On the no prior time condition, why does the zero point exist?

I’m sorry, I thought you were already aware of this. If not, you may need to catch up. Start at The Other Problem with Nothing, which you even mention here, so it perplexes me that you don’t know that it answers your question or links to the articles that do. Maybe you need to start from the beginning: The Problem with Nothing.

For the present article, the answer is irrelevant. It does not matter to the specified complexity and structural incoherence of then supernatural why an initial zero point might exist, and whether it exists is simply one hypothesis among many, not one that anyone need commit to here.

Are these metaphors you use to say that out of infinite logical possibilities, only one is that nothing ever exists?

Yes. We don’t have language for things we have no experience with and never could. So we have to borrow language that approximates or analogizes. Most language is like that actually, even for ordinary things. That’s why language is efficient. But it does mean you need to abstract away the irrelevant material to understand what is being said, as when we say “the sun just came up,” we have to abstract away the implication that the sun moves and understand the analogy is to relative and not absolute motion. No one is saying the sun moves when they say it is moving across the sky (except actual flat earthers; everyone else understands the analogy meant).

So in the existential case, there is no time at which a decision is made. What exists is simply automatically decided by the metaphysically entailed reality that if nothing exists to make one outcome more probable than another, every outcome is equally likely, which entails some non-nothing infinite series of events will exist (to infinite probability). It does not come to exist at some time. It just exists. And all we are explaining is what will exist on that condition.

Dr. Carrier,

Thank you for your answers!

You wrote that on the “no prior time” condition, the zero point collapses into either no time at all (so there only ever is just one point of time and therefore nothing else comes to exist) or some extension of time (a universe). Logic then entails the latter is infinitely more likely. But there is always a finite time ago.

On the no prior time condition, why does the zero point exist? If it began to exist without a cause and shortly after collapsed into an infinite multiverse, why not renounce the claim that the zero point existed at all and say that the infinite multiverse began to exist without a cause?

You also wrote that on the “past infinite time” condition, the existential selection does not occur at “a” time; it collapses across all infinite time atemporally. This makes me think about what you say in The Other Problem with Nothing: the Argument from Nothing provides a naturalist metaphysics for why anything exists at all, and why this thing and not some other. It’s a random selection effect—whether that happened at some specific time in the past, or is simply the atemporal “dice-roll” whereby what would exist was selected to be.

I don’t really understand what you mean by the existential selection collapsing across all infinite time atemporally, or by the atemporal “dice-roll” whereby what would exist was selected to be. Are these metaphors you use to say that out of infinite logical possibilities, only one is that nothing ever exists?

P.S. I keep reading your blog posts. They are quite long, but also very interesting. I will probably ask you some questions about what I read, but I will do so in the comment sections of these posts.

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On the first question, that is all explained in my study of the very methodology you are asking out: Proving History. You may need to consult that.

The tl;dr is that objective probability is ontological probability (the physical probability of a thing), while epistemic probability is the closest we can get to that with the information available. As information increases, EP approaches OP. But as omniscience and infallibility never exist, EP never equals OP (though it can get so close as to make no consequential difference in their values).

I avoid the phrase “subjective” probability because it is misleading and results in a lot of errors when people use or argue from it. But in a sound application, “subjective” means POV, i.e. epistemic probability, the probability that H given what you know at time T. It does not mean arbitrary or opinion or feelings or intuition. All epistemic probabilities are constrained by objective evidence. All of them. Given B and E, P(H|E&B) follows objectively. The only subjective element is that, as an individual, your access to the contents of E and B are limited to what you have access to. So P(H|E&B) can differ from person to person if they do not have equal access to information. In academic subjects that doesn’t usually matter though. This isn’t like a criminal case or corporate secrecy where some parties have access to information the rest don’t. In this matter all information is public. You can therefore either account for it or ignore it; and accounting for it implicates only objective entailments (you are validly deriving results from facts), while ignoring it can only generate epistemically invalid results (then you are basing probabilities on vacuous intuition or feelings).

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I wrote that if spacetime must always exist, and the spacetime point briefly existed before anything else did, it would seem to follow that the spacetime point existed an infinite amount of time ago.

