No serious mathematical understanding, aptitude, or even interest is required to enjoy this post. There’s a fascinating thing that I want to share with you, but there’s a bit of mathematical throat clearing we need to get through up front.

Here’s an example of a differential equation (seriously, this isn’t on the test):

This differential equation describes a damped oscillator. Imagine a weight on a spring. Drop the weight, and it bounces up and down, but less each time until it comes to a stop. That motion is described by this equation. Here it is in graphical form:

Equation 2 is a simplified representation of equation 1 (the dots represent a derivative with respect to time):

Move some terms around for one last simplification:

Analog computers

Okay, now it gets interesting. Decades before the early room-sized electronic digital computers like ENIAC, there were analog computers. They solve differential equations like this one.

Analog computers are made from elements like integrators, multipliers, and adders (I leave as an exercise for the reader why integrators make much more sense than differentiators).

To solve the equation above, we first assume that we have ẍ.

Crazy, right? We just proceed blithely along after first assuming that we already have the second derivative of the thing we’re trying to find.

Stick with me and see how this turns out. First, integrate it twice (each integration removes a dot—that is, one derivative of time). The signal moves from left to right through two integrators:

Okay, we’re almost there. We use the analog computer to create the right side of equation 3:

Magic time!

And here’s the fun part. We’ve now computed the right side of equation 3. But wait a minute—that’s equal to ẍ ! So that bizarre, unfounded assumption—we just assume that we have what we don’t have—was actually justified. We feed that output back in as ẍ and we’re done. Here’s the final layout:

Ah, if only faith worked like that in religion.

Augustine’s contribution to differential equations

Augustine (354–430 CE) didn’t have much to say on this subject, but see if this sounds like our analog computer project: “Seek not to understand that you may believe, but believe that you may understand.”

Just believe. Don’t worry about it making any sense—understanding will come with time. It’s like solving a differential equation with an analog computer: assume the result, and you will be rewarded.

The problem, of course, is that it actually works with an analog computer. Every time. By contrast, “just believe” is terrible advice when evaluating a claim with poor evidence—fairies, leprechauns, Oz, the Force, and so on.

Begging the question, Christian style

We see a similar assumption of the conclusion with many responses to challenges against Christianity. For example, we see in the gospels just what we’d expect to see if the resurrection were true. Therefore, the Christian apologist says, the gospels are important evidence for the resurrection being true.

Or, take the order and beauty we see in the world. The apologist tells us that this is just what we’d expect if there were a god.

But is this approach justified? Take an analogous argument:

1. If space aliens caused car accidents, we’d see car accidents.
2. We do see car accidents.
3. Conclusion: we now have more evidence that space aliens cause car accidents.

The Gigantic If

Or (for a different kind of rationalization) take the Problem of Evil, the puzzle of why an all-good god allows so much bad in the world. An all-knowing god could have his reasons, couldn’t he? That you skeptics don’t understand is hardly surprising—your finite mind may just be incapable of understanding it from that god’s perspective.

In other words, assume the Christian position and rearrange evidence to support it rather than start with the evidence and then reach a conclusion. This is the Christians’ Gigantic If: an argument that begins, “if God exists . . .” or “if objective morality exists . . .” or “if Jesus resurrected. . . .” (I’ve discussed this in more detail as the Hypothetical God Fallacy.)

Yes, Mr. Christian, if God exists then you win the argument, but you don’t get to just assume God or any other fanciful claim. Simply showing that your claim is compatible with the facts counts for nothing. You must do it the hard way, like a scientist or historian, showing the evidence that leads us unavoidably to your conclusion. I’ve seen the Gigantic If so often that it’s like fingernails on a blackboard for me, and I hope that it will be for you, too.

Assuming the conclusion works great when solving differential equations, since we have evidence that it works. The opposite is true for supernatural claims.

 In a universe of electrons and selfish genes, 
blind physical forces and genetic replication, 
some people are going to get hurt, 
other people are going to get lucky, 
and you won’t find any rhyme or reason in it, nor any justice. 
— Richard Dawkins

(This is an update of a post that originally appeared 12/11/13.)

