Religion

## The paradox of rational theology

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Nicholas of Cusa (1401-1464) isn't a household name, even among households steeped in the Judeo-Christian theological tradition. He tends to get lost in the shuffle—dwarfed by the late medieval giants who preceded him such as Maimonides, Aquinas, and Ockham, and obscured by the Reformation apologists who followed such as Luther, Calvin, and Hooker. Yet Cusa's mystical intuitions about the nature of God are among the most eerie and profound ever put to paper. Inadvertently, though, he may have sounded the death knell of rational theology.

To make sense of God, Cusa turned not only to holy scripture but to plane geometry. Here is where his main contribution lies. The axioms of geometry forced him to wrestle with the mind-boggling difficulties of infinity. Cusa began by supposing that God must be infinite—in his words, the "Absolute Maximum." It was a traditional notion in Cusa's time. Saint Anselm, four centuries earlier, had described God as "that than which none greater can be thought." But Cusa pushed the idea of God's infinite nature farther, zeroing in on the logical paradoxes that resulted from actual infinity.

Think of a circle, he said, and then think of a straight line. By definition, the circle is not a line, and the line is not a circle. Now suppose that you're sitting on a sand beach, with a wood stick in your hand, about to draw the circumference of a circle that is exactly one foot in diameter. So you start at the bottom, and you curl upwards after only a moment—after all, the circle is only one foot in diameter. If you don't start curling upwards soon enough, the circle will wind up too large. On the other hand, if the diameter of the circle you're about to draw is 10 feet, your upward curl will be more gradual. It's going to take longer. You're going to have to stand up and walk the stick around the circumference of the circle. The larger the diameter of the circle you are about to draw, the slower your upward curl is going to be. To draw a circle with a 100 foot diameter, you're going to have to drag the stick through the sand with an upward curl so gradual it will seem at first almost indiscernible.

Now think of an infinite circle, a circle whose diameter equals infinity. If the diameter of the circle is infinite, think what that would do to the circumference of the circle. If you try to draw an infinite circle in the sand, starting at the bottom, you'll never even begin to curve upwards. For the moment you begin to curve upwards, you limit the diameter of the circle—you render it finite.

Except that if you never begin to curve upwards, but just go on and on, you're drawing a straight line, not a circle. You will go on and on towards infinity in a straight line without ever curving upwards. That's how Cusa came to the conclusion that an infinite circle is an infinite line. By definition, of course, a circle is not a line. But at infinity, a circle is what it is not. Only at the point of infinity, Cusa argues, are contradictories reconciled.

It was at the point of infinity that Cusa found God. God is the Coincidentia Oppositorum—the Coincidence of Opposites. He is where things become what they are not. "God is the absolute maximumness and absolute unity," Cusa writes, "preceding and uniting things that are absolutely different and distant, for example, contradictories, between which there is no mean." In other words, God is the point at which contradictions merge into identities, at which is and is not become one.

The infinite nature of God cannot be grasped by the logic of the finite human mind, according to Cusa, but it can be glimpsed by way of another geometric metaphor. Imagine a circle, not an infinite circle this time but a run-of-the-mill circle. Now think of a square inside the circle. The square and the circle are, obviously, different. The square has four equal sides, and the circle has no sides. That's the reason you can never square a circle; you'd have to draw the circle with sides. But a circle with sides is a contradiction in terms; it's nonsensical. If it has sides, it's not a circle.

Now, again, think of that square inside that circle. Except now, in your mind, add a side to the square. Make it a pentagon, with five sides, instead of a square with four. So now you are imagining a pentagon inside a circle. Notice that the pentagon looks more like the circle than the square did.

Now imagine an octagon, which has eight sides. Imagine it inside the circle. It would look even more like the circle than the pentagon did; a dodecagon, which is a 12-sided plane figure, would look even more like the circle than the octagon did. Notice that the more sides you add to the plane figure inside the circle, the more closely it comes to resemble the circle.

But a circle has no sides.

The greater the number of sides, the nearer you come to zero sides. If you imagine a plane figure with a million sides, it becomes almost indistinguishable from a circle with zero sides. Yet it's still not a circle. It never quite becomes a circle until the number of sides becomes infinite. But the number of sides can never become actually infinite. Infinity, by definition, cannot be reached. It cannot be actualized. You can get closer and closer, but you can never quite finish it off.

Which is Cusa's point. The act of adding sides to a plane figure brings you closer to both an infinite number of sides and to zero sides. Infinity, therefore, is the unachievable, inconceivable moment at which contradictory extremes are unified. The moment at which the greatest number and the least number become one and the same.

That's also, according to Cusa, how the finite human mind glimpses, but does not grasp, the infinite nature of God. Rational thought and language fail at infinity because contradictories become identities. Human reason cannot grasp God, Cusa believes, because it is crippled by the law of non-contradiction. "Since reason cannot leap over contradictories," he writes, "there is, in accord with reason's movement, no name to which another is not opposed." The fact that the rational mind thinks in terms of finite oppositions—Socrates either is or is not mortal—rather than in terms of infinite unities keeps us from full comprehension of the ultimate Truth.

Cusa, who oozed piety in every sentence, regarded his geometric analogies as signs of God's infinite glory. Despite his intentions, however, he was laying the groundwork for an airtight proof of God's nonexistence.

That proof continues with a brief tour of the basic laws of thought. There are four: the law of identity (a thing is whatever it is); the law of non-contradiction (a thing cannot simultaneously be and not be); the law of excluded middle (a thing must either be or not be), and the law of causality (for every condition or event, there must be a cause). Despite the occasional yelps from multiculturalists and postmodernists, the laws of thought are universal. No human being has ever lived, no human society has ever existed, that did not accept and rely upon the validity of the laws of thought; they are the foundation of  reasoning and knowing. Descartes, for example, held that epistemology began with the proposition "I think, therefore I am." Yet even that rests upon three prior suppositions. Descartes took for granted that he couldn't exist and not exist simultaneously. That means he presupposed the law of non-contradiction. He also took for granted that he either had to exist or not exist, one or the other. That means he presupposed the law of excluded middle. So, too, he took for granted that he was who and what he was—that the I of "I think" was the same as the I of "I am." That means he presupposed the law of identity. Even a proposition as basic as "I think, therefore I am" invokes three of the first four laws of thought.

The laws of thought don't merely describe the way the human mind works; they're not just in-here rules. They're out-there rules as well. The world itself operates in accordance with them. They're the first and final arbiters of possibility—a point that can be illustrated using the fourth law of thought, the law of causality.

The year was 1996. TWA Flight 800, a passenger jet with 230 passengers and crew aboard, was flying off the coast of Long Island, New York when it vanished from air traffic control radar screens. The wreckage was soon discovered in the water. Eyewitnesses on the ground reported that the plane blew up in midair. But in the aftermath of the tragedy, there was no clear indication what had brought the plane down. Many theories were advanced. The National Transportation Safety Board (NTSB), charged with conducting the investigation, considered each theory one by one  and, one by one, the NTSB ruled each one out. Conspiracy buffs thought the plane had been accidentally shot down by an American fighter jet, but none was reported in the area. Plus, the fuselage of the airliner, which was painstakingly reassembled by NTSB investigators on the ground, showed no sign of missile damage.

That fact also ruled out terrorists on the ground firing a shoulder-launched surface-to-air missile—and, in any case, the altitude of the plane put it beyond the reach of such a weapon. There was no forensic evidence of a bomb on board, so that explanation was also nixed. Every probable cause of a midair explosion was ruled out. Once the probable causes were exhausted, the NTSB turned to highly improbable, unprecedented explanations. Perhaps a sudden, catastrophic structural failure caused the plane to snap in half—except the wrecked fuselage showed no signs of metal fatigue. Or perhaps a missile had detonated near the plane, and a random fragment penetrated the fuel tank, triggering an onboard conflagration—except, again, where would the missile have come from? In the end, the NTSB concluded that the likeliest cause of the crash was an explosion in the fuel tank adjacent to the left wing. But the investigators puzzled over an ignition source; they couldn't figure out what could have set off such an explosion. They speculated that faulty wiring might have generated a spark. But there was no evidence of that. As a matter of fact, faulty-wiring-in-the-fuel-tank became the official explanation only because the NTSB investigators couldn't definitively rule it out. In the final analysis, it was the only explanation left standing.

But was that a legitimate logical move? Why couldn't the NTSB have concluded that TWA Flight 800 had exploded without a cause? What if the investigators had filed a report declaring that the aircraft was flying along as usual, with nothing wrong, and then it just blew up for no reason whatsoever? Could that have happened?

The answer, of course, is no. The idea of an effect—in this case, the sudden flaming disintegration of a passenger jet—without a cause is inconceivable in the literal sense of the word. Your mind rules it out with a degree of certainty that equals, or at minimum comes very near, the certainty with which it rules out a logical contradiction. You'll entertain the possibility that a space alien from Mars transported into the jet and struck a match in the fuel tank before you'll accept the conclusion that the plane crashed for no reason whatsoever. The Martian scenario strains credibility, but at least it's thinkable. You can imagine it. The uncaused effect scenario, on the contrary, is utterly unthinkable.

To be sure, the NTSB could've decided that there was a cause of the crash, but that it is unknown at the present time—and that it likely will remain unknown. To suppose an unknown cause is an altogether rational conclusion. It's not very satisfying, but it doesn't violate the law of causality.

The law of causality, in other words, is axiomatic. It's a sine qua non of rational thought. Along with the laws of identity, non-contradiction, and excluded middle, the law of causality forms the ground floor of knowledge, the bedrock certainty that underlies all subsequent rational certainties.

The certainty and universality of the laws of thought collide headlong with the requisites of a rational theology. For such a theology cannot skirt the problem of actual infinity: Actual infinity does not and cannot exist. Here is where Cusa's happy piety begins to turn on itself. What he stumbled upon half a millennium ago was not a metaphor for God's limitless grandeur but an intimation of God's non-existence.

The claim that actual infinity does not and cannot exist sounds strange, of course. Many things are potentially infinite. For example, a line potentially may be divided an infinite number of times, but at no point will the actual number of divisions total infinity. Likewise a line potentially may be extended an infinite distance, but at no point will its actual length stretch to infinity. To leave the world of plane geometry, future time may be thought of as another potential infinite. Revolutions of the earth around the sun, for example, can be added one by one ad infinitum, but at no point in the future, regardless how distant, will the actual number of revolutions add up to infinity. (Plus, astronomers assure us that both the earth and the sun will be lost along the way.)

The reason infinity can never be actualized is that it's a numeric plural, a hypothetical sequence of ever-increasing values. It isn't a single amount, a very large number, x, but an endless series of very large numbers: x, x+1, x+2, x+3, and so on. To say that a thing is actually infinite is thus to say that it's x and x+1 simultaneously. But x+1 is also, by definition, not-x. Saying that a thing is x and not-x simultaneously violates the law of non-contradiction. Except the law of non-contradiction cannot be violated. Remember that the universality of the laws of thought constitutes our bedrock certainty.

