Among the things you’re sure of, which are you surest of? For Richard Dawkins, writing in the Wall Street Journal, it’s the theory of evolution:

We know, as certainly as we know anything in science, that [evolution] is the process that has generated life on our own planet.

Now, I would be thunderstruck if the theory of evolution turned out to be fundamentally wrong, but not nearly so thunderstruck as if arithmetic turned out to be inconsistent. In fact, I can think of quite a few things I’m more sure about than evolution. For example:

**1. The consistency of arithmetic.** (This amounts to saying that a single arithmetic problem can’t have two different correct answers.)

**2. The existence of conscious beings other than myself.**

**3. The fact that the North won the American Civil War.** (That is, historians are not universally mistaken about this. I am *not* interested in quibbling about what constitutes a “win”; I mean to assert that the North won in the everyday sense of the word, as reported in all the history texts.)

**4. The consistency of higher mathematics.** (The math geeks in the audience can take this to mean the consistency of Zermelo-Frankel set theory.)

**5. The special theory of relativity.** (The science geeks in the audience can take this to mean that the laws of physics are locally Lorentz invariant.)

**6.The efficiency of the price system.** (The econ geeks in the audience can interpret this as the truth and appropriate applicability of the first and second fundamental theorems of welfare economics.)

And then somewhere down the list—though still way above anything I significantly doubt—we have:

**7. The theory of evolution.** (That is, all—or nearly all—living things evolved from simpler things, largely through some process involving reproduction, mutation and selection.)

I’m not at all sure I’m right about this ordering, and I’d probably have chosen a different ordering five minutes ago or five minutes from now.

What would your ordering be?

Is your point that you think Dawkins is being hyperbolic? This may be true, but note the context. Dawkins (in his latest book) notes that 40% of Americans and a nearly as high number of Europeans FUNDAMENTALLY doubt the truth of evolution, and believe things flatly in contradiction with evolution. In contradistinction, virtually no one doubts #1-3 in your list, and no one who has any significant exposure to them doubts #4-6. Even those without exposure to 4-6 don’t claim they are false, merely that they don’t know enough to say.

Perhaps Dawkins should have claimed that no scientific theory is more clearly shown by overwhelming amounts of evidence to be true and simultaneously thought by so many to be false.

RL: My point in quoting Dawkins was not to pick a fight with him; it was just a way of leading into the (hopefully interesting) question of how best to order these and other near-certainties. Sorry if that was unclear.

where would the judeo christian god (or any random diety from the major religions of the world) fit in on this scheme? 8? or 88…or is it so far down the list we may as well forget about it.

I’m surprised special relativity is so far up there (I was similarly surprised when you thought it was natural for you daughter to deduce special relativity in Fair Play) — do you have any personal experience with observations that the speed of light is constant (therefore causing time to vary)? I would think the assumption would be the opposite (time is constant), only discarded when evidence from very careful and precise experiments proves it surprisingly incorrect.

Or is that the point, and you’re not really that sure (relatively) about the efficiency of the price system?

Ben writes:

do you have any personal experience with observations that the speed of light is constantNo, but neither do I have any personal experience of the North’s having won the Civil War, or for that matter of simple life forms evolving into more complex ones.

I believe these things partly because they explain so many pheneomena that I *have* observed (frogs, in the case of evolution, or magnets, in the case of relativity), partly because of their extraordinary simplicity compared to the vast number of phenomena they seem to explain, and largely because they are endorsed by vast numbers of people who are much smarter than I am and/or have examined a lot more evidence than I have.

The thing I’m surest of is the fact that I’m not absolutely, 100% sure of anything.

In fact, the more educated I have become (BS in mechanical engineering) and the more I learn and read (especially in the area of science), the more I am sure of the existence of God.

I just can’t wrap my mind around the concept that everything I see came about on its own, basically by random chance.

Oh, another thing I’m sure of is the fact that I love reading this blog because it always makes me think, even when I disagree with something.

This is just the sort of Big Question that I like to answer, even though, like our distinguished host, my answer might change; which means that, like Jeff (and Socrates before him), I am not 100% sure about anything; which probably means that the thing I am most sure of is the Münchhausen Trilemma:

http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma

Apart from that, I am more confident in logic and mathematics than in empirical sciences. My ranking within logic and mathematics would be based on Gödel’s incompleteness theorems, if I understood them better; which means that I am pretty sure of Gödel’s theorems.

