A conversation regarding origins

14 Comments
Posted November 20th, 2008 in Philosophy. Tags: , , , , .

Reythia says:

Let me ask a question to all you atheists out there: if some sort of God didn’t create the universe (or at least the laws behind it), then what did? How did our universe get here? And, by the way, the answer, “It’s always existed,” isn’t an answer at all. After all, that’s the same as saying, “God’s always existed,” and if a good atheist can’t believe that, then he shouldn’t believe “the universe’s always existed” anymore!

It wasn’t exactly aimed at me, but I love the sound of my own voice/keyboard so much that I couldn’t resist answering.


You can use these links to jump to various points in the discussion. Or, ignore them and just keep reading.

My first response

Reythia’s first reply

My second response

Reythia’s second reply

My third response


Written by Dumb Scientist

Well, I used to be qualified to answer that question, and my theological views have changed little since I was an atheist– I’ve only really altered my criteria for certainty. That is, I’m much more cautious nowadays.

Anyway, my short answer as a weak agnostic is– unsurprisingly– that I simply don’t know how to solve what I call the problem of Origins. Even when I was a strong atheist I never pretended to know where the universe came from. I’ve come to terms with my ignorance– I’d rather continue to search for answers, instead of accepting an answer that might be wrong. (I’m not saying theists are necessarily being hasty– they’ve probably already examined the issue on a deeper level than me, and found answers to the problems that are confusing me.)

But, now for the longer answer: the reasons why I don’t know how to solve the Origins problem.

First of all, I think an atheist would be wrong to believe that the universe has always existed– experiments show that it popped into existence about 13.7 thousand million years ago. I also agree that it makes at least a little more sense to say that God’s “eternal” because we have no evidence that He ever began existing at any particular point in time. His other qualities are infinite, so it’d be consistent for His existence to extend infinitely in at least one direction in time (if not both).

But I’m not convinced that “God did it” solves the Origins problem either. I realize that God’s existence has no clear beginning, so causality as we know it doesn’t exactly apply to Him. But given that time started with the Big Bang, I’m not sure that causality applies to it either. So I’m confused as to why God is supposed to make a particularly compelling choice for the First Cause. Why exactly is it preferable to leave God’s existence unexplained rather than leaving something else unexplained? (Other than the fact that He’s defined to be the First Cause; that argument seems similar to ontological arguments which I find wholly unsatisfying.)

My confusion centers around the fact that many theologians say that God is “eternal” and (as we all know) eternal objects are self-explanatory because they never had beginnings. So even though it’s obviously silly to believe that the universe’s existence needs no explanation, God’s existence is an a priori fact because He belongs to a special class of objects with the property “eternal” that basically explain themselves.

This is where I get lost. How do we know that eternal objects even exist, let alone know anything about their properties?

  • Has anyone ever found evidence of an eternal anything? (Aside from God– referring to Him to justify the properties of eternal objects seems a bit circular in this context.)

  • Our logic seems reasonably effective at describing a universe that is ancient and vast (but finite in age if not in spatial extent) and seems to be filled exclusively with transient objects. But why should I believe that logic can be so easily extended to assess the self-explanatory capabilities of eternal objects?

  • Is this an obvious fact that I’m simply supposed to understand at a glance? “God is eternal, therefore by means of a proof so simple it doesn’t need to be stated, His origin needs no explanation.”

Frankly, I don’t understand why some theists seem to think that God solves the Origins problem. It seems like they’ve merely traded one arbitrary assertion for another, so I’ve got to be missing something. It wouldn’t be the first time I’ve missed a crucial detail that everyone else sees… please, any theologians out there– help me!

The reason I say it’s an arbitrary assertion is that I can think of at least one other possible solution. Suppose that instead of choosing a First Cause based on temporal characteristics (i.e. eternal vs. transient), I select it based on logical necessity. Using this criterion, it seems like an ideal First Cause would be the laws of math.

In other words, I’m saying that “1+1=2” is the only type of statement I’m willing to accept as true without evidence. I’m proposing that the question of Origins might be answered by a literal form of mathematical realism.

My choice of First Cause is just as arbitrary as the theists’, but I’m drawn to it on an almost instinctual level. Math just feels more fundamental than anything else I’ve studied because it involves no arbitrary assumptions– at least none that I recognize. For instance, I can’t imagine how “1+1=2” could be changed, but I think I can imagine a universe with different physical laws, or no universe existing at all. I even think I can imagine a universe without a deity, or a universe with multiple deities. The laws of math, on the other hand, seem like immutable certainties to me– more certain than any other statement except “I think, therefore I am.”

The problem now (for me, I guess) is to work “upwards” from the laws of math and see if the laws of physics can be derived from them in a way that explains all the “fine-tuned” constants that litter our theories. In other words, a single physics theory would not only need to be capable of explaining all experiments, it also has to be rigorously justified– without any extra assumptions along the way– all the way back to mathematical axioms. (Incidentally, I believe that if fine-tuned constants are explained by the existence of many parallel universes with different constants, these parallel universes need to be falsifiable somehow.)

I won’t consider the Origins problem solved until physicists have a theory of everything that works like this:

  1. Start by selecting a set of mathematical axioms. (I can’t yet say which set.)

  2. Insert lots of reasoning here, including potentially very complicated mathematics– all of which flows from the axioms in #1.

    (But don’t include experimental data or unfalsifiable assumptions about parallel universes in order to account for fine-tuning of any physical constants.)

  3. The result is a set of predictions for all physical constants and any possible experiment.

To be honest, this seems like such a difficult goal that I probably won’t live to see it achieved– and that’s only if it’s possible at all! I’m interested to see if there’s a quicker or easier way to approach the Origins question. Anyone?


Written by Reythia

Okay, so what you’re arguing makes perfect sense. Specifically, the part about:

On the other hand, I don’t think “God did it” solves the Origins problem either. I realize that God’s existence has no clear beginning, so causality as we know it doesn’t exactly apply to Him. But given that time started with the Big Bang, I’m not sure that causality applies to it either. So I’m confused as to why God is supposed to make a particularly compelling choice for the First Cause. Why exactly is it preferable to leave God’s existence unexplained rather than leaving something else unexplained?

I agree completely: God is no more a compelling choice for a First Cause than the (incomplete) physics behind the Big Bang or any other physics-based universe creation story. But to turn your logic on its head, neither does the state of modern physics produce a more compelling choice for a First Cause than the answer “God” gives!

I’ve read a bunch of things by Carl Sagan (I own most of his non-technical works, actually) and one of the things that always struck me about his discussions on the formation of the universe and so forth is his flat-out insistance that no God/gods exist. Now, you can make a pretty compelling case that a specific, human-like God (or direct speaker of God) like Jesus, Mohammad, Abraham, etc, etc didn’t exist or weren’t really gods. But saying “there was no Creator” isn’t as simple. I mean, you can use physics to go back an awful long way in time… and yet you still can’t say what “started” the universe. Even if we eventually understand the full principles of the last fraction of a second after the creation of the universe (the first 1e-40 of a second after creation, or so), we’re still going to be left with the question: who or what set up all the “rules” for the universe?

Now, an atheist would answer, “Something we don’t understand yet.” And that’s a perfectly valid answer to me. Trouble is, I don’t see ANY difference at all between saying that and saying, “God.” After all, what is “God” (in the general sense, not the specific human-like named deity sense) besides “something we don’t understand yet”??? And that’s my problem with hard-core atheists like Sagan: they recognize that there’s something they don’t understand, but get angry (or, more often, stubbornly arrogant) when others admit the same thing and give it the name “God”. It becomes a great debate of semantics and labelling, in my opinion.