To illustrate this idea in a more familiar way, consider that it's impossible for a man to be two ages at the same time. Even as he's getting older, he can never be, say, 33 and 34 years old simultaneously. The instant he turns 34, he ceases to be 33. The reason is that 34 is, by definition, not-33. His age cannot be 33 and not-33 simultaneously because that would violate the law of non-contradiction. So, too, with actual infinity. Since it's a numeric plural, x and not-x, infinity cannot be actualized. An actual infinity, in other words, would be a logical contradiction, an impossibility.

Which means, first of all, that the world itself cannot have always existed. If the world had always existed, it's age at the present moment—whether measured in milliseconds or millennia—would amount to an actual infinity. As an aside, Thomas Aquinas, who perhaps saw where the logic was pointing, twisted himself into knots trying to avoid this very conclusion; he argued that since one year replaces another year, we don't need to add them up as if they existed at once. However, calculating a sum always supposes the simultaneous existence of units, whether the units are temporal (milliseconds or millennia) or physical (marbles or melons). That's the nature of arithmetic. The mental act of adding them together for the sake of measurement supposes that the units accumulate rather than replace one another. Past time, therefore, must be measured as a simultaneous existence—whether that past time stretches back to a well-known point, say, the number of years since the New York Jets won the Super Bowl, or that past time encompasses the entire duration of the world.

The law of non-contradiction tells us that the world cannot have always existed. Thus, it must have come into existence in the beginning. Furthermore, the law of causality tells us it cannot have come into existence uncaused. The existence of the world, in other words, demands a Cause.

But not so fast.

There's still that problem of actual infinity.

The beginning of the world is demonstrable since the only other possibility, a world that has always existed, isn't a possibility at all. We can rule that out because it would violate the law of non-contradiction; it would necessitate an actual infinity.

But if the world came into existence in the beginning, then the cause of its coming into existence either: 1) requires a cause of its own, or 2) has itself always existed. Which means you're still staring at the prospect of an actual infinity. Either you've got an actually infinite regress of causes (a cause of a cause of a cause—with no first cause—which, taken together, amounts to an infinite multitude of causes); or you've got a first cause of actually infinite duration (an accumulation of milliseconds or millennia—stretching back endlessly—which, taken together, amounts to an infinite multitude of temporal units).

So pick your poison: Whether you choose an infinite regress of causes, or a first cause of infinite duration, the result is an actual infinity. Except the law of non-contradiction, one of the bedrock certainties of human reason, dictates that an actual infinity cannot exist. Nevertheless, there is a choice to be made. For even though both alternatives—an infinite regress of causes, and a first cause of infinite duration—result in a violation of the law of non-contradiction, their logical consequences are strikingly different.

The first alternative, an infinite regress of causes, entails the existence of an actual infinity which includes the knowable world—since the knowable world would stand as the latest effect in the sequence. But that cannot be the case; it is not possible. To suggest the reality of that which, by definition, is not possible would result in the annihilation of rational thought. The law of non-contradiction must remain universally binding in order for rational thought to retain the distinction between assertion and denial.

Consider: If an actual infinity were possible, then a logical contradiction, any logical contradiction, would also be possible. For example, a sentient stone—a "sentient non-sentient thing"—would also be possible. But a logical contradiction is not possible. The laws of thought are the laws of possibility. If a thing can simultaneously be and not-be, then it no longer makes sense even to talk about it. Again, if I assert that Socrates is mortal, I must also deny that he's immortal—or else the initial statement had no content, no meaning. If a logical contradiction can be reconciled, then an assertion, any assertion, can be reconciled with its denial. Possibility becomes indistinguishable from impossibility.

But, of course, if you can rule out an infinite regress of causes because it would entail an actual infinity, why wouldn't the same reasoning apply always and everywhere? After ruling out an infinite regress of causes, how can you then turn around and accept a first cause with no beginning–since that would also entail an actual infinity?

That indeed is the second alternative, which is the only alternative to an infinite regress of causes: a first cause, or First Cause, that spans an actually infinite duration. Once you rule out a cause of a cause of a cause ad infinitum, you're stuck with a First Cause with no beginning. That First Cause's duration would necessarily stretch across an infinite multitude of temporal units, whether milliseconds or millennia.

There used to be a loophole for this predicament, one that hinged on an ancient philosophical distinction—found in the writings of Augustine, Boethius, and Aquinas, among others—between infinite duration and eternality. Because God exists outside of time, their argument goes, He doesn't have any duration whatsoever. He's eternal, not infinitely old. Aquinas describes eternality as "the simultaneously-whole and perfect possession of interminable life." From God's eternal perspective, the moment of creation is simultaneous with the moment of your reading these words. God doesn't look back at creation, nor forward to your finishing this essay. The two events are simultaneously present from His viewpoint, whereas, from our temporal point of view, creation far precedes the moment of your reading these words. History appears to us an ongoing movie, with events happening at different times. To God, history appears more like an all-inclusive snapshot in which past, present, and future events happen at once.

The eternality loophole remained viable until 1905 when Albert Einstein unveiled his Theory of Special Relativity. Simultaneity and duration, Einstein demonstrated, are always relative judgments. Imagine a pair of twin brothers, Jacob and Esau. Jacob cannot bear their constant squabbling, so he takes off in a rocket that travels at almost the speed of light; Esau stays behind on earth. Twenty years pass on earth—which means 20 years pass from Esau's perspective. Then Jacob's rocket returns to earth. But from Jacob's perspective, only 10 years have passed. Esau is now 10 years older than Jacob. They're still twins; they were still born the same day. Neither of them is wrong about his age. It's just that the duration of Esau's life is now 10 years longer than the duration of Jacob's life. The notion that time slows down at high speeds is counterintuitive, but the phenomenon has been verified many times by experiment. Atomic clocks mounted inside high-speed jets actually lose miniscule fractions of a second by the time the jets land. Duration is indeed relative.

How does that bear on our present discussion? Consider: Even if, from God's eternal frame of reference, the notion of duration is meaningless, from our perspective, from the perspective of the temporal world, duration is real. God might be eternal to Himself; to us, His eternality amounts to infinite age. Einstein taught us that measurement of duration depends on the frame of reference of the measurer.

Einstein, to be sure, was talking about objects located in space and time. So it might be argued that the concepts of space and time cannot be applied to God's eternal existence. That, remember, is how Aquinas tried to dodge the problem of an actually infinite duration—if eternal existence doesn't admit change, then it doesn't admit time. But what the theory of special relativity does is noose up that loophole. Whether or not God experiences time is irrelevant. What's relevant is that we do. Time might not move from past to present to future from God's eternal perspective, but it does from ours. From our perspective, therefore, God does have duration. The theory of special relativity, moreover, dictates that our temporal perspective is every bit as substantial, every bit as real, as His. So if God has no beginning, which is the only way to avoid an actually infinite regress of causes, His duration must be actually infinite. (Again, from our frame of reference.) Right now, at this very moment, measured in milliseconds or millennia, God's duration must be actually infinite.

Except an actual infinity cannot be: It violates the law of non-contradiction. By definition, it is not possible.

We know that an actual infinity violates the law of non-contradiction. For that reason, we can rule out an actually infinite regress of causes—in other words, a cause of a cause of a cause ad infinitum. But that means we're stuck with a First Cause of actually infinite duration.

Like an infinite regress of causes, an infinite multitude of temporal units entails a logical impossibility. So at first glance the second alternative would seem no more satisfactory than the first if the actual infinity of temporal units were located within the realm of possibility.

Therein lies the wiggle room.

You can have an actual infinity outside the realm of possibility. You can locate a First Cause of infinite duration there. But "locate" must not be taken in the literal sense of the word. That First Cause, which, for the sake of convenience I'll call God, cannot be located in space or time or, as it turns out, possibility. Even if God cannot be spatially or temporally located, however, He can be conceptually located. He can be conceptually located outside the realm of possibility. Now the "realm of possibility" sounds rather like a Disney Kingdom. But in truth it's the most comprehensive logical category. The realm of possibility is broader than the physical world—that is, the totality of stuff—for it encompasses not only whatever is but also whatever can be. Indeed, the realm of possibility extends as far as the verb to be, as far as predicates attach to their subjects, as far as what's possible can be distinguished what's not possible.

The point is that an infinite accumulation of temporal units, an infinite accumulation of any sort, constitutes an actual infinity—which is not possible. It therefore cannot be since it would introduce an impossibility into the realm of possibility. However, there's no need to locate (again, so to speak) this singular case of an actual infinity within the realm of possibility. If we locate the Cause of the world outside the realm of possibility, that Cause becomes the Impossibility that accounts for possibility, the Nothing by which and out of which all things emerged.

Nothing, as in no thing.

However, to recognize (another inconvenient word) the Cause of the world as a logical impossibility, or rather to absent Him from the realm of possibility, is also to detach Him from rational language. We cannot speak of an actual infinity as if it were bound by the laws of thought. Actual infinity by definition defies the laws of thought. It is impossible. If the realm of possibility includes whatever is or can be, impossibility includes only whatever is not and cannot be. The latter qualification, that which "cannot be," is crucial. Impossibility consists entirely of non-being, of the impossible reconciliation of contradictories. Impossibility, in short, consists of nothing.

Here, then, is what atheism got right: God is nothing.

That is, God is no thing in the narrow sense that "thing-ness," the starting point of every rationally meaningful statement, and the baseline quality of existence, cannot be stipulated of Him. So He must be conceived as inconceivable. Posited as impossible. God, in short, does not exist. That which is no thing is not and cannot be. The realm of possibility excludes nothing—literally. Nothing is beyond the laws of thought, which circumscribe possibility, and which are invoked in every assertion or denial. Thus: God.

But without the law of non-contradiction, you cannot make true (or untrue) statements about God; they have no logical traction. You can neither assert nor deny. This was the insight that Cusa intuited but did not, and perhaps could not, confront. If I assert that God is just, I must also deny that God is unjust—or else the initial assertion was empty. But once a subject has been absented from the realm of possibility, any assertion can be simultaneously denied; whatever God is, He is not. Just and unjust. Loving and unloving. Eternal and not eternal, since God's eternality is reconcilable with its logical contradiction. God, in essence, can "be" both eternal and not eternal at once—which effectively voids the initial assertion that He is eternal. Whatever is said is simultaneously unsaid. That "is" (and even the word is here must be qualified) the nature of the non-being that precedes being, the Nothing or Nihil that caused the world.

Here, then, is what atheism got wrong: "In the beginning, God created the heavens and the earth."

That is, the first line of Genesis can be deduced from the laws of thought. The world cannot be infinitely old; therefore, it must have come into existence at a definite point in the past. The world cannot have come into existence without a cause; therefore, it requires an infinite Cause to account for its existence. But an actual infinity violates the laws of thought and cannot exist; therefore, even though God does not exist, God created the world.
Wrestle, for a moment, with that paradox: God does not exist . . . and God created the world. The two propositions seem irreconcilable; indeed, they seem mutually exclusive. But each one is dead certain, as dead certain as the laws of thought themselves.

It is a paradox that tells us as much about the limits of human reason and rational language as it does about God. Just as a sentient stone is not a thing because its definition asserts what it denies, so too God, absented from the realm of possibility, is not a thing. God's nothingness would permit the simultaneous assertion and denial of any predicate—for example, His "omniscient ignorance" or "omnipotent powerlessness" or "omnipresent absence."

