First he would have to ask what e is, then pi, then i. That might take a while. Sooner or later, he would ask the five year old's question, "How do you know?"
Actually he could ask many such questions. How do you know what the value of e is? How do you know what the value of pi is? What is an imaginary number and how do you use it as an exponent? He could continue to ask "Why?" and "How do you know?" and it would be like peeling the layers of an onion. This particularly onion would take him through calculus, trigonometry, complex analysis and basic algebra, before winding up at addition.
Side note: If he were serious about actually understanding the answers to all of the various why and how questions down the ladder, the process of asking and answering would likely take him years. More likely, the person explaining it to him would start at the bottom and work his way up to it so by the end, he would have a rather complete understanding of math. Which goes to show that just because there is an explanation, it doesn't necessarily follow that you have the ability to understand it and confirm its validity for yourself. If you're going to ask hard questions, this is a real practical problem worth keeping in mind. At some point, you are going to have to find a way to trust experts to give you information you're not capable of verifying for yourself; there's just not enough days in a lifetime.
Ignoring the practical problems, does the chain of why and how questions proceed ad infinitum or is there an end. The answer is there is an end. You reach a point where the claims are so atomically simple that you cannot justify them in terms of simpler claims. You run into the situation you ran into above with the flat earther, just saying, "They're true, just trust me." They're called axioms. They're not proven because we don't have any simpler statements we can use to derive them, so they're a kind of assumption that float around ungrounded in the intellectual ether.
Fortunately, these propositions are not in dispute. They're statements of kind "there is a number called 1", "parallel lines in a plane never cross", "if you change the order of addition the answer doesn't change." (that's a + b = b + a, remember it because we'll return to it shortly.) The list would fill about a page and you can figure out all of mathematics from them, with some definitions added in mostly for brevity and convenience.
The process of reducing math to the smallest number of these statements is called axiomatization. It's an intellectually macho exercise - a kind of nerd contest - where you try to use as few of these axioms as possible. This minimalism exists primarily for aesthetic reasons. Since the facts form a coherent network, and the higher level facts just fall out with enough of what a professor of mine called "Squigglies".
Many have asked the question of whether it's possible to eliminate the axioms; to have a coherent system that contains no assumptions. It was actually one of the great unanswered questions at the end of the Nineteenth Century.
The answer, it turns out, is a definitive NO. The "Incompleteness Theorem", proven by Kurt Gödel in the 1930s (pronounced Girdle) demonstrates that it's an impossible task. Remember that math is the only domain where it's actually possible to prove things to be impossible. The rest of the world just has to settle for degrees of uncertainty. Although even in mathematics, we don't have absolute certainty, because when someone "proves" a result, there's always a non-zero probability that there's a mistake in the argument and no amount of peer review can reduce the chances of a mistake absolutely to zero.
Of course, it may worry some people that the whole of mathematics (and therefore huge chunks of the rest of science) rests on "unproven assumptions." You may have noticed that the mathematics community at large hasn't jumped on board endorsing Matt's presuppositional argument, and they show no evidence of loosing any sleep over it either. What's their escape?
Can you guess? It's observation... evidence. The e-word a presup must shy away from. The real world (whatever you mean by real) is the get out of jail free card. You don't have to have perfectly valid deductive logic. You just have to poke your head out the window to see if your conclusions line up with reality. Trial and error, a kind of evolutionof ideas by rational selection, is what is responsible for most of our knowledge. Remember all of Edison's failed attempts at that lightbulb.
Let's look at the axiom from before:
a + b = b + a *
*This is only one of the axioms. You'd have to give each one its own separate similar treatment.
This is an unproven statement - the sort of thing that makes Matt and Eric and Sye Ten drool. But it's mutually agreed upon by everyone in the field as being true by the following process: imagine two rows of stones; the first row contains a stones, the second row contains b stones (I realize I'm being pedantic, but Matt brought it up.) Now if you want to find the total. You move the two rows of stones close together, then count the total number of stones starting from one and stopping when you run out of stones... this is how addition works boys and girls (remember... Matt asked for this; it's his fault.)