Now then, as to your comments about the glories of math as a First Cause. Here’s my problem: math is a completely arbitrary system humans defined to meaningfully discuss the things around them. That doesn’t mean it’s “wrong”, per se, but there’s nothing fundamental about it, which makes me very skeptical of using it as any sort of an axiom. Really, it’s no different than language, and just as two people can speak equally accurately in two different languages without using any of the same words, two people could choose to describe the same real, physical phenomenon differently just by using different sets and definitions in mathematics.

Two simple examples:

  1. You chose “1 + 1 = 2” as an example of something that is ALWAYS true. But it’s not. In fact, it would be equally correct for me to write: “1 + 1 = 10”. Why? Because I would be using binary, not decimal notation. I use this rather silly example as proof that math is only a human “language” and is therefore completely arbitrary. The system the math is defining may be non-arbitrary, of course, but the math itself is nothing more than a convenient way of describing that system, not the ONLY way.

  2. The classic “find the distance between two points” problem. Let’s say we have two points on a grid, one at (x,y) = (0,0) and the other at (1,1). How far are they apart? Well, the usual way to solve the problem is to say the distance d is found via: d^2 = delx^2 + dely^2. Or in other words, d = sqrt(2). But that’s just because we defined math that way. If instead, I used the “taxi cab metric”, where you can only move straight up/down and sideways, rather than diagonally, then the distance becomes d_taxicab = delx + dely = 2. These answers aren’t identical, but they ARE both valid ways of measuring distance. Another example of the arbitrary-ness of math.

A more “realistic” example of this problem would be asking “How far away from Boston is Chicago?” Most people would pull out a map and get the answer directly from there. But that would only tell you how far AROUND THE SURFACE OF THE EARTH the two cities are apart. Why do we use that measurement over the “direct” line of measurement (which goes through the Earth, of course)? After all, it’s the 3D equivalent of using the taxicab metric!

Well, because for most activities, it’s more USEFUL. Math is very good at being useful. That’s what we designed it (and language) for. But “the most useful way” doesn’t mean “the only way”, as I’ve tried to show here. And if even the “fundamentals” of math can be easily and equally-validly defined to mean numerous different things, then I am very skeptical of the ability of those fundamentals to serve as a valid set of axioms to base the mysteries of the universe upon!

In truth, if you’re going to go this route: to declare the the proper “unknown” to choose to describe things is not “God” but “math”, I would suggest you alter your choice of “math” to “the underlying physics”. After all, what you really want to base your structure on is the “laws” which run the universe, right? Well, math isn’t those laws. The laws are typically defined in terms of math, yes, but that’s about it. Math doesn’t make the universe work, it just describes it (in an arbitrary but commonly-used fashion).


Written by Dumb Scientist

I agree completely: God is no more a compelling choice for a First Cause than the (incomplete) physics behind the Big Bang or any other physics-based universe creation story. But to turn your logic on its head, neither does the state of modern physics produce a more compelling choice for a First Cause than the answer “God” gives!

They’re equally arbitrary, I agree. I’m just personally more drawn to mathematical realism out of a vague “Occam’s Razor” feeling.

I mean, you can use physics to go back an awful long way in time… and yet you still can’t say what “started” the universe. Even if we eventually understand the full principles of the last fraction of a second after the creation of the universe (the first 1e-40 of a second after creation, or so), we’re still going to be left with the question: who or what set up all the “rules” for the universe?

That’s exactly the kind of question I’m trying to answer. Just to be clear, I think the process of setting up all the “rules” for the universe would look like this:

  1. Choose a particular subset of math to be embodied in physical law. For example, undergraduate quantum mechanics takes place in an infinite-dimensional Hilbert space and gravity is described by 4D differential geometry curved by a stress-energy tensor. Quantum electrodynamics is described by an abelian (i.e. commutative, I believe) gauge theory with the symmetry group U(1)– the symmetry of a rotating circle.

    (Probably none of these subsets are actually embodied in physical law. They’re more likely to be subsets which contain physical laws that are close enough to fool our crude experiments.)

  2. Once a subset of math is chosen, the arbitrary constants that parameterize those physical laws need to be fine-tuned to allow for life.

    (Or, at least, the apparent fine-tuning needs to be explained in a falsifiable manner.)

So a full explanation of “how the rules were set up” would require understanding why the physics we see are contained within one subset of math rather than another random subset. This problem seems insurmountable to me: I don’t know that universes based on different subsets of math can even exist, let alone how that idea could be falsified.

I’m completely ignoring the possibility that the underlying laws of physics aren’t mathematical at all for much the same reason.

Arbitrary fine-tuned constants, on the other hand, seem a little easier to approach. The existence of universes that embody the same physical laws but have different physical constants might be testable by experiment one day. Otherwise, this “fine-tuning” would eventually seem like the result of design. It’d be nice to see proof that there’s no need for fine-tuning because (for instance) many universes exist, each with different values for these constants.

This position is similar to the reason I’m not surprised that Earth is comfortable– there are lots of inhospitable planets out there that we simply didn’t evolve on. Currently the singleton “fine-tuned universe” situation seems more analogous to a cosmos that’s empty except for the Sun and Earth. In that case, Earth’s idyllic nature would seem suspiciously fine-tuned– anthropic principle notwithstanding.

Now, an atheist would answer, “Something we don’t understand yet.” And that’s a perfectly valid answer to me. Trouble is, I don’t see ANY difference at all between saying that and saying, “God.” After all, what is “God” (in the general sense, not the specific human-like named deity sense) besides “something we don’t understand yet”??? And that’s my problem with hard-core atheists like Sagan: they recognize that there’s something they don’t understand, but get angry (or, more often, stubbornly arrogant) when others admit the same thing and give it the name “God”. It becomes a great debate of semantics and labelling, in my opinion.

If a pantheist claimed that the unknown “something” was God, I’d probably agree.

But a theist who believes in a personal God is making a more complicated claim: by identifying that “something” as God, that “something” comes packaged with all kinds of attributes like a personality, goal-directed behavior, omnipotence, omniscience, omnibenevolence, etc.

Frankly, all I know is that “something we don’t understand yet” created the universe. People can believe whatever they want, of course, and it never makes me angry. Confused, yes… I just don’t know how all these extra qualities are justified based on the topic at hand.

I realize you’re using the word “God” in a more general sense here but I’ve got to admit that very few people who’ve talked to me about their belief in God seem to be strict pantheists. In my opinion, pantheists are the only ones who wouldn’t be pulling a “bait-and-switch” maneuver by using the Origins problem to argue for the existence of God.

Now then, as to your comments about the glories of math as a First Cause. Here’s my problem: math is a completely arbitrary system humans defined to meaningfully discuss the things around them. That doesn’t mean it’s “wrong”, per se, but there’s nothing fundamental about it, which makes me very skeptical of using it as any sort of an axiom. Really, it’s no different than language, and just as two people can speak equally accurately in two different languages without using any of the same words, two people could choose to describe the same real, physical phenomenon differently just by using different sets and definitions in mathematics.

Short version: I disagree.

Long version:

Math may seem arbitrary when used in physics, but I think that’s only because it’s hard to select the subset of math which contains a completely accurate physical theory. It’s easy to choose a subset that results in predictions close enough to fool contemporary experiments. For example, Newton believed gravity could be described by a 3D vector field, but Einstein showed us how to make more accurate predictions using a subset of math that’s far stranger. Quantum gravity will probably be even weirder. Who knows if we’re smart enough as a species to obtain the final theory of everything, and what would its math subset look like?