That doesn't mean that thinking and talking about God, as human beings have been doing for millennia, is pointless. It's just not logically binding. Reason must continue to regard God as a thing—though, again, thing-ness supposes possibility. As Aquinas himself notes, in the relationship between being and non-being, human reason "apprehends non-being as an extreme." That's another way of saying that the mind attributes being to non-being (or, if you prefer, thing-ness to nothingness) in the process of thinking and talking about it; we superimpose possibility on impossibility. Logically, this is illegitimate. Practically, it's unavoidable. The instant we begin to speak about God, the instant the word "is" enters the discussion, we engage absurdities. Assertions blur into their own denials. Whatever God is, He isn't. The verb "to be" has been stretched too far.

That isn't where theology ends, of course.

But it is where rational theology ends.

Mark Goldblatt teaches religious history at Fashion Institute of Technology of the State University of New York. His latest novel, Sloth, was published by Greenpoint Press last year.

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1. Read our new novel, Left Behind: Geometry Class.

2. Holy crap. That’s a lot of ink spilt in the name of jibber jabber.

1. tl;dr

3. I havent made it all the way thru the article but its clear that Cusa wasnt familiar with limits.

Maybe he would have done better if he come after the invention of calculus.

1. I made it less far than I thought I did, I didnt even make it thru page 1.

Goldblatt, Goedel. Goedel, oh, you dont need to meet him. But he really needs to meet you.

2. My head hurts! Actually, a very interesting article.

The limit does not say infinity exists, it says that as you approach infinity, then a relationship approaches a certain value or can be reduced to another relationship.

4. He died in 1464 and sounded the death knell for rational theology? How long is this rational theology thingy gonna linger on? 647 years is a long time to be kicking after the bell has rung.

1. There is a difference between rational theology and rationalized theology.

1. Man is a rational animal, therefore he rationalizes.

1. Man is a rational animal

[citation needed]

1. I publish, therefore, I am.

1. Cogito cogito, ergo cogito sum?

1. Um, Auditum feci, ergo sum.

1. Gunter glieben glauben globen

1. Surdi Pardus.

2. …of Ulm.

3. Cie la vie.

Cie la guerre.

Say no more.

2. Ren? Descartes was a drunken fart. “I drink; therefore, I am.”

1. I stink, therefore, I am

2. SugarFree|8.22.11 @ 12:22PM|#
Man is a rational animal
[citation needed]

You prove it by asking for proof.

2. 547 years….

5. Also:

Apparently Cusa and/or Goldblatt never read Flatland. Cusa has an excuse, what with being dead before it was published.

6. Mark Goldblatt teaches the Bible in the History of Ideas at the Fashion Institute of Technology of the State University of New York.

I’m sure this dorm-room plays much better with his student body than it will on H&R.

1. That should be “dorm-room bullshit.”

1. That didn’t play well.

2. What?

7. gonna have to disagree on a few things

quantum mechanics involves a lack of the causality principle in a few of its concepts. It might be wrong, but people most certainly can conceive of it. Specifically, the electron is just “randomly” moving in the probability cloud area or whatever.

and as per the laws – I wouldn’t really explain them as being laws of reality so much as our description of reality. They pretty much describe the limits of semantics. They only describe the limits of reality to the extent that language accurately describes reality.

1. There is a cause. And the cause of its final, “instantiated” position is the observer.

1. Maybe, but where the particle appears “just happens”. It will probably be near the last place you saw it, but exactly where it will be is random. In fact, it may be anywhere the next time you look.

1. So the result of the cause is statistical rather than specific?
OK, what are you arguing?

2. Cop: Do you know how fast you were going?

Heisenberg: No, but I know where I am.

2. Exactly. Seems the problem here is the ironclad assumption of the truth of these laws. The limits of our reasoning power have to do with our own limits of understanding. The universe is not bound to be comprehensible to us.

1. well like I said, it’s not a matter of whether or not the world is strictly comprehensible to us; the laws themselves really only describe semantics

1. “the laws themselves really only describe semantics”

Uh,

3. Please don’t talk about things you know absolutely nothing about. This is something almost all popular accounts get wrong about quantum mechanics. Quantum mechanics obeys causality. In fact, it obeys multiple versions of casuality. There are variations of it that obey Galilean relativity (the standard run-of-the-mill kind of casuality), Einsteinian (special) relativity, and there are attempts to incorporate it with Einsteinian general relativity. That’s where all the stuff about string theory and quantum gravity comes from. The causality applies to the wavefunction of the particle, however. Concepts like “position” and “momentum” are ill-defined concepts in quantum mechanics; sometimes they are well-behaved properties of a system, sometimes they aren’t. But this doesn’t not mean that quantum mechanics is some kind of post modern hippie paradise. It means that asking “What is the position of a particle?” is sometimes like asking “What is the IQ of a piece of wood?”; a question that is inherently meaningless.

1. pwnd

2. Thanks for your explanation – very insightful.

3. I will report this account to others. Wait! I wouldn’t know what I’m talking about so I probably shouldn’t say anything!

4. yup.

they can conceive of it. otoh, wasn’t it feynman who said “NOBODY understands quantum physics?”

1. That no one understands quantum mechanics is a running joke among physicists because when you study quantum mechanics (and the experiments that corroborate it) you see a lot things that don’t (at first) make sense. They don’t make sense because our intuitions about what matter is made of at a macroscopic level lead to wrong conclusions at the microscopic level of quantum physics. No one understands on an intuitive level–at least at first.

If you’re fairly smart and really want to understand Quantum Physics at a basic level, you can. Here’s a good primer:
http://lesswrong.com/lw/r5/the….._sequence/

I’m kinda disappointed I haven’t seen an “Introduction to Quantum Physics” at my local universities that covers this material with the aim of teaching it to non physics and/or math majors.

5. I doubt the explanation of quantum mechanics offers. It is a useful model given what little we know about subatomic relationships. Imagine this though:

You’re a being that is observing the earth. You live for a vast period of time 100,000 + years, and time passes very rapidly for you. Further, your current technology only allows you to perceive nuclear explosions, you cannot detect humanity. From your perspective, the nuclear explosions would appear causeless and random. You might even come up with nonsense explanations along the lines of quantum mechanics, and as you develop your theory, they might have some ability to predict the explosions (perhaps an explosion will happen every 100 years or so).

In any event, quantum mechanics is a useful model, but it should not be taken as a counterexample to reality.

8. How sophomoric.

9. reading further i see he’s talking about the creation of the world.
However, he sloppily applies the 4 laws as laws of reality. Again, things outside of them can be conceieved. The current understandings of the big bang involve the universe just coming into being, almost as a consequence of space-time itself. But that space-time itself is just assumed. How the universe itself was caused may not even be a scientific qwuestrion, and the assumption of causality could itself be considered a kind of bias.

If anythingg all this really explores is the limits of science. It becomes pretty clear that science cannot answer every single question – the issue of causality will always bring up the issue “Well, then what caused THAT” once the cause of something is discovered

1. M-theory can account for a non-causal creation.

2. The universe may adhere to certain ‘laws’. This in no way means subsequent (or previous) universes, assuming there can be such, must adhere to the same ‘laws’. As far as other universes, what existed before the ‘big bang’. What will exist when this universe implodes? (Again, there are many assumption as to the validity of current theory, etc.)

1. This in no way means subsequent (or previous) universes, assuming there can be such, must adhere to the same ‘laws’. As far as other universes, what existed before the ‘big bang’. What will exist when this universe implodes? (Again, there are many assumption as to the validity of current theory, etc.)”

Other than the fact that this universe exists.

3. We understand more about what “caused” the universe than most people think.

For instance the total energy of the universe is zero: youtu.be/7ImvlS8PLIo

1. Link didn’t work; try again?

4. Yes, my immediate thought was, putting aside theology, God, whatever,-it seems to (at least to)me, that you still have the question of what caused the universe to come into being; and, if the theory that a huge mass of basses existed before the universe, where did THAT come from? Also, My understanding of quantum mechanics was that particles are in constant flux, so all we perceive is what we think we’ll see, not the actual state of the particle.

10. So the poster tried to mathematically prove that his deity is unknowable to man using circular logic (yes, intended). Except it proves nothing. Math is a tool, not an end. You can’t mathematically prove the existence of god simply using geometrical tricks (or at all for that matter). It’s beyond absurd.

12. the whole talk about the world not being able to have been there forever being impossible assumes it has to have an age. That’s a big assumption that’s also false. Maybe the universe just has existed forever, end of story. The whole concept of a progression of time involves entropy more than anything else, time in a general sense is really only the capability of change in the universe.

1. And that ignores the possibility that what we perceive as time is just slices of an extant unchanging reality that already exists — that everything, past and present and future, exists simultaneously and unchangingly.

2. “That’s a big assumption that’s also false”
Cite missing.

13. I can’t tell who this guy hates more Physicists or Mathematicians.

“There are four: the law of identity (a thing is whatever it is)” – Except when it isn’t, see “virtual particles”, or for a a little more nuance, “entanglement”.

“the law of non-contradiction (a thing cannot simultaneously be and not be)” -this definitely happens, it’s called “Superposition”.

“the law of excluded middle (a thing must either be or not be)” – Again, see “superposition”.

“and the law of causality (for every condition or event, there must be a cause).” – Again, see “virtual particles” who show up randomly then disappear. These 100% exist and we have evidence.

For all this blah blah blah about infinity, he really glosses over the fact that there are two distinct infinities within formal logic, countable and uncountable. And, yeah, one is bigger than the other. Wacky, huh?

I’m pretty sure he hates physicists the most in general, but you gotta think he has a special load of hate for Kurt Goedel specifically.

1. There are an infinite hierarchy of infinities.

1. Yes, but they are all equivalent to one of the two mentioned above.

1. aleph-null, and aleph-1, are distinct and I have some vague idea about them. That these two are the only infinities that can be concieved I hadn’t heard postulated. Has someone tried to prove that? It seems a much stronger statement than the continuum hypothesis.

And the article – more about semantics than anything else – but vaguely interesting.

2. There are an infinite number of distinct infinities. Given any one infinity, you can construct a larger one by raising, say, 2 to the power of the given infinity. Cantor first showed this in the 19th century. The only open question is how one should apply them to thought and logic.

1. No, there aren’t, there’s just the two. I don’t know what you read by Cantor, but I assure you that isn’t what his results were. Countably infinite is the infinity most are familiar with (the cardinality of the set of natural numbers, etc.) Uncountably infinite is the power set of set of countably infinite cardinality. Or the cardinality of the set of real numbers (also the cardinality of the reals inbetween zero and one). So, no, countably infinite raised to the 2nd power is still countably infinite. Only the power set of a set who’s cardinality is countably infinite has a distinct and infinite cardinality, namely, uncountably infinite.

This is math, and there is no debatable opinion, you’re simply wrong.

1. Mike, you are wrong. Aleph-null is the countable infinity and Aleph-one is the uncountable infinity corresponding to the power set of the countable infinity. Subsequent infinities can be constructed by taking the power set of the previous one. So there are (at least) a countably infinite number of infinities. It is true that all infinities after aleph-null are uncountable, so in that sense there are only countable and uncountable infinities.