This all depends on your semantic meaning. If by “always exist” you mean infinite time, then yes, you are simply describing a tautology. But if by “always exist” you mean exists at every time there is, then that is compatible with there only being a finite time. If no time existed before T = 0 and no time exists after T = n, than anything that exists in between 0 and n “always exists,” because it exists at every time there ever was or will be. It exists at “all times.” That does not entail or even imply “all times” is an infinite number of times. And if it is past finite (if there is no time before T = 0) it cannot refer to “an infinite amount of time ago.”

So whether there has been a finite or infinite amount of time ago is unresolvable on the facts at hand. No evidence exists to tell us which condition we are in. But my model works for either condition. On the “no prior time” condition, the zero point collapses into either no time at all (so there only ever is just one point of time and therefore nothing else comes to exist) or some extension of time (a universe). Logic then entails the latter is infinitely more likely. But there is always a finite time ago. On the “past infinite time” condition, the existential selection does not occur at “a” time; it collapses across all infinite time atemporally (as it must be decided what will exist, and “nothing ever exists” is one of the possibilities, but there are infinitely many “infinite timelines” that could exist instead, so it is infinity to one that one of them will exist instead of nothing).

As to whether “only if the B-theory of time is also true” that’s not true for the purpose here. A theory entails the same outcomes: if time has been running infinitely there was no first time and thus never a nothing-state, and in that condition, which infinite A series exists must have been existentially selected at random, and that entails some infinite A time series will be infinitely more likely to exist than no series at all and thus nothing existing at all; and if time started at some past point, what happened at A = 1 is entailed by random selection again, only this time at A = 1, and the selected timeline will proceed from there (in which case what is selected is a “rolling condition,” i.e. every future time’s contents is causally decided by its prior time’s contents, but all starting at the random selection of one set of contents at A = 1).

Dr. Carrier,

Thank you for answering my questions! Your responses clarified a lot for me.

I particularly liked the response to my question about Parson’s claims. In that answer, you use concepts such as (a) objective probability, (b) epistemic probability, and (c) arbitrary (probability). Another related concept that I’ve come across is (d) subjective probability. The way I’ve heard it, if we’re adopting the subjective interpretation of probability, we ought to be willing to say that different agents can have different values for their epistemic probabilities, even if the information available to them is the same. I.e., different agents can have different values for P(hypothesis/backround knowledge), even if the hypothesis and the background knowledge express the same propositions for all agents. In your response to my question, I think you contrast objective probability with epistemic probability rather than with subjective probability. Could you please explain the relationship among the four concepts I mentioned?

In my fifth question, I wrote that if spacetime must always exist, and the spacetime point briefly existed before anything else did, it would seem to follow that the spacetime point existed an infinite amount of time ago. You pointed out that this doesn’t follow. If it existed at all, it can’t have lasted more than a fraction of a second. Therefore, it logically necessarily will always exist a finite amount of time ago. The scenario I was thinking about is one in which the following claims are true: (a) spacetime must always exist, (b) the spacetime point didn’t come into existence without explanation/cause, and (c) the spacetime point’s existence was very brief. I thought this implied that the past is infinite. But since I was wrong, it must be the case that (d) the past is finite. The scenario in which (a), (b), (c), and (d) are all true seems possible to me, but only if the B-theory of time is also true. Would you agree?

Shouldn’t it possess information…

Everything possesses information. That is a logically necessary consequence of existing.

You may have been framed by Christian propaganda regarding the word “information” here. Information always attends existents, i.e. any time anything exists for any reason whatever, so does the corresponding information. Information is therefore not a mental object. It is just a set of physical facts. See Is God Needed for “Information” and “Laws”?

Are you referring to the spacetime point’s specified complexity?

Yes.

Fewer ontological facts are needed to describe or specify it.

If one asks, “But isn’t a zero infinitely specified?” they will be close to understanding the existential version of the argument (The Other Problem with Nothing): if absolute zero (total simplicity) is infinitely specified and therefore the least likely thing to be selected to exist, a random chaos is most likely to be selected to exist instead. My whole argument follows.

