Posts from August 1997

The Big Rock Conundrum

Can God create a rock so heavy that he cannot lift it?

This is known as the Big Rock conundrum. It is often used by atheists seeking to disprove the possibility of the Christian god, and any other purportedly omnipotent god. Sadly, it is logically flawed.

Remember that omnipotence means the ability perform all tasks. However, tasks that are logically impossible, such as creating square circles, are not really tasks at all; they are nonexistent, the null set. Thus they are not real actions for an omnipotent entity to perform. The Big Rock conundrum disappears when you consider this. In argument form:

Given:

  1. U: The Universal set of tasks
  2. A: A proposed task
  3. B: A proposed omnipotent entity
  4. r: A rock
  5. Cx: Proposed task of creating object x
  6. Mx: Proposed task of moving object x

Assuming:

  1. Omnipotence is the ability to perform all tasks. (All members of U)
  2. If the definition of proposed task A is self-contradictory, then A is not a member of U.
  3. If A is not a member of U, then A is not a task.
  4. Any entity X can only perform real tasks (elements of U)

One can infer that:

  1. If A is logically impossible, then A is not a task (prem. 2-3)
  2. B has the ability to perform all tasks (prem 1)
  3. B only has the ability to perform real tasks (prem 4)
  4. B does not have the ability to perform nontasks (inf 3)
  5. B has the ability to perform all members of U (prem 1)
  6. If B performed Cr such that Mr is a nontask, B could not perform Mr (inf 4)
  7. If B can perform all Mr, then B cannot perform Cr such that Mr is a nontask (inf 4)

In conclusion:

  1. Either B can perform Mr for all r xor B can perform Cr such that Mr is a nontask.

The argument leads to the conclusion that an omnipotent being could rationally be able to do one xor the other and still be omnipotent. The conclusion to this argument is (A xor ~A), which simplifies to TRUE. IOW, this is a tautology. And proves the argument to be valid rather than contradictory (in which case it would end in a direct contradiction, (A and not-A), or a paradox of self-reference, (A implies not-A).

The obvious points of attack are premises 1 and 4. However, if you assume that an omnipotent entity is able to perform both tasks and nontasks, you will ALWAYS end up with logical contradictions or paradoces of self-reference. To borrow a phrase from computer science, garbage in, garbage out. So, I submit that such a definition of omnipotence is inherently empty and will not get you anywhere with relatively rational theists. Another avenue of attack to this definition is to analyze it from the perspective of set algebra: from this view, it does not make a jot of difference whether you define omnipotence to include logically impossible or not; nonexistant tasks form the null set (∅), and the union of any set A with ∅ is always that set A (A ∪ ∅ = A). Thus, either way you still end up with the same set U of possible tasks.

If there is a contradictory conclusion of omnipotence, it lies elsewhere.

I’m unsure when this piece first appeared on the web. It was adapted from a post that I made to talk.atheism on 3 March 1997. The Internet Archive’s first record of the web version is from 12 August 1997. —C.J. 2006-07-10.

The Argument from Design and Anthropic Principle are Worthless

The Argument from Design, also known as the teleological argument, and the fundamentally identical Theistic Anthropic Principle are two of the arguments bandied about by fundies perhaps more often than any other in defense of their god figure. The Argument from Design, which only very loosely qualifies as an argument, basically states that due to the incredible order of the Universe, or the incredible odds against abiogenesis causing life on Earth, it seems unlikely in the extreme that the Universe was not designed by a Creator.

This argument has several critical flaws. Its first is that it is based on an extremely geocentric/anthropocentric view of the Universe, in its form arguing against undesigned abiogenesis. In this form, it posits that the probability of abiogenesis occurring without design is tiny to the point of absurdity. The flaw in this is that such a view is only on the planetary scale; given the chances of abiogenesis occurring at any given point in the Universe (rather than just on the planetary scale) multiplied by the size of the Universe and the amount of time in the Universe’s lifeline (so as to account for all possible timespace locations of abiogenesis), the probability becomes much more palatable. Life could have just as easily arisen on Planet Zeetar in the fifteenth sector of the galaxy Drizzlefump as on Earth. The abiogenesis version also hinges on the probability of Earth-pattern life, which is not at all the only form of life possible. As an example, it has been posited that life could arise from silicon-based molecules rather than carbon-based. Also, every single probabilistic model I have ever seen on the possibility of abiogenesis is based upon something along the lines of the random formation of some large organic molecule (often a strand of DNA) from scratch. The ridiculous and critical errors here are twofold:

  1. Chemical reactions are not random and therefore basing your probabilistic model on random assemblage is invalid.
  2. Abiogenesis does not state that complex organic molecules like DNA appeared from primordial scratch. The simpler organic molecules formed first, and once they formed, any measure of probability of the DNA and other complex molecules forming would show an increase.

The Argument from Design is often summed up in the Watchmaker Analogy, which runs something like:

If one finds a watch sitting on the beach, its orderliness would cause one to assume that there was a Watchmaker. In the same way, the incredible order of the Universe would seem to imply a Creator.

There are several flaws in this form of the argument. For example, when the analogy is applied to life, the watch is not a self-replicating structure with factors to modify the structure and selective pressures to regulate which structures are preserved (Dawkins’ Blind Watchmaker), while life and pre-living self-replicating molecules are. Because of this, they have a form that is semi-designed via the principle of the chaos game: when unpredictable input is fed through a regular system of rules, it tends to produce predictable patterns (although there is no guarantee of any given result: there is just a liklihood of large-scale patterns). When the analogy applied to the Universe as a whole, what makes it truly worthless is that the assertion that the Universe is strikingly orderly is absolutely without basis, due to the fact that there is no backdrop to which we can compare the Universe. In the Watchmaker Analogy, the watchmaker is assumed because the watch stands out against the seemingly random backdrop of nature. However, there is absolutely no backdrop to which we can compare the Universe.

The Anthropic Principle is basically the Argument from Design’s abiogenesis version, slightly reworded and placed in something approaching argument form. However, the underlying premise is the same; the Anthropic Principle posits that there are some two dozen Universal constants which are necessary to hold the values that they do for life on Earth to arise, which, the proponents of the argument hold, makes undesigned abiogenesis unlikely in the extreme.

Since the Anthropic Principle hinges on universal constants, rather than on mere chance, it does not suffer from the same geocentric problems as the Argument from Design does. However, it does suffer from the same confusion of Earth-pattern life with all possible forms of life.

However, the most critical flaw in these two nearly identical arguments is that they are based on a faulty understanding of probability. The flaw in the reasoning is best illustrated in an analogy:

Assume that one has 1,000,000,000,000,000 (one quadrillion) dice. All these dice are cast in a fair roll. The result that came up is incredibly unlikely (there are 61,000,000,000,000,000 possible outcomes), so much so that an Argument from Design regarding the outcome of the roll would posit that such an incredibly unlikely outcome would indicate that each die was placed face up to the right number. However, the roll must have a result, and this one happened to be the one that came up. And, in fact, any other outcome would have been equally unlikely.

Of course, all of this ignores the problem that the probability for the outcome has not been and cannot be determined until you first define all the possible outcomes. If physics determined that our current Universe’s parameters were the only possible outcome, then the arguments would seem quite silly. Indeed, they would if the chances were found to be anything but astronomical.

For further reading:

  • Dawkins, Richard: The Blind Watchmaker
  • Dawkins, Richard: Climbing Mount Improbable
  • matthew: The alt.atheism FAQ

I first wrote this piece some time in 1997, but I’m unsure of the precise date. The first recorded appearance of the page in the Internet Archive is on 12 August 1997. –C.J., 2006-07-11.

The Lord, Liar, Lunatic Trilemma

The Lord, Liar, Lunatic trilemma has been proposed by several Christian apologists, including the noted layman’s theologian C. S. Lewis. It seeks to argue that Jesus Christ was Lord, Savior, and all those other wonderful things he said he was in the New Testament. It goes about this by proposing something of a trilemma regarding Jesus:

Assuming that Jesus existed, and that he said he was the Lord, there are three possibilities regarding his claims: either he was

  1. telling the truth (he was LORD),
  2. lying (he was a liar), or
  3. insane (he was a lunatic).