2. In fact, the “law of the excluded middle” is more of an opinion than a law. Perfectly good systems of logic can be constructed which deny the law of the excluded middle. (See L. Brouwer and intuitionistic logic,for example.) Too bad Mr. Goldblatt relies so heavily on it.

14. “the instant the word ‘is’ enters the discussion, we engage absurdities.”

Dude, that’s what I’ve been trying to tell you!

1. If you want any of the stuff I’m smoking, just ask. I obviously have lots.

1. Not even I could make a bong big enough to make Goldblatt make sense.

1. That’s so funny – you kill me!

Wait – no you didn’t. Now I’m confused.

No, I’m not.

1. If you’re having existential discussions about nothing, you could at least mention my name. Or not.

1. Did someone mention Being and Nothingness?

1. Hey, what are you guys talking about?

1. Nothing.

15. this entire article is rife with instances of the author proposing a law, and then applying it repeatedly over and over again and listing off in pseudo-logic, without ever checking back to see if his assumption doesn’t apply in some context. It’s the sort of nonsensical pseudo-logical wandering endemic of libertarians, so it’s no surprise that’s it appears in reason magazine as some sort of disproof of God.

Some similar logical gems I’ve heard from libertarians: things have to either be property or people with full rights, so your kids are your property. If a woman employee stays on the job after you grope her, she’s consenting, and so you’re not violating her rights. If you have the right to own something, you have the right to defend it, and if you have the right to defend it, it wouldn’t make sense to say you defended it too fiercely, because how could you have the right to defend it if you can be censured for that action later? Therefore, you can kill anyone or do anything to them for even the slightest transgression, so that guy who actually murdered a kid just for walking across his lawn isn’t a murderer, he was just defending his property.

Libertarians clearly don’t thoroughly grasp the concepts of logic and reasonable dialogue. They’re smart enough to follow logic to a certain extent, being kind of nerdy, and so they find it stimulating to do, and they get stuck on the process/math and end up ignoring the actual concepts contained therein.

1. Yes, good call. Libertarians really think this blah blah blah.

Maybe you should try reading the comments where everyone calls this a pile of bullshit before assuming everyone has bought it.

1. Also, some other things you may want to consider and keep in mind for future reference:

1. Some libertarians do believe in God
2. Not all libertarians agree on most topics
3. Most libertarians do not make generalizations about non-libertarians

Since you’re so good at logic, please provide me with the proof that shows that an article posted on reason.com means that everyone who has read it agrees with it.

1. those are actual positions that libertarians have held repeatedly both on these threads and elsewhere

I never said that all libertarians agree with this article, but it is showing of the kind of butchered logic that libertarians frequently use

You said :”Libertarians clearly don’t thoroughly grasp the concepts of logic and reasonable dialogue. ”

“but it is showing of the kind of butchered logic that libertarians frequently use”

Who? In which instances?

2. It’s the sort of nonsensical pseudo-logical wandering endemic of libertarians, so it’s no surprise that’s it appears in reason magazine as some sort of disproof of God.

Libertarians clearly don’t thoroughly grasp the concepts of logic and reasonable dialogue.

I guess I missed the part of these two quotes where you proved that this article being on reason.com means that it is the standard libertarian position.

NB: I am neither a (true) libertarian nor do I believe in a god.

1. “this article being on reason.com means that it is the standard libertarian position.”

those phrases don’t imply that.

Again, it was a general statement on libertarian “logic”.

See? You suck at logic.

1. It was a demonstrably false set of statements not in accord with reality.

So, yes, someone sucks at logic. His name starts with “e” and ironically ends with “win”.

1. I dunno what you’re saying but I was commenting on crappy libertarian pseudo-logic in general. Again, this whole article is rife with it, and his basic mistakes are not surprising.

2. “Who? In which instances?”

I gave a few examples right there.

1. No, Edwin, you did not. You always claim “libertarians say..” and never indicate anything more specific beyond that.
That’s textbook generalization, buddy.

1. it was just last week Old Mexican and other posters were re-affirming that Mugrage guy’s right to murder that kid for walking across his lawn. Matter of fact, they were claiming the whole thing is some kind of conspiracy on my part for me to justify “taking whatever I want”…. when we’re talking about a guy that fucking shot a kid for no good reason.

1. “fucking shot a kid for no good reason.”

Do you have a link? Just curious. would like to read up on it.

3. derp

2. Why are you picking on libertarians? Almost no one thoroughly grasps the concepts of logic and reasonable dialogue. I think you are probably right about libertarians, but regular old liberals and conservatives are even worse in my experience. Blog comments are not a good way to find out about these things in any case.

3. Libertarians clearly don’t thoroughly grasp the concepts of logic and reasonable dialogue.

1. generalized phrases aren’t meant to be absolute and apply unanimously to groups. And groups can indeed have tendencies and qualities in aggregate. Forests and trees and all that.

If you really understood logic and semantics, you’d understand that. But you don’t, and you’re trying to take a childish swipe.

4. Good job writing about the problems with the article. But man, you hang around with some wacky libertarians! I’ve never heard any of those propositions being put forward by intelligent libertarians, although they are the type of ideas presented by trolls posing as libertarians on message boards.

I recommend following Reason Online for a while to get an idea how libertarians think when they are engaged with reality.

1. it was just last week Old Mexican and other posters were re-affirming that Mugrage guy’s right to murder that kid for walking across his lawn. Matter of fact, they were claiming the whole thing is some kind of conspiracy on my part for me to justify “taking whatever I want”…. when we’re talking about a guy that fucking shot a kid for no good reason

the secretary-groping thing was also backed by numerous posters here a few months ago

1. no matter the group of libertarians, these sick-fuck positions come up and are held by a few within the group. Given how few libertarians there are andf the consistency of the phenomenon, along with the screwiness of more basic libertarian posoitions, the phenomenon is significant. Again, it reveals a butchered logic.

1. Oh man, I can’t believe I just wasted a minute of my life reading this arguement. I wish I had been travelling so damn fast at the time it was only 30 seconds wasted.

3. So.. take it up with them and stop collectivizing. If your mind cannot comprehend what an individual is, that’s your problem.

16. Seems to me that if we accept the universal truth of the ‘laws of human thought’ then he’s successfully proved that a finite universe of limited duration cannot exist, because it must be caused by something that can’t exist (infinite causes or a cause of infinite duration). Something’s got to be wrong with that logic given the universe does in fact exist.

Further towards the end, he falls into the typical semantic traps of all theists, defining ‘whatever it is that caused all of this’ as God, and by implication all of the things we traditionally associate with ‘God’ (all powerful, all knowing, non-corporeal, morally good etc.). No reason to suppose that a first cause or infinite cause actually needs to have those properties (other than by logical non-sequitors that assume if I use the word “God” to define something then it also contains all the other meanings of “God”). I could equally define the first cause as the “Giant PB&J Sandwich” and then go on to assert that my worship of PB&J sandwhiches is justified by logic.

1. Apart from those of us who are allergic to peanuts, worship of PB&J sandwiches IS justified by logic!

17. Well….[time from my life I’ll never get back, etc. etc. etc.]

18. Theology is a device for enabling agnostics to remain within the church…enough said.

19. The Octagon. Wasn’t Chuck Norris in that?

20. Things that both are and are not are quite common in quantum mechanics. A light wave is split and goes down two paths until the photon is measured, then it is on one side only. Actual infinities exist until they are measured. It is the measurement that makes them finite. The author is trying to measure God, and since it is and actual infinity, he can’t.

21. Things that both are and are not are quite common in quantum mechanics. A light wave is split and goes down two paths until the photon is measured, then it is on one side only. Actual infinities exist until they are measured. It is the measurement that makes them finite. The author is trying to measure God, and since it is and actual infinity, he can’t.

1. Yes! Excellent point.

2. “The author is trying to measure God, and since it is and actual infinity, he can’t.”

Truly a stupid claim.

22. Here is true rational theology: we cannot know anything about God except what He chooses to reveal to us about Himself. And how do we distinguish what He revealed about Himself from that which is falsely purported to be about Him? By the occurrence of events outside the realm of possibility – i.e., miracles. This is the essence of the rationale given by both Peter (Acts 2:32,36) and Paul (Acts 17:31) to both Jewish and Greek audiences.

1. Feel free to prove that such miracles happened.

1. That’s where the faith part comes in. Although the book of Acts is almost certianly historical at its core.

1. I think this was all before Mary joined the band so maybe that’s part of the problem.

2. From “The Devil’s Dictionary”:

Faith: n. Belief without evidence in what is told by one who speaks without knowledge, of things without parallel.

1. Faith: Things our puny, small, limited rational minds can’t prove that are outside of our comfort zones or belief systems that includes Atheism.
I have talked to men of science who were Atheist, they have admitted even to me they will never discover every principle, law, etc. in the universe, that it is impossible. Me I am agnostic, this just confirms to me that my agnosticism is correct.

2. Both men I mentioned point mainly to the resurrection of Christ as the sign of his divinity. There is no record of any serious attempt to refute the validity of the resurrection, even by those who stood to lose much by its spread (including Jewish religious leaders and even the Roman occupiers). Many people have believed it *couldn’t* happen, but it’s hard to say it *didn’t* happen.

1. “…but it’s hard to say it *didn’t* happen.”

Given that Logic 101 states you cannot prove a negative, asking someone to prove the resurrection DIDN’T happen would be like me asking you to prove you’re not a pedophile.

2. Did Resurrection Myth Precede Jesus?

“The way the early church fathers defended against the mystery religions showed that they knew these pagan myths antedated the Christian ones. Justin Martyr (c160-165) claimed that the devil plagiarized Christianity by anticipation with the pagan religions in order to lead people from the true faith. He claimed the myth of the virgin birth of Perseus, an ancient Greek legend that preceded Christianity, was pre-copied by the “deceiving serpent” (Dialogue with Trypho: 70). Similarly he asserted that the cultic rites of Mithraism had a diabolical origin (Apology 1:66). Tertulian (c160-c225) made the same claim: that it was the devil that provided this ‘mimicry’ [notes omitted].”

3. Both men I mentioned point mainly to the resurrection of Christ as the sign of his divinity.

If your evidence is some quotes in the Book of Acts, then you’re using the Bible as evidence for the truth of the Bible.

There is no record of any serious attempt to refute the validity of the resurrection, even by those who stood to lose much by its spread (including Jewish religious leaders and even the Roman occupiers).

Really? Celsus seemed obsessed with the subject.

Many people have believed it *couldn’t* happen, but it’s hard to say it *didn’t* happen.

1. Let’s try the link again. http://heterodoxhomosexual.blo…..ncept.html

2. “This is the essence of the rationale given by both Peter (Acts 2:32,36) and Paul (Acts 17:31) to both Jewish and Greek audiences.”
Don’t forget Mary!

3. Kevin L|8.22.11 @ 1:10PM|#
“Here is true rational theology: we cannot know anything about God except what He chooses to reveal to us about Himself.”

Theology you got, not even close to rational.

23. I’m guessing that the Fashion Institute of Technology doesn’t have any required courses in either quantum mechanics or transfinite numbers.

1. Though I’ll lay odds that a few transfinites attend the Fashion Institute of Technology…

1. dude, that’s funny!

24. I’m lost. Somehow he thinks he shows the world wasn’t caused, but hasn’t always existed.

Pages and pages of this guy tying himself into logical knots. After the last couple paragraphs I can’t even figure out if the guy believes in God or not.