In truth every exclusive random possibility is infinitely specified, so their relative probabilities cancel out. Hence the net specified complexity of nothing becoming a random something is near zero. That’s why nothing cannot remain nothing. Because that would entail infinite specified complexity—just as selecting a God would. And that’s even assuming gods are logically possible (see The God Impossible).

If we replace the spacetime point with a spacetime volume the size of a particle (e.g., a proton), how much more complex would it be compared with the spacetime point?

Note that volume is relative. So you first have to specify what you mean by the size you are describing. If nothing else exists, relative volumes don’t exist, and so nothing “has a volume.”

In logical terms, however, a zero point contains only one geometric point. You can imagine a space that has only two geometric points, and so on. The complexity goes up with the number of points (exponentially, because the arrangements of those points are permutative).

Though whether that is even possible is in question, because there is a principle in topographical logics that as soon as there is any extension of space (any nonzero amount of it, no matter how small), it can be mapped to infinite distinct geometric points.

So, for example, if the zero point expanded to allow two points, that would actually create infinitely many points. For example, geometrically, a proton has infinitely many distinct locations inside its volume. So does a planet. That’s the funny thing about infinities: they are all equal in size (until you count permutations a la Cantor but that ends in the same insight: some infinities are larger than other infinities, but at each “size” of infinity there are infinitely many infinities the same size as each other).

So to specify a volume out of all possible volumes is really only marginally more complex than a zero point, because every nonzero volume has the same complexity, it’s just more complex than a zero point. When you start specifying structure within that volume (e.g. is the volume a proton or an electron or a rabbit or a planet or a universe) the specified complexity starts skyrocketing.

However, simple physical volumes, though they can have a huge specified complexity, will always have a vastly smaller specified complexity than a god. An empty volume of space awash with virtual particles is simpler than a rock of the same volume; a rock is simpler than the brain of a worm; the brain of a worm is simpler than the brain of a cat; the brain of a cat is simpler than the brain of a human; the brain of a human is simpler than future superintelligent computer; which is all necessarily simpler than a God brain. Ergo God’s mind has to have vastly more specified complexity than even a tiny nonzero volume of empty space.

When you get to cosmologies like Inflation, they trade on a simple nonzero starting volume that necessarily expands into a multiverse. One can say that the start point for Inflationary cosmology has a high specified complexity (there have been estimates; it’s huge, but nowhere near infinite), but a God has infinitely more. So the relative probability of an Inflationary bubble just existing for no reason is infinitely larger than that of a God just existing for no reason. Inflation is therefore infinitely more likely than God.

If it is the case that my logically-necessarily-unstable nothing-point existing for no reason is vastly (but not infinitely) more likely than Inflation owing to being so much simpler in its components, then Inflation would have to be an outcome of my model. But that still leaves us with Inflation as the most likely explanation of observations. God doesn’t even have a chance.

I think you’re saying that because humans use their brain (which is located in spacetime) to imagine or intuit things, they cannot imagine or intuit anything with no spatiotemporal location.

Correct.

As explained for disembodied minds (that’s in what you must have read by now), one cannot prove disembodied minds are possible by using an embodied mind to imagine one, because that remains only possible with an embodied mind (so far as you can observe).

So, too “existing nowhere.” You cannot prove “existing nowhere” is possible by imagining it somewhere (like in your mind, which has a location, in both space and time).

it would seem to follow that the spacetime point existed an infinite amount of time ago

That doesn’t follow. If it existed at all, it can’t have lasted more than a fraction of a second. Therefore, it logically necessarily will always exist a finite amount of time ago.

The only way to have a past eternal timeline is if there was never nothing (and thus never an absolute zero point). That is the existential condition that I treat in The Other Problem. It’s possible. No evidence currently can rule it out. So both models compete with God. And both models are vastly more likely than God. And they are roughly epistemically equally likely to each other (because we have no evidence at the moment to rule one more likely than the other).

the paradoxes that threaten the logical possibility of an infinite past can be resolved, but only by saying that the infinite past has no beginning.

Correct. That’s a tautology. To say “infinite past” is identical to saying “no beginning.”