Image credit: Bryan Alexander, flickr, CC

We conclude our responses to the Transcendental Argument (TAG) here. I introduced the argument and begin in part 1.

9. Transcendental Argument for theNon-existence of God (TANG)

TANG is a variant on TAG. It supposes that God created everything, including logic. But then logic is dependent on God—it’s contingent. Said another way, logic isn’t logically necessary. The laws of logic are then arbitrary, and God could’ve made them something else. X and not-X could both be true, for example.

You may enjoy logic as we know it, but TAG says that it’s not as absolute as you thought.

10. Some things don’t need supernatural explanations

I’ve always found the claim, “Well, if there are moral or logical laws, there must be a lawgiver!” to be a mindless applause line.

When falling sand in an hourglass forms a cone, does that require a supernatural cone maker? When a river changes course as it meanders over a flat valley, does that demand a river designer? When there is an earthquake, must the timing and placement of that be supernaturally ordained? No, there natural explanations for all these things.

Similarly, the question “Why these fundamental laws and not others?” doesn’t demand the supernatural. To support a claim of supernatural grounding, we need the evidence.

11. An answer without evidence is no answer

“God did it” explains everything. Therefore, it explains nothing. “God did it” is a solution searching for a problem, and apologists thinks they’ve found one with “What grounds logic?”

But “God did it” is simply a repackaging of “I don’t know.” It tells us nothing new. I’m no smarter after hearing “God did it” than before. How did God do it? Why did God do it? Did he break any scientific laws to do it? Who is this guy and where did he come from? This is an answer that just brings forth yet more questions, and it never comes with any evidence to back it up. Since the apologist answers “I don’t know” to each of these new fundamental questions, let’s just save a step and avoid replacing a natural “I don’t know” with a supernatural one.

And which scientists, on hearing and believing TAG, say, “Well, I guess my job is pointless now, so I’ll go be a plumber”? That “explanation” doesn’t explain anything; it simply relabels “We don’t know.”

12. TAG asks a poor question

The Edge had an interesting list of scientists’ musings on a similar topic. I’ll summarize a few points from physicists Sean Carroll and Jeremy Bernstein.

We’re used to asking questions about nature. What causes earthquakes? Why do the continents move? Why is the sun hot? It seems natural to then ask, “Why does logic work?”

But that’s a different kind of question. Earthquakes, continents, stars, molecules, and the elements of nature are part of a larger whole. Asking about the fundamental properties of reality is instead asking about the whole.

The demand to explain the laws of reality is malformed—explain in terms of what? There’s no larger context in which to explain them. The buck stops with these fundamental properties.

Caltrop arguments

I first heard the TAG argument when it was given as a challenge by apologist Matt Slick during a live radio interview ten years ago. Here’s a tip: a radio interview is not the best place to hear a new argument against your position.

And that’s the point. That’s why TAG is a good argument—not that it’s accurate but that it’s confusing.

I call this category of argument caltrop arguments—arguments made simply to slow down an opponent. They’re good for scoring rhetorical points, not for revealing the truth.

You can make your argument so simple that there are obviously no errors. Or you can make it so complicated that there are no obvious errors (Hoare’s Dictum). Said more colloquially, if you can’t dazzle them with brilliance, baffle them with bullshit.

Gods are fragile things; 
they may be killed by a whiff of science 
or a dose of common sense. 
— Chapman Cohen

(This is an update of a post that originally appeared 12/9/13.)

Photo credit: Wikimedia

What grounds the laws of logic and mathematics? We know that they work, but why? The Transcendental Argument (TAG) says that they exist because of and are sustained by God.

I introduced the argument and explored the first responses in Part 1. Let’s continue.

6. You ask “why?” but I ask “why not?”

When we look at reality, we usually explain things in terms of more primitive laws or principles, but eventually you come to the bottom. These few elementary principles, which can’t be defined in terms of anything more fundamental, are called axioms.

Apologists claim that they can do better than this—they rest everything on just “God did it.”

The first problem is that this is stated as a theological claim, not as evidence. Second, they’ve simply replaced natural axioms with a supernatural one. There are still axioms at the bottom, so this is no improvement.