If this ultimate subset of math is ever identified, I think that any remaining “arbitrariness” is merely an uninteresting matter of notation. In other words, I could write the equations with an extra factor of 3 multiplying both sides, or do my arithmetic in base 2 as you suggest, or use a different metric, or choose a different set of axes… These examples do seem like semantics– mere translation problems.

You see, when I talked about math earlier, I used “1+1=2” as a quick example. I really wanted to list more fundamental concepts like identity and transitivity. I wanted to mention theorems of existence and uniqueness. Because what I’m ultimately searching for is an existence theorem showing that the Big Bang is inevitable once certain math assumptions are made, followed by a uniqueness theorem that explains the apparent fine-tuning of the universe (or a falsifiable multiverse theory– I’m not picky).

It’d be nice to know why that subset of math was embodied rather than any other, but that’s an intimidating problem. Also, any set of math axioms faces challenges from Gödel’s incompleteness theorems. I just don’t understand these theorems well enough yet to assess the damage. Any logicists are welcome to show me that my approach is doomed, though. I don’t want to waste my time!

I realize that many subsets of math contain approximately valid physical theories. I just can’t imagine a universe in which two theories based on non-intersecting math subsets turn out to be equally effective at describing all physical laws down to the last decimal place. In that sense, math is more than just a language to me. Math is a guiding light that constrains my search for knowledge almost as effectively as comparing predictions to experiments.

In truth, if you’re going to go this route: to declare the the proper “unknown” to choose to describe things is not “God” but “math”, I would suggest you alter your choice of “math” to “the underlying physics”. After all, what you really want to base your structure on is the “laws” which run the universe, right?

When I think of “the underlying physics,” I think of the particular subset of math that’s embodied into physical law, as well as the particular values of the constants that parameterize those laws. I don’t want to consider them to be the First Cause for precisely the reason you gave: I’d have to wonder where those arbitrary constants came from in the first place.

That’s why I’m setting my goal higher– I want to start with some particular subset of math (I can’t yet say which subset). Then I want to somehow derive the laws of physics from that subset in a way that falsifiably explains all the fine-tuned constants we observe.

I don’t want to base my logical structure on the “laws which run the universe” so much as I want to base it on laws which I can’t imagine being any different. I can imagine physical laws embodying different subsets of math, and I can imagine physical constants being different. So I’m not willing to leave physical laws unexplained– it seems like they could have been different, and if they were even slightly different we might not be having this conversation because life wouldn’t exist.


Written by Reythia

Of course, if our universe is just one of many universes with slightly different “rules”, then it’s likely that the formation of the universe(s) is going to remain a problem which we don’t — or maybe even can’t — understand. After all, if our universe was created outside itself (which, if there are multiple different universes, would almost have to be the case), then it was surely created using a set of “rules” which were meaningful wherever it was created. And since nothing in our experience suggests that the creation of universes following different sets of “rules” is permissable from within our universe, that suggests that the “rules” at hand during creation are not exactly those which our universe follows. So, even if we someday come to completely understand the “rules” of our universe, that won’t help us in the least to understand the rules outside it!

And I still disagree with you about the relative importance of math or physics when it comes to specifying what these “rules” are. Math and physics are both tools. Good tools, in my opinion, but still just tools which we can use to define the real “rules”. Now, I think you can make a decent argument that physics (or science in general) is supposed to be a full conceptual understanding of those “rules”, and thus, the ideal perfected state of science is an accurate representation of the “rules” themselves. But math isn’t supposed to be a representation of anything! Math is just… math. A tool.

I had the same math professor in undergrad for 1.5 years, so I got to know him pretty well. He came into class one day absolutely hopping mad. About ten minutes into lecture, he broke off in the middle of a problem and announced, “I can’t believe it! Those STUPID physicists took MY math and actually used it! I’d written my whole dissertation on a beautifullly obscure piece of mathematics and they turned it into part of string theory! It was perfect, PURE! And they went and USED it!”

Now, I admit that the whole class laughed at him because of his obvious pique (and I’m still shaking my head in remembrance now), but the point of the story is that math CAN be “pure” and unrelated to those “rules” we were talking about. That’s because it’s just a tool, and tools’ usefulness depends on how we use them. (Much the same as the way a hammer is still a hammer even if you’re only using it as a paperweight.) Your theory about using math to define those “rules” is nice — and even right, I think. But only because we’ve learned how to use our mathematical “hammer” with precision and without (much!) confusion. The part that makes that math useful in terms of figuring out those “rules” isn’t the math itself, it’s the rationale BEHIND that math. And we typically call that understanding “science”.


Written by Dumb Scientist

And since nothing in our experience suggests that the creation of universes following different sets of “rules” is permissable from within our universe, that suggests that the “rules” at hand during creation are not exactly those which our universe follows.

I’m intrigued by the idea that black hole formation spawns a spacetime orthogonal to ours. It’s even been suggested that this process alters physical constants (by some mechanism I don’t understand), resulting in a “daughter universe” with different physical constants. This idea might even be falsifiable– it may have left a “fingerprint” on the inflation rate of the early universe, for instance.

Even more bizarrely, universes may be subject to their own type of natural selection if they have to compete for resources or “space” (in some higher-dimensional sense). If this is true, it’s ironic that they wouldn’t be selected for compatibility with life, but rather for the most efficient creation of black holes…

This is just a crazy hypothesis– I mention it only because it seems relevant. You’re right to say that multiple sets of rules may eventually be necessary– we haven’t even begun to properly study these questions so at this point very little can be ruled out.

… the point of the story is that math CAN be “pure” and unrelated to those “rules” we were talking about.

I agree. 3D vector fields are “pure” but they only seem to describe gravity– the actual rules are quite different. Also, there are likely many “pure” subsets of math that don’t contain approximations of any physical laws. In other words, the set of all math is probably larger than the union of all subsets of math which contain structures resembling physical laws. (I say this because physics has an additional constraint that math doesn’t share: experiment.)

I think the real problem is that we’re having this conversation a few centuries too early. Currently, it is possible to look at math as an arbitrary human tool that merely gives approximate answers. But my gut instinct is that the fundamental rules of the universe must be based on math. And I can’t conceive of an outcome in which the universe is equally well described by two (or more) different sets of physical laws (each with the same number of axioms) down to arbitrary precision.

As a result, I use math as a guide to knowledge. For instance, I abandoned the Copenhagen interpretation of quantum mechanics in favor of the Many Worlds interpretation based solely on MW’s mathematical consistency and streamlined set of axioms.

Again, my own personal intuition is the only reason I choose mathematical realism as my First Cause. I’m glad that others do take a different approach to the problem of Origins. I say this because if I’m wrong, my search for knowledge is ultimately doomed to failure. While that possibility saddens me, I find solace in the fact that others would carry on the search in different directions.

To them I say this: learn from my mistakes to avoid making similar ones yourself. Attack my ideas repeatedly and read all the works of my critics with an open mind. Never assume that I know what I’m talking about. Because I usually don’t.


a

Update:

As if on cue, here’s more evidence that I don’t know what I’m talking about. I’ve been using the term “First Cause,” but after reviewing Aquinas’s Five Proofs, the term “Necessary Being” seems more appropriate. I say this because my position depends on contingency rather than causality.

It’s still inaccurate because the word “being” implies personhood, but I can’t think of a better term. Sorry for the confusion…

Last modified June 12th, 2012
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14 Responses to “A conversation regarding origins”

  1. (Ed. note: I emailed The Famous Brett Watson and asked him to comment on this article because he did such a superb job here.)

    I just tried to answer the question "If God didn't create the universe, what DID?"