Keith Parsons in which he expressed his skepticism regarding the use of probability theory outside empirical contexts

Which is often sound thinking. But not always. Because you can ramify a logical possibility space without making it exist empirically. In fact, all frequentist statistics used in all the sciences constantly do this (ramify counterfactual possibility space into distinct probabilities) in order to produce usable probabilities even with empirical data.

But one can reframe the Parsons objection differently: the problem is not that unempirical probabilities are meaningless or useless; the problem is that to claim something exists for which no data exists and vast data exists that lack it is to make an unramifiable claim. For example, we can empirically ramify the relative probability of all the causes of a plane crashing that we have observed (we have known data points of how often it’s pilot failure, mechanical failure, unavoidable collision, or weather event). But if you come in and say “I think a magical flying monkey flew into the cockpit and strangled the pilots,” you can’t even give us a fringe probability of that: its probability is unramifiable because we have no examples of any of the relevant things that evokes. All we can do is set an upper bound based on things we do know (e.g. monkeys probably don’t fly, magic probably doesn’t exist, etc.), and the end result is going to be an extremely small probability, so small as to render the claim moot on present evidence. But we can imagine an extraordinarily complex array of evidence being gathered sufficient to establish that such monkeys and magic do exist and do do that sort of thing. So the probability is not entirely inaccessible. It’s recoverable in the complexity and compound probability of the conjunction of things required for those monkeys to exist (the prior probability is simply the inverse ratio of the likelihood that would be sufficient to prove it).

I don’t think Parsons was well versed in Bayesian epistemology so he likely did not know any of this. He was just reacting to the consequential fact that unempirical probabilities are always going to be too small to matter and thus are usually foolish to argue from.

So, statements like probabilities “have no meaning at all when we leave behind any possible empirical context” are literally false, because you can specify a counterfactual model to replace the expected empirical context (you can simply hypothesize an empirical context), and in fact we necessarily do this all the time (especially in the sciences). I think what he was trying to get at (but lacked the resources to articulate specifically) is that hypothesizing highly convoluted and presumptious hypothetical contexts is simply foolish, because even insofar as it can be done (and usually people doing this are so lazy and noncommittal they don’t even do the specification required to derive a probability from), the result is always going to be useless: convoluted counterfactuals simply have vanishingly small probabilities and therefore are rarely worth the bother of considering. It’s a waste of time. And that is a thing Parsons said generally about philosophy of religion. He’s largely right about that.

“Whatever exists as the ultimate brute fact is neither probable nor improbable. It just is.”

That’s logically impossible. Parsons evidently did not think this through. There is always a rationally necessary ordering of any permutation space.

He is making the same mistake as the guy who said the LHC will destroy the Earth because it had a 50% chance of making a black hole capable of eating it, because “it either will or it won’t, therefore it’s 50%,” which is not how probability works. If the LHC can make a million different particles, they can’t each be 50% likely, because the sum of their probabilities must be 1. So the probability of making the expected kind of black hole has to be well below millions to one (in fact it’s far, far lower than that—almost as near to zero as the LHC spontaneously duplicating a whole cup of tea).

When you exhaust the logical possibilities in a set, and have no evidence favoring any over the other being the case, the probability of each is simply one divided by their number. That is a logically necessary fact. And that is a probability. And it won’t be 50%—unless there are only two things in the set (for a probability of either of 1/2), which would require those things to exhaust all logical possibilities, and for there to be no evidence (none whatsoever) making either more likely than the other.

What I think Parsons was reacting to is, rather, that when the possibility space is infinite or quasi-infinite (vast), and no evidence favoring any one possibility, necessarily no one can say one is more likely than another, nor that any one is even likely at all, only that there will be one—not which one. Which is correct.

If there are a million logically possible arrangements of hats in my closet, and you have no evidence favoring any arrangement, then the probability that you will find an arrangement of hats in my closet is 100%, but the probability that you will find a specific arrangement of them is a million to one against. So you cannot say, staring at my closed closet that any arrangement is more likely. Nor can you say any one of them is likely at all (they are all maximally unlikely). All you can say is that there will be one. Which is uninformative. That’s like saying, “There’s a 100& chance that there is either a god, or a million other things instead.” That leaves God maximally unlikely. Without arriving at any knowledge of what is the case. Both are true at the same time. Parsons is criticizing people who confuse this state of affairs as an argument for God being likely. It’s the opposite.