Now if instead of calculating a + b, you wanted to calculate b + a. You can imagine standing up and walking around the stones to stand on the other side. You are looking at the same stones and they haven't moved but you're now counting them in the opposite order. You get the same number of stones. Case closed, you've proven it.
No, you haven't.
This is only an observational fact - anecdotal evidence, the worst kind of evidence - and we have no way of knowing if it's true for any number of stones. We can try the experiment many times counting small numbers of stones (say less than 100). We can imagine what the experiment would look like with very large numbers of stones and imagine getting the same answer. But there could be a certain number of stones where this is no longer the case; where walking around the stones to look at them from the other side changes their number. (Okay, I can't imagine it. I can imagine trying to imagine it.)
I might also be able to imagine in place of stones, some sort of quantum mechanical particles, where the act of "looking" at the particles actually changes the number of particles present. ("Looking" in quantum mechanics looks nothing like the looking you're used to looking at... trust me.) Or if you wanted to switch from a plus b to a times b, there are lots of mathematical objects, more complicated than ordinary numbers, that when multiplied in different orders give different answers. So it's not impossible to imagine a world where the order of addition matters; it's just difficult.
So the presuppositionalist has stumbled onto a very real problem. You can't have a complete logical system without at least some axioms. When we dig down deep enough, we hit a kind of intellectual bedrock below which there is no logical foundation.
Now quickly, before a dishonest presuppositionalist quotes the above out of context and implies that I've conceded his position, I'll offer two solutions:
The first is a practical solution. You may not be able to prove that a + b always equals b + a even though you strongly suspect it's true for all a and b. But you can estimate the probability that it is universally true. That estimate might be a 99.9% with so many repeating 9's that it's indistinguishable from 100% certainty to anyone except the most anal philosopher, but it will never truly be 100%. But if you ran into someone in the street who was sweating and fretting that perhaps it might turn out to be a false assumption sometime soon, you can confidently tell him to chill out, go get some ice cream and forget the whole silly idea. So with the same level of confidence, you can take a young presuppositionalist and tell him to chill out, go get some ice cream and forget the whole silly idea.... Although with my luck there will be a ban on ice cream tucked in the sillier parts between Deuteronomy and Numbers; those books ruin all the fun stuff.
The second is a more philosophical solution. When looked at from a distance, this axiom can be seen as a type of symmetry in the universe. Now all of the conservation laws (energy, momentum, electric charge, etc) have a symmetry associated with them, which basically assume that from moment to moment and place to place, the processes that govern the universe (it's misleading to call them laws, because that brings the temptation to invoke a law giver) are the same. They become the basis of what creationists pejoratively refer to as uniformitarianism.
Once this fundamental reliance on the observed regularities is noticed, it will quickly become apparent that all of the axioms of mathematics and logic are just abstractions of this regularity into linguistic terms. The "Law of Non Contradiction" (to choose an example randomly) is not a fundamental principle, but is a generalization derived from the natural world.
As near as we can tell, uniformitarianism is a necessary precondition for life. We can't wake up tomorrow and discover that God has enacted a new fundamental law, say "The Law of Conservation of Twerk". Imagine a world where new particles spontaneously popped into and out of existence (violating what we call the "laws" of mathematics and physics) or spontaneously transmuted into other particles. A creature who might wake up one morning to find important parts of its heart had poofed out of existence, or that some of the H20 in its blood had magically been replaced with cyanide would not last long. Unpredictability is deadly to life forms and so we require a universe in which these types of "laws" operate just to make it past breakfast.
This may sound familiar... it's the Anthropic Principle: The problem that you can only find intelligent and reflective creatures in a universe where it's possible for intelligent and reflective creatures can exist. And since we have absolutely no way of gathering any information about universes in which we cannot exist, or about what goes on "outside" our universe, anyone who claims to know anything about these situations, or even claims to know they are properly posed questions is either lying or a moron... or both.