    I'm not sure what I can contribute to this line of inquiry. A brief glance through suggests to me that there are a lot of underlying assumptions in play, and I don't know which of them you consider fundamental, or which of them are just de facto positions that you haven't thought to question.

    I find that it's more productive to argue with at least some knowledge of the other person's fundamental beliefs, because this is what defines "rational" for them. I know some of your brand of rationality, but not enough to apply it to the question you've posed. Instead of taking a systematic approach, then, I'll scan through the article and make some random comments, just to stir the pot a bit. (I'm not going to focus on your remarks, in particular — I'll just comment on whatever looks commentable.)

    if some sort of God didn't create the universe (or at least the laws behind it), then what did?

    The question itself brings some assumptions to the table, and not very clear ones at that. What do we mean by "create"? What do we mean by "the universe"? I think the former question hides the more controversy. If nothing else, the question assumes that some kind of creative agency is necessary.

    There's a kind of causality-based thinking here which is problematic in itself. The argument from contingency classifies some things as contingent and others as necessary, and requires a necessity to act as a foundation for the contingent, thus producing the idea of a Necessary Being. I'm inclined to pull a kind of Kantian wildcard on this line of thought, and question whether the categories of "contingent" and "necessary" are only valid when applied within certain bounds. By that interpretation, the concept of the Necessary Being is not sufficient to prove it exists: the absence of the Necessary Being would simply prove that we've over-stepped the proper bounds of reason somewhere.

    Maybe I'm just a tad sceptical about the concept of Necessity. My scepticism tends to grow in proportion to the alleged universality of the principle. Maybe the whole "contingency/necessity" thing is a way in which we categorise the world, and is suitable only for classifying objects of experience, not for deriving Ultimate Truths.

    I also agree that it makes at least a little more sense to say that God's "eternal" because we have no evidence that He ever began existing at any particular point in time.

    Theists who use the word "eternal" tend not to mean that God's existence extends infinitely along both directions of the time axis. They imply that time itself is a finite dimension with a t=0 prior to which the dimension does not even exist. Spacetime is thus finitely bounded in at least one direction. I don't know which model of spacetime is currently in vogue amongst those who like to ponder that sort of thing, but you should at least be familiar with the concept, yes?

    With this in mind, "eternal" means that God exists outside the dimensions of spacetime with which we are familiar. Also, we have a special relationship with the time dimension in that we perceive ourselves as being in motion along it. An eternal being has no such relationship with time, or at least not with the dimension we call "time".

    My confusion centers around the fact that many theologians say that God is "eternal" and– as we all know– eternal objects are self-explanatory because they never had beginnings.

    Self explanatory? Not my choice of words. If you hypothesise dimensions beyond our own, it's not clear what sort of science you can do on them, so "beyond scientific explanation" might be more apt. If natural science (the study of nature) is your only tool, of course, this arbitrary placing of things out of (your) reach won't sit comfortably. On the other hand, if you start with "science is the answer", I suppose you'll have to rule out a few questions.

    I won't consider the Origins problem solved until physicists have a theory of everything that works like this:

    I see a problem with your research programme. Although the programme of physics is (at present) to describe all events in the universe in mathematical terms, it's not at all clear that mathematics can imply anything about the universe. As a thought experiment, ask yourself "what impact would it have on mathematics if there were no physical universe as such?" Clearly this would have an impact on mathematicians — there would be none — but if there were no time, no space, and no laws of physics, would mathematics itself be even slightly fazed? Would "1+1=2" be even slightly less certain?

    If mathematics is compatible with the non-existence of everything else, then it can't sufficiently explain the universe as it is, can it? You'd additionally need to prove (at least) that it is necessary for something to exist, and such a necessity is not mathematical in nature.

    I think that mathematics is like a set of train tracks: it provides the road on which the freight can be carried, but tells us nothing of the freight itself. Given a train on the tracks at some point, you can tell where it's going, but the tracks themselves don't give you the train.

    After all, what is "God" (in the general sense, not the specific human-like named deity sense) besides "something we don't understand yet"???

    I have to say I find this statement pretty baffling. Why use "God" in two wildly different senses like this? There are numerous other words that one could use for the concept, "something we don't understand yet", like "mystery". Not all mysteries demand "God" as an explanation. Consider the question, "hey, who ate the last slice of pizza?" A mystery it may be to the person posing the question, but I doubt that anyone but a cartoonist would suggest "God" as the answer.

    Of course, the deal with atheists like Carl Sagan and Richard Dawkins is that in their view of things God is superfluous. When they speak of mysteries, the only mysteries they allow are "laws of physics yet to be discerned". The origin of the universe is such a mystery to them. For an Orthodox Jew, on the other hand (given my understanding of Judaism), the origin of the universe is no mystery at all: God spoke, and it was. The disagreement that follows between the two parties rests on the sort of thing which they accept as an explanation. Sagan and Dawkins reject the Jewish explanation purely because it's not the kind of thing they permit as a law of physics.

    Frankly, all I know is that "something we don't understand yet" created the universe. People can believe whatever they want, of course, and it never makes me angry. Confused, yes… I just don't know how all these extra qualities are justified based on the topic at hand.

    This is a product of your approach to answering the question. You want to be able to reach a conclusion using the combination of your brainpower and observation of the world around you. Sometimes that approach leads to theism, sometimes (as in your case) it doesn't. I can only conclude that the result is under-determined by the method. There's probably a lot of personal taste entering into the process undetected. You don't see the need for God to be a person; others can't see how "personhood" can exist at all unless it is a property of God. I'm not sure how one can decide between those two positions other than to adopt the one to which one feels the most inclination, as Mill puts it.

    You see, when I talked about math earlier, I used "1+1=2? as a quick example. I really wanted to list more fundamental concepts like identity and transitivity.

    How about the law of the excluded middle? Not all logics accept it, "fundamental" (to some of them) though it be.

    It'd be nice to know why that subset of math was embodied rather than any other, but that's an intimidating problem.

    It's also contingent on the laws of physics remaining unchanged. We already have some reason to question the constancy of certain fundamental "constants", like the speed of light. Then again, maybe these things are actually variables which have settled down into steady states. That's a different twist on your research programme: not that constants are constants by mathematical necessity, but that they would tend towards certain constants if they were variable!

    Also, any set of math axioms faces challenges from Gödel's incompleteness theorems.

    Only if it's trying to prove itself complete and consistent, in which case Gödel will give your nice set of axioms an atomic wedgie.

    Math is a guiding light that constrains my search for knowledge almost as effectively as comparing predictions to experiments.

    In which case you should be a man of many doubts. Simple things like the three-body problem should leave you in a state of despair. Most of the laws of physics as we formulate them lead to non-computable results. Oh sure, we can approximate them, but sometimes approximation is about like throwing a dart at a map. Most real-world systems are not just non-computable, but also chaotic. All that mathematics adds up to a mass of unpredictable results, even before you add quantum nondeterminism into the mix.

    I don't want to base my logical structure on the "laws which run the universe" so much as I want to base it on laws which I can't imagine being any different.

    Is this going to tell us more about the universe, or about the limits of your imagination?

    Of course, if our universe is just one of many universes with slightly different "rules", then it's likely that the formation of the universe(s) is going to remain a problem which we don't — or maybe even can't — understand.

    Personally, I can explain the existence of n universes for n=0. I have roughly equal amounts of trouble with all other values of n. Maybe some folks think the problem is easier for an indefinite n, such as "anything that can exist, does exist". Maybe that makes for an easier description of what exists, but it completely fails to address the question of why the heck anything can exist at all.

    That will do for now. See if there's anything in that pile of random commentary that inspires anything.

