Proof From Intelligence (1)

Proof from Intelligence

There.

What you just did is quite unique in the history of life. The act of reading, so far as we can tell, was first done within our species. This is rather astonishing, since life has been loafing around for four billion years, and complex land-based multicellular life popped up sometime around four hundred million years ago. The odds of some other species coming up with our neat trick should be pretty high, and yet none did.

We don’t just read, though. We collect reading like crows or octopuses[34] collect shiny toys, enshrining them in large buildings called “libraries.” We then leverage them to do all sorts of stupendous things, like build telescopes or launch hunks of metal into outer space.

This fits into a greater pattern: those books, telescopes, and metal bits all exist to gather knowledge, which we then sift through in search of patterns and more knowledge. This perpetual cycle of gathering and interpreting is a sign of intelligence, something that just seems to be lacking in other animals. It’s richly rewarded us, by doubling our life span, freeing our spare time for more knowledge gathering, and building us some very cool toys.

If it’s been such a help to us, though, why haven’t other animals jumped on the intelligence bandwagon? Perhaps this is something exclusive to our species, something that took a divine touch to bring about.

Definitions

There are two ideas hidden behind this proof. Homo Sapiens Sapiens[35] has intelligence, while other species don’t, so we must be special. And since intelligence couldn’t possibly have evolved via small steps, it can only have come from god. To rebut these, I have to show that other species have some intelligence, and that there’s nothing we have that they don’t in smaller doses.

Note that I don’t have to show that other animals are smarter. The Fangtooth fish may have the longest teeth in proportion to its body size,[36] but no one would argue this proves it was blessed by a deity. In fact, we’d prefer to find a wide variety of intelligence in the animal kingdom; just like comparing other species’ eyes to infer the eye’s evolution, we can trace the development of intelligence by snooping on other intelligent beings.

But before I can show intelligence in other species, we need to get one thing straight: What is intelligence?

This may seem like a simple problem, but it has haunted philosophers and scientists for centuries. Everyone “knows” it when they see it, yet they struggle to describe it:

Individuals differ from one another in their ability to understand complex ideas, to adapt effectively to the environment, to learn from experience, to engage in various forms of reasoning, to overcome obstacles by taking thought. Although these individual differences can be substantial, they are never entirely consistent: a given person’s intellectual performance will vary on different occasions, in different domains, as judged by different criteria. Concepts of “intelligence” are attempts to clarify and organize this complex set of phenomena. Although considerable clarity has been achieved in some areas, no such conceptualization has yet answered all the important questions, and none commands universal assent. Indeed, when two dozen prominent theorists were recently asked to define intelligence, they gave two dozen, somewhat different, definitions.

(Ulric Neisser et al, “Intelligence: Knowns and Unknowns,” American Psychologist , February 1996)

 And without a clear definition, there is ample wiggle room to define “intelligence” in a way that’s convenient for you. An example: I can state as a fact that I believe a god exists. This might seem impossible for an atheist:

  Atheist \A"the*ist\, n. [Gr. ? without god; 'a priv. + ? god: cf. F. ath['e]iste.]
     1. One who disbelieves or denies the existence of a God, or supreme intelligent Being.
     2. A godless person. [Obs.]
     Syn: Infidel; unbeliever.

(Webster’s Dictionary, 1913 edition)

And yet there’s no conflict here. Look up “believe” in a thesaurus, and you’ll find “assume” right next to it. While both words refer to a fact that is true despite a lack of evidence, a “belief” is implied to be absolutely true, while an “assumption” is only relatively true. Assumptions can be easily discarded if proven false, and you’re free to pretend they were false if you’d like. Beliefs should remain true no matter what facts come to light, and thus should never change. Nonetheless, both meanings are close enough to be confused and interchanged, which is exactly what I did.

“God” has traditionally meant a powerful conscious being, but that definition has been expanded over the years. Pantheists reject that meaning, for instance, as well as the concept of souls. Instead, they define “god” as the entirety of the universe. Since the universe is just a definition, as per my remarks in Cosmological, that’s entirely consistent with my world-view.

So while I said

I believe that a god exists,

my true meaning was closer to

I assume that a universe exists,

which is quite compatible with atheism. The lesson is obvious: without a consistent, clear definition for “intelligence,” it’s easy to shift the meaning of the word around to suit your whim and dodge whatever argument you’re facing.

That doesn’t make it impossible to counter-argue, though. Look over the various definitions of intelligence, and you’ll note they’re usually a mix of mental attributes, such as logical thinking and tool use. By examining each potential component separately, I can check most definitions of intelligence without defining the term.

The most popular test of intelligence is the “psychometric approach,” for the simple reason that it can be easily tested. The victim is given a set of problems to work on, and asked to solve as many as possible until the clock runs out. Anything that can be fit on a sheet of paper has been on an intelligence test at some point, ranging from word vocabulary to picture patterns. Today these tests focus on abstract logic and reasoning, mathematics, and solving novel problems.

As implied, they usually split apart intelligence into several sub-components. For instance, the popular Cattell-Horn-Carroll theory uses ten categories:

  • Quantitative Knowledge: In a word, mathematics.
  • Short-Term Memory: The ability to remember things for a few seconds.
  • Long-Term Storage and Retrieval.
  • Reading/Writing: The ability to read and write, and all skills directly related to that.
  • Visual Processing: Dealing with visual patterns, by analysing, remembering or creating them.
  • Auditory Processing: Much like the above, though this also includes speech.
  • Processing Speed: How well someone can repeat a mental task.
  • Reaction Time: How quickly a person can respond to some input.
  • Fluid Intelligence: Reasoning with new problems or information.
  • Crystallized Intelligence: Reasoning with old problems or information, as well as the amount of information already known and the ability to share that with others.

(Most of us would group those last two categories as “problem solving,” and in the interest of keeping my workload down I’ll take full advantage.)

Other researchers have rejected easy tests of intelligence, and broadened the definition still further. Howard Gardner’s theory of multiple intelligences includes:

  • Logic and Mathematics.
  • Linguistic: Reading and writing, plus the ability to use speech.
  • Spatial: The ability to picture and analyse a scene, be it real or a product of the mind.
  • Kinesthetic: How well people can control their own bodies, including how quickly they react and memorize sequences of movement.
  • Musical: Recognizing or producing a pitch or beat, and the ability to play or write music.
  • Intrapersonal: How well someone knows their emotions, desires, and abilities.
  • Interpersonal: The ability to interact with society, including recognizing another person’s intrapersonal content and sharing information with others.
  • Naturalistic: Interacting with other species, and the ability to nurture.

I myself will add on another few categories, to catch a few other talents that have been flagged as unique to our species:

  • Tool Use
  • Play
  • Culture
  • Altruism
  • Lying
  • Long-term Planning
  • Creativity

[34] Yes, that’s really the plural form of “octopus.” While “octopodes” is the correct Greek plural, it’s so rarely used that dictonaries either bury it as the last candidate or don’t mention it at all. “Octopi” is completely wrong.

[35] Homo Sapiens means “Wise Man;” anthropologists have begun tacking on an extra “Wise” to make room for a potential sub- or co-branch of our species, and given our messy origins I think this is a Wise idea.

[36]  They’re so long that if it closed its mouth like other creatures do, its front teeth would stab through the brain and create an impressive set of horns poking out of its forehead.

Proof from Logical Necessity, or the Ontological Proof (3)

Kant-er Arguments

Obviously, I’m not the only one with objections. Immanuel Kant, most notably, spent eleven pages in “Critique of Pure Reason” poking holes in the Ontological proof. He uses much more robust reasoning than I do, so if nothing I’ve said so far has convinced you, I’d recommend you give his arguments a go.[28] I’ll attempt to summarize the entire thing here.

Kant’s critique comes in four separate parts. First off, he points out that “God is something greater than we can think of” has a hidden assumption: god exists. If god did not exist, then we can say anything about it without contradicting ourselves. “Unicorns are made of gold” is just as truthful as “Unicorns are not made of gold,” but only “Coelacanths[29] are not made of Gold” is true. Since we can say anything we want about non-existent beings, we can prove anything we want about them too.