25. I got all the way to the 4th page of this when I realized that I wasn’t in the other room kissing my girlfriend and enjoying my finite span of life on this miserable planet.

1. That’s funny you were typing this while I was trying to make the same basic point:)

26. Looks like several people beat me to particle-wave duality and the Uncertainty Principle.

That being said how does any of this help me get drunk or laid? This is why I quit reading theology and philosophy. It’s a total waste of time as evidenced be the time the author spent trying to link all this BS together. I mean what is rational theology? Also, I think the Council of Nicea and the whole Trinity nonsense smashed all of these concepts to hell (pardon the pun) long before Nicolas was even born.

1. That’s the point of studying theology and philosophy…to wrap your mind in circles to the point that you throw your hands up in disgust.

Then you don’t have to think about it ever again and you’re much happier than everybody else who still thinks about it.

1. Good point

27. I love it when the mathematically illiterate use incorrectly to prop up a bias they hold dear.

28. As a phD candidate in mathematics (specializing in algebraic geometry and algebraic number theory), I have to take issue with his use of infinity. The development of limits, introduced by Newton and Leibniz and placed on firm footing by Cauchy and Riemann, and Cantor’s development of set theory belie the assumptions presented within this article. In particular, their ample usage of infinities and their practical utility within the sciences (limits are the foundation for calculus, which is utilized throughout science and engineering; set theory is the basis for computer science) shows that the understanding of infinity presented herein is incorrect.

I say this as an atheist scientist with no particular love for rational theology.

1. I don’t really understand why it took calculus to debunk thought experiments like the “octagon inside a circle” one.

I have never thought of a circle as having 0 sides. I always thought it had 1 side – a curved lined described by a pretty straightforward formula, R*Pi. And they had that formula even back in Ancient Greece. So it’s not infinity sides turning into 0 sides, it’s infinity sides turning into 1 side. Right?

1. Or, if you understand limits, you always think it has infinity sides.

1. Pretty much thought that was the definition of a circle; (infinite) sides, each a point of zero dimension.

2. Infinity has its own problems in set theory re: Wittgenstein; infinities in calculus seem a little different. I’m not convinced that calculus deals with infinity so much as arbitrarily large or arbitrarily small quantities.

1. Calculus is all about what happens at infinity. Read through Kolmogorov & Fomin or Rudin.

Wittgenstein’s criticisms of infinity were basically the same as Brouwer’s. However, those areas of mathematics that are entirely predicated upon transfinite arithmetic (such as topology and analysis) have resisted formulation through finitist methods and have been necessary in many applications outside of mathematics, ranging from quantum mechanics and general relativity to electrical circuit analysis. The finitist and intuitionist schools of mathematics have essentially died out for lack of utility within both mathematical theory and application. Hence, most mathematicians take either Hilbert’s or Plato’s views on the philosophy of mathematics. I side with Hilbert here, but both are widely represented both within my department and within the worldwide mathematical community, and stand in distinct contrast to the finitist views espoused by Wittgenstein.

Hence, the marketplace of ideas finds finitism and intuitionism lacking in explanatory utility when compared with views that are compatible with ideas descended from Cantor.

29. Good job everyone; way to impose 20th century perspectives on a 15th century thinker. Now it’s time to wreck the ludicrous ramblings of that idiot Ptolemy.

1. Best comment so far, purely for laughs.

1. Boy, was I wrong!

30. Modern physics demolishes your weak argument. Consider: “But was that a legitimate logical move? Why couldn’t the NTSB have concluded that TWA Flight 800 had exploded without a cause? What if the investigators had filed a report declaring that the aircraft was flying along as usual, with nothing wrong, and then it just blew up for no reason whatsoever? Could that have happened?”

As it happens, the answer is yes. In quantum theory, a partical can be here one instant and there the next. There is a small but nonzero probability that a moment from now you’ll be in St. Louis, or on the surface of the moon.

This is science. Better brush up on it before posting more late-night-dorm-room drivel like this article.

1. Not that this has anything to do with your comment, but I’ve worked with several former TWA employees in the aviation MX field, and they’re very adamant that the official story is full of bullshit.

1. Curious – what do they think really happened?

1. That it was shot out of the sky, basically. The coworker that I worked with most frequently told me some of the flight and maintenance crews did in fact see an object collide with the plane. I can’t recall much else from the conversations other than he was most adamant about what he and others saw.

1. should read: “worked with the most frequently”

2. Sy|8.22.11 @ 2:18PM|#
“That it was shot out of the sky, basically.”

Goody for them.
They’re wrong; unicorns landed on the wings and ruined the lift.

1. Yes, so the feds and FAA have repeatedly said.

2. No, they realized the futility of existence and simply ceased to be.

31. “That proof continues with a brief tour of the basic laws of thought”

Since there are limits to what the human mind can comprehend, it seems rather illogical to use contrived human laws of logic to try to contain a discussion about the infinite.

1. I agree completely.

32. Wait. The author teaches “religious history at Fashion Institute of Technology??” That’s funnier than the rest of this silly piece.

History of theology at FIT: From “Oh my God to “Oh my God Oh my God!”

1. > History of theology at FIT: From “Oh my God to “Oh my God Oh my God!”

Very good!

33. Honestly, this is just shabby:
“No human being has ever lived, no human society has ever existed, that did not accept and rely upon the validity of the laws of thought; they are the foundation of reasoning and knowing. Descartes, for example, held that epistemology began with the proposition ‘I think, therefore I am.'”

I call bullshit. Plenty of people have doubted the veracity and validity of their own thoughts and perceptions. Descartes was one of them. That’s why they built formal systems of rules for logic and evidence. Societies that practiced trial by ordeal recognized the law of thought? Shabby thinking.

34. Theology as the teaser said is not dead. Bonhoefer’s “Cost of Discipleship” is incredibly meaningful even though it was written nearly a century ago. JP2’s theology of the culture of life vs the culture of death stimulates one to reconsider the Un-PC aspects of our modern culture.

Our churches would rather spew leftwing politics from the pulpit or repeat the basic tenets of Christianity over and over till they become meaningless, than celebrate and teach the great theologic advances of the recent century and the current day.

35. Obviously, Goldblatt never studied Set Theory in Mathematics. Nor even basic calculus. Go read about the Axiom of Choice (or Zorn’s Lemma), Goedels proofs, cardinality of infinite sets, convergent infinite series, etc. Dunno who edited this one, but it certainly wasn’t John Derbyshire. Yuck.

36. You gotta love how, after four pages he just throws up his hands and comes up with this gem:

“Here, then, is what atheism got wrong: “In the beginning, God created the heavens and the earth.”

Shorter Goldblatt: I believe in God and cannot be bothered by rational thought.

Pathetic.

1. Pretty much what god-talkers do.

37. Geebus how sophmoric. I was expecting to see history on Cusa and his writings, that would have been atleast somewhat intersting given the time period and the context. Instead we get a few mentions of him, and then three and a half pages of pre-calculus, gifted grade school student level meditation. Geee thanks for describing a square and a circle in such details. Way to step up to the plate with quality reading material, Reason

38. This is why no one should graduate from high school without understanding calculus.

1. I’m fairly sure that a huge percentage of the population is utterly incapable of understanding calculus.

Perhaps you should have said that no one should be able to matriculate without understanding calculus.

But then where would we get education majors?

39. This is embarrassingly bad. A nonsensical attempt to shoot down a crudely constructed mash-up of the cosmological and ontological arguments for the existence of God. The “loophole” you think you have tightened is actually wide open, my friend. Go read William Lane Craig’s treatments on the actual infinite and the Kalam for a much more coherent discussion of space-time and theology.

40. Nobody tell this guy that a parabola is really an ellipse with infinite eccentricity, or his head might explode.

41. “But x+1 is also, by definition, not-x.”
Not generally true. In fact,
x + 1 is equivalent to x (mod 1) for all x. Whether x+1 is equal to x or not very much depends on the structure of the objects you are working with.
In the case of the size of infinite sets, adding or removing one or any finite number of elements from the set does not change the size of the set. One could vaguely translate this to say that for any finite number A, and for any non finite value(cardinality) INF, INF + A = INF – A = INF, although I am not presently aware of any accepted standard for doing arithmetic with non finite values. Most likely this is because it is not very useful since many operations are not defined (the difference between two equal cardinalities cannot be defined much like division by 0 cannot be defined), but it could also be because it leads to inconsistencies (I’m not aware of any so far).

1. There is a way to do it: define numbers strictly as cardinalities of sets, and then define: a + b as “the cardinality of a set C composed of the union of A and B, where A and B are disjoint and A has cardinality a and B has cardinality b”. That way, all the transfinite cardinalities are properly defined as numbers, and you have ?? + 1 = ??, etc.

42. That was a lot of words burned to say, “Rational theology is an oxymoron.”

43. The paradox of rational theology
Rational Theology….what the hell is that???

44. Most religious believers take revelation and reason rationally from the principles. They never claim to be arguing from empirical fact.

If the author had figured that out, he’d have saved the time of writing this article. Nicholas of Cusa has the excuse of having written before the Enlightenment. The rest of us have no excuse.

Honestly, don’t even atheists prefer it when religious people at least *try* to argue rationally rather than irrationally, even if their premises are in empirical dispute? Isn’t it better than nothing? Better “man is born into original sin, therefore we must limit the power of individuals” than “I see the image of Christ burned into my holy toast!”

Wait until one of them god damn fundies in the Republican Party replaces that sack of shit with big ears.

1. Wait until one of them god damn fundies in the Republican Party replaces that sack of shit with big ears.

You overestimate the sincerity of politically motivated proclamations by candidates for public office. That’s assuming you can find any that actually support your ideas of what ‘fundies in the Republican Party’ want.

1. Regardless of the duplicity on the part of Republican candidates, there is a multitude of fundies in the electrate that will vote them in.

2. “Wait until one of them god damn fundies in the Republican Party replaces that sack of shit with big ears.”

And how do you define the sack of shit? Seems he spent a good bit of time with a whacko ‘preacher’,

1. The sack of shit and the “whaco preacher” are not fundies in the religious sense. They are socialists and racists. They both hate Capitalism and whites.

46. References to quantum theory are good.

The whole Mandelbrot set (which is infinite, assuming infinite precision) is contained in a (very definitely) finite generator function.

At the very beginning of the observable Universe (Big Bang Theory) even the laws of physics weren’t the same as now, so any logical axioms taken over from current physical reality are suspect.

47. Man, this is terrible. “Fashion Institute of Technology”? You teach this crap to budding supermodels or something?

“That’s the reason you can never square a circle; you’d have to draw the circle with sides.”

Er, what? The phrase “squaring the circle” refers to the ancient struggle to geometrically construct a square with the same area as a given circle, and the reason you can’t do it is because it happens to be equivalent to showing that pi is the root of a polynomial with rational coefficients, which it ain’t. It has nothing to do with trying to “draw the circle with sides.”

And there is no “law of causality”. The idea of an absence of causality may make us uneasy, but why expect the world to behave in a relaxing fashion? There are real physical theories that say that sometimes specific events do just happen, with no specific cause that we can ever possibly determine even in principle. They’re some of the most successful physical theories ever conceived.