“I see no reasonable basis for assigning objective a priori probabilities to any posit.”

He is here confusing objective with epistemic probabilities.

But even with objective probabilities, there is always a logically necessary probability of every possibility given some set of information. So, for example, if the set of information is only “tautological information,” then every singular (not compound) possibility is equally likely. If there are infinite possibilities, each has a probability of infinity to one against. That’s still a probability. So I think he is confusing useless probabilities (like infinity to one) with no probabilities. But even infinitesimal probabilities have a mathematical system to them that can be analyzed. Science runs infinite sums of infinitesimal probabilities all the time. All frequentist calculus is doing that, in every study ever published.

“Any answer you give would seem arbitrary, or, I think, simply meaningless.”

This is closer to saying something correct. He is still confused. “Arbitrary” means selecting without reason (so, just “declaring” God has a 37% chance of existing is “arbitrary”). Rational ordering of probabilities in a permutation space is not arbitrary. But it can be described as “meaningless” if you are using that word over loosely. “Meaningless” usually refers to a proposition without content. But here he is using the word more like “an idea without utility.” For example “infinitely unlikely” is not meaningless (that has a definable content that can even be used in functional mathematics). But it is often useless. There is no way to claim an infinitely unlikely thing exists, unless you are admitting which infinitely unlikely thing exists was decided at random, and therefore cannot be a specific thing like “God.” Until you get enough evidence, but then you are outside what Parsons is talking about (as then you have some of the “nontautological information” he was excluding).

What do you think about Parsons’ comments, given that the spacetime point you call Nothing is an ultimate posit?

His remarks don’t have any applicability to my argument. My probability argument is rationally ramified. So it avoids all his concerns about uselessness or undefinability.

Dr. Carrier,

Thank you for replying to my comment and for providing the links for further reading!

I have read the sections you recommended, and I have also read The Problem with Nothing and The Argument from Non-Locality. Some of what you wrote is a bit difficult for me to understand. That said, I have a few questions I’d like you to please answer.

1. In the post Theism, Naturalism, and Explanatory Power, you say that Spacetime “knows” everything in the sense that everything that exists or happens does to its direct eyewitness, and everything that could be, can only be through some other arrangement of it; but as it has no mental properties of itself, it doesn’t know anything in the sense required by Howard and Alander.

Also, in the post The Problem with Nothing, you say that here we are just working out what must necessarily be the case if there was ever a state of total nothing, the most empty nothing logically possible. And that means such a nothing-state will be a hypersphere of zero size in all dimensions, with no contents, and governed by no rules or laws, except the laws of logical necessity.

By random chance alone, the spacetime point you call Nothing can spontaneously produce any logically possible thing, but it also has no contents. Shouldn’t it possess information about what it can spontaneously produce stored somewhere? (I don’t understand why spontaneous creation by random chance precludes the need for such information.)

2. At the end of The Problem with Nothing, you say that Nothing as here defined is unarguably far far simpler than God as an explanatory entity. Are you referring to the spacetime point’s specified complexity?

3. If we replace the spacetime point with a spacetime volume the size of a particle (e.g., a proton), how much more complex would it be compared with the spacetime point?

4. In the post The Argument from Non-Locality, you write that we can’t say “But I can imagine God existing nowhere,” because that statement will be literally false: to imagine anything at all, you have to use a brain, which has a location. It is logically impossible for you to imagine something without a location. You are always imagining things in a location.

Could you please expand on this? I think you’re saying that because humans use their brain (which is located in spacetime) to imagine or intuit things, they cannot imagine or intuit anything with no spatiotemporal location.

5. In the post The Argument from Non-Locality, you make the case that probably spacetime must exist in all logically possible worlds. According to the argument from Nothing, a spacetime point explains the existence of the universe we are observing. That point immediately changed into something else (most likely an infinite or quasi-infinite multiverse made of a random collection of universes). If spacetime must always exist, and the spacetime point briefly existed before anything else did, it would seem to follow that the spacetime point existed an infinite amount of time ago. Doesn’t this mean that the past is both infinite and had a beginning? To my knowledge, the paradoxes that threaten the logical possibility of an infinite past can be resolved, but only by saying that the infinite past has no beginning.