My ranking within the empirical sciences is based on both falsifiability and empirical evidence, which means that I am much more confident about falsified theories being false than I am about commonly accepted theories being true. It also means that I am pretty sure about Popper’s epistemology: more sure than I could be about any empirical theory, because I could not justify any empirical theory without reference to Popper.

Enough for now: I’ll add a few more thoughts later.

What is your decision procedure for ranking two beliefs, both of which are almost certainly true, in order of their likelihood of being true? Why, for example, do you list #3 ahead of #4? What does it even mean to say you believe the truth of special relativity more than the truth of the efficacy of the price system but less than the truth of the evolution of life?

I speculate Dawkins would consider only 5, 6, and 7 to be “things in science” (assuming he allows that economics is a science). But maybe we should ask him whether he’s more sure of evolution, than he is of what he had for breakfast this morning, or that there exists a bijection between the set containing Nelson’s legs, with the union of the set containing Nelson’s eye with the set containing his arm (Whitehead & Russell, 1910, 54.43).

It’s an interesting list. Looking at it, (1) and (4) are theorems (at least under appropriate restrictions), so they seem pretty definite: a system of “arithmetic” that wasn’t consistent wouldn’t be the same system of arithmetic we mean. (2) is a convenient assumption: one can always make an argument for solipsism, but it doesn’t lead anywhere. Might was well assume there’s something else. (3) seems definitional and somewhat circular, or if you like tautologous: you have a set of facts and a definition of “win” and the set of facts is consistent with the proposition. That basically deductively true.

SR and evolution are adductive; attempts to falsify them have failed, but there is no certainty that some future experiment might not falsify them in whole or part. We can determine experimentally that what we expect to see as a consequence of Lorentz invariance is observed locally; the various attempts to model varying c all depend on very much non-local observations, and would be consistent with SR in a local framework. Is this the same as the “certainty” you feel about ZF?

Response to RL: I take it as a definition that I am more sure of A than of B if I would feel more shocked to learn that A is false than to learn that B is false. My decision procedure is, in each case, to try to imagine how shocked I would feel if any of the various items on this list proved to be false. Of course, my imagination is constantly changing its mind, which is why I say I might hvae ordered things differently five minutes sooner or later. In fact, I moved things up and down several times while composing this post.

Response to Charlie: (1) and (4) are theorems only if you start from assumptions that are less inherently plausible than (1) and (4) themselves. There is much on this topic in

The Big Questions.As for (3), it is not, I think, definitional. It’s at least possible that at Appomattox, Lee handed his sword to Grant rather than the other way around, and Jefferson Davis was then inaugurated as President of the United States. If I were to discover that those things were true, I would conclude that (3) is false; if there are circumstances in which I might conclude that it’s false, then it can’t be definitional.

Regarding SR, I interpret the statement to mean something like: Any any future physical model that retains anything like our current notions of space and time, and that is not contradicted by experiment, will incorporate local Lorentz invariance.

I certainly feel far surer of the consistency of arithmetic than of special relativity, but I probably feel surer of special relativity than of evolution.

Hmmm. I don’t think I buy your argument on 1,4, although since my copy of TBQ hasn’t arrived I can’t be sure. But based on this short statement, at least, I don’t buy it. Axiomatizing arithmetic, as eg with Peano’s Axioms, proceeded more or less as did geometry and other similar systems: we had observations and wondered about the simplest rules that would explain them. We found a set: I’m not sure how to measure “more obvious” but it’s hard to imagine something that acts like a “number” that wouldn’t satisfy them. I guess the notion that axioms should seem “more obvious” than the observations from which they’re derived just seems inherently flawed: can you provide an example of

anyaxiomatized system that would meet your criteria?On “definitional” I think I just wasn’t clear: given

boththe definition of “win” and the agreed-on facts. it seems conclusive. If we assume different facts, it no longer would be. But the notion that it’s “possible” that, eg, Jeff Davis was the President seems a use of “possible” with which I’m unfamiliar.Steve

Regarding #5, is it Lorentz _invariant or Lorentz _covariant_? I was reading Michio Kaku’s book on Einstein and he uses the latter terminology all through the book.