Second, the ontological proof is supposed to be a proof of god’s existence, yet as noted above Anselm had to assume god existed to write his proof. This is allowed in proofs, if you use a  technique known as “reductio ad absurdum;” you assume something, derive a contradiction from that assumption, and are forced to conclude that assumption is false. Of course, any proof that applies “proof from contradiction” to the assumption “god exists” would have to conclude god does not exist, which seems counter-productive in this case.

Third, we don’t toss around “being” and “exist” lightly. We know that coelacanths exist because we’ve found fossils of them, photographed a few of them swimming about, held them in our hands, and even tasted them. [30] We don’t say they exist because they are “beings,” or have a property called “existence.” Anselm calls god a “being” and says he “exists,” but offers no evidence beyond his proof to back that up. God hasn’t earned either of those labels, yet most Ontological proofs assume he has.

Fourth, we can describe what a unicorn is in physical terms, and set up various tests and experiments to try and catch one. Since we could pin them down as “beings” in the same way as we’ve done to the coelacanth, we can debate their existence in a meaningful way even if no-one’s actually seen a unicorn in the wild. The rational god of Avicenna will never jump into a fishing net or be lured out by hay. Not only do we lack any tangible proof of its existence, we could never find any. God will never be a “being,” no matter how badly an Ontological proof wants him to be.

All of the “distilled” proofs provided by the Encyclopaedia of Philosophy trip up one at least one of Kant’s counter-arguments, and all of them trip up on the last two.

Those last two, in fact, apply to all variations of the Ontological proof. You cannot show something exists in the real world without referring to the real world in some way. Remember my kitten example from the introduction? Until I began defining the physical characteristics of a kitten, you had no way to prove its existence and no reason to take the idea seriously. Conceptual ideas can only be defined within a logical system, and only when that system relies on assumptions that are a close match to the laws of reality do those ideas happen to coincide with reality. For instance, zero-order logic is not permitted to use the concept of sets, and those seem to be an essential abstraction for understanding the real world.

As a direct example, take the third “distilled”[31] proof from the Encyclopaedia of Philosophy, which claims any god is not contingent. While this dodges most of the objections outlined above, it treats existence as if it was an arbitrary label and not something justified via tangible evidence. Since existence is contingent, and this proof says a god has the property of existence, god must be contingent after all.

The Ontological proof tries to use concepts and logic alone to prove the existence of something physical and tangible. It’s impossible, plain and simple.

Gödel’s Proof, and the Problem of Infinity

Simplicity is rare in Ontological proofs, though.

As I mentioned in the introduction, long and complicated chains of reasoning seem more impressive than short, simple ones. In reality, long proofs are more likely to suffer from small errors in logic, and less open to cleaning them out.

A perfect example of this is Gödel’s Ontological proof. To start at the beginning, his insistence on positive properties is suspicious. We tend to make negative properties the verbal negation of positive ones because we prefer to think about the positive, not because one method is inherently better; compare “non-corrupt” and “corrupt“ to “just” and “non-just.” If we apply Gödel’s argument to “negative, morally aesthetic properties” instead, we can prove a god’s existence via the same line of reasoning, since if none of the positive properties conflict then neither can the negative ones, but we’re forced to conclude this god is “perfectly corrupt,” “all-weak,” “merciless,” and an “absolutely amoral” deity.[32] The restriction on “positive” properties is in place to ensure Gödel proves the existence of a god he wants to exist, not because it’s necessary for the proof.

Speaking of which, why does Gödel go to great lengths to use the pure, rational logic to formulate his proof, yet use such a loose definition of “morally aesthetic?” That’s like trying to build a rock-solid building on a swamp. A logical proof is no stronger than its weakest part, and the definitions form the bedrock of the entire argument.

Note as well a subtle problem with Definition 1 and Assumption 3:

Definition 1: An object has the “God-like” property if, and only if, that object has every property in P.

Assumption 3: The “God-like” property is in P.

If you’ve read my take on the Cosmological proof, this should twig an alarm bell. I demonstrated that a container of things is not automatically a thing itself. If the “God-like” property is a property, then it was already in P and thus assigning an object the “God-like” property means that it must already have the “God-like” property to begin with! We could also define a “God-God” property, which requires every property in P including “God-like,” a “God-God-God” property via similar means, and so on.

Even if you object to the above lines of reasoning, Gödel’s proof has a gaping hole. The Epicurean Paradox[33] is the same size as that hole:

If God is willing to prevent evil, but is not able to, then He is not omnipotent.
If He is able, but not willing, then He is malevolent.
If He is both able and willing, then whence cometh evil?
If He is neither able nor willing, then why call Him God?

(“Dialogues Concerning Natural Religion,” by David Hume)

So is this paradox:

If God is perfectly just, no-one is punished less than they deserve.
If God is merciful, someone must be punished less than they deserve.
Therefore, God cannot be perfectly just and merciful.

Same here:

If God is omnipotent, can he perform an action that he cannot perform?

Gödel is careful to prevent simple contradictions from derailing his proof, but does nothing to keep out more complicated ones. These conflicts lead to a definition of a god that contradicts itself, rendering it nearly useless.

I say “nearly” because there is one way out; instead of combining multiple attributes into a single god, you could place a strict limit of one property per god. Most believers will reject that outright, at the time of this writing, since most believers are monotheistic. It also denies any composite property such as “good” from being a god, since that would include the contradictory properties “merciful” and “just,” among others. It also suggests that any property we could come up with has a god associated with it, including “fortitude,” “ambidexterity,” “radical-ness,” and “ability to explain mathematics without sounding condescending.” Even polytheists have their limits, and the vast majority would reject thousands of gods, let alone a potentially infinite number.

Ignoring that escape route, believers dismiss the contractions as not applying to a god because they are beyond rational thought, or as proving that the person asking the question doesn’t understand the type of infinity that the gods posses. The first reply also dismisses the Ontological proof, since it relies on the target god being rational. The second instead proves that the believer doesn’t understand what they’re asking for. Here, let me remind you of a few definitions:

Omnipotent \Om*nip"o*tent\, a. [F., fr.L. omnipotens, -entis;
     omnis all + potens powerful, potent. See {Potent}.]
     1. Able in every respect and for every work; unlimited in
        ability; all-powerful; almighty; as, the Being that can
        create worlds must be omnipotent.
     2. Having unlimited power of a particular kind; as,
        omnipotent love. --Shak.
Omniscient \Om*nis"cient\, a. [Omni- + L. sciens, -entis, p. pr.
     of scire to know: cf. F. omniscient. See {Science}.]
     Having universal knowledge; knowing all things; infinitely
     knowing or wise; as, the omniscient God. --
     {Om*nis"cient*ly}, adv.

(Webster’s Revised Unabridged Dictionary, 1913 edition)

Note that no restrictions are placed on the chosen god, in either case. If a god can do any action, then even the contradictory ones must be doable. If the god can know everything, it must know about things you’d rather keep private. If god is infinitely just, then she must punish fairly in every case, no matter how much mercy you’d like him to grant.

There’s only one escape from this quagmire: redefine the words to place a limit on your god. This is quite dishonest, because people expect the words to mean roughly what a dictionary says they do and thus will misunderstand you. It’s far better to use a different phrase to avoid confusion, though I’ll admit “effectively omnipotent” or “really, really, really super powerful” don’t have the same ring.

A limited god is still a god, mind you. The two definitions I outlined in the introduction do not make reference to infinite power, as you’ll recall. We can still bless a god with enough power to create the universe, or do any number of incredible feats. But note that all versions of Ontological make reference to infinity, either by directly describing an unlimited being, or indirectly implying an infinite number of traits that are infinitely more perfect than any other being can claim. You can’t have your infinity and eat it too.

That doesn’t stop Ontological proofs from trying. All the ones I’ve seen merely introduce more errors, above and beyond the pair related to existence.

The Proof that God Does Not Exist

I can’t leave this proof without sharing my favourite variation. Instead of spending most of a chapter developing objections, Douglas Gasking just cuts to the point by using the same reasoning to prove god doesn’t exist:

  1. The creation of everything is the most marvellous achievement imaginable.
  2. The merit of an achievement is the product of (a) its intrinsic quality, and (b) the ability of its creator.
  3. The greater the disability (or handicap) of the creator, the more impressive the achievement.
  4. The most formidable handicap for a creator would be non-existence.
  5. Therefore if we suppose that the universe is the product of an existent creator we can conceive a greater being — namely, one who created everything while not existing.
  6. Therefore, God does not exist.