6. Before The Secular Frontier replaced The Secular Outpost, I read some comments by Keith Parsons in which he expressed his skepticism regarding the use of probability theory outside empirical contexts. Below are some of the things he wrote:

“[C]oncepts like probability, that have clear meaning in empirical contexts, have no meaning at all when we leave behind any possible empirical context […].”

“[W]hen we are talking about ultimate posits–whether God, the universe, or anything–we have no basis for assigning any prior probabilities at all. Whatever exists as the ultimate brute fact is neither probable nor improbable. It just is.”

“When you have prescinded from all possible empirical (nontautological) information, I see no reasonable basis for assigning objective a priori probabilities to any posit. For any h whatsoever, what is p(h), considered with respect to absolutely no background information at all? Any answer you give would seem arbitrary, or, I think, simply meaningless.”

“I think that in such circumstances, our thinking has become dialectical in Kant’s sense and that we are trying to employ the concept of probability out of any context that would give it meaning.”

Basically, the axioms of probability theory establish a formal model, but its applicability in given contexts is not determinable by the model itself. Therefore, we cannot take it for granted that the probabilities of ultimate posits will be determined by the principles we employ in empirical contexts (e.g., simplicity).

      What do you think about Parsons’ comments, given that the spacetime point you call Nothing is an ultimate posit?

Yeah. That appeared in Philo decades ago. It’s important for someone doing a dissertation on the topic but it’s largely obsolete for current debates.

This is for two reasons.

First, the current apologetical trend is to defend Swinburnian simplicity, which that paper does not address.

Second, current apologetics commonly conflates two different senses of simplicity to activate equivocation fallacies in this domain.

Ontological simplicity is not the same thing as epistemic simplicity. The latter is also known as “theoretical” simplicity and counts all the assumptions not proved in evidence that one must adopt to get a theory to fit the totality of evidence. An ontological simple can still be theoretically complex; and that matters for any attempt at Bayesian theology. See my discussion here. The trick often pulled is to insist on ontological simplicity (a feature not proven in any credible way, just presumed or insisted upon) and then claim that entails epistemic/theoretical simplicity which isn’t the case.

When we return to the first item, Swinburnian simplicity is an argument to ontological simplicity, but it is inherently fallacious, because it requires maximum specified complexity (a perfect and boundless mind), and tries to steal that in by supposing omnipotence would automatically produce it, but that’s a bootstrap error: you would need the perfect boundless mind to know how to reliably deploy boundless power to produce a perfect boundless mind, which is a chicken-egg paradox that can’t be logically solved. Whereas boundless power without a mind is simply nature (nature contains all possible things as potentials and thus contains all powers, it just can’t activate them all, or any of them intelligently, because it is mindless).

Which is why the debate between atheists and theists is really a debate over whether the ground of all being has thoughts and feelings or not. And there is just no logically valid way to get “thoughts and feelings” to be ontologically simple.

I cover aspects of this in various places. You are already at one of them here (The Argument from Specified Complexity against Supernaturalism). But also read Swinburne’s Absurdly Complex Simplicity (which is mainly about the epistemic problem but does discuss its relation to the ontological problem), and then my discussions under Explanatory Power: The Other Weird Argument from Trope Theory followed by The Logical Entailment of God’s Properties.

This post is a worthy contribution to the debate about God’s simplicity. As I was reading it, I remembered a paper by Graham Oppy that I read a few years ago: The Devilish Complexities of Divine Simplicity. Perhaps you read it as well, but in case you haven’t, Oppy actually defends the doctrine of divine simplicity with an account based on a truthmaker theory.

The article is freely available:
https://www.academia.edu/23446298/The_Devilish_Complexities_of_Divine_Simplicity?sm=b&rhid=42392055981

If you have read it or will at some point, please let me know your thoughts on it. Thank you!

Thanks for pointing this out so quickly!

Last update of WordPress deprecated the original code affecting earlier articles. I fixed this one (so it should work now) but likely there are others, I’m checking now.