    Regards,

    TFBW

    • Wow, thanks! You’ve raised a lot of very interesting points. I need to give your comments some serious thought before I respond…

    • I find that it’s more productive to argue with at least some knowledge of the other person’s fundamental beliefs, because this is what defines “rational” for them. I know some of your brand of rationality, but not enough to apply it to the question you’ve posed.

      I’ve tried to summarize my fundamental beliefs in this article.

      Self explanatory? Not my choice of words. If you hypothesise dimensions beyond our own, it's not clear what sort of science you can do on them, so "beyond scientific explanation" might be more apt. If natural science (the study of nature) is your only tool, of course, this arbitrary placing of things out of (your) reach won't sit comfortably.

      I’m really only uncomfortable with the claim that the Origins problem is proof of the existence of God. People who make this claim seem to ignore that the problem’s simply been swept under the rug– that they now have to explain why God exists. If they address this issue at all, they do so by saying that it’s absurd to question God’s existence because He’s eternal.

      I’m not bothered that many people choose to resolve the Origins question in this manner. (I’m certainly ignoring some problems in my attempts to answer the Origins question, so that’d be hypocritical of me.) I’m just curious to know why they seem to think it’s anything but an arbitrary choice. (Note that I’m not necessarily including you in that group of people.)

      On the other hand, if you start with "science is the answer", I suppose you'll have to rule out a few questions.

      I’d rather say that science is a good method for producing models which correctly predict the results of experiments and observations. I don’t think science is an answer… it doesn’t even provide answers like religions claim to. Science can only give us models that are constantly updated with new evidence.

      If mathematics is compatible with the non-existence of everything else, then it can't sufficiently explain the universe as it is, can it? You'd additionally need to prove (at least) that it is necessary for something to exist, and such a necessity is not mathematical in nature.

      Nice thought experiment! I think you’ve identified another intimidating question that belongs with “What if the laws of physics aren’t mathematical?” and “Why are the laws of physics contained within this math subset rather than another?”

      As you say, it seems impossible to predict anything about the universe based on pure math. I guess my goals are more humble; I’m more interested in removing roadblocks that stand in the way of describing the universe completely in terms of math. These roadblocks include:

      • The existence of fine-tuned constants in our theories of physics. I want to see some evidence or a good logical argument that this fine-tuning isn’t an astonishing coincidence. (The anthropic principle doesn’t impress me.)

      • Where did all the energy in the universe come from? Before we found that the universe is accelerating, I didn’t think this was a problem. That’s because a universe that re-collapses has negative gravitational energy that balances out the positive mass energy of all the stars and planets. But an accelerating universe isn’t so easily explained. (Any smarter physicist want to help me out here?)

      • The Big Bang isn’t explained to my satisfaction. While evidence that it happened is overwhelming, I’d like to see a coherent, falsifiable explanation of how it happened. Because it seems like time didn’t exist prior to the Big Bang, this explanation probably won’t hinge on causality.

      • We can’t describe all fundamental physical processes in the universe with the same theory. Different phenomena have to be described by theories that can’t be combined without inconsistencies. How embarrassing!

      My approach is limited in the sense that I’ll probably never be able to say why the universe exists at all, or why the universe doesn’t use some other set of laws. But if these roadblocks are ever removed, I’d be able to say that everything in the universe– at the most fundamental level– is just a manifestation of mathematics. Galaxies, planets and people would simply be emergent properties of that subset of math.

      I recognize that this type of explanation appeals to me only because I find it conceptually beautiful. And just to be clear, even though I say that I can’t see a way to solve certain problems, I’m not saying that they’re “out of reach” for anyone except me. I would never declare something to be “unknowable.” All I’ll say is that these mysteries are beyond my meager skills.

      Anyway, thanks for pointing out that problem. I’d never heard such a clear explanation of the analytic-synthetic distinction before.

      This is a product of your approach to answering the question. You want to be able to reach a conclusion using the combination of your brainpower and observation of the world around you. Sometimes that approach leads to theism, sometimes (as in your case) it doesn't. I can only conclude that the result is under-determined by the method. There's probably a lot of personal taste entering into the process undetected.

      I mostly agree with you here. I’ve met too many intelligent theists to believe that there’s an “obviously correct” theology. The conclusions we reach are based on the assumptions we make, which can’t be evaluated by reason because reason depends on those very assumptions in order to function.

      It seems to me that the taste involved is more cultural than personal, though. Otherwise people wouldn’t be so likely to share the religion of their parents.

      You don't see the need for God to be a person; others can't see how "personhood" can exist at all unless it is a property of God.

      Just to be clear, I don’t see the need for the “Necessary Being” to be a conscious person based solely on the problem of Origins. Other approaches could succeed, though. For instance, credible historical evidence of divine intervention would be evidence that the Necessary Being is a person (called God). I say this because I don’t think Spinoza’s God would’ve parted the Red Sea, whereas it’d be in character for Yahweh.

      It sounds like you agree, because your justification of God’s personhood seems to be based on something other than the Origins problem. I’m not entirely sure I understand what you’re saying, though, so I might be wrong.

      How about the law of the excluded middle? Not all logics accept it, "fundamental" (to some of them) though it be.

      The law of the excluded middle is a good example of a math axiom I don’t understand well enough yet to declare it “obviously true.”

      Also, any set of math axioms faces challenges from Gödel's incompleteness theorems.

      Only if it's trying to prove itself complete and consistent, in which case Gödel will give your nice set of axioms an atomic wedgie.

      I’m worried that assuming the existence of a theory of everything is equivalent to proving that theory complete and consistent.

      (Also, I don’t think the phrase “atomic wedgie” is used often enough in philosophy debates. *slow clap*)

      In which case you should be a man of many doubts.

      Like you wouldn’t believe…

      Simple things like the three-body problem should leave you in a state of despair. Most of the laws of physics as we formulate them lead to non-computable results. Oh sure, we can approximate them, but sometimes approximation is about like throwing a dart at a map. Most real-world systems are not just non-computable, but also chaotic. All that mathematics adds up to a mass of unpredictable results, even before you add quantum nondeterminism into the mix.

      I only turn to math when experiments/observations are unavailable or ambiguous when I’m trying to compare two theories. In that case, I think it’s helpful to examine each theory for mathematical consistency, and see which theory has fewer axioms.

      The problems you describe are serious pragmatic hurdles; I deal with them in my day job as a computational physicist. But they don’t bother me philosophically because they just seem like evidence of our inability to make perfectly accurate measurements and perform simulations with infinite precision.

      I don't want to base my logical structure on the "laws which run the universe" so much as I want to base it on laws which I can't imagine being any different.

      Is this going to tell us more about the universe, or about the limits of your imagination?

      This is certainly a serious ambiguity. I’m just not sure what else to rely on when approaching questions like this. Someone else’s imagination, perhaps?

  2. Here are a few points which are by no means adequate — from philosophy and from cosmology — but which have become accepted by quite a few careful thinkers (certainly not all) on this subject (among them cosmologists, philosophers and theologians) as the, so far, least inadequate understanding of origins.

    First of all there are two different origin questions: that of the temporal origin (when did physical reality as we know it begin?) and the ontological origin (what is the ultimate source or explanation of reality?). These are very different, and the second is obviously much more fundamental. It is possible, as Thomas Aquinas and other medieval theologians recognized, that there may not have been a beginning to the universe or to physical material reality as we know it. But that does not mean that it explains itself, or has no further explanation. It still needs to be grounded in its existence and in the order and properties it manifests. That’s simply because it is clear that it doesn’t explain itself. That is, it still needs an ontological origin. The idea here is that whatever the ontological origin is, it effectively gives existence and order to the universe from all eternity. It is its ultimate and continuing source of being and ordered activity — or one may say that the universe participates in, and derives its existence, order and dynamism from this ultimate ontological origin or source. It is clear that this does not in any way demand a temporal origin — though it does not rule it out.