Like naturalists, apologists agree that you’ve got to stop somewhere; it’s just that their stopping point is based on nothing. It has no evidence to support it. Contrast that with the naturalists’ logical and mathematical axioms. Unlike God, these aren’t taken on faith but are tested continually. Why would we want to ground the one that is strongly confirmed with evidence (logic) with the one that isn’t (God)? Why demand something solid to hold up the fundamental axioms but then use faith to hold up God?

I’ll admit that “that’s just the way reality is” isn’t completely satisfying, but “God did it” resolves nothing. The apologist won’t tell us why or how God exists; he just exists. This informs us as much as “fairies did it.” But if the Christian can have a fundamental assumption about reality (God), so can the naturalist (natural axioms).

Show me that the laws of logic are optional or different in an alternate universe. Otherwise, we can presume that the logic that we have is universal.

Let’s say instead that reality just has properties. Or: properties are a consequence of reality. A universe with zero axioms is a universe without properties. Could such a universe even exist? Is that what a godless universe would look like? I await the evidence.

See also: The Parable of the Mathematician and the Theologian

7. TAG undercuts itself

Apologists jump into a TAG presentation using logic. At the end of their argument, they conclude that God exists.

But wait a minute—was that a valid argument? The apologists will certainly say so. But it was made using logic without a presumption of God! The TAG proponents themselves argue that logic can be reliably used without assuming God.

(I believe that this is Timothy Pew’s argument.)

8. Logic needs a vessel, like a mind

One variant of TAG says that logic requires a vessel. Logic can’t be just free-floating truth but must reside in a mind. Before humans, logic must still have been in force, but what held it? God’s mind, of course.

One popular example of this is the argument that gravity is a ghost in Zen and the Art of Motorcycle Maintenance. Before humans, there was no mind to hold the law of gravity. It had no mass or energy. How much more nonexistent could it be?

The problem here is that gravity and the law of gravity aren’t the same thing. Before Newton, Newton’s Law of Gravity didn’t exist. But gravity did. Similarly, you don’t need a mind for time to exist, but you do for “September” or “ten o’clock.” And you don’t need a mind for logic to exist, but you do for the laws of logic.

Said another way, logic and math are languages. We didn’t need to invent English for rocks to exist, we didn’t need to invent physics for gravity to exist, and we didn’t need to invent math for 1 + 1 to equal 2.

Gravity, time, and logic are properties of the universe, and no mind is required.

Concluded in part 3.

Atheism is the arrogant belief 
that the entire Universe 
was not created for our benefit.
— Michael Nugent

(This is an update of a post that originally appeared 12/4/13.)

Photo credit: Wikimedia

We’re exploring ten tough questions from Christian apologist J. Warner Wallace that supposedly provide strong evidence for the Christian claim. Let’s continue.

4. Why Does There Appear to Be Evidence of Intelligence in Biology?

“Most scientists are quick to agree that biological systems often ‘appear’ to be designed. There are many examples of biological ‘machines’ that appear to be irreducibly complex, a sure sign of design. . . . Perhaps the most important evidence suggesting the involvement of an intelligent agent is the presence of DNA and the guiding role that this DNA plays in the formation of biological systems.”

Appearances can be deceiving. ELIZA was a computer program with which users could have a typed conversation, as if with an attentive friend. Originally written in 1966, it could be assigned as a homework problem today. It convincingly mimics intelligence, though it contains none. Perhaps we’re seeing an ELIZA effect when we look at DNA, imagining intelligence where there is none.

Is the marvelous complexity we see in the cell a clue to an omniscient designer? Or is this clumsy, non-optimal Rube Goldberg machine actually evidence for evolution? Biologists are satisfied that evolution explains it. Laymen have no grounds by which to reject the scientific consensus as the best provisional explanation we have (more here).

The claim of irreducible complexity doesn’t convince biologists either. I’ve written more on that here.

As for DNA being strong evidence for intelligence, guess again. In fact, DNA alone demolishes this Argument from Design. DNA is a record of evolution’s sloppy progress, not the perfect blueprint of an omniscient designer.