The reason you cling to such non-laws is not because all rational thought depends on them, but because your wild flight of fancy seems to.

And you call yourself “rational”? You throw that word around like a politician with “principles”.

Similarly you don’t actually present an argument that infinity cannot exist. You merely insist that it doesn’t, like some camp designer throwing a hissy fit. You assert that for the universe to have an infinite age, it must first be constructed by ageing steadily from a finite beginning. But therefore you have simply assumed that it is finite to begin with – you’ve begged the question. What if it is and always has been infinite in size and age? There is no need for it to become infinite from a finite origin.

Plainly it is permanently impossible to tell whether or not the real physical universe – including the parts we cannot perceive – is infinite in age or extent, and hence the possibility remains that it may be.

Also your understanding of Special Relativity seems to halt at about 1907, just before Minkowski made his vital contribution that later inspired Einstein’s General Theory. If we take space and time coordinates as referring to “events” in a combined 4-dimensional space-time, then there is no disagreement between observers. The subjective “relativity” vanishes and we have restored a shared picture of independent reality. The space-time analogue of the distance between two points is called the “interval” between two “events”, and if two observers convert their observations into this form, they agree perfectly. So if it pleases theists to claim that their god has a universal perspective, Relativity has nothing to say against it.

If I were you, I’d stick to proving that vertical stripes make you look thin. Keep it vocational.

48. I used to wonder why I had to take Calculus and physics classes to be a doctor. Well, I still do, but now I know why they need to require it for theology majors. Infinity is not some nebulus impossibility, it is an important principle to solve some of mankinds most perplexing problems:)
Like what if my interest were compounded countinously – or what is the optimal size of soup can. You see if you add up an infinitly small particle an infinite number of times you get something.

This article does nothing to clarify exogenesis, calculus or infinity. Pure garbage

1. “This article does nothing to clarify exogenesis, calculus or infinity. Pure garbage”

Says a bleever, by any chance?

49. So I guess we can conclude that the only thing this article achieved was a Rickroll of the H&R community.

50. You can’t fool me, sonny! It’s turtles all the way down!

51. Fashion Institute of Technology? That’s a joke right?

52. Fashion Institute of Technology? That’s a joke right?

1. Also known as Frock U.

1. +7

53. That rationality does not comprehend the Gospel. That Jesus Christ existed is an indisputable fact. The history and eyewitness accounts are sufficient in a court of law. As C.S. Lewis said, We have three choices than.

1. Jesus is who He said He is–God
2. He is a liar-contrary to the evidence
3. He was deluded-contrary to the evidence.

God came into the creation as a man, through a virgin birth, paid the penalty for humans that sinned against a Holy God, and through faith are reconciled to God.

1. In what way are 2 and 3 contrary to the evidence?

2. Jesus claimed to be the Messiah (like a number of his contemporaries), but in his Jewish culture, the messiah was not necessarily thought to be “God in human form.” I’m not aware of any biblical quotes in which he clearly claimed to be God in human form. Can you cite a passage?

Then there is the question of whether the gospels, written long after Jesus died, correctly quoted his words.

So there are a few more choices:

4. Jesus did not say he was God
5. He said he was God, but he did not mean that all of God was contained within his human form, but rather, meant something else (e.g., that the spirit in each of us is God).

Also, what contemporary records are there of Jesus’ existence? That he existed is only an indisputable fact if (1) he’s referenced in contemporary writings, and (2) we have proof that the person so referenced is the same dude that the gospels were talking about.

Personally, I think he was probably real, and was just one of several rabbis of his day teaching about love, forgiveness, and not judging others, and/or claiming the mantle of “Messiah.” But his teachings were not unique, even with respect to Jewish philosophy. Look at Hillel, for example.

1. “Before Abraham was born, I AM.” ~ John 8:58

Just saying.

1. Thanks for the cite. It does sound like the author of John included quotes to support the idea that Jesus did claim to be God. Of course, that still doesn’t solve the problem of whether the quotes were accurate, especially since they are in John, often considered the least historically accurate of the four gospels. If Jesus clearly claimed to be God, I would expect the synoptic gospels to include that claim as well. It’s an odd thing to leave out.

1. You’re claiming there is a “least historically accurate” gospel?
Try Ehrman: “Lost Christianities”.
There is not a shred of evidence of any accuracy in any of the gospels.

2. Steve Premo|8.22.11 @ 5:12PM|#
“Jesus claimed to be the Messiah…”

Right.
Care to point to *any* historical corroboration for the existence of junior?

3. “Personally, I think he was probably real”

Yeah, and most of us bleeved in Santa Claus.
Until we were 5YO or so……..

3. oft|8.22.11 @ 4:30PM|#
“That Jesus Christ existed is an indisputable fact…”

That’s GREAT! I’ll bet you got a million of ’em!
Bullshit.

54. I think I’ll have a beer.

55. I think not.

56. What he is arguing against are paradoxes and paradoxes are very real. One needs to simply look at G?del’s incompleteness theorems to see some examples.

This exact same argument can be used to say that we don’t exist either, you run into the same problem of “the beginning”. Since I am thinking, I must exist. Since I exist then there is a problem with this argument. Where the problem lies is the question and like all paradoxes there is not a way to tell where the problem is at.

A question for Mr. Goldblatt: where do these four laws of thought originate? (Antony Flew asked a similar question regarding the laws of physics.) As for the nature of God, Mr. Godblatt ignores existing answers from East to West: Taoism’s Founder, Loa Tzu: “The Tao that can be spoken is not the eternal Tao/ The name that can be named is not the eternal name,” and Jewish Medieval philosopher, Maimonides’ “Apophatic theology” or Negative Attributes. So, Mr. Goldblatt can argue that Positivistic (but not all rational) philosophies are create an appearance of paradox, but he is incorrect in stating rational theology is dead.

1. “but he is incorrect in stating rational theology is dead.”

58. Oh good grief.
My thoughts leading me to belief stemmed simply from “If God is spiritual, then only by spiritual observation could I determine His existence (or lack thereof) and nature.” No need for all this nonsense.
And I couldn’t quite tell why a finitely old universe would need to be created by an infinitely old source.

59. i like matt and trey’s take on it.

the only thing stupider than believing god exists, is looking at all the stuff (more things in heaven and earth) around us and claiming that it happened “just because” without a god.

it saves us paragraph after paragraph of strained pseudointellectual bullshit

1. “the only thing stupider than believing god exists, is looking at all the stuff (more things in heaven and earth) around us and claiming that it happened “just because” without a god.”

Shorter:
“I don’t understand it, therefore a god must be involved.”

1. If you don’t start believing soon, Mr. dunphy might get his “buddies in blue” to try and “change your mind”. By which I mean they’ll kick your ass.

60. There are major problems here, as is often the case with such QED!!! articles that attempt to prove sweeping claims in a few thousand words (see, Richard Dawkins). There is a reason good analytic philosophers teach their students to value the word ‘seems’ above all others.

As far as the author’s ‘law of causation’, that ‘for every condition or event, there must be a cause’, it is not a law as such, but rather his assertion of the theory of Causal Determinism as law. The nature and relata of causation are far from decided, much less a law of thought. Perhaps his biggest mistake is in claiming that uncaused events are inconceivable. They are not (see, Michael Jubien).

And, as other posters have commented, the author seems to lack awareness about Godel’s incompleteness theorems, without which any discussion of modality and set theory is a non-starter.

61. My parents have a neighbor who suffers from manic depression. Sometimes when he goes off his meds and has a manic episode, he stays up all night and writes things like this.

Oh, by the way, did you know that there are philosophers who specialize in metaphysics and religion who actually have worthwhile things to say about this topic?

Hint: Mark Goldblatt is not one of them.

62. This essay was just silly. There is no such thing as “rational” theology. There never was and there never will be. Isn’t it obvious that belief in God or Allah or whatever is based on faith and tradition? It always has been and apparently always will be. Theology is not dead. But I can say with certainty that as long as there is religious belief there will be attempts to explain it. This is what theology is about. Countless individuals have tried throughout human history to explain religious belief and all have failed. Just as an aside religious belief has nothing to do with geometry, that’s just wacky. I used to belong to the Reason foundation when I lived in Santa Monica. I understand where you are coming from but your chosen task makes Sisyphus look like a slacker. In my 53 years on Earth I have learned that people, all people, need to believe in something bigger than themselves, and that goes for atheists as well. It’s a complicated and contentious issue that is not going away. So keep your day job.
PS: I thought your rules of thought were tendentious and created a dispute where there is none. How many people think of their religious faith in this way? I’d wager it is close to zero out of 6 billion people. Worst of all is that this circular, non argument has nothing to say about why religion is so important to humanity and always has been. It is navel gazing at its’ worst.

1. “In my 53 years on Earth I have learned that people, all people, need to believe in something bigger than themselves, and that goes for atheists as well.”

Uh, as an atheist, I’d *love* to read how you’ll defend *that* statement.

63. THANK U

64. Ren? Descartes walks into a pub and the bartenders asks, “What will it be, the usual?

Ren? Descartes says, ” I think not” and promptly vanishes.

65. Just to make it clear:
There is not one shred of evidence for a sky-daddy or a mud-mama.
The universe exists and some part of the relationships of the parts of that universe are now understood, due to this (post-hunter-gatherer) human endeavor called “science”.
It has two wonderful attributes: It is communicable to other humans (doesn’t rely on personal ‘revelations’) and it does a pretty good job of prediction.
When any one of you bleevers comes up with a single airplane that flys ’cause the sky-daddy said so, or a single internet that works ’cause mud-mama says so, I’ll listen.

1. I take it from your wording that you’re talking about our existence, our realities. Now, can you show me where it is confirmed that only our reality can exist. That there can be no other reality, no alternate existence.

You follow the reasoning of the creationist, who insists that God must exist in our reality, when there is no proof that such applies.

As far as we know there could very well be a reality with God, and that this God is in contact with our reality. For we inhabit but one of a possible infinity of realities, and some of these reality contradict what we know to be true.

1. Alan Kellogg|8.22.11 @ 11:12PM|#
“I take it from your wording that you’re talking about our existence, our realities. Now, can you show me where it is confirmed that only our reality can exist.”

No, I can’t. Can you give any evidence otherwise other than silly bleeving?

2. When you demand the standard of Sola Empirica! you’re making a metaphysical claim, which by your standard is bullshit. You may want to actually learn a little philosophy. Also, Aquinas’ theory of consciousness actually holds up pretty well in light of modern neuroscience and the big bang theory originated with a priest. Just to name two useful contributions from “bleevers”. And if those were the only two contributions they’ve already contributed more than the new atheist movement ever will.

66. No, I haven’t read all the comment, but I have read enough to note a theme going through so many of them. The idea that our reality is the only reality, and that there can be no other.

Mark specifically spoke about alternate realities, in fact about one particular reality which is not our reality where such contradictions as God and infinity can and do exist.

Now the existence of this alternate reality depends on one proposition that whatever we imagine, no matter how implausible or non-sensical, exist in the meta-reality holding our reality. This is an hypothesis that cannot be, at the present time, tested, and so cannot be proved or disproved.

In short, there are more things in Heaven and Earth than are expressed in your philosophy.

