Creation, Probability and Something for Nothing? Part V

 Let's Carry on Carriering Part V

This is my continuing critique of an article by commercial historian and unquenchable blowhard Richard Carrier. In his article Richard believes he has used probability calculus to show that "No god [is] needed" to create a universe. Well, in this instance there is no need for me to argue either for or against atheism; for the purposes of this post it is sufficient for me to show that Richard's misunderstanding and mishandling of probability and randomness hamstrings his polemic completely.  In Part II I pointed out where his argument comes off the rails and from that point on he constructs a teetering house of cards. 

The other parts of this series can be found here....

Quantum Non-Linearity: Let's Carry on Carriering Part I

Quantum Non-Linearity: Let's Carry on Carriering Part II

Quantum Non-Linearity: Let's Carry on Carriering Part III

Quantum Non-Linearity: Let's Carry on Carriering Part IV

On the whole Richard started his article well. In the first part of this series we saw Richard defining what he referred to as Nothing; note the capitalized N. Richard tells us that this kind of Nothing is what you are left with when all mere logical contingencies have been removed and one is left with a bare minimum of logical truisms, truisms which can't be removed without logical contradiction. I had no problems with this proposal. I also agreed that many of the classical "proofs" for God's existence are very dubious to say the least.  But I noted that Richard said nothing about the actual content of this exotic and mysterious placeholder he calls "Nothing" and I went on to say that this omission allows theism to slip in by the back door. Richard might have attempted to lock and bolt the front door but he's left the back door wide open. However, for my current purposes there is no need for me here to smuggle in God using "back door theism" because my focus is on his foundational logical errors, errors which bring his house of cards crashing down, never mind that he's actually failed to even lock the front door.

Let me finish this opening section with this: As I might have said before, theism, particularly Christian theism, is at the very least a mythological world view which for me is the abductive narrative making a whole lot of retrospective sense of an otherwise very perplexing and meaningless world. Moreover, it provides compelling insights into the human predicament; for me personally it is a successful "Weltenschauung"  (world-view) which is actually more than mythology; it is mythology++. However, we must concede that world-views attempt to encompass and synthesize a very wide field of proprietary experience and unique personal histories and therefore Worldview analysis is a rather subjective and contentious business on which the agreement theorem hits the rocks.

Although I would recommend Christianity to atheists even if they are to regard it as only a compelling mythological world-view, I nevertheless respect and understand their perspective given the cosmic context which has developed in our consciousness since the enlightenment  ...although I have little sympathy with the kind of flawed and triumphalist polemic we get from Richard Carrier. 

***

RICHARD: Probability of Something from Nothing. Proposition 8 holds that “when there is Nothing,” then “every possible number of universes that can appear has an equal probability of occurring,” and Proposition 9 holds that therefore “the probability of Nothing remaining nothing equals the ratio of one to n, where n is the largest logically possible number of universes that can appear.” We can therefore calculate limits on how likely it is that something would exist now, given the assumption that once upon a time there was Nothing—not a god or quantum fluctuation or anything else, but literally in fact Nothing.

MY COMMENT: I've already covered propositions 8 and 9 in part IV but I'll outline again Richard's two main embarrassments here. 

In the above Richard has assumed that if he is given a probability this implies he has in his hands an objective source capable of randomly creating outcomes. This is an error on at least two counts as we will see. I can, however, accept  this:

Proposition 8 holds that “when there is Nothing,” then “every possible number of universes that can appear has an equal probability of occurring,”

But then this doesn't follow:

Proposition 9 holds that therefore “the probability of Nothing remaining nothing equals