So there you have it, Matt. I hope you slogged through it. 5000 words and you can see that your argument is just a re-hash of the Anthropic problem. This is not a new issue. I heard about it in a Stephen Hawking book from the 80s and it wasn't new then. So you can rest easy knowing that an army of physicists around the world is working on the problem, racing to be the first to have an answer for you. (Kind of makes you feel special, doesn't it?)
I don't have an answer for the anthropic problem. It continues to make my head hurt. I'm comfortable enough to admit I don't know the answer, and also knowledgeable enough to know that you don't have the answer either, nor will you be able to find it in any book presently available. Remember that you can determine that an answer is wrong even if you don't have the right answer.
I guess that all we have left now is to go out for ice cream.
An idiot's guide to apologetics
For those of you that didn't go out for ice cream and are still reading, I offer some tidbits of advice for anyone who wants to try and defend their faith in the public square. I watch, read and listen to a lot of this stuff and thought I would offer some helpful hints to reduce the amount of mockery you have to deal with. Just my 2 cents. Hope you can make use of them.
1. Leave your ego at the door
A religious person, almost by definition, considers himself special. He, and the universe he grew up in, were created by a deity (cause apparently god needed a cheerleading squad to tell her how great she was.) That means someone consciously decided that she wanted to have a human playmate to have some kind of relationship with. He has a soul, and the ability to live on in some kind of afterlife - something not available to any other animal we know of. And 99.% of species ever discovered have gone extinct.
Of course there are about 4,000 different religions in the world (it really depends on how you count; I'm not married to that number. Suffice it to say it's more than twenty.) But of course a religious person is safe because he picked the correct one. On top of that Christianity itself can be subdivided into tens of thousands of sects, but you've still you've managed to find the correct one... even without examining 99% of the alternatives; which is like mad skillz dawg!
Undaunted by large numbers, the entire universe was created as part of this "plan" as well. The number of stars in the visible universe is twenty-five digits long. They don't do much except provide shiny lights to base our horoscopes on. (Although Scientology made up a use for them.)
Or much more likely, just incredibly biased. If your conclusion happens to end with the good news that you're part of a divine plan and are in some sense the centre of the universe created by someone who notes whether or not you say she exists, don't expect anyone to take you seriously. You need to develop a more reasonable evaluation of your place in the universe.
Develop an appreciation for the limitations of your knowledge and cognitive faculties. Know how quickly and easily you can slip into self-deception and reach fallacious conclusions (if you need help reaching this state of mind, go watch a magic show. It's an intellectually liberating experience.)
Turn the lame "what percentage of the world's knowledge would you say you have?" back on yourself and accept that the next book you pick up could completely change your worldview... and pick up the book anyway. And accept the corollary to that, which is your incredulity or lack of understanding can't be used as the basis for a refutation for someone actually studying in a given field. (There's no shame in admitting that. We have to accept that life has gotten too complicated for individual humans to master everything in a single lifetime and we need to work together and share knowledge. But at the end of the day, the only people whose opinions about quantum physics matter are people who've seriously studied quantum physics. Business people are fond of saying, "You don't count votes, you weigh them.")
And never assume (or speak in such a tone so that people will think you assume) that because you aren't familiar with the refutation of your argument, that such a refutation doesn't exist. You'd be amazed how often I stumble across 20 and 30 year old references that contain perfect rebuttals to creationist questions. You'd be even more amazed how many of them are dealt with directly in Origin of Species... which you probably never bothered to read.
And don't presume that your question will give atheists nightmares. Even if the answer really is "I don't know," remember that we don't mind "I don't know" as an answer.
I can live with doubt. I think it’s much more interesting to live not knowing then to have answers that might be wrong.
2. Avoid simplistic ideas and generalizations
Life is complicated. If you can explain the origin of the universe, the origin of life, the basis for morality and what happens to you after you die with a single theory simple enough to be grasped by a second grader, you do not have an accurate picture of the world.