1. “Mark specifically spoke about alternate realities, in fact about one particular reality which is not our reality where such contradictions as God and infinity can and do exist.”

And the unicorn Sam told me you’re full of shit.

1. You would consider only the stockyard and ignore the whole of the farm.

1. “You would consider only the stockyard and ignore the whole of the farm”

You invent fantasies an hope that ignoramuses bleeve them.

2. Oh, and Mark is also full of shit.

1. For an argument to be persuasive it must not only be succinct, it must also be pertinent.

1. “For an argument to be persuasive it must not only be succinct, it must also be pertinent.”

3. “In short, there are more things in Heaven and Earth than are expressed in your philosophy.”

In short Allan can invent bullshit and hope that someone buys it.
Please tell us of the evidence for “heaven”.
I’m waiting…….

67. From the fact that a limit may have different properties than any of the objects in the sequence we get… talking rocks !?!. Really? To quote:

“If an actual infinity were possible, then a logical contradiction, any logical contradiction, would also be possible. For example, a sentient stone?a “sentient non-sentient thing”?would also be possible.”

1. But if it has limits, then how can it be an infinity?

Since our reality, by its very nature, forbids infinity in its contradictions, then for infinity to exist there must be a reality where infinity is not a contradiction. And since our reality is one where infinity is contradictory, then it can’t be our reality that has infinity

1. I am using the word limit in the mathematical sense. If we have an infinite sequence which (in some sense) approach a different object we call the object that it is approaching a limit. For instance, the example given in the article of a square embedded in the circle. We then keep adding sides to the square getting a pentagon then a octagon and so on. In the limit (when the number of sides approach infinity) we are left with a circle.

Similarly, is we take a sequence of circles of increasing diameter then (in a certain sense) the circle can be though of as approaching a line as described in the article as well.

Why this means that our reality forbids infinite I do not understand. I am not saying that reality allows infinity (I am not a physicist). How ever these examples do not generate contradictions and certainly not on the level that the author is implying.

I mean… talking rocks!?!

1. Pretty sure you’re wasting time here, but, hey, I do the same with xian-bleevers and mud-mama-bleevers.
It can be amusing.

2. Why this means that our reality forbids infinite I do not understand. I am not saying that reality allows infinity (I am not a physicist). How ever these examples do not generate contradictions and certainly not on the level that the author is implying.

I couldn’t figure out whether or not the article was intended as an introduction to negative theology. And having a math geek as a best friend I know enough to know that his math is bad and his examples worse.

About the only good thing about the article is that I’ll probably read Nicholas of Cusa to see how badly the arguments were muddled.

68. “Since our reality, by its very nature, forbids infinity in its contradictions,”

Since it does not, please try some other bullshit.

1. Yeah, dude, you have all the answers. Only you know what is real and what isn’t real. Sounds pretty dogmatic to me.

69. The argument is based on false categories, and limited in its sense of both time, eternity identity and causality. Reason can foolishly boxes itself and then complain that it cannot see beyond its own boxes.

The so-called “laws of thought” are not as categorical as Mr. Goldblatt contends.

The law of identity (a thing is whatever it is) — Identity is violated by a tree. A tree has leaves. The leaf is not the tree; but the leaf is the tree. A leaf is, and is not, at least within the realm of being a tree.

The law of non-contradiction (a thing cannot simultaneously be and not be).

A tree violates this “law” also. A twig is not a tree and at the same time the twig is a tree.

The law of excluded middle (a thing must either be or not be).

One cannot say with definity, or by other than arbitrary distinction, where the tree and the branch are distinguished, but the branch is distinguished from the tree, but the mean between them is continuous and not excluded.

The law of causality (for every condition or event, there must be a cause).

A tree is the subject of multiple causes — which are also its ends — a previous tree that gave the seed, to which end the growing tree itself seeks to generate seed; water is a cause of germination and growth and an end the tree’s roots seek in that growth. Sunlight causes and orients the growth, but is also an end that the tree seeks in its growth.

Man fell in seeking the fruit of a tree unsuited to his unaided nature.

Jesus said “I am the Vine; you are the branches.” “No one comes to the Father except by Me.”

Mr. Goldblatt is correct, we cannot of our own power reach even the ideas of eternality, much less the reality. We require a mediator between what is impossible for us, and what is possible for God.
The life of man is more like a tree than it is not, in terms of the redoubtable “laws of thought.”

Our petty realm of imaginable possibility is mapped onto His unimaginable and unimaginably vast realm of possibility but in one and only one locus — and only because He offered Himself for that purpose — Jesus Christ.

70. What if C-A-T really spelled dog?

71. Those four “basic rules of thought” are just that— basic rules not of REALITY, but of thought. Man is a rational animal— that is to say, an animal whose thought is limited to certain pragmatic rules.

Modern logic recognized dialethism, something that spiritual traditions also recognize, and which modern physics validates. Our notions of being are so limited.

I suppose the bottom line is that this “Squaring the Circle” Gnostic, Randian babble demonstrates not true understanding, but a dogmatic and religious opposition to dogmatism and religion.

1. AndyK: “Our notions of being are so limited.”

This literary comment was fascinating and topical:

“The doorknocker asked, ‘Where do Vanished objects go?’
‘Into non being, which is to say, everything,’ replied Professor McGonagall.
‘Nicely phrased,’ replied the eagle door knocker, and the door swung open.”

In other words, when an object vanishes, or ‘ceases to exist’ as we might say, it does not actually cease its being — it enters non-being, which is not a loss of being but a joining of its distinct being to all being, not nothingness — merely losing its ready distinction from everything else.

Connections are deeper and more meaningful than distinctions, without dismissing the reality of the distinctions.

Guilllermo Suarez: “The change ,of the change, of the change ,……. regardless of change ,the change is the same(constantly iterating into infinity yields a constant answer).”

72. The function “e” can be infinitely differentiated ie the process(derivative) can be repeated an infinite(what ever that may be) number of times for all time(what ever that is) and yet it always equals the original function. Ubiquitous , and unassailable tool for understanding ,predicting,and explaining the Universe. The change ,of the change, of the change ,……. regardless of change ,the change is the same(constantly iterating into infinity yields a constant answer). A paradox ? Contradictory in scope and range , conclusion which we can’t explain. Just a thought regressing into infinity.

73. It’s not clear that the author’s law of causality is axiomatic like the previous 3 laws of logic. If it is such that all things that exist must have come into existence or have not previously existed at some definite point, this contradicts his reasoning regarding the 3 logical axioms. Being axiomatic, they must always exist. This also brings into question as to the cause of the law of causality–which appears to be a contradiction. The author’s definition of the law of causality is overloaded. In his argument, the author uses an indefinite term, “world” to describe that which must have come into existence by a cause, and that the world has a certain definite beginning. If the author means “The Planet Earth” instead of “world”, this is reasonable scope, at least regarding the object being caused. However, it still assumes too much. If he is equivocating Existence as such with “world”, then he sows the destruction of his own position. Existence as such, i.e., the sum of all things (including the axioms) must be, and must always be. They cannot be caused to be, because the causing agent would also be part of that which exists. All that exists, by being the sum of all things, cannot have a cause. This eliminates the problem of infinite regression of causes. It also eliminates the possibility of transcendent beings (aka “gods”) that can exist outside of existence (another contradiction). If one takes this position, the axioms hold. Causality itself is not axiomatic, but rather an aspect of these laws of thought and Existence. A good reference would be part of Rand’s metaphysics outlined by Dr. Leonard Peikoff. I think he provides a strong argument for this position. Unfortunately, I’m just paraphrasing. Their axiomatic and causal concepts circumvent these problems regarding infinity as well as others that have plagued philosophy. I believe Dr. Peikoff also uses similar examples by Aristotle as to why infinity can be only a potential and not an actual, especially regarding the problem of Xeno’s paradoxes.

1. Actually, causality has only been established to any degree by observation (and of a infinitesimal proportion of events) of physical phenomena, so I agree that he’s overloaded the axiom. Mental phenomena have not been shown to have any such chain of causation.

However, I would dispute the claim that axioms “exist”. The symbolic representation of axioms exist, but axioms themselves are descriptions; adjectives and adverbs, not nouns. Nor is it valid to subject “Existence”, that is, the collection of all existent things, to this sort of analysis. This is because trying to make it into a single object is illegitimate; “Existence” is just a shorthand, implying a descriptor, “those things that exist”. Essentially your argument rests on an illegitimate semantic trick. We, and only we, sum all of existence together; those things which exist are not, themselves, a sum. Models are not reality.

Four pages, and all that Goldblatt has managed to do is show that
God, if He exists, cannot exist within the rules and bounds of the physical universe as we know it.

But that’s kind of the point of the whole God thing, innit?

75. The law of causality is not a “law of thought”, it is merely a theory supported by inductive evidence, and really, a tremendous number of assumptions, and discounting still mysterious action of consciousness. Further, the law of the excluded middle is denied by constructivists, as is proof by double negation. Therefore, two of your assumptions are controversial. However, even accepting your premises, something caused by nothing has no cause, and as such, you appear to be using contradictions to prove a contradiction. Why, then, should we prefer your contradiction to the others?

76. The TriPrimality:

“Bob” is.
“Bob” becomes.
“Bob” is not.
Nothing is; Nothing becomes;
Nothing is not.

Thus: Nothing Is Everything.
Therefore: Everything is “Bob.”

77. Nothing Is Everything.

78. What’s most interesting: Nobody cares

79. The “whole story compressed and quick”:
(3.3 billenia aprx ago, Gabrielnews) yes telepaty from campanulaflower plants, eye-portals on some creatures, “etc”…
Lillibeth, the former Addam’s wife, a Goddess (of reproduction plentity…”), after doorway teletransport Addam&Eve; for such ossady, joinned (publicly) the Archangel of the eternities (4 of 1 billion/years each: Eden, Eter, Elba and Atlas, “great sign: “Noah’s” flood), you know, the fallen one…
The Goddess still using timeweaponry to punish mankind, the dark Archangel tryes to apeace her hate, he has enough with God’s loyals to “deal with” and the (ET joinning loyal Celestials are not helping… Mars, the “new power rising” has a ET RAY CUT you can see forever on Martian ecuador… usual Celestial “touch”)…
more… some other time…

80. I’m afraid there are several issues with this article. In particular a terrible notion regarding infinite. For instance, the author stated that a circle with an infinite diameter cannot be drawn, therefore, infinite is impossible. Following that line of thought, zero does not exist, since a circle with a diameter of zero cannot be drawn. By destroying zero, you have collapsed logic itself. Suddenly, 2-2 does not exist. The absence of objects is only possible in my imagination: everything exists.

I don’t want to bore all of you with deep mathematical notions but I’d recommend reading the fantastic book by Charles Seife: Zero, The Biography of a Dangerous Idea. This material will give you an idea of the mistakes of logic done here.