Since his words are very profound, they can hardly be discounted as the words of a raving lunatic. He could not have been a liar because he was willing to die for his beliefs, as were many of his followers; this hardly seem like the acts of a liar. Therefore, since the other two options have been eliminated, he must have been LORD.

There are a number of flaws with this argument, starting at the most fundamental level of the assumptions. The assumptions need not be accepted at all; there are a number of other options. If the historical figure of Jesus did not exist at all (which is possible, but not overly likely given a conservative approach to the evidence), then the argument is superficially ludicrous. If Jesus did exist, then he may not have ever said he was LORD, but rather the early Christians such as Saul/Paul and the New Testament Gospel authors merely fit the semi-historical person of Yeshua/Iesos to fit their Messiah god Xristos. The most likely scenario, I think, is that he never said he was LORD, but was merely a Jewish religious reformer, and that his teachings were encrusted and embellished with miraculous life narratives and salvation myths as his followers shifted from the original Jewish reformers to the apocalyptic mystery cult of Christianity.

The next significant flaw is that of trifurcation; it proposes only three options when there are in fact more. One of the most likely is that Jesus and/or his followers sincerely believed what they said, but were not correct. It is quite possible that, whether Yeshua ever said anything about being LORD or not, Saul/Paul and the various other authors of early Christian books sincerely believed that Yeshua was the Messiah in the form of Xristos.

The final significant flaw in this argument is that it seeks to eliminate the options of liar and lunatic, but fails to do so adequately. If Yeshua was delusional as to his godhood, that does not in anyway preclude his abilities to make cogent moral and religious observations; delusions of godhood do not rule out functional sanity in other fields of life, and even were he totally insane there are still several cases of insane or marginally loony people putting out observations that seem profound to some (eg, Nietzsche, who produced his final works the last year before he became clinically insane). The argument against liar is even less convincing; history has been littered with people making huge sacrifices for liars and lunatics. Was David Koresh truely the Second Coming of Christ? Are all those Scientologists shelling out thousands of dollars doing so for true revelation? In fact, the reasons given to rule out liar and lunatic can easily be applied to most other would-be prophets and saviors; many have fought and died for Muhammed, and his moral teachings could be argued to be as profound as those of Yeshua. Was then Muhammed truely the prophet of Al-Lah?

I am unsure of the date of this piece. It dates back to some time in 1997; the first record of it in the Internet Archive is from 12 August 1997. –C.J. 2006-07-09.

Pascal’s Wager is Worthless

Pascal’s Wager, put in its most famous form by the brilliant French mathematician and philosopher Blaise Pascal, is one of the most common and one of the most logically flawed arguments used by evangelists. It is properly conceived as an argument for belief in God rather than as an argument for the existence of God. In essence, it goes:

  1. Either God exists or He does not.
  2. If there is no God, whether you believe in God or not, all that occurs after death is oblivion.
  3. If there is a God, and you believe in God, you go to Heaven.
  4. If there is a God, but you do not believe in God, you go to Hell.
  5. By statements 2-4, if you approach belief as a wager, betting on God’s existence is a win-draw proposal: either you gain eternal bliss or end up with oblivion like all other betters.
  6. By statements 2-4, if you approach belief as a wager, betting on God’s nonexistence is a draw-lose proposal: either you end up with oblivion like all other betters, or you suffer eternal hellfire.
  7. Thusly, belief is the superior choice from a wagering perspective.

The reason why Pascal’s Wager is so pathetically fallacious should be obvious upon a little examination. There are two ways to look at the argument, each with its own problems: assess statements 1-4 as assumptions, 5-6 as inferences, and 7 as a conclusion, or else assess 1 as an assumption, 2-6 as inferences, and 7 as a conclusion.