Can we assume that #3 is meant as a representative example, i.e. that learning of the non-existence of the Roman Empire would be about as shocking as learning that the South won the Civil War?

Snorri wrote:

Can we assume that #3 is meant as a representative example, i.e. that learning of the non-existence of the Roman Empire would be about as shocking as learning that the South won the Civil War?Answer: Yes.

Charlie (Colorado) wrote:

But the notion that it’s “possible” that, eg, Jeff Davis was the President seems a use of “possible” with which I’m unfamiliar.Yet learning this would still shock me less than learning of an inconsistency in arithmetic.

I’m curious how you can be surer of (2) than of evolution, since the truth of (2) seems to me a consequence of the truth of evolution.

Maurizio:

The greenness of grass is a consequence of its containing chlorophyll, but I am more sure that grass is green than that it contains chlorophyll.

“This amounts to saying that a single arithmetic problem can’t have two

different correct answers.” Either this is very oversimplifed, or I am

about to demolish your certainty. It is true that 1+1 has only one

correct answer (2 in case there was doubt). However, 7 + 2 * sqrt(9)

can be answered correctly by 13 or by 1.

Ron: sqrt steps outside what a logician would consider arithmetic. You only get to add, multiply, subtract and divide.

Charlie: actually, if the consistency of arithmetic is a theorem of arithmetic, then arithmetic is *not* consistent. This result is precisely Goedel’s second incompleteness theorem, assuming we take “arithmetic” to mean (in layman’s terms) “some formal system encompassing arithmetic”.

There do exist formal systems which can prove the consistency of *other* formal systems that contain arithmetic. But then the value of this proof relies on the consistency of the first formal system, so you’re still stuck *guessing* that some system or other is consistent. Of course this is an educated guess, based on the fact that nobody has yet published any contradiction in any of the commonly-used formalisations of integer arithmetic. Same goes for the Z-F axioms, with or without the Axiom of Choice.

Steve Landsurg: I think Ron’s objection is perfectly fair. “Find a solution to the equation x * x = 1″ is clearly an arithmetic problem, and equally clearly it has two different correct answers. “Find an integer greater than 12″ is an arithmetic problem with infinitely many correct answers.

The usual definition of “consistent” is that there does not exist a statement S such that both S and (not S) are provable. Without loss of generality, we can probably take S to be of the form “x is the only correct solution of the following problem…”. So arithmetic is inconsistent if we can find two different solutions to a problem which provably only has a single solution.

Steve:

So arithmetic is inconsistent if we can find two different solutions to a problem which provably only has a single solution.And equivalently, arithmetic is inconsistent if (and only if) we can find two different numbers that are both equal to some given expression containing only numbers, addition signs and multiplication signs. Finding the values of such expressions is what I meant by “arithmetic problems”. Perhaps I should have made that clearer.

RE: The North won the Civil War

It’s important to consider what the word “won” means. The Civil War was probably a Pyrrhic victory for the North. Slavery likely could have been effectively ended at a much less devastating cost if the North had allowed the South to secede, set up open borders, and declared that any slave that entered the North was free.

Of course, if the North’s primary goal was to keep the Union together, then we should by all means consider the deaths of roughly half a million people and the destruction of a large percentage of the capital stock a victory.

As far as what I am most sure of, I would be quite shocked to find out that I don’t exist.

It sounds like Dawkins is of the opinion that levels of certainty in science are fairly fuzzy, especially at the top, and so there’s just this “as certainly as we know anything” level rather than any hope of discrete ordering. And I think that’s entirely fair. I don’t see much defensible basis for saying that special relativity is more or less certain than evolution. Both have a large convergence of interlocking but independently derived lines of evidence pointing not only at the same conclusion, but the same fine details. That’s as good as science can possibly get (which is to say: still not ever certain).

Which is why I think adding in things like math is sort of off whatever scale Dawkins was thinking about (which seems to be narrower than simply “surest”). The consistency of arithmetic isn’t _simply_ empirically provable (i.e. we can test putting 2 rocks next to 2 other rocks and find that we always then end up with 4 rocks), it’s formally, logically provable in a way that outstrips anything that’s even _possible_ with most scientific claims about empirical reality. Dawkins hedged his bets by slipping “science” in there to narrow the question. All, I’m sure, so that he could tout the particular scientific thing he’s best known for touting.