    Secondly, it is, from a purely philosophical perspective (which was eventually taken over into Jewish, Christian and Islamic theology) that this ontological origin is what most theologians and many philosophers would mean by “God.” “God” for them is much more than this, of course, as one who is revealed through prophets, saving persons, and community experiences as personal, loving, and in ongoing interaction with the believing communities, but God is also conceived certainly at least the Creator in this sense of ultimate ontological origin. We cannot have anything like an adequate concept of God — God is above and beyond our concepts. However, that does not mean that we cannot say something about God, and conclude that we need something like God as ultimate ontological origin to account for existence and order. Otherwise there is no answer to what certainly seem like legitimate questions: Why is there something rather than nothing? And Why this type of basic order — or any order at all — rather than some other kind? Otherwise we have to abandon the fundamental principle of sufficient reason at this point. What it does mean is that, though we can speak about God to some extent and what God does, we cannot come close to understanding or conceiving God — comprehending God.

    In your first response to Reythia, you mention that “causality as we know it doesn’t exactly apply to Him (God).” That’s perfectly correct! That’s why in applying causality to God as the source of existence and order, we do so metaphorically or analogically. And refer to God as “the First or Primary cause” not because God is “first” temporally, but because God is the most basic, and as such unlike any other cause. God enables all other (secondary) causes, but does not substitute for them. Instead God as creator enables or empowers other things to be what they are — and gives them the relative autonomy and causal efficacy to operate according to their own innate dynamisms. We might say that as Creator God is the necessary condition for everything, but the sufficient condition for nothing.

    If we now go to contemporary cosmology, it is clear scientifically that the Big Bang is first of all not an event, and secondly not the temporal beginning of the universe. In fact, it is simply the past limit of the hotter, denser phases of the universe as we go back into the past, according to the standard, general relativistic model of space-time (Einstein). But it is clear that this model breaks down at very high energies (temperatures) — above 1032 K for three spatial dimensions. The Big Bang singularity is symptomatic of this break-down. And so quantum cosmologists are exploring other models which may eventually provide a reliable model of space-time in this high-energy, totally quantized regime. On the basis of these new insights, people have proposed many types of pre-Big-Bang scenarios, postulating an array of possible pre-Big-Bang physics and physical states, with the possibility that even time itself as we know it may not be a fundamental physical reality, but derivative of some primordial completely quantized configuration. The Wheeler-DeWitt equation for instance, which describes in semi-classical terms the wavefunction of the universe, does not contain time as parameter in its basic formulation.

    The points here are:

    1. The Big Bang is not either a temporal origin, nor, obviously, an ultimate ontological origin — it cannot and does not explain itself or what emerges from it.
    2. Any physical state in reality is preceded by another physical state.
    3. No physical configuration or cause, no matter how primordial provides — or can provide — an ultimate ontological explanation for existence or for order. To do that it would have be self-sufficient in its existence, and be self-explanatory in its characteristics and its ordered activity.

    Thus, though what we can determine about origins from physics and cosmology is limited, we can engage and describe those limits, and ask philosophical questions which transcend what physics can deal with. We can also postulate what is needed to answer those questions of origin, and say something — however inadequate –about what characteristics that source or ontological origin would have to possess. Philosophically, how do we determine whether that educated speculation is worthwhile or valid? Certainly not scientifically or mathematically! But if it leads to consistency — within the terms and uncertainties of the concepts, which we have to be very careful about! — and if it provides a secure basis for other philosophical investigations and accords with critiqued experience over the long term, and if no other competitors equal its explanatory success, then it seems to be that it does provide the least inadequate explanation for existence and order. Certainly its application in theology has also provided that discipline with singular successes — once you purify that from the gross distortions which have visited upon it.

    Furthermore, it is clear from this, too, that what the sciences discover and what philosophy and theology conclude — if they are properly pursued, interpreted and understood — cannot be in essential conflict. If they seem to be, then there has been a failure on one side or the other (or on both sides!) — often involving the overstepping of the limits of the disciplines themselves.

    These are a few points which may shed some light on origins.

    All the best!

    Bill

    • Thanks for your insights; I really appreciate you taking the time to help me.

      This is the first I’ve heard of the Wheeler-DeWitt equation and pre-Big Bang cosmologies. The notion that time could extend before the Big Bang is likewise news to me. How fascinating!

      I think I understand what you mean when you say the Big Bang isn’t an event. If I’m right, you’re saying that the Big Bang isn’t a clearly delineated event as much as a barrier to our current physical theories, like the “sound barrier” was. A more accurate physical theory will presumably reveal the Big Bang to be a an era of the universe which isn’t qualitatively different than our own era– just hotter and denser.

      I’m still digesting most of the philosophy you discussed, but these points immediately spring to mind:

      But that does not mean that it [the universe] explains itself, or has no further explanation. It still needs to be grounded in its existence and in the order and properties it manifests. That’s simply because it is clear that it doesn’t explain itself.

      I agree with you here, but the problem is that I don’t know why I agree with you. I don’t know why I consider, say, the arbitrary constants that define our universe to be coincidences requiring explanation. For example, their current life-sustaining values might be the only logically possible values, eliminating the “fine-tuned” coincidence. Perhaps life can exist even in universes that seem inhospitable to us, albeit in a drastically different form. I just don’t know.

      More abstractly, I’m having trouble putting into words the reason why I don’t consider the universe to be self-explanatory. This might sound pedantic, but until I know what criteria I’m subconsciously applying to this question, I can’t trust my judgment. How could I ever identify a “self-explanatory” entity if I don’t know why I’m rejecting some entities as “non-self-explanatory”?

      To do that it would have be self-sufficient in its existence, and be self-explanatory in its characteristics and its ordered activity.

      I also think I agree with this statement. My confusion centers around the fact that nearly all theologians consider these characteristics to be synonymous with a personal God. They also assert that no other being can be self-explanatory– that a personal God is the unique solution to the Origins problem. They might be correct to say this, but I’m not convinced yet…

      Otherwise we have to abandon the fundamental principle of sufficient reason at this point.

      I’m considering this possibility, radical though it may seem. I tend to agree with The Famous Brett Watson (above) when he says:

      Maybe I’m just a tad sceptical about the concept of Necessity. My scepticism tends to grow in proportion to the alleged universality of the principle. Maybe the whole “contingency/necessity” thing is a way in which we categorise the world, and is suitable only for classifying objects of experience, not for deriving Ultimate Truths.

      Likewise, the principle of sufficient reason seems effective at handling most mysteries. But I’m not sure what the bounds of its proper application are.

      • The question of whether the Principle of Sufficient Reason has bounds on its proper application leaves us with an interesting choice.

        If the Principle is strictly universal, then there is an infinite regress of reasons. If every event must have a prior cause, and every entity must have a proper origin, then there is no escape. This is often rejected for both empirical and rational reasons. Experience gives us the law of increasing entropy, which makes us doubt the possibility that the chain of cause and effect can be infinite. If entropy always increases (and we know of no exceptions to this, given a closed system), then the chain of events must be bounded at least by maximum and minimum possible entropy. From a purely rational perspective, the infinite regress raises the question as to the strict universality of the Principle, particularly when applied to itself. That is, if the Principle of Sufficient Reason is true, there must be a reason why it is true. Infinite regress can not supply this fundamental reason: it can only place the reason beyond reach at infinity.