The implications are pretty clear. If you can prove and disprove something using the same line of thought, there’s something wrong with your line of thought.

[28] “Critique of Pure Reason” has long since dropped out of copyright, so there are a number of translations available online. The same is true of most of the documents I’ve mentioned, so feel free to analyse them for yourself.

[29] A fish thought to have gone extinct with the dinosaurs, until one jumped into an African fishing net in 1938.

[30] From what I’ve read, they’re very fishy.

[31] As quoted from the Encyclopaedia: “These are mostly toy examples. But they serve to highlight the deficiencies which more complex examples also share.”

[32] Not even Satanists would worship this god. They value personal responsibility, knowledge, justice, and individuality.

[33] Ironically, Epicurus never came up with his paradox. A critic of his, Lactantius, incorrectly attributed it to him four centuries later. Epicurus is sometimes labelled an atheist, again thanks to Lactantius, but was more deist.

Proof from Logical Necessity, or the Ontological Proof (2)

Existence is not Great

A core assertion of Ontological is that it’s better to physically exist than to be a concept. I’m not convinced, and to help illustrate the point I propose a simple thought experiment.

  1. Picture a vertical line, which we’ll declare to be one unit high.
  2. Place a circle around it with a diameter of exactly that line; if you’ve pictured this correctly, you’ll have a circle split in two.
  3. Now, mentally undo the part of the circle that touches the bottom of the line, as well as the top part of the line on the left side. Unwrap it counter-clockwise from the top, keeping the left-most portion anchored to the top of the vertical line, until the line is perfectly horizontal and at a right angle to the original line.
  4. You now have two sides of a rectangle. Complete it by extending a horizontal line from the bottom of the vertical line with the same length as the upper horizontal line, and a vertical line from the end of the upper horizontal line with the length of one unit.

The area for a rectangle is the width times the height. We know the circumference, or length around a circle is π times the diameter of that circle, which in this case is π units. So with a width of π units and a height of our circle’s diameter, or one unit, that rectangle has an area of exactly π square units.

If you had difficulty, the following diagram should help you. Conveniently, this diagram will also prove my point:

Creating a rectangle pi units long by unwrapping a circle.

The final rectangle in your mind is exactly π square units big. The rectangle in this diagram is not. In fact, no real-world diagram will ever be exactly π square units.

For argument’s sake, we’ll say the rectangle is exactly 10cm wide, and the diagram is printed at 472dots per centimetre.[26] The width of this rectangle is thus 4,720 dots, and the height is 1502 dots, for an area of 7,089,440 dots. To convert that to “units,” we need to divide by the size of one square unit in dots, which is 1,502×1,502 or 2,256,004 dots. According to my math, that rectangle is about 3.142477 square units in size. This differs from π after the third decimal place.

The reason is pretty clear. π is an irrational number with an infinite number of decimal places; by definition, it can never be represented by one integer divided by another, or by counting a finite number of elements. And yet if we construct this diagram in the real world, both the width and the height must be finite numbers. Even if the width of the rectangle was the size of the visible universe, it would still be a finite number of atoms in area, and our answer would be wrong somewhere around the 36th decimal place.

There’s no escape from this problem, either. No matter how you try to represent π in the real world, you’ll be forced to use a finite number of decimal places to represent a number with an infinite number of them. And yet, what’s impossible in the real world is easy in your head. You don’t need to convert π to a decimal number, you can treat it as a concept and dodge around the problem. As a consequence, the rectangle in your head is exactly π square units in area.

This confirms something I’ve observed as an artist. Like Anselm’s painter, I too have had a vision of a finished drawing or photo in my head; unlike him, the finished product is rarely more than a shadow of what’s in my head. Something always goes wrong; a line falls out of place, a photo has a branch that’s poorly placed, and so on. The exceptions are usually because I accidentally found an improvement while creating the work, and not through perfect execution.

The Triumph of Irrationality

I’ve also got a beef with another assertion of Ontological, that it’s impossible to think of any being greater than god.

If you’ve heard of Buddhism, you’ve likely heard of its most famous variation, Zen. Part of that sect’s seductive quality comes from an emphasis on “kōans,” or questions that have no rational answer but instead are intended to provoke an enlightened train of thought. Here’s the most famous of them:

“Two hands clap and there is a sound. What is the sound of one hand?”

(Hakuin Ekaku)

That question cannot be logically answered,[27] yet Hakuin had no problems asking it and we had no problems contemplating it. Given a little thought, you should be able to come up with your own kōans: What is the colour of an object in perfect darkness? What is the sound of empty space?

Kōans show that we have no problem thinking irrational thoughts. The Ontological proof uses reason to prove god, however. In order to do this, it assumes that god must be rational. If he is not, he could not be described by reason, and if he could not be described by reason, he could not be proven by it either.

But if a god must be rational, and our thoughts don’t need to be, we can contemplate things greater than the gods. Let’s try it: There is something greater than a god. The consequences of that sentence are not logically valid, yet I had no problems writing it and you had no problems understanding it. If we shift our assumptions, we can make it valid; I’ll use this in the Morality proof later on, for instance.

If we’re not bound by rationality, while god is, then we can easily think of something greater than god, and another assertion is shot down.

Anselm realized this loophole, and tried to close it in Chapter 4 of Proslogion. He separates thought into two categories:

For a thing is thought in one way when the words signifying it are thought, and it is thought in quite another way when the thing signified is understood. God can be thought not to exist in the first way but not in the second. For no one who understands what God is can think that he does not exist.

(Chapter 4: “How the Fool Managed to Say in His Heart That Which Cannot be Thought”, as translated by David Burr)

The problem with Anselm’s counter-counter is that it doesn’t address the counter-argument at all. He clearly wants to put “a being greater than god” in the “signified but not understood” category, where he can safely ignore it, but he doesn’t say why it belongs there, let alone why his categories exist in the first place.

In order to decide which category that sentence goes into, you have to understand the sentence first. For instance, which of the two gets “Yd.p. lprxaxnf co br Ire?” That might be a meaningless statement, making it impossible to understand, or it might have meaning in a language or code you’re not familiar with. In contrast, “There is something greater than god” can be easily understood and thus placed in a category. But because you understood it, there’s only one possible placement: things that are “signified” and “understood.”

You may not be aware of all the rational implications of that statement, or you might know them better then I do, but the underlying concepts must be clear to you before you can make a rational decision. Irrational decisions are another beast, but they only prove my point: the irrational trumps the rational.

Anselm’s defence doesn’t work, and my counter-example still stands.

This cuts the other way, as well. Merely being able to state something does not make it rational or logically justified. The fourth “distilled” proof falls into this trap. “The existent perfect being is existent” is true, in the same way that “the existent @#^*$ is existent” is:

  • “The existent ___ is existent” depends on the assumption “a ___ exists.”
  • If that assumption is true, then there’s no need for the proof!
  • If that assumption is false, then the proof is contradictory and we can conclude anything we wish from it, including the existence of whatever we want.

The fifth earns a medal from me for squashing three separate proofs into one. There’s proof from Witness (“if one person is convinced a god exists, god exists”), proof from Popularity (“multiple believers can’t be wrong”), and just a sprig of Ontological (“the word ‘God’ only means something if a god exists”). Unfortunately, it falls flat on that last assertion, as the trio of Faust, Bilbo Baggins and the Jabberwocky will swear to. We’re surrounded by fictional, non-existent things that provide us with meaning, by setting an example or just giving us a good time. This extends to science as well; Niels Bohr expanded on Ernest Rutherford’s model of the atom to create the boringly-named Rutherford-Bohr model, which has very little in common with the real layout of an atom but is easy to teach. And so it is taught.

[26] For readers who think in imperial units, that’s 3 15/16ths inches and 1200dpi respectively.

[27] It’s a common misconception that kōans have no answer. To the contrary, every kōan has an answer, though that answer varies from Buddhist Master to Buddist Master. For instance, Zhàozhōu’s answer to “Does a dog have Buddha-nature or not?” to one of his students was “Wú,” Japanese for “no.” To another, he replied “yes.”

Proof from Logical Necessity, or the Ontological Proof (1)

Proof from Logical Necessity, or the Ontological Proof

I’m going to need your help with this one. Relax and get comfortable.