The Christian might point out that for every instance of information, we find an intelligence behind it. That may be so, but for every instance of intelligently caused information, that intelligence is natural, not supernatural.

Given the long list of things we thought were supernatural but are actually natural (disease, earthquakes, and so on), you’d think that apologists would be more cautious. But no, once science resolves a puzzle, they’ll just retreat to another unanswered question to defend their God of the Gaps.

5. How Did Human Consciousness Come Into Being?

“[As evolution proceeds, naturalists must] imagine that spatially-arranged matter somehow organized itself to produce non-spatial, immaterial mental states. Naturalism has no reasonable explanation for how this might come to pass.”

Ah, but it does: emergent properties. Consider a water molecule. It doesn’t have the properties of wetness, fluidity, or surface tension, but once you get trillions of trillions of them, then these properties emerge.

Or take the human brain. Our brains have roughly 100 billion (that’s 10¹¹) neurons. A single neuron doesn’t think 10^–11 times as fast; it doesn’t think at all. Thinking is another emergent phenomenon. (I’ve written more on that here.)

If the point is that we have plenty to learn about consciousness, that’s certainly true. Again, science’s long to-do list of unanswered questions does nothing to support the Christian claim.

Wallace also insists on the existence of the mind as something separate from the brain, but he gives no evidence of this dualism. For every instance that we know of, a mind is supported by a physical brain.

Remember the story of Phineas Gage, the man who had a steel rod shot through his head while working on a railroad tunnel (more here)? Or consider an Alzheimer’s patient. As the physical brain is damaged or deteriorates, the mind is also damaged. The “mind” is simply what the brain does.

If Wallace thinks that the mind (or soul) is something separate or that consciousness is not the inevitable end result of a sufficiently large brain, he needs to show evidence.

6. Where Does Free Will Come From?

Wallace imagines various philosophical problems with free will and then solves them with God as the first mover. Of course, he doesn’t explain the new puzzles that the God hypothesis introduces—where God came from or how God could always have existed or what laws of nature (if any) God breaks to do his miracles. This hypothesis teaches us nothing new. God becomes a synonym for “I don’t know.”

If God is the reason that we have free will, then Wallace is saying that a godless universe would have no free will. I await evidence of this claim.

I have little interest in philosophical puzzles. In the apologetics context, they seem like nothing more than smoke screens. (More here.)

7. Why Are Humans So Contradictory in Nature?

Humans can be altruistic and compassionate, but we can also be hateful and murderous. “Philosophical Naturalism struggles to explain how creatures capable of genocide and cruelty are also capable of compassion and sacrificial generosity.”

What’s puzzling? Humans have a large palette of personality traits and drives. They came from evolution, and we’re stuck with them, though we can try to adapt to modern Western norms.

These drives, both “good” ones like patience and perseverance and “bad” ones like lust or envy, can be useful. The problem arises when any are used too much.

For example, generosity is a good trait because we usually aren’t generous enough, but you need to be a bit selfish so that you don’t damage your own life by giving away too much. Anger is a bad trait because we can be angry too often, but the focus and drive that it gives can be useful occasionally when righting a wrong.

Different conditions create a wide variety of norms (the Nazi prison guard is a classic example) that encourage actions inconceivable in healthy modern society. We don’t need to handwave about Mankind’s fall to explain the good and bad we see in human actions.

Concluded in part 3.

In dark ages people are best guided by religion, 
as in a pitch-black night a blind man is the best guide; 
he knows the roads and paths better than a man who can see. 
When daylight comes, however, 
it is foolish to use blind, old men as guides. 
— Heinrich Heine

(This is an update of a post that originally appeared 11/20/13.)

Photo credit: Z S, flickr, CC

No one can demand a proof that God does (or doesn’t) exist, but where does the evidence point? Following the evidence without bias is the best we can hope to do.

A number of apologists defend Christianity with the thinking of a courtroom lawyer or detective. One of these is J. Warner Wallace. In his essay “The Christian Worldview is the Best Explanation”* he gives ten tough questions to which he claims Christianity has the better answer. Let’s take a look.