        This gives rise to our second possibility: that the Principle is nearly universal. Due to the difficulty associated with the strictly universal view, we add an exception to the rule: the First Cause or Uncaused Cause. Under this revised formulation of the Principle, there is one exception: God. (This gives rise to the Cosmological Argument for the existence of God.) This solves the experiential difficulties by denying that the universe is infinite: instead, it has an origin which transcends the law of entropy. Similarly, this provides the Principle with a reason of its own: the Principle of Sufficient Reason is true because it reflects the will of God in his creation. That seems like an ad hoc explanation because it is an ad hoc explanation: once you have admitted that the Principle of Sufficient Reason can’t be applied to God, then you’re stuck with “because God wills it” or something similarly lame once you make that final leap backwards to the first cause.

        The third possibility is to deny the universality of the Principle of Sufficient Reason, or at least to be openly doubtful as to its universality. This is akin to the “nearly universal” position, except that the “nearly” is deliberately vague. The trap here is that we don’t really know whether any particular event, entity, or proposition has a reason behind it. Experience gives us evidence that everything happens with cause, but experience can never give us Universal Truths. Furthermore, when we extrapolate backwards from effect to cause, we have no way to determine whether our extrapolation is valid or not. If there was no prior cause, then the extrapolation is invalid, but that doesn’t prevent us from reaching a conclusion: it merely results in an invalid conclusion (and no general means to detect the error). The major implications of this modest Principle of Sufficient Reason are twofold: first, it throws into doubt the validity of the Cosmological Argument for the existence of God; second, it throws into doubt most of science — particularly the portions of it which rest heavily on principles of Uniformity (such as anything to do with long ages or far reaches).

        A fourth possibility is to deny reason altogether. Neither proper science or proper philosophy are possible without reason, so this position doesn’t require a lot of explanation. In fact, the position itself is one of strong anti-rationality, and can not be rationally explained without defeating itself.

        My observation here is that most Scientific Rationalists (and Dawkins in particular) tend to operate under the nearly universal model of Sufficient Reason. They tend to think that their cause-and-effect brand of thinking is absolutely best of breed — right up until they hit the Cosmological Argument for the existence of God. At that point, they abruptly switch into the more modest model of Sufficient Reason which doubts the validity of this argument. If they were consistent, they would either accept the Cosmological Argument, or be more sceptical of the validity of science itself when applied to long ages and far reaches (which assume not only Sufficient Reason but also much broader traits of universality and immutability).

        Is that a fair criticism? Does that four-way subdivision help clarify matters at all?

      • Sorry for being so late with this response. I was at a scientific conference when you posted, and went home immediately for Christmas where I was a little distracted. I also wanted to do your comment justice, because as usual your insightful analysis definitely helped clarify matters.

        If the Principle is strictly universal, then there is an infinite regress of reasons. If every event must have a prior cause, and every entity must have a proper origin, then there is no escape. This is often rejected for both empirical and rational reasons. Experience gives us the law of increasing entropy, which makes us doubt the possibility that the chain of cause and effect can be infinite. If entropy always increases (and we know of no exceptions to this, given a closed system), then the chain of events must be bounded at least by maximum and minimum possible entropy. From a purely rational perspective, the infinite regress raises the question as to the strict universality of the Principle, particularly when applied to itself. That is, if the Principle of Sufficient Reason is true, there must be a reason why it is true. Infinite regress can not supply this fundamental reason: it can only place the reason beyond reach at infinity.

        I don’t see how entropy applies to this problem. I usually regard Boltzmann’s definition of entropy as being most fundamental. When I think about an infinite regress of cause/effect, I can’t identify any microstates which are macroscopically indistinguishable. As a result, I don’t see how entropy has anything to do with the principle of sufficient reason.

        Having said that, I completely agree that the principle of sufficient reason can’t be strictly universal because, as you say, then there would have to be another reason why the Principle is true.

        This gives rise to our second possibility: that the Principle is nearly universal. Due to the difficulty associated with the strictly universal view, we add an exception to the rule: the First Cause or Uncaused Cause. Under this revised formulation of the Principle, there is one exception: God. (This gives rise to the Cosmological Argument for the existence of God.) This solves the experiential difficulties by denying that the universe is infinite: instead, it has an origin which transcends the law of entropy. Similarly, this provides the Principle with a reason of its own: the Principle of Sufficient Reason is true because it reflects the will of God in his creation. That seems like an ad hoc explanation because it is an ad hoc explanation: once you have admitted that the Principle of Sufficient Reason can’t be applied to God, then you’re stuck with “because God wills it” or something similarly lame once you make that final leap backwards to the first cause.

        This seems like a valid (but arbitrary, as you say) point at which to terminate the infinite regress of cause and effect. Out of all the alternatives you listed, this one sounds closest to my position. One important difference, though, is that I see no reason to think that the First Cause is a conscious person.

        The third possibility is to deny the universality of the Principle of Sufficient Reason, or at least to be openly doubtful as to its universality. This is akin to the “nearly universal” position, except that the “nearly” is deliberately vague. The trap here is that we don’t really know whether any particular event, entity, or proposition has a reason behind it. Experience gives us evidence that everything happens with cause, but experience can never give us Universal Truths. Furthermore, when we extrapolate backwards from effect to cause, we have no way to determine whether our extrapolation is valid or not. If there was no prior cause, then the extrapolation is invalid, but that doesn’t prevent us from reaching a conclusion: it merely results in an invalid conclusion (and no general means to detect the error). The major implications of this modest Principle of Sufficient Reason are twofold: first, it throws into doubt the validity of the Cosmological Argument for the existence of God; second, it throws into doubt most of science — particularly the portions of it which rest heavily on principles of Uniformity (such as anything to do with long ages or far reaches).

        My observation here is that most Scientific Rationalists (and Dawkins in particular) tend to operate under the nearly universal model of Sufficient Reason. They tend to think that their cause-and-effect brand of thinking is absolutely best of breed — right up until they hit the Cosmological Argument for the existence of God. At that point, they abruptly switch into the more modest model of Sufficient Reason which doubts the validity of this argument. If they were consistent, they would either accept the Cosmological Argument, or be more sceptical of the validity of science itself when applied to long ages and far reaches (which assume not only Sufficient Reason but also much broader traits of universality and immutability).

        I can’t speak for anyone but myself; my problem with the Cosmological Argument isn’t the abrupt truncation of cause-and-effect based reasoning that you believe bothers Dawkins. It’s clear that the principle has to be truncated, and that truncation point might as well be called a First Cause. What confuses me is that I don’t see any reason to believe that the First Cause has to be a conscious, omnibenevolent person like Yahweh or Allah.

        I strenuously disagree that “long ages” are based on an untestable assumption of uniformity. Uniformity isn’t an assumption, it’s a provisional conclusion drawn from centuries of astronomical observation. This conclusion is falsifiable because a single counter-example could prove it wrong.

        However, I agree that an assumption of immutability (what I call the assumption of a strictly objective reality) is an extraordinary claim that isn’t sufficiently supported by evidence right now. All I’m willing to say is that I’ve never seen evidence contradicting a strictly objective reality, but I’m not reckless enough to make such a sweeping claim about the nature of reality based on my meager experiences.

        My preferred version of the principle of sufficient reason makes distinctions between entities, propositions and events:

        1. Every entity has a sufficient explanation for its existence. I don’t see a reason to add any caveats to this version of the principle.

        2. Every proposition with non-contradictory alternatives has a sufficient explanation for why it’s true. Thus I see no reason to justify “1+1=2” because I see no alternatives, but I do see a need to justify the statement “water at standard pressure boils at 100 °C” because it seems like that proposition could be expressed differently without logical contradictions.