81. many enemies has have mankind, pluss the “actual times” (thru time): any kind of “\$ocial leaders”, auuthoritie\$, conventional comunist enemies, their acorn\$ terror states, dictatorships (accepted/tolerated instead of Mosse’s Bush enlightments, etc), neolibtiCAL\$, rinoliphant\$, not accepting A DAUGHTER OF EVE SHALL BE A GOOD CHOICE AGAINST too many “formidable” mounstruos levels globalwarmed FRAUD OF MANKIND candidates, SUN CONTROLS WARM/COLD 3 years cycles, Jupiter makes warm and sun’s blackspot activities, and the other cause: polar magnetic axis angle, up: hot, down like now moves: cold.
But now, the megatreason helping sharialaw (org\$, wich destroyed ussr(‘u\$ neolibland, BLACKPAN TIES IMPUNITY, acorn, hammas, ayatola and castros preffer bhorK instead of Bush…)… makes visible any anti-American (oil, coal, gas, nuke, culture, not assymetriCAL castrocoyote/auuthority santuaries without God at schools instead of sodomic prision jam/any rap assymetrical culture of death/violence, etc, surely a “descendence of lilibeth’s mankind… “reproduction plentity sodomic abortion rule”… even “on to the ending of the world”…
A daughter of Eve, not a “divine deity gov “speakers or Hogan’s heroes campgard schultz, powers, or summer warmings, from other worlds…
Na, na na, we EAT chicken, we need A STRONG NEST, straight shooters, sWORD masters, tot govsmarta\$\$e\$, we need God back INTO HIS/HER, NO “MIDDLETERMS”, ah!, yeah, SPIRIT, we don’t need a castro preffered instead of Bush telepropter lecturer, no “sophi\$tiKaTED social thing\$”, just family under God, no more than a woman who can cryout for the future and life’s children, loud, from TEA TO SHINNING TEA women like Sara Palin or Michele Backman is what THE PLANET NEEDS, the mother… Earth, TEA MOTHER EARTH…

82. ah!, the female (is called the winged woman of war, announced Jesus, the son of Mother Mary) archangel Gabriel was still talking to Mars rebelion to surrender and recieve considerations, when like on Helmsdeep, but an ET “just shot the Ray against the Martian ecuador”… oops…
ah!, dinosaurs where so inmortaly strong, they survived mostly of them, the global fire/water tsunamies… but the size of the asteroid was “perfect” to change down the polaraxis, making “big” megaiceages, medium and minies ones…

83. I’m sorry Kara…

1. ooops: sWORD masters, tot govsmarta\$\$e\$, sWORD masters, NOT (more)govma\$ter\$…

84. Likewise a line potentially may be extended an infinite distance, but at no point will its actual length stretch to infinity

What the hell? I thought that lines by definition are infinite!

Actually, this was a very interesting article – particularly the metaphor of God as a circle of infinite radius. Cusa is hardly the only person to make that analogy; Jorge Luis Borges’ The Fearful Sphere of Pascal traces that idea (or, actually, the idea that God is a sphere of infinite radius) through a number of thinkers, all the way back to Xenophanes of Colophone, 2500+ years ago!

85. Just awful. Treatment of actual infinity completely wrong…conflation of quantity with possibility. Just one mess of nonsense from beginning to end. Reason magazine..stay out of the theology business!

86. I don’t think very highly of this article, for many of the particulars gone over above. My real comment is how did this get through the editor to publish?

87. I enjoyed the article until: “The world cannot have come into existence without a cause; therefore, it requires an infinite Cause to account for its existence.” Why the hell an INFINITE cause?

1. I think (and I hate to sound like I am defending this badly written article) that he is referring to every cause then needing a cause. If the universe began with a big bang, what caused the bang? What caused the cause of the bang to cause the bang? The “uncaused cause” as it is sometimes called goes on and on, which is why you need an “infinite cause.”

Basically this article butchers physics and mathematics and brings up an obscure theologian (who is probably not very well known for a good reason) in order to present Pascals Gambit in a really convoluted and annoying way.

88. This was interesting to read, but some logical blunders beginning on the second page wound up leaving the argument hollow.

To avoid unnecessary length, let’s just look at the initial blunders on the second page. You claim that infinity nowhere exists actually, but only potentially. Your train of thought skips the rails in two (chief) places.

First, you keep limiting the “actual” existence of infinity to mere “potentialities” of infinity. But, this limiting actually has its genesis in your own fallacious application of finite and concrete ideas to necessarily infinite and abstract ones.

Consider one of your examples. You say a line can “potentially” be divided an infinite number of times, “but at no point will the number of divisions” we make, equal infinity. This is not at all relevant to the actual, present and complete existence of infinity within even this finite line. Where has your argument broken down?

Well, of course humans will never finish making or noting an “infinite” number of divisions in a line. We’re finite and experience time in a succession, and so from our perspective there is always a theoretically greater number of divisions to mark, and hence we never reach the “infinite” number so long as there is yet more time and yet more divisions to make. But, this doesn’t mean the infinite number of divisions isn’t already there, it just means our finitude is not capable of exhausting their notation in the finite experience of space-time.

More importantly, though, this shows how you have framed the concept of infinity in entirely faulty premises. Because you think of infinity as an “ever-increasing” numeric plurality, you mistakenly conclude that no man will ever be able to say he has yet finished making the infinite divisions.

*Yet.* There’s the trick! You superimpose concrete, finite concepts of human activity and experience of space time, upon the abstract concept of the actual and paradoxical infinitude of the line. You mistakenly conclude from this that the infinity is “potential.” It’s not – it’s only the human conceptualization of this infinity in your concrete terms, that is potential. The infinity is right there, conceptually and abstractly, whether we could ever mark it or not. We already know and perceive that there are infinite number of divisions groupings in the line; the infinity is actual and even perceivable, abstractly.

The heart of your error lies in phrases like this: “The reason infinity can never be actualized is that it’s a numeric plural, a hypothetical sequence of ever-increasing values.” This is not at all what infinity is, and it shows that you are not trying hard enough to abstract the concept of infinitude from our concrete experience of number and limit. “Ever-increasing” already introduces the concept of measurement. “Numeric plural” indicates a total failure to really grasp what is meant by infinity. Infinitude is not a “sequence of ever-increasing values,” still less a “numerical plurality.” It by definition excludes such concepts. The closest approximation we can get to conceptualizing an infinitude, is to conceive of it as an integral whole beyond our ability to measure or quantify in any way (and so an inability to speak of “plural” or “increasing,” etc.). In fact, if you read some of the great Greek Fathers of the Church, they describe how, ultimately, infinity is even beyond the concept of a “unity,” since it is not only beyond all concept of plurality, but is even beyond the concept of “one” and number altogether, and so beyond even concepts of integrity, wholeness and unity.

Don’t take my criticism personally; these topics are fun to explore, but we have to be doubly careful to sharpen our powers of abstract thought. It is an easy and natural mistake, to allow our concrete experience of things to intrude upon concepts that must, essentially, be considered in the abstract. By all means, keep up the discipline and enjoyment of contemplating such topics, and strive for greater purity in your abstract considerations of this topic.

In Christ,
Fr. Augustine

1. Well said Fr. Augustine. I wish I didn’t have to read through every comment to have made it to yours. But, you seem to ignore in your example that although a finite object may be abstractly infinitely divisible, is much different than saying that time may trace back infinitely. One appears to be more abstract than the other. In fact, saying that time traces back infinitely is in many ways quite concrete (unless one takes time to be an illusion altogether). I’m uncertain that your argument actually fells the heart of the author’s logic. All human experience does in fact point to time as “ever increasing,” and because of that, it isn’t all that inappropriate to ascribe units of time to an act such as marking divisions in a line, when one is in fact positing that the infinitude of time is the impossibility. If time had begun an infinite amount of time ago, we would never have made it to this point in time.

Of course, then we get to the entire argument about God being “in time” or totally outside it. If outside it, then the author’s conclusion marries quite well I would say. After all, he is really just saying that within the rational constructs of our universe, God does not exist, which could be extrapolated to mean he is outside our Time as well.

You seem well versed in this field, probably more so than myself, so I only mean this in friendly rebuttal.

1. A point is infinitely small but exists…

Perhaps God, being THE platonic ideal of Being-ness, is qualitative and thus need not bother with NUMERICAL notions of infinity.

89. 1) Something cannot be brought into existence by Nothing.

2)Something exists.

3)Therefore, Something has always existed.

The fact of eternal existence is an example of actual infinity.

90. If time traces back infinitely, then this moment would have never been reached. No point in time could ever be reached for that matter. This is the paradox of an infinite history.

Your proof begs the question. You would have to define both “Something” and “Nothing” in order to have a meaningful statement there.

91. I didn’t say anything about “infinite history”. You have made the mistake of assuming that time is a property of all existence. Time began with the big bang. Existence is not limited to time and space

92. You still have not defined “Something” and “Nothing.”

As was posted earlier, if one takes existence to not be limited to time and space, then the original author’s point stands: God may exist outside it. But, if existence is not limited to time and space, then the word “always” is meaningless as it relates to “something,” being a temporal word.

93. “But, if existence is not limited to time and space, then the word “always” is meaningless as it relates to “something,” being a temporal word.”

Semantics. Human beings are bound by space and time, and human language reflects that. The notion of “a time before time” only seems nonsensical because of the limits of language. Logic, and the Big Bang theory, tells us that time and space did have a beginning, which means they didn’t always exist. That doesn’t mean Nothing (the absence of any thing or being) existed. Theists believe God is the eternal Being that constituted existence before spacetime. They maybe wrong, but the existence of some type of being “before” (or if you prefer,”beyond”) spacetime is a logical fact.

94. I would also have liked to see the history of Cusa.Sounds a marvellous man for his time.
I thought you were being arbitrary as Reason writers on purpose!
You serve well,but cannot find the end story suitable somehow.Never mind.
After all 6sense is a great find for me ,but that is spiritual ,so i cannot marry the two up as equal things- humanist,God-love.
Best,
N.

95. I don’t see the logic in an infinity being a contradiction, since infinity is not a number it cannot be represented by a number x, or x+1. An infinity is by definition a thing that IS, since it cannot be said in any way to not be, since anything finite must not be something. So is it not just as or even more logical then to prove that God does exist by this line of thought? Plus, God is described as absolute Being (shall we say infinite being.) As a thing that entirely IS, God cannot be a being that isn’t. The definition of evil is nothing, classically.

One more thing, if God is infinite, He is infinitely fast, hence omnipresent and of infinite duration. But since He is supposed to have created time/space etc., then it makes no sense that He would in any way be thus constrained…

96. One more thing I would like to point out. If God is where opposites meet, that does not mean he is a logical contradiction. For there can be two types of “opposite”, one being something and not-something (good and evil), the other being things equal but opposite, and thus contradictories (Infinite mercy and Infinite Justice). Since the example of a circle becoming a line is an example of the latter (for a cicle is not by definition the idea of not-line, nor a line by definition the absence of circle-ness). So the arguments that say God is where contradictions meet is not illogical, since the ideas, of, say, infinite mercy versus infinite justice ARE in fact resolved (hence Christ). Good and evil (that is, the absence of good) are opposites but not equal, not mirrors. Thus God is logical. Rational Theology can’t be killed (see my other posts for more aguments.)

97. The existence of at least one person proves this essay wrong: Graham Priest, who has spent a lifetime demolishing the law of noncontradiction. I just responded to this.

98. Goldblatt is not only completely at sea in concept analysis, he also knows next to nothing about Cusa. He has so completely misread Cusa—& read so little by Cusa—that it is a shame the Editors chose to print this.