1. How Did the Universe Come Into Being?

Our universe had a beginning, but what caused it? Why is there something instead of nothing?

I don’t know what caused the universe. I don’t even know if asking about a cause (which implies an action through time) even makes sense before time existed. (And I say “I don’t know” simply because I’m parroting the consensus view of physics. If that changes, so will my opinion.)

But there’s nothing embarrassing about pointing out where we don’t know things. Science has plenty of unanswered questions, and highlighting them shows where work needs to be done. It’s not like we’ve ever learned anything new about nature through holy books or divine revelation.

That science doesn’t know something doesn’t mean that Christians do. They still must deliver evidence for the claim “God did it.” Believing by faith won’t do.

Note also that quantum events may not have causes, and the Big Bang was a quantum event. There’s no reason to demand a Big Banger, some supernatural First Cause.

As for “Why is there something instead of nothing?” show us why nothing is the default. Show us that nothing is what a godless universe would contain. In fact, physicist Lawrence Krauss argues the opposite: that nothing is unstable and would spontaneously produce something. (More here.)

More could be said on this and the other questions here, but I’ll keep it short for space reasons. Apologies in advance when I shortchange one or both sides of the argument.

2. Why Does There Appear to Be Design (Fine Tuning) in the Universe?

The constants that govern our universe appear to be remarkably fine-tuned to allow life. What explains that if not a supernatural intelligence?

I’ve responded to the fine-tuning argument before (here, here, and here). The quick answer to this question is the multiverse—an almost infinite number of other universes defined by different constants. Most of them might be sterile, but there are enough to make one or more life giving.

The Christian might imagine frustrated atheists lamenting how the appearance of deliberate fine tuning makes a deity unavoidable and then hitting on the crazy idea of bazillions of universes so that by sheer luck at least one of them will be tuned to allow life. But that’s not how it happened. A multiverse is predicted by well-established physics—both string theory and inflation.

Note also that events and objects aren’t unique in physics. There’s more than one photon, more than one electron, more than one star, more than one object influenced by gravity, and so on. Why must we be limited to one Big Bang?

Wallace says that explaining the appearance of design “is a problem for philosophical naturalists only because they are precluded from considering the possibility of a designer.” If someone is closed minded to the evidence, I agree that that’s a problem. However, I’m happy to follow the evidence where it leads. Science has studied supernatural claims but found only natural causes.

And how designed does the universe look? The vast majority of the universe is hostile to any kind of life that we’re familiar with. Does creating hundreds of billions of galaxies sound like what a cosmic designer would do if life on a single lonely planet was the goal?

Wallace says, “The Christian worldview is founded on the existence and creative activity of a Master Designer, and for this reason, it does not have to struggle with the appearance of design.” Show us that this is grounded with evidence and it’ll be more than just an ancient myth. Until then, not so much.

3. How Did Life Originate?

“Philosophical naturalists are still unable to explain how life began, and more importantly, their work in this area simply reveals how difficult the problem is to explain. . . . This scientifically inexplicable event can be described as nothing short of miraculous; the Christian worldview explains how the long odds against the emergence of life were overcome.”

No, the Christian worldview explains nothing. Christians can show how their theology is compatible with the question, but this isn’t evidence.

The origin of life is called abiogenesis. Though science has lots of ideas, it doesn’t have a good theory. Nevertheless, science not having an answer gives nothing to the Christian side of the question.

And Wallace’s “inexplicable” is a very bold claim. I’m sure biologists will be eager to hear his proof that abiogenesis is impossible by natural means.

Do Christians think that this or any of the scientific questions are fundamental parts of their argument? I doubt it. When science reaches a consensus on any puzzle—and science’s track record for finding answers to nature’s questions is remarkable—they’ll just drop that question and pick up something new and hope that no one notices the switch. Their argument then becomes “Science has unanswered questions; therefore God.”

Continue with part 2.

* The link to this 2012 article at www.pleaseconvinceme.com is now broken.

The universe is simply one of those things 
that happens from time to time.
— physicist Edward P. Tryon

(This is an update of a post that originally appeared 11/18/13.)

Photo credit: Wikimedia