        3. Every event that could have occurred differently has a sufficient explanation for why it occurred. Thus I’m concerned by “fine tuned constants” inherent in the Big Bang, but I’ll be satisfied with the Big Bang if those constants can eventually be shown to be the only logically consistent values. (Or I’d like to see a falsifiable multiverse theory– either discovery would provide a provisional answer to the question of Origins, in my opinion.)

        I don’t see any compelling reason to declare the existence of God exempt from the principle in the same way “1+1=2” is– there could be no God, one God, or multiple gods. As a result I’m uneasy with the claim that God’s existence is outside the bounds of the principle of sufficient reason.

        This approach is necessarily subjective; other people will undoubtedly argue that “1+1=2” could be different, or that God’s existence is somehow axiomatically certain. My approach also doesn’t really solve the Origins problem as you noted: I might be able to reduce the entire Universe to mathematics, but I’d never be able to explain why the Universe existed at all. But I think that these flaws are not unique to my approach, and I personally prefer my ad hoc bounds on the principle of sufficient reason.

      • @BlackPhysicists tweeted about a relevant paper by Sara Imari Walker: The Descent of Math.

  3. Jimmy posted on 2009-07-03 at 00:34

    I was reading a bunch of articles on your website. It led me to wonder about the effects of inflation and dark energy on black holes. I know the answer is probably either “we don’t know enough to figure it out” or “the effect is too small to be significant.” However, it can’t hurt to ask. :-)

    From what I understand, dark energy comes from space itself. So in a black hole, in the space between the singularity and the event horizon, shouldn’t the dark energy contribute to the black hole’s total mass (because of E=mc^2, of course)? But dark energy causes space to expand, so shouldn’t the diameter of the event horizon increase as space expands? I guess this effect, if it occurs, is too small to be important in regular black holes and the expansion of space right now. However, during the early universe, wouldn’t inflation cause any primordial black holes to increase in size the same way? Of course, if the primordial black holes created after the period of inflation, then this doesn’t matter, right?

    • I was reading a bunch of articles on your website. It led me to wonder about the effects of inflation and dark energy on black holes. I know the answer is probably either “we don’t know enough to figure it out” or “the effect is too small to be significant.” However, it can’t hurt to ask. :-)

      Actually, there probably is someone capable of figuring this out. Unfortunately, I’m not that person. I have yet to take any serious graduate-level courses on general relativity, and I only barely understand the evidence for dark energy. Competing variants of dark energy such as quintessence and a resurrected cosmological constant are over my head.

      From what I understand, dark energy comes from space itself.

      I haven’t seen any evidence for dark energy inhomogeneity, unlike dark matter which seems to exist mainly in halos around galaxies. Quintessence is one variant of dark energy that can vary spatially and temporally, so if that’s the correct model then dark energy isn’t necessarily uniform.

      So in a black hole, in the space between the singularity and the event horizon, shouldn’t the dark energy contribute to the black hole’s total mass (because of E=mc^2, of course)?

      Mass alone defines an object’s gravitational field in Newton’s theory, but gravity in general relativity is produced by the stress-energy tensor which also depends on the pressure. Since dark energy’s pressure is negative, I think it would cause a black hole to be smaller but that depends on how much pressure each joule of dark energy exerts to see if its pressure contribution is larger than its mass-energy contribution.

      But dark energy causes space to expand, so shouldn’t the diameter of the event horizon increase as space expands?

      Technically dark energy causes the expansion of the universe as a whole to accelerate. However, this is only known to be true about the universe on a very large scale– where individual galaxies are too small to worry about. I’m not sure that the conclusions drawn from our current measurements can meaningfully be extended to relatively tiny objects such as supermassive black holes, let alone their stellar mass cousins.

      I guess this effect, if it occurs, is too small to be important in regular black holes and the expansion of space right now.

      It’s definitely not observable with today’s technology, because we’d need some way to estimate the mass inside a black hole independently of the size of its event horizon. It might change the energy at which particle accelerators like the LHC would create miniature black holes but I don’t even know the sign of this change, let alone how to begin estimating its magnitude.

      However, during the early universe, wouldn’t inflation cause any primordial black holes to increase in size the same way?

      I don’t know. Maybe they would, but then again maybe they’d increase in size during inflation and then return to normal afterward. I’m no cosmologist, but I’ll try to contact one and see what he thinks.

      Of course, if the primordial black holes created after the period of inflation, then this doesn’t matter, right?

      Inflation supposedly took place 10-36 seconds after the Big Bang. I’ve never seen any estimate of when primordial black hole production peaked. Since they were created by density fluctuations, it might be possible to obtain a limit on their creation time using the size of the fluctuations in the cosmic microwave background radiation.

      On a similar note, I’ve long been fascinated by the idea that black hole formation spawns a new universe.

      I’ve recently been toying with the idea that the Big Bang was caused by the collapse of a star in another universe. If that’s true, could inflation itself have been caused by something like the infalling matter hitting the singularity or any inwardly-directed gravitational radiation emitted during the balding phase that immediately follows the formation of the event horizon? Would there be any way to experimentally verify a connection like this by comparing the nature of inflation to simulations of gravitational collapse? (Even if this isn’t complete nonsense, quantum gravity would probably be needed to describe these events.)

      • Jimmy posted on 2009-07-03 at 00:45

        I’ve been fascinated by that idea that black holes spawn new universes too. I’m often skeptical that it is like the “cyclic universe” – a cool idea that probably wouldn’t work. In any case, if black holes do evaporate due to Hawking radiation, then I would wonder if our own universe eventually evaporated away like that!

        I forgot that dark energy’s negative pressure would have an effect. It seems like a complicated problem.

      • I’m often skeptical that it is like the “cyclic universe” – a cool idea that probably wouldn’t work.

        Personally, I lost interest in the cyclic universe (also known as the oscillatory universe) when the expansion of the universe was shown to be accelerating.

        Since oscillations seem to require Big Crunches, these models don’t make much sense to me unless dark energy eventually changes sign and causes a Big Crunch which leads to the next oscillation. On the other hand, the wikipedia page points out that the Baum-Framptom model includes dark energy in its oscillations, and it was recently published in 2007.

      • The simple answer to your main question is that there is really no connection at all between dark energy and black holes. Black holes are the ultimate collapsed state of normal mass-energy. If dark energy turns out to be vacuum energy (the cosmological constant), as appears the most likely alternative, it cannot clump at all. It remains perfectly homogeneous throughout the universe. If dark energy is something else, it may clump, but would not directly be connected with the formation or constitution of black holes.

        There is, of course, a much deeper connection between inflation and dark energy. The only way we can really conceive of inflation occurring in the early universe is under the influence of a large amount of vacuum energy, which is a type of dark energy. This dark energy must be quickly transformed into the particles and radiation at the end of inflation. So, it’s not at all clear if there is a relationship between the dark energy which drove inflation and the dark energy which we have evidence is driving the gentle acceleration of cosmic expansion now. It may be that the dark energy now may be a remnant of the dark energy left over from the very early universe.

  4. Galactus posted on 2012-02-20 at 00:24

    The origins of the universe are irrelevant to the existence of god or being an atheist. Atheists don’t need to know the origins of the universe or “Believe” in anything. Atheists have educated hypotheses based on hard facts and data, no matter what the atheist’s hypothesis or personal conclusion on the origins of the universe are, it has no relation to the argument of God/god/gods.—If an atheist comes to the conclusion that the Universe always existed, because of the evidence he finds, it doesn’t give religious folk a free pass to use the same statement. Religion’s claims are arbitrary, unfounded, and irrelevant, because they are not derived from the process of logic; the claims are made up out of ‘thin air.’

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