Now, I’d like you to imagine the most perfect being. One that embodies all the qualities you’d like to be in a conscious entity. A perfectly-balanced sense of judgement, say, or a deep pool of empathy and caring, or a graceful ability to forgive and move on, or a wisdom well beyond its years. Picture an entity that manages all that, better than anything that has or will exist.

It’s a lovely thought, isn’t it? Don’t you wish such an entity existed?

I bet you’d agree that it’s better to exist than not exist, right? A being that has all those traits would be more perfect if it existed than a similar being that did not. And yet, you had no problems picturing that perfect entity, didn’t you? How could you have pictured perfection without including every portion of that perfection, including the ability to exist?

The ease of picturing perfection, therefore, must mean that perfection exists. And since a god matches that perfection to a tee, that must mean the gods exist.

No Really, It’s Quite Popular With Some People

Most of you are scratching your heads right now. “Really? That’s a proof?”

It is, and it’s been a favourite of philosophers for some time. Despite the “-logical” suffix, most scholars do not think this proof was dreamed up by a Greek. I’m not so sure; while it’s true that I can’t find a single example within their works, you’ll note that it bears a strong resemblance to the Cosmological proof, which was quite popular with them. Indeed, my description above is almost identical to variation of Cosmological. Instead of stepping up one degree of perfection, however, I stepped sideways and invoke the property of “existence.” Thus Ontological proofs do not “step outside” the universe, and are immune to that particular counter-argument.

There’s a better argument for this proof’s origins, that a fan of Greek learning came up with this twist. Avicenna[22] was a Persian philosopher who lived roughly 1.5 millennia after the Greeks, but was one of the few people in the world to have access to their written texts. He claims to have memorized the entire Qur’an by age ten and outsmarted his teachers by age fourteen, which sounds unlikely until you start cataloguing his accomplishments. Avicenna pioneered the use of clinical trials, knew the heart worked as a valve, discovered Newton’s first law of motion, reasoned that light had a finite speed, came pretty close to inventing Germ Theory, was the first psychologist, published a book of medicine that was used for 600 years in Europe, and during a moment of boredom invented the refrigerated coil and scented oils. As if to further rub it in, half of his surviving work is
written in verse.

A lover of Aristotle, Avicenna extended the old Greek’s philosophy and applied it to Islam. I can track down several scholars, such as M. E. Marmura and Parviz Morewedge, who make it quite clear that Avicenna’s proof differed from his classical hero by focusing more on logic and existence, independent of physical reality:

It is not in any sense a proof that infers God’s existence from the observation of His handiwork. On this Avicenna is explicit. After giving one version of his proof from contingency, for example, he writes: “Reflect on how our proof for the existence and oneness of the First and His being free from attributes did not require reflection on anything except his existence itself and how it did not require any consideration of His creation and acting, even though the latter [provide] evidential proof (dalīl) for Him. This mode, however, is more reliable and noble, that is, where when we consider the state of existence, we find that existence inasmuch as it is existence bears witness to Him, while He thereafter bears witness to all that comes after Him in existence” (Ešārāt, p. 482).

(M. E. Marmura, Encyclopædia Iranica, http://www.iranica.com/articles/avicenna-iv, retrieved April 30th 2011)

Other scholars dispute Avicenna’s departure, and unfortunately I can’t track down a translated version of his Šefāʾ or Ešārāt to decide for myself.

I can track down the original texts of Anselm of Canterbury, however. His book Proslogion is universally accepted as a true proof from Logical Necessity. Anselm had a rather interesting life, most notably feuding with two kings of England and being forced into exile twice. It’s a shame the topic of this book doesn’t permit me to go into more details, because those decades of political intrigue would be easier to sort out than Anselm’s writing:

In fact, it [God] so undoubtedly exists that it cannot be thought of as not existing. For one can think there exists something that cannot be thought of as not existing, and that would be greater than something which can be thought of as not existing. For if that greater than which cannot be thought can be thought of as not existing, then that greater than which cannot be thought is not that greater than which cannot be thought, which does not make sense. Thus that than which nothing can be thought so undoubtedly exists that it cannot even be thought of as not existing.

(Proslogion, Chapter 3: “That God Cannot be Thought Not to Exist”, as translated by David Burr)

Since I’m not a cruel person, I’ll spare you from having to parse the original and write up my own translation:

Chapter 2: That God Really Exists

1. No being is greater than God. Even a fool who would deny God recognizes this.

2. That fool has only a partial understanding, however, since he does not understand such a being to exist.

3. Consider a painter’s thoughts of his or her next masterpiece, to the finished masterpiece itself. They have a rough sketch of the painting within their minds, but since it does not physically exist they cannot fully understand that painting.

4. It follows from 3. that it is greater for any object to exist that to not exist.

5. But if point 4. is true, then it would be impossible to think of the greatest possible being unless that being existed. Otherwise, there could exist a greater being, having all the attributes you gave to your greatest being plus the attribute of existence.

Chapter 3: That God Cannot be Thought Not to Exist

6. We can think of a being that must exist, and this being must be greater than one that we cannot think of as existing.

7. By that reasoning, if that being from 4. couldn’t exist, it would be lesser than another thing in our thoughts that could exist in reality.

8. Thus, we’ve reinforced point 5: that being must exist in reality.

9. By extension of points 6 through 8, we cannot even think of this being as not existing.[23]

10. We can’t think of anything greater than God.

11. This “being” we’ve been referring to must be God, otherwise we’d contradict point 10.

12. Praise God, isn’t He wonderful, etc. etc. etc.

Philosophers fell in love with this style of proof. The possibility of finding a proof for god using nothing but logic is like finding a long-forgotten civilization without leaving the house. A number of big-names have come up with their own versions, such as Gottfried Leibniz, Kurt Gödel, and René Descartes. The Stanford Encyclopaedia of Philosophy lists five more “distilled” variations on it:

1. God is a being which has every perfection. (This is true as a matter of definition.) Existence is a perfection. Hence God exists.

2. [24]

3. It is possible that God exists. God is not a contingent being, i.e., either it is not possible that God exists, or it is necessary that God exists. Hence, it is necessary that God exists. Hence, God exists.

4. [It is analytic, necessary and a priori that][25] Each instance of the schema “The F G is F” expresses a truth. Hence the sentence “The existent perfect being is existent” expresses a truth. Hence, the existent perfect being is existent. Hence, God is existent, i.e. God exists. (The last step is justified by the observation that, as a matter of definition, if there is exactly one existent perfect being, then that being is God.)

5. The word ‘God’ has a meaning that is revealed in religious experience. The word ‘God’ has a meaning only if God exists. Hence, God exists.

6. I exist. Therefore something exists. Whenever a bunch of things exist, their mereological sum also exists. Therefore the sum of all things exists. Therefore God—the sum of all things—exists.

(http://plato.stanford.edu/entries/ontological-arguments/ , retrieved April 30th 2011)

Missing from that list is Leibniz’s Monad theory, which borrows an ancient Greek idea. A “monad” is a super-atom of sorts; they make up every substance and contain consciousness, yet cannot be changed or destroyed, only divided into infinitely small pieces. No two are alike. They’re classified by the abstract properties they’ve been granted; “Entelechies” do little more than move, “Souls” have the added ability to remember things, and “Spirits” are permitted to reason. While all modads are tied to physical bodies, Leibniz claims there’s a special monad out there that is not attached to a body, and does nothing but continually create new monads. This god monad is stopped from just cranking out “Spirits” by the laws of nature. This system cannot be improved on, according to Leibniz.

None of Leibniz’s contemporaries agreed on that point.

The sixth on that list is a close match for Descartes’ “proof” for God. The scare-quotes are because Descartes would probably object to that argument being called a proof, let alone one of his own. In general, he thought God’s existence was obvious via intuition, instead of rational arguments. As a result he never bothered to write up a formal rationale, but instead randomly scattered bits of logical argument and informal reasons throughout his work. He took full advantage of this sloppiness, by throwing out many variations and forcing his critics to comb through his entire work to clean up his “proofs.” Fortunately for me, his arguments boil down to a mix of proofs that I have or will cover in this book, so I don’t need to elaborate further.

Gödel’s proof, by comparison, is both much better and much worse. Instead of dealing with “perfections” or simplistic “attributes,” his proof works on “positive, morally aesthetic properties;” examples of these include “perfectly just,” “all-powerful,” “merciful,” and “absolutely moral.”