Stop seeing the world in black and white and learn to appreciate that on complex issues we try to take nuanced positions, and view the world not just in shades of grey, but all of the fabulous colours. Learn to parse the difference between the magic p-words possible: plausible, probable and proven. Learn how to distinguish between correlation and causation. Learn the difference between refutation and repudiation. Don't generalize conditional statements to biconditional statements without evidence to support them Remember that nature is far more clever than you ever could be; problems tend to have more than one solution. Learn the difference between skepticism and cynicism. Learn the difference between an authority and an expert. Learn the difference between someone admitting that they could be wrong and demonstrating that they are, in fact, wrong.
To mention the video above (finally) don't assume that because something was not designed by an intelligence, that it doesn't work. True, you can argue for why producing something intelligently, is more likely to create something that works. It's a fully unjustified leap to conclude that that intelligent forethought from draughting table direct to finished product is the only way to arrive at working design. This is especially true since an alternative was discovered 150 years ago and has been actively researched ever since.
3. Learn the Real Scientific Method
This is the one flaw that I think the scientific community can take the full blame for. Historically, scientists have been lousy communicators to the lay public. Scientists have even been guilty of looking down on those people who tried to share their love of science with the public (think of Carl Sagan or Stephen Hawking). Media coverage of scientific discoveries is dreadful being overhyped and misleading, making many events sound more important and more certain than they actually are. Ironically, if you go to primary scientific source material, the language is much more conservative. You'll never find the phrase "earth shattering breakthrough" in a real scientific document. And anyone so says that scientists "prove" things is misled, stupid or both.
Okay, that's not literally true. Certain scientists will deductively prove theorems about the mathematical relationships between quantities measured in physics. That's not quite the same as mathematical proof because the assumptions aren't axiomatic in nature.
And the state of science education in schools is sorely lacking (it's even worse in schools where teachers are trying to faust stultifying nonsense like the universe is 6000 years old.)
I would wager that less than 1 in 20 people stopped randomly in the street could give an accurate description of the scientific method. And yes, that's a real problem that still needs to be dealt with.
Rather than try to give you my definition of the scientific, I will offer you the definitive explanation of the scientific method by a Nobel Prize winning physicist, Richard Feynman. Thanks to the generosity of Bill Gates, the lecture is available to watch for free on the Project Tuva website. The lecture of primary importance to this discussion is #7: Seeking New Laws. Of course the rest of them are marvellous as well, so if it's a rainy day, go nuts.
And learning about science will teach you how ideas get overturned in science. Restating the thesis in a derisive tone does not constitute a convincing refutation. I'm thinking of your "You believe that Hydrogen Gas turns into people given billions of years." line of argument. While you could semantically argue it's true that we believe, you omit the things that drive the process (like gravity, nuclear physics and chemistry) and that hydrogen gas didn't even form for the first 300,000 years because the universe was too hot. There was stuff before that, which was even cooler. I'll refer you to a great book on the subject.
4. Learn history
I'm thinking specifically of the history of science, although you can't go wrong with history in general (it would help you get over nonsense like America is a Christian nation and the bible is historically accurate). Science is far more than a collection of facts, it's also the stories of the people who made discoveries through cleverness, accident and happenstance.
And if god were real, science would just be the story of us fixing god's mistakes. Body not intelligently designed? Let's invent some medical science for that, perhaps some clothes and buildings to protect us from the elements while we're at it.
You'll discover just how badass and clever humans can be. You'll also learn things that disconcert you and make you reevaluate your preconceptions. There also four things that you should take particular note of:
1. Major discoveries are always the result of hard work. We may look back and them and spin them into narratives with "Aha!" moments. But if you look at the stories, you notice that the glorious "Aha!" always has some lengthy and arduous work process, and many discarded failed attempts associated with it that gets left out of the movies. Darwin didn't stroll off a boat, sketch a few finches and think "I'll write a book about this." You should see the notes he kept between artificial selection of plants and pigeons, his mollusk stuff... Really awesome.