As for special relativity, while I think we can be certain about the math, I’m not sure we can really be very sure yet that we have the right conception of its actual implications: what the math and experiments are really describing is happening. That is to say that while I’m quite certain that the fundamental claims of special relativity are as well established and verified as anything can be, I’m not sure I really comprehend what they are describing on the whole (in part because SR is likely to be just one odd slice of solutions to much bigger puzzle that we’re still missing a great deal of). With evolution I have a much clearer picture of what’s basically been going on and why we can know it.

“Consistency of arithmetic” sounds obvious if you restrict yourself to everyday numbers– but there’s an inductive assumption in arithmetic that makes it all not-so-obvious.

And even finite sequences can get problematical. Do you know about the “Busy Beaver” sequence? See this essay for information on it. So… suppose you had arithmetic operators acting on numbers that are too large to be computed, ever, under

anycircumstances. What does ‘consistency’ mean in that context?MattF: I am aware of the Busy Beaver sequence, and in fact I’m familiar with the essay you pointed to. But I don’t think this presents a problem for defining the consistency of arithmetic: Arithmetic is consistent if there does not exist a finite string of symbols that constitutes a proof that 0=1. (This is equivalent to the definition I gave in the post.) Our ability to

findthat string is a separate question. No?What I’m saying is that an assertion that arithmetic is consistent is stronger and more abstract than one might think, and possibly stronger and more abstract than necessary.

I suppose my view is that the $64 questions here are not about arithmetic, but about the world. Attaching numbers to collections of apples and oranges will yield consistent results about collections of apples and oranges– and that’s a fundamental and important fact. But why should that fact determine what you mean by ‘arithmetic’?

MattF: I understand you to be saying this (correct me if I’m wrong): 1) I am quite certain that there is no inconsistency in what I’ll call the “accessible part” of arithmetic, and 2) I am, perhaps, mistaking that certainty for a certainty that there’s no inconsistency in the rest of arithmetic either.

Or to make this operational: If I were to learn (from some unspecified miraculous source) that there is an inconsistency in the “inaccessible part” of arithmetic, I might not be as shocked as I think I’d be. Maybe even less shocked than if I learned that the theory of evolution is false.

You might be right, but I’m pretty sure you’re wrong (regarding your forecast of my reaction). I do have a more or less Platonist view of the natural numbers as existing independently of human invention, and if anything like that view is correct, then there can be no contradictions in any part of arithmetic. Now maybe that view is completely unjustified, or even completely wrong—but I continue to believe that I’d be shocked to the core by that discovery.

1. Sense perception. I like to think DesCartes was close but missed the mark. Rather than doubting everything, we should rank our doubts as you have here. What can I doubt less than what I directly perceive? Everything else that I think I know I have come to ascertain through my senses (whatever my senses are). So, the visual/audio/tactile/etc. “data stream” coming in to my awareness is that which I can doubt the least.

2. Basic physical properties, in space and time. That rocks, when dropped, go downward, not upward, that two solid objects cannot occupy the same space, that water seeks its own level, that the sun is hot, that the stars move through the sky, and so on. These are the things, like ancient man, which I know most directly about the physical world. They constitute the vast majority of what I know. But my knowledge of the physical world is inherently dynamic. I do not perceive the world as a series of freeze-frames, but rather, as a flowing movie which only makes sense exactly because it keeps moving. In other words, my brain forms expectations about the future state of the physical world. The relationships between events in space and events in time are equally fundamental. But the essence of time is expectation or prediction which is inherently metaphysical since that which we predict does not (and may never) exist, yet it is what guides our actions (consider the lowly housefly which predicts the incoming swat of the magazine and makes a hasty retreat). In other words, abstraction (dare I say, metaphysics?) emerges from prediction about the physical world.

3. Other stuff. Logic, math, physics, and so on. These are all stylized/ritualized/formalized extensions of the basic properties of the physical world that I know through immediate sense perception. Most important is to realize that science is a subset of my immediate knowledge about the physical world… every theorem of science known to modern man is bound up in the simple act of throwing a rock. Similarly, mathematics is a subset of natural language, since every math theorem ever invented can, with sufficient effort, be translated to ordinary, natural language without loss of information but not vice-versa.