Out of all the Ontologicals I’ve presented, Gödel’s is easily my favourite. It’s much better than Descartes’ “proof” because it is a well-structured logical argument, presented in a formal logical system with well-defined rules. It’s also much worse, for the same reason:

Godel's Ontological Proof

That chart-junk is called “modal logic,” and is a little tough to understand without study. Would another translation help?

Assumption 1: No property in collection P will be the inverse of another property also in P.
Assumption 2: If a property is in P, and if for all objects with that property that implies the existence of some other property in every possible situation, then the collection P also contains the other property.
Theorem 1: If a property is in P, an object might exist with that property.
Definition 1: An object has the “God-like” property if, and only if, that object has every property in P.
Assumption 3: The “God-like” property is in P.
Theorem 2: At least one object might have the “God-like” property.
Definition 2: A property is an “essential property” of an object if, and only if, every property that object has must be implied by the essential property, in every possible situation.
Assumption 4: Any property in P must be within P in every situation.
Theorem 3: If an object has the “God-like” property, that property must be an essential property.
Definition 3: An object has the “Anselmian God” property if, and only if, all its essential properties imply that, in every possible situation, an object exists with that essential property.
Assumption 5: The “Anselmian God” property is in P.
Theorem 4: There must exist an object with the “God-like” property in every situation.

I think this is enough examples to begin pulling out some common threads. To begin with, Ontological proofs ignore concepts grounded in reality and instead focus on using pure logic. The only potential exception is “existence,” depending on whether or not you think ideas have an existence outside or independent of the universe. From there, they start rattling off attributes and properties of god, and through some carefully-constructed logic come to the conclusion “god exists” by proving something god-like has the attribute of “existence.”

[22] This is the Latinized version of his name; in the Middle East, he was known as Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā, which was sensibly shortened down to Ibn Sīnā.

[23] Points 6 through 9 match up with the section of Proslogion that I quoted earlier, so you can decide how accurate my attempts at translation were for yourself.

[24] The second version is the rephrasing of Anselm’s argument I quoted earlier.

[25] My best translation from philosopher-ese is “it follows from and is proven from prior knowledge that…”

Proof of God: The Cosmological Proof (4)

Absolutely Nothing

But that isn’t the only nothing out there. I’ve described the best “nothing” we have evidence for. Some of the religious argue this is the wrong “nothing” to be thinking about. Take this review of Laurence Krauss’s book “A Universe from Nothing,” written by Robin Schumacher:

You would think that by the title of Krauss’ book he answers the question that Leibniz posed, but he doesn’t. Instead, he redefines what ‘nothing’ is. ‘Nothing’ to Dr. Krauss would be empty space or the quantum vacuum. Neil DeGrasse Tyson, who is an astrophysicist at the American Museum of Natural History, says in his brief review of the book: “Nothing is not nothing. Nothing is something. That’s how a cosmos can be spawned from the void — a profound idea conveyed in A Universe From Nothing that unsettles some yet enlightens others. Meanwhile, it’s just another day on the job for physicist Lawrence Krauss.” [21]

Fair enough, let’s consider a more basic nothing. First on the agenda is demonstrating that it exists. Here, we stumble badly; Schumacher’s review asserts all “the scientific evidence points to the universe exploding out of true nothingness,” yet as I’ve shown above there is no evidence for this, and we can never find any by definition.

Think about it: we define things by partitioning the universe into “parts of X” and “not parts of X.” A definition of “nothing” cannot throw anything into one of those partitions, because the instant it does our “nothing” consists of at least one thing. Everything we know of must go into the other partition, which means that we are perpetually finding evidence for things that are not nothing. Thus we will never have evidence for that definition of “nothing.”

Let’s ignore those trivial details, though. What would this “nothing” be like? Well, nothing, of course. The scientist’s version of nothing, as I outlined above, includes rules like “Heisenburg’s Uncertainty Principle” and the “Conservation of Energy;” these would have to go. You’d also have to toss out all the rules of logic, as they too are something.

Which means we also have to toss out “something cannot come from nothing” from this nothing. But if there is no rule that prevents something from forming from nothing, then why couldn’t something spontaniously arise? It’s not against the rules, as there are none.

So even if we accept Schumacher’s “nothing” as possibly existing, it’s still possible for something to arise from it!

So Bad It’s Not Even Wrong

Even if you can somehow find a way past all those problems and patch up Cosmological, you face a minor problem.

The conclusion of Kalam is that the universe was caused… and that’s it. At no part of the argument does it say what that cause was. Do we need a god to cause a universe to exist? As we have no clue how to cause a universe, we don’t know. This opens up the possibility of a non-god creator, which we cannot rule out unless we offer up evidence (which, as I’ve argued, will never arrive).

In other words, Cosmological doesn’t even prove the existence of a god! Its continued popularity in religious circles should be an embarrassment to believers the world over, for that reason alone.

[21] http://carm.org/lawrence-krauss-atheist-definition-of-nothing

BBC’s “Transgender Kids, Who Knows Best?” p1: You got Autism in my Gender Dysphoria!

This series on BBC’s “Transgender Kids: Who Knows Best?” is co-authored by HJ Hornbeck and Siobhan O’Leary. It attempts to fact-check and explore the many claims of the documentary concerning gender variant youth. You can follow the rest of the series here:

  1. Part One: You got Autism in my Gender Dysphoria!
  2. Part Two: Say it with me now…
  3. Part Three: My old friend, eighty percent
  4. Part Four: Dirty Sexy Brains

 

Petitions seem as common as pennies, but this one stood out to me (emphasis in original).

The BBC is set to broadcast a documentary on BBC Two on the 12th January 2017 at 9pm called ‘Transgender Kids: Who Knows Best?‘. The documentary is based on the controversial views of Dr. Kenneth Zucker, who believes that Gender Dysphoria in children should be treated as a mental health issue.

In simpler terms, Dr. Zucker thinks that being/querying being Transgender as a child is not valid, and should be classed as a mental health issue. […]

To clarify, this petition is not to stop this program for being broadcast entirely; however no transgender experts in the UK have watched over this program, which potentially may have a transphobic undertone. We simply don’t know what to expect from the program, however from his history and the synopsis available online, we can make an educated guess that it won’t be in support of Transgender Rights for Children.

That last paragraph is striking; who makes a documentary about a group of people without consulting experts, let alone gets it aired on national TV? It helps explain why a petition over something that hadn’t happened yet earned 11,000+ signatures.

Now if you’ve checked your watch, you’ve probably noticed the documentary came and went. I’ve been keeping an eye out for reviews, and they fall into two camps: enthusiastic support…

So it’s a good thing BBC didn’t listen to those claiming this documentary shouldn’t have run. As it turns out, it’s an informative, sophisticated, and generally fair treatment of an incredibly complex and fraught subject.

… and enthusiastic opposition …

The show seems to have been designed to cause maximum harm to #trans children and their families. I can hardly begin to tackle here the number of areas in which the show was inaccurate, misleading, demonising, damaging and plain false.

… but I have yet to see someone do an in-depth analysis of the claims made in this specific documentary. So Siobhan is doing precisely that, in a series of blog posts.
[Read more…]

Proof of God: The Cosmological Proof (3)

There Are No Stupid Questions

While Hume has me in a philosophical bent, let me ask a question of my own. Can you prove to me that the universe exists?

It sounds like a trivial question. Shouldn’t the keyboard under my fingers, the photons smacking into my eyeballs, or my ability to think about myself suggest an obvious answer?

But think about it a little more. That keyboard is not the universe, but something that exists within a universe. The same can be said for those photons and even my thoughts.[16] In fact, at no point in my life will I ever interact with the universe, I will only deal with the things contained in it.

We can’t say the same about my keyboard, those photons, or the thoughts bouncing around my skull. I can verify my keyboard exists by looking at it, test my eyes’ ability to detect light by comparing where it says my hands are to what my body has to say about the matter, and hook myself up to a brain scanner and watch the activation patterns of my neurons change over time. These aren’t absolute proofs of existence, true, but by combining multiple lines of evidence I can push my uncertainty down to an arbitrarily low level.

As this simple question demonstrates, the universe is qualitatively different than any physical thing. It is an abstract container, which can only be properly described by referring to the things within it. And yet Cosmological wants us to treat it the same as any other physical object. The sloppy nature of language hides this conflict from us, making the proof seem more rational than it actually is.