2. Realize that major advances are always sparked by the discovery of new evidence. (Good quality evidence is always lacking in religious argumentation... and no, your bible doesn't count as evidence.) The germs were discovered by analyzing hospital statistics. Relativity was developed because of a confusing experimental result about the speed of light (then validated experimentally years afterwards). Kepler realized the earth went around the sun after painstaking measurements of the solar system through his new telescope. Hubble discovered the universe was expanding by making observations of starlight through spectroscopy. The list goes on.
You'll also start to understand what constitutes good evidence. Learning that people get things wrong when they use their gut or rely on bad evidence (like say eyewitness testimony or hearsay). And see how evidence can be misinterpreted. Witches were executed with mountains of well documented "evidence" and we have confirmed eyewitness testimony Joseph Smith and his golden tablets. Then there's UFOs.... If we're able to reject those despite the quantity of evidence, a 2000 year old book doesn't stand a chance.
3. Understand that significant advances in science have always been counterintuitive. The heliocentric theory, universal gravitation, the germ theory of disease, evolution by natural selection, just about any result in statistics, relativity, quantum mechanics, atomic theory, Newton's laws of motion... All of this stuff runs completely against the grain of how we "think" the world ought to work.
4. A HUGE number of phenomena were, at one point in time, attributed to the actions of conscious, anthropomorphic supernatural agents (gods) and the majority of them are now well understood as the results of mindless natural processes. Similarly many processes were deemed to be beyond human understanding and they turned out to be wrong. (I think even Bill O'Reilly knows why the tides go in by now.) If you use history as a guide, asserting something is due to a supernatural cause is undeniably a loosing bet.
5. Learn to talk the talk
It's extremely easy to spot someone who doesn't know what they're talking about (and therefore will not be taken seriously) and that's because they use words without knowing what they mean.
You need to learn to separate atheism, evolution, abiogenesis, particle physics and cosmology. For example, evolution only deals with the nonrandom survival of randomly varying replicators, while having nothing to say on the subject of where the original replicators came from. Cosmology can explain how a whole bunch of energy develops into stars and planets and puppies. The big bang is a theory that unifies a bunch of observations within cosmology.
If you say "Evolutionists believe..." followed by a statement about cosmology or the multiverse, or refer to the big bang as an "explosion", you sound incompetent. Even though you may be using the terms "evolutionist", "the religion of atheism" or "the religion of evolution" as a term of derision, the unintended consequence is to make you seem less articulate and less credible.
I realize that if you change "evolutionists believe" to "serious scientists who have spent decades studying biology believe" then it's much harder to form a compelling argument. No one said life was easy.
Being clear and specific is essential for science. So within science, words like uncertainty, energy, nothing, information, and mutation all have extremely specific meanings, often different from the way those words are used in every day speech. Using words in non-traditional (like applying "faith" to scientific theories or "information" to the organization of DNA molecules) also costs you major credibility.
And keep in mind the limits of language; that lots of things have misleading names because in the past we knew less than we knew now. So the big bang as neither big, nor did it bang. Electric eels aren't eels. Tin foil is made of aluminium. Pencil lead is made from carbon. And Creation Science has nothing to do with science.
You also need to learn to reign in your analogies. It's not enough to find a useful analogy, you also have to know what its limits are, where it breaks down. An atheist is exactly like a soda can fizzing, if by exactly, you mean it's neo-post-modern definition of not at all.
If you don't understand analogies, don't use them. It's like a pig on a tightrope.
If you're trying to persuade people with words but don't seem to understand the words coming out of your own mouth, you will be dismissed and mocked. I get that proselytizing is as much about getting the slap on the back from your fellow Christians and you're talking as much to them, if not more, than you are to the unbelievers you might hope to sway. But you should take the high road; be and sound smart for it's own sake. Being smart is awesome.
He said heading off to watch NPH host The Emmys... Hope there's a big dance number!