In the first approach, it rests entirely upon four assumptions that are highly contestable. Premises 3-4 are essentially a statement of Christian belief, which means the only people that will accept them are Christians. Thus, the argument reduces to “if you are a Christian, then belief in God is superior from a wagering perspective,” a rather superficially silly tautology that results in an argument that only convinces the convinced. Further, premises 2-4 commit the fallacy of bifurcation: they state that there are only two possibilities when there are in fact more. In this case, it posits that either the Xian model is true or the secular humanist one is. However, many other options come to mind. For instance, if Allah is supreme, then both the believing Xian and the atheist are doomed to eternal hellfire.

In the second approach, inferences 2-4 derive information from nowhere, thus violating information entropy. All that is assumed is that God either does or does not exist. This says nothing about whether God is benevolent to those who believe in Him and condemning of those that don’t, or whether there is a God who rewards the skeptics and punishes the sheep, or whether there is a God who rewards all, or any number of other possibilities. Because of this, inferences 2-4 are not logically connected to assumption 1, thus causing a non sequitur.

I’m unsure of the date of this piece. 12 August 1997 is when it first shows up in the Internet archive, but it may date back as far as 1996 for all I know. –C.J., 2006-07-09.

First Cause and Kalaam’s Cosmology Argument are Vomitous Filth

The First Cause argument has been spewed many times by many different theists, ranging in intelligence from a1nonly to Saint Thomas Aquinas. It basically goes:

  1. All events have a cause.
  2. All beginnings are events.
  3. The Universe has a beginning.
  4. An event cannot cause itself.
  5. Therefore, the Universe has a First Cause.
  6. By premise four, that cause must be something outside of the Universe.
  7. This implies that something outside of the Universe, that is, a God, must have created the Universe

The problems with this arguement are manifold. Firstly, Quantum Mechanics has all but totally disproven the first premise. Secondly, the beginning of the Universe is, by definition, also the beginning of time. Since causality requires a temporal referrant (A causes B implies a time progression), by definition the beginning of time, and thus the beginning of the Universe has no cause.

However, even if one ignores the problems with those premises, there are still more problems. Premise three is questioned by some, although a lot of modern cosmology points to a Universe with a definite beginning point. OTOH, Stephen Hawking, one of the foremost minds in modern physics, supports a circular-time model with no definite beginning. The logical implications of asserting that the Universe has a beginning are also theologically troublesome, as many can respond by asking why the Universe needs a beginning but God doesn’t.

Finally, the conclusion is a non sequitur, in that it automatically assumes that the Universe’s cause is necessarily a God. Something transcendental to the Universe could just as easily be the Force or the Tao as a conscious entity.

Kalaam’s Cosmology Argument is a slightly dressed up version of the First Cause argument. It goes, basically:

  1. A causes B implies that A exists at the time A causes B
  2. Net entropy in a closed system must always increase towards the maximum.
  3. The Universe must either be eternal, have caused itself, or been caused by an external force.
  4. The Universe is a closed system.
  5. The Universe has not yet reached maximum entropy.
  6. Before something is caused, it does not exist.
  7. By premise two, a closed system which has been in existence forever would have at any present point in time P already been in maximum entropy for an infinitely long period of time.
  8. By premise four, if the Universe were eternal, it would have reached maximum entropy by this present point in time P.
  9. Thus, the Universe cannot be eternal by premise five.
  10. By the law of noncontradiction, something cannot both exist and not exist at the same time (not (A and not A)).
  11. If something caused itself, it would have to both exist, by premise one, and not exist, by premise six, at the same time.
  12. Thus, something cannot cause itself.
  13. Thus, the Universe could not have caused itself.
  14. By premise three, this leaves only the possibility that the Universe was caused by an external force, which would be a God.

This shares the same misunderstanding of cauasality as the First Cause, although it no longer contains the problem of assuming that the Universe could not have always existed, but rather demonstrating it by using the Second Law of Thermodynamics. However, premises two and four are still somewhat questionable. Also, one could argue that an eternal Universe would, by definition, be infinite in its extent and not a closed system.

Finally, Kalaam’s Cosmology makes the same blunder of assuming that a transcendental force is necessarily a conscious entity, rather than admitting the possibility that it could also be a nonsentient force.

I am unsure of the date of this piece. It dates back to some time in 1997; the first record of it in the Internet Archive is from 12 August 1997. –C.J. 2006-07-10.