It’s a Mad, Mad, Mad, Mad World

All that would be bad enough, but so far all I’ve discussed is theory. Wouldn’t it be nice if there was also some hard physical evidence that the Cosmological proof fails?

There might be, but it’s going to take a little explaining.

Remember the phrase “you can’t get something from nothing?” Imagine we’re able to break that rule, exactly once. Something would pop out of nowhere, and set off a chain of causes, moves, and so on. This would form its own hierarchy that might intersect the primary one at some point, but would still lead back to separate single “mover.” Applying the Cosmological proof to this tree would result in two gods, one per tree. This is a bit of a problem if you only believe in one god.

Polytheists would be fine with it, but even they have limits. The highest number of gods I’ve heard of is in the 300 million range, for Hinduism, but this seems to be an estimate of historical and forgotten gods instead of the number actively worshipped. Nonetheless, once we get into the trillions of trillions of gods it becomes difficult to keep a straight face. If this exception can happen with no limit, those numbers are easy to reach.

So if we could find some way to get “something from nothing,” we’ve again broken Cosmological. I can think of two: the Casimir Effect has been well-demonstrated but only goes half-way, while Dark Energy is probably a clean break but needs further study to prove this.

Bring two metal flat metal plates really close together, to within a few thousand widths of an atom, then attach a force gauge to at least one. You’ll measure a force tugging the two together, even if there’s no electric or magnetic fields to draw them together, and everything is in a complete vacuum. What’s creating the Casimir Effect is likely virtual particles popping out of empty space unevenly.

Wait, empty space is creating particles? It’s strange, but true. To explain how, I have to tackle a much more fundamental problem: energy.

Philosophers had long thought there was some sort of force or fluid driving life. From the time of Gottfried Leibniz in the 1600’s to the work of Lord Kelvin in the late 1800’s, this definition became more and more abstract:

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. [17] The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

(The Feynman Lectures on Physics, 1961)

The best metaphor I can think of is money. It used to be a physical thing, a solid coin or token you carried, but in my time it’s been reduced down to a few magnetic disturbances on a computer hard drive in some far-off land. You could exchange some “cash” for tea, chocolate, or a good massage. Likewise, by selling tea or giving a massage you can earn some of this abstract quantity back. Just like energy, money only becomes useful when it’s transformed into an action or something material.

Also like energy, it’s a positive quantity; you cannot have less than zero dollars,[18] and once you reach zero dollars you’re stuck until someone gives you a donation. Forces can front you some funds; if you hold up a ball above the surface of the Earth, it has some money/energy “stored” thanks to gravity, and once you let go it hurriedly starts converting that into motion. The two Relativity theories say that matter itself can also supply some currency, like in a nuclear reactor or radioactive decay.

In empty space, where forces like gravity and magnetism are absent and matter doesn’t exist, you’d expect the bank balance to be firmly at zero. This makes sense; otherwise, you could use empty space to do some useful work, by creating something out of nothing.

There’s another possibility, though. Canada used to have “Vagrancy Laws” which mandated that every citizen must carry a certain amount of change on their person.[19] On the surface, both lead to the same results since you can’t spend below your limit, whether it’s zero or a greater amount. There are some subtle differences, though. For instance, you could temporarily go below the legal amount when consolidating your change at the bank, or during a private card game. If you had no cash on you, however, both scenarios would be impossible. This doesn’t have to break the law, though, so long as you always end up above the limit while in public.

Werner Heisenberg added a key feature to Quantum Mechanics in 1926. His “Uncertainty Principle” states that there are limits to how defined some quantities could be. If you knew the momentum of a particle very well, for instance, you couldn’t be very precise about its location. This perpetual uncertainty is not the fault of the experimenter, but built right into the fabric of the cosmos.

The Uncertainty Principle applies to empty space, too. Thus a perfect vacuum cannot have an energy level of zero, because then you would know its value with certainty. In fact, not only must it contain some energy, but that energy must fluctuate too lest it be known with certainty. So while every other physical theory we know of views an empty void as, well, an empty void, Quantum Mechanics views it as a perpetually churning, frothing hotbed of action.

Just like in our metaphor, a non-zero minimum energy has some side-effects. The twin Relativity theories point out that energy and matter are interchangeable, so the fluctuations in a perfect vacuum wind up creating “virtual” particles that live for incredibly short periods of time before popping back out of existence. These don’t have to play by the rules of normal matter, leading to such oddities as negative energy and time travel. The kind and strength of these particles depends on the size of the void, and this leads to the Casimir Effect. The tiny distance between the two metal plates constrains what particles can pop out of the vacuum, yet the open space behind the two plates does not. The pressure of the interior particles can be less than or greater than those of the outside, depending on the exact distance, and thus the two plates are forced together or apart.

This sounds like a clear violation of the Conservation of Energy, but remember the money analogy. If everyone has the minimum amount of cash, then everyone’s equally poor and no work can be done. Likewise, all that virtual particle action averages out to a minimum value, which cannot be borrowed against.

Does it make sense to call this an “empty void,” then, if it isn’t empty?

This is where “something from nothing” begins to break down. If we call this void “nothing,” then it clearly is creating “something” in the form of matter and forces. It’s tempting to declare it to be “something” and dodge this bullet, but then what can we call “nothing?” If no such thing exists, then the “something from nothing” argument is meaningless since there must always be something!

There is a way around this counter-argument, though. If we redefine “something” as anything above this minimal vacuum energy, then the contraction goes away. Since these virtual particles are exactly at the minimum, we can dismiss them as averaging out to nothing in the long run. I’m not certain the Casimir Effect can be waved away so easily, but some physicists like Robert Jaffe think it can be explained without needing to invoke virtual particles. This would mean the void is not producing force, and thus not producing “something.” The Casimir Effect is very small and difficult to study, so it could take some time to sort out who’s right.

Or, we could look for the answer in the stars.

The calculations of Edwin Hubble[20] and others before him have been tested, re-tested, and verified via other means. Physicists and astronomers are convinced the universe is growing in size. On this grand a scale, the only force that can effect expansion should be gravity; the weak and strong forces have no effect here, and all charged particles average out to zero electromagnetic force. Gravity may be the weakest force on the block, but it only pulls; over long distances, this adds up and has the effect of pulling the universe back together. We should see the rate of expansion slowing down over time, as a result.

Instead, it is accelerating. Two competing teams first discovered this around 1998, and other observations have backed them up. Something within the universe is pumping out extra force and energy that is pushing everything away from everything else, and yet the source of this isn’t visible from our lonely planet. The prime suspect behind this “Dark Energy” is the energy of empty space, as I just described above. These virtual particles create a force or pressure that drives matter apart, and more virtual particles are created as the size of the universe increases. It’s a tidy explanation, which also vindicates the Casimir Effect as I described it.

It isn’t a perfect explanation, though. For one thing, the energy of empty space is at least 1050 times greater than Dark Energy’s observed value, and could even be a staggering 10120 times too strong. It also leads to problems in the early universe, where this energy suddenly turns into an attractive force, and there are some observations related to the density of our cosmic neighbourhood that further muddy things up.

Still, it’s the best explanation we have right now. And no matter what the true answer is, we know that we have something currently within our universe that’s creating energy out of nothing, in clear violation of the “something from nothing” assertion.

Yet again, we find the Cosmological Proof amounts to nothing.

[16] That last one depends on my counter-arguments for the proof from Mathematics, specifically the section on dualism. Feel free to skip ahead, if you’re feeling sceptical.

[17] Feynman may have gotten this wrong. I’ll get to the details shortly.

[18] Yes, some Canadian citizens owe more than they own due to credit and loans, but for this metaphor I’m ignoring those messy details.

[19] That portion was repealed in 1972. In theory, it was to ensure each citizen could call someone to get out of trouble. In practice, it was used to punish the poor and homeless.

[20] Hubble would make a good subject for a book. He was a handsome, charismatic athlete who hung out with Hollywood stars, yet still lied to fluff up his resume and seems remarkably ignorant of the theories his data was supporting or refuting.

Proof of God: The Cosmological Proof (2)

Hume’s Trip to the Pole

This line of thought brings up another objection, one that was first noted by David Hume.