Since this discussion is still going on, I’d like to add that, rationally, one ought to be more confident in evolution than in specifically Darwinian evolution. That means that one ought to be more confident that Creationism is wrong, than that Darwinian evolution is right.

Similarly, I am much more confident that socialism is a failure than I am that the free market is optimally efficient (in the real world, as opposed to the theorems of welfare economics); and, perhaps like JLA above, I am more confident that the South lost the Civil War, than that the North won it.

Another distinction is between random mutation + natural selection as an optimization algorithm and as a theory of biological evolution. I have more confidence in it as an optimization algorithm; but only slightly, because this confidence is based to a large extent on biological evolution providing a proof of concept.

I am with Snorri Godhi that Creationism is more wrong that Darwinism is right (though I am a big fan of Darwin and his inspired stream of research) and that socialism is more of a failure than the free market is efficient (though I find little fault with the 1st fundamental theorem of welfare).

Also, I think that something representative of the physical world clearly should be higher than some included on the list. For instance, I am quite certain that hitting my thumb with a hammer hurts. And that is a greater certainty (at least without pain-killing drugs) than the efficiency of free markets.

It is interesting that you included a historical event: the north having won the civil war. It got me to thinking about the historical events that stupid/insane people like to dispute (but which I’m pretty sure of):

1) the holocaust happened

2) Oswald shot Kennedy

3) the moon landings were real

4) Obama was born in Hawaii

On a related note, which movie based on the second and third denials was more inane “Capricorn I” or “JFK”. (I suggest it’s JFK.)

>> I believe these things partly because they explain so many pheneomena that I *have* observed

Would it then be fair to generalize and say that the strength of your beliefs is directly related to the ratio of net change in explained phenomena to the complexity of the explanation? If so, wouldn’t the existence of an intelligent creator being have a high ratio? Or perhaps you think that proposal raises more questions than it answers? If not, how do you think your strength-of-belief algorithm differs?

Dr. Landsburg,

Just got your book and am enjoying it so far but am having trouble with one of your arguments that I’d love to address before I continue on…

I love your breakdown of Biology (baggage + chemistry), chemistry (baggage + physics) and physics (baggage + math).

Here’s my question. Could it be that math is baggage + logic? For example, multiplication is simply human defined process for calculation purposes… so Multiplication = baggage plus addition… addition = baggage + logic. The set of natural numbers = baggage + addition…. addition = baggage + logic.

I argue that the CONCEPT of the set of natural numbers is not complex at all… just follow one rule of logic (add 1 each time).

You say on pg 19 that mathematics “contains the most complex patterns ever observed”. Are those patterns really the math? Or are they human applications of the logic laws?

I could be wrong, but mathematics could be extremely un-complex. It’s just that our brains have discovered ways to classify logical laws, adding complexity to a simple set of logical truths.

I guess when I think of measuring complexity, I would have to define “the amount” of complexity to be the minimal amount of information (bits on a computer for example) needed to define it.

I feel you are not distinguishing between the complexity of a set of logical truths (math – baggage) and the infinite complex manifestations of those logical truths.

The concept of the number 294892849324 is simply baggage + logic.

Please set me straight!

Kindest Regards,

Bill T.

Where would I rank the idea that Jamie Coulson has at least the sense God gave a wombat? Probably at around #57455345.

Typical of evolutionists, Dawkins never discusses which parts of the theory are accurate and which parts aren’t. Creationists divide the evolutionary process into two steps, and following economics calls them microevolution and macroevolution. Micro involves changes from one species to another within a family of animals. The evidence for micro is overwhelming and no creationist denies it. Dawkins would like to convince everyone that creationists deny it, but he is dishonest. Microevolution is nothing but selective breeding, which every Christian farmer/rancher practices daily.

Macroevolution is the change from one family of animals to another, such as a change from dogs to horses. The evidence for macro, and therefore its scientific validity, is almost non-existent. See Roger Lewin’s book “Bones of Contention” if you disagree. Lewin is a devout evolutionist, so you Darwinians don’t have to be afraid that he will try to destroy your faith in evolution. He just happens to be an honest scientist, unlike Dawkins.

Fundamentalist – is that what Creationists are saying nowadays? That microevolution is a change within but not beyond a family (or a genus)? Because I remember the official line being, “Microevolution is a change within but not beyond a species.”