trees to support the delusional forest. It's how the media discovered Trump was a Russian spy, or how our intelligence community found out Hunter's laptop was Russian disinformation.

I'm going to highlight a number of passages that arrested my attention for one reason or another. There's nothing complete or consistent about them. Or, perhaps there will be once we specify them; in other words, maybe we'll discern a pattern. 

Starting with the theorem(s), they represent "the most significant mathematical truth of the century," the "staggeringly brilliant and paradoxical proof" to the effect that -- wait for it -- "no formal mathematical system will ever capture every mathematical truth within its own bounds."

I'm no doubt missing something, because this strikes me as common sense, and I'm no logician, let alone brilliant, although I have been known to stagger.  But if you know what the soul is and the intellect does, obviously they transcend any mathematical or computational system. The mind is not a computer. Sure, a lot of experts talk about artificial intelligence, but this is only because they are genuinely stupid. Or at least ignorant of Gödel.

Speaking of which, although the theorems were published in the early 1930s, there was no popular book on the subject until the late 1950s. Then they were used by anyone and everyone to prove anything and everything (similar to how people take the Theory of Relativity to mean everything's relative, when it implies the opposite). Deepak no doubt uses Gödel to prove that our minds create reality. 

More generally, there are people who loved the implications and people who hated them, but both camps tended to misunderstand them.

Although Gödel was a member of the famous "Vienna Circle," he ended up placing intellectual dynamite under its absurdly pretentious and narrow-minded empiricism and positivism; although he mostly kept it to himself, he inclined to

the deeper conviction that there were truths to be found not just in the empirically perceivable, but perhaps more beautiful and enduring ones in the realm of abstract conceptions, where they awaited human discovery not through tangible perception, but by thought alone.

Okay, prove it!

The rest is history. Although his proofs still haven't managed to vanquish scientism, reductionism, materialism, Marxism, atheism, naturalism, humanism, evolutionism, et al. To be sure, they've been defeated, only they don't yet know it and don't want to know: matter over mind!

For Gödel, mathematics is not a human invention but a human discovery, a proposition that has literally infinite pansophical implications. "Mathematical objects and a priori truth were as real to him as anything the senses could perceive." Same. Well, maybe not the former, since I'm no math wiz. But a priori truths are as real to me as reality, since there is no reality without them.

Gödel regarded mathematics as "a search for truth, and more specifically a search for pre-existing truths that inhabited a reality separate from the human mind."

What?! A reality separate from the human mind? Yes, it's called reality for short. It's that thing that doesn't go away even when progressives refuse to acknowledge it.

Gödel once made a gag that "It's just as hard to be wrong about everything as it is to be right about everything."

St. Thomas would approve, for it is only possible for man to be right about anything because he cannot in principle be right about everything. The first follows from the second; ideologies that pretend to be right about everything (e.g., Marxism) are inevitably wrong about everything, or at least the most important things.

This post has gone on long enough. It's not complete, but I think it's pretty consistent.