Hume, who lived from 1711 to 1776, was one of the first philosophers to examine proofs of god with a sceptical eye. As my future self will mention, my thoughts on miracles will be little more than his thoughts with a light dusting of cheese and vinegar. He also examined the Design proof, and weighed in on Cosmological as well. While he gives several objections to the last one, I’d like to focus on this one:

… The WHOLE, you say, wants a cause. I answer, that the uniting of these parts into a whole, like the uniting of several distinct counties into one kingdom, or several distinct members into one body, is performed merely by an arbitrary act of mind, and has no influence on the nature of things. Did I show you the particular cause of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts.

(Dialogues Concerning Natural Religion, Part 9)

As I’ve mentioned before, at the core of Cosmological’s argument is a hierarchy. I can turn this into a visual metaphor by drawing a series of ever-branching pipes:

[diagram of a tree of pipes]

As we follow the flow down these pipes, we jump from cause to effect, or from mover to moved, or from creator to created, or along whatever relation was used to construct this version of Cosmological.

[diagram of an arrow flowing down these pipes]

Since these pipes have a finite length, we can attach a rope to one point, then swim around the pipes until we run out of pipe but still have some rope in hand. We can just as easily picture the rope attached to the top of this pipe hierarchy, and then pull ourselves along it until we reach the very source of all the flow.

[diagram of a rope feeding through these pipes, acting like a measure of time]

Thanks to the rope trick, it’s easy to ignore the branches and just think of it as one pipe with a well-defined beginning. Note that we don’t care about an ending; so long as there’s a beginning, we can always pull ourselves towards it. In contrast, consider a long pipe with no beginning or ending at all.

[diagram of an infinite but straight pipe]

If we attach the rope and explore, we’ll run out of rope no matter how much swimming we do. Likewise, if we pull ourselves along an attached rope, we’ll still have plenty of places to explore once we’ve reached the end of it.

Cosmological compares these two layouts, and rejects the second one. It claims an infinite pipe or chain of relations is an absurd idea, and faced with no other alternative claims the hierarchical version is the only way to go.

But are those two the only possible choices? Consider instead a loop of pipe, like so:

[diagram of a pipe bent into a donut shape]

We have a finite length of pipe, which satisfies Cosmological’s rejection of the infinite, and yet at the same time there’s no beginning or end to this pipe! If we pull ourselves along a rope we find drifting in the current, we’ll again be faced with a void that we’re free to explore. We can use this rope as a measure of how far we are from the “beginning.” If we just float and let the rope spool out, we note that we get further and further away. If instead we pull ourselves up, our rope gets shorter and shorter until we run out of rope. From this point, everything is after the beginning, since we need to let out some rope to move away from this point. This will come in handy later.

[diagram of a donut pipe with a rope attached to one point]

But for now, we’ve found a third way, one that avoids infinite spaces while also avoiding the need to stop at a First Mover. This derails Cosmological, since it was counting on finite space implying a First Mover, and again renders the proof useless.

No doubt you’re sceptical of my metaphor. We know our universe had a definite beginning, because we’ve found the evidence in and between the stars. Real life is not a one-dimensional loop, but a four-dimensional expanse of space and time. How can the two be similar?

Very easily, in fact, so long as you think four-dimensionally.

Back in 1905, Albert Einstein published his theory of Special Relativity. In this landmark paper, he proposed that space and time are actually the same thing, differing only in what direction you look, and that both of these are warped by gravity. It sounds crazy, but one hundred years of observation have backed up Einstein’s claim, and Special Relativity 2.0 (better known as General Relativity) has become one of the most successful theories ever proposed. [A]

The standard metaphor for General Relativity, handed from generation to generation, is the rubber sheet. Plunk a heavy round object, like a bowling ball, on one that’s been suspended in air, and it’ll sink down and pull the sheet with it. Take a smaller round object, say a marble, and roll it across the sheet towards the big one. It’ll go in a straight line until it reaches a bent part of the sheet, where it’ll veer towards the heavy object. Do this well enough, and you can get the marble to orbit the big ball before friction ruins the fun.

If we’re allowed to warp the sheet, however, what’s stopping us from warping it around until it touches itself? We’ve just reached the other standard cosmology metaphor: the rubber balloon. This is usually used to explain the Big Bang, by showing how space stretches and makes everything look like it’s rushing away from you. But we could also think of it as a potential model for how the universe is shaped. It has a finite area, even if you continue to inflate it, but at the same time you could walk around this shape without ever reaching an edge. This is exactly like the ring of pipes I outlined above, only in two dimensions.

A three dimensional version is too big for me to visualize, unfortunately. That one-dimensional version is actually in three dimensions; I needed to twist the pipe around so that it would meet itself, and the only way to visualize that from the outside is to invoke another dimension, and I also implied the dimension of time indirectly by having our metaphorical swimmer swim. This diver within the pipe has no way of accessing the second spacial dimension, let along proving it exists, so I haven’t spoiled the metaphor. Likewise, to explain the two-dimensional version I really used four dimensions to get the point across. I need one more dimension to describe a three-dimensional extension, but my poor brain was only designed to work in four dimensions and fails miserably when dealing with five.

And yet that hasn’t stopped similar brains from thinking about higher dimensions. Einstein was able to cope with a four-dimensional space-time by using math as a crutch, and other scientists have used the same trick to think about our world in eleven or more dimensions. To name an example, Stephen Hawking has proposed a theory that would visualize time as a sphere like the Earth, with the “North Pole” label replaced with “Big Bang.”

I was never built to be comfortable with higher dimensions, but that doesn’t rule out their existence. We humans were convinced the world was flat for a very long time, until a few of us realized we actually lived on a very, very, very, very big sphere. It only looked flat from our limited perspective. Cosmological makes the mistake of assuming its narrow perspective is the only one, that there must only be two ways to organize the world.

All this talk of spheres brings up another good rebuttal, though. Let’s return to my pipe metaphor again, with the rope attached to the head of Cosmological’s hierarchy. The proof asks us to pull ourselves hand-over-hand up the rope, until we run out of space and rope. It then asks what would happen if you tried to take up one more length of rope. It points out this would take you outside the pipe, and that the only thing which could survive out there is a god. Ergo, god exists.

But does that make sense? In our metaphor, we are constrained to follow the pipes, and to always have a length of rope greater than or equal to zero. We have no way to get outside out of either limit, and yet Cosmological is asking us to think about what’s on the outside. That doesn’t fit into our metaphor at all! David Hume indirectly realized this; since you can’t reach outside of the pipe, once you’ve swam around and reached every point within the pipe, you don’t have any place left to go. If you understand everything within the pipe, you understand everything.

[diagram of person banging on pipe, from the inside]

Let’s now extend the metaphor back to the proof. Note that “cause” and “effect” are exclusive; one object cannot be the cause of, and the effect of, another object. The same applies to creation, movement, and any other system used by variations of Cosmological to organize the hierarchy. This not only creates Cosmological’s hierarchy, it also defines a direction; if we just let things play out naturally then creators create, movers move, and so on. Having established all this, the proof asks us to go against the natural flow and walk back up the hierarchy to the top, being careful never to backtrack. Once it runs out of universe and reaches the pinnacle, it tries to take one more step. The universe defines where we can and cannot go, however, so this is the same as asking us to step outside the universe. The result is nonsense, even though every step before then seems perfectly reasonable.

This assumes a hierarchy, of course, which has a definite start. If our universe is more like a circular pipe or spherical balloon, our choice of start is arbitrary. Fix our metaphorical rope to whatever place you wish to call the start, and then take a stroll. Sometimes the rope will lengthen, sometimes it’ll shorten, but in no direction will you be forced to go beyond the “start.” Even if you make a beeline straight for it, the rope will merely shrink down to nothing then immediately lengthen again, without forcing you to backtrack.

This fits perfectly with our modern view of the universe. Relativity makes time and space interchangeable, so any physical metaphor works equally well with time. While asking “what happened before the universe” seems to be a valid question at first, it’s actually the same as asking “what’s beyond the end of the rope,” “what happened before time existed,” or “what’s North of the North Pole,” all of which are absolute nonsense.

And yet the Cosmological proof requires us to ask those questions, and requires us to think of them as perfectly valid, otherwise it has no place to insert a god. We’ve found another flaw in the proof, only this time there’s no escape hatch.

[A] Whoops, past me screwed this one up. As Rob Grigjanis points out, the Special Relativity papers of 1905 ignored gravity. I also misunderstood spacetime a bit. While space and time are integrated, there’s a difference between purely spatial paths and purely temporal paths through this space. I think one of Brian Cox’s book covers this well for a lay audience.

Proof of God: The Cosmological Proof (1)

Proof from First Cause, or the Cosmological Proof

Have a quick look around you.

Are you sitting in a chair? Did you ever wonder how that chair got there?

I’m willing to bet you or someone else placed it there. I doubt you created it, though; more likely, a team of people fashioned it out of wood and metal, gave it to another group who transported it to a store or warehouse, where another bunch helped deliver it to you. Where did that first team get their materials, though? The wood was probably harvested from a forest, the metal dug up from a mine. The trees got their nutrients from the soil and the sun. No matter which path you take, both trace back to the Earth or the Sun.

So far, everything we’ve discussed has come from something else. The materials came from elsewhere, and somebody or some process helped shape it. The chair was “caused” by human effort and the proper materials, the tree was “caused” (in a loose sense) by sunshine and nutrients gathering in the right place and the right way. We can do this thought experiment for every object in the universe.

We should be able to do this for the universe itself. It’s a material thing, after all, though perhaps a little larger and more complicated than our chair.

At this point, the chain of causes breaks down. We can’t name anything within the universe as a cause, since by definition that’s a part of the universe itself. Any potential cause must come from outside. But what lies outside the universe, in a place we can never hope to explore?

There’s only one being we know of that could live outside the universe. God, after all, is the only possible being with enough power to create a universe, and in countless religions she does exactly that:

In the beginning God created the heaven and the earth.

(Genesis 1:1, Jewish Old Testament, King James translation)

They say it happened long ago when there were no people nor anything, and when earth and the black sky did not exist “Let us make the earth and the black sky,” he said. He began to study and talk about how both the earth and sky might be made.

(“Myths and tales from the San Carlos Apache”, collected by Pliny Earle Goddard)

Nights, days, weeks and seasons; wind, water, fire and the nether regions—in the midst of these, He established the earth as a home for Dharma. [11]

(from the Sikh religious text “Siri Guru Granth Sahib”, translated by Singh Sahib Sant Singh Khalsa)

Then, at last, slowly uprises Tane-mahuta, the god and father of forests, of birds, and of insects, and he struggles. With his parents; in vain he strives to rend them apart with his hands and arms. Lo, he pauses; his head is now firmly planted on his mother the earth, his feet he raises up and rests against his father the skies, he strains his back and limbs with mighty effort. Now are rent apart Rangi and Papa, and with cries and groans of woe they shriek aloud: ‘Wherefore slay you thus your parents? Why commit you so dreadful a crime as to slay us, as to rend your parents apart? But Tane-mahuta pauses not, he regards not their shrieks and cries; far, far beneath him he presses down the earth; far, far above him he thrusts up the sky.

(“Polynesian Mythology & Ancient Traditional History of the New Zealanders,” collected by Sir George Grey)

Therefore, there’s only one possible cause for the universe, and that’s god.

Golden Oldies

The Cosmological proof is, without a doubt, the most popular of its class. Surprisingly, it’s also one of the earliest formal arguments we know of, dating back to Plato’s last work, Laws. In the tenth chapter of this dialogue, the wise “Athenian[12] ” scoffs at those who deny the existence of the gods, who claim they were man-made inventions that bend to human whims. To show their folly, he builds a simple proof by cataloguing the types of motion that exist in the universe. After ticking off nine, the “Athenian” describes a tenth type, that is capable of moving itself and other objects. He then points out this tenth must be the greatest of all, and reaches the core of his argument:

ATHENIAN: I mean this: when one thing changes another, and that another, of such will there be any primary changing element? How can a thing which is moved by another ever be the beginning of change? Impossible. But when the self-moved changes other, and that again other, and thus thousands upon tens of thousands of bodies are set in motion, must not the beginning of all this motion be the change of the self-moving principle?

CLEINIAS: Very true, and I quite agree.

ATHENIAN: Or, to put the question in another way, making answer to ourselves: If, as most of these philosophers have the audacity to affirm, all things were at rest in one mass, which of the above-mentioned principles of motion would first spring up among them?

CLEINIAS: Clearly the self-moving; for there could be no change in them arising out of any external cause; the change must first take place in themselves.

ATHENIAN: Then we must say that self-motion being the origin of all motions, and the first which arises among things at rest as well as among things in motion, is the eldest and mightiest principle of change, and that which is changed by another and yet moves other is second.

(Laws, Book X, translated by Benjamin Jowett)

From there, the “Athenian” needs only a little bit of hand-waving to turn this primary mover into what he calls a “soul,” but modern readers would recognize as a god.

The argument next appeared roughly 1,300 years later, in Avicenna’s studies of ancient Greek thought, only this time it proved the existence of Allah instead of the Greek gods. Later scholars, most notably the influential Al-Ghazali, would condemn all of Plato and Avicenna’s work as a corrupting influence, but retained the handy Cosmological proof.

Thomas Aquinas independently claimed Cosmological for Christianity some 200 years after Avicenna, in his Summa Theologica. Aquinas’ version shows why this proof continues to be so popular. Not content to merely repeat Plato’s chain of movers, he created three more variations of the same proof and claimed each as a newcomer. One is the chain of causation I used in my introduction to Cosmological; another is a chain of creation, which traces back to singular creator; and the last is a chain of perfection, leading to the most perfect being possible.

Plato’s original argument has endured because it is so very plastic. To come up with your own variant, all you need is some way to organize every object in the world into a hierarchy.[13] You then claim that an infinitely deep hierarchy is absurd or impossible, then place atop this tower of induction the god of your choice. In the 2,500 years since it left Plato’s mind, Cosmological has been polished down to an invincible single sentence:[14]

You can’t create something from nothing, unless you’re a god.

Because I Said So

It would help if we had a more formal version of Cosmological to run through point-by-point. The Kalām[15] version of Cosmological, as promoted by William Lane Craig, seems like a good start:

  1. Whatever begins to exist has a cause.
  2. The universe began to exist.
  3. Therefore, the universe has a cause.

We can easily modify this to cover all other versions of Cosmological:

  1. Whatever begins to exist was created has a cause creator.
  2. The universe began to exist. A finite number of movers must exist.
  3. Therefore, the universe has a cause. a being more perfect than all must exist.

Returning to Plato, he rejected the idea of an infinite chain of movers or causes because he didn’t think infinite things existed in the real world. Most thinkers who invoke the Cosmological proof agree, and like Plato stop this infinitely long cascade by placing an infinitely-powerful being in its path. Thus in order to stop an infinite thing from existing in the world… they propose the existence of an infinite thing in the world. Hmm.

And looming over it all is a cherry of a contradiction that Cosmological tries to ignore. If everything has a creator or mover or what-have-you, and god is something, then what created/moved god? After all, this proof rests heavily on the idea that everything can be put into a hierarchy, with no exceptions, but then it turns around and grants one exception. Doesn’t this derail the entire train of thought? If we’re allowed to grant exceptions, what prevents me from saying the universe is an exception too? Philosophers have been fine labeling their god of choice the “First Mover” without any evidence to justify it, so I fail to see why I can’t slap the same label on the universe, given an equal amount of evidence.

[11] “Dharma” probably means “religious path” here, but in other contexts it could be closer to “religious law” or “social structure.”

[12]  Scholars suspect this mysterious Stranger from Athens was supposed to be Socrates. Plato never named the character directly because he bore little resemblance to the Socrates from Plato’s earlier dialogs. The youthful version was perpetually questioning and dripping with excessive humility, while the later one knows the truth and kindly shares his lessons with lesser people.

[13] Why a hierarchy? Let’s take creation as an example: a lump of clay can be used to create many things, like pots or plates, while those pots or plates have only one creator, the clay. The same one-to-many branching applies to causes, movers, or whatever other mapping you use, and when laid out on paper naturally leads to a hierarchy.

[14] Sorry, that’s a lie. The ancient Greek Parmenides nailed it when he said “ex nihilo nihil fit,” and he pre-dated Plato!

[15] “Kalām” refers to an early school of Islam, that valued knowledge and thought theological arguments were best settled by debating it out. I approve, if only because it cuts down on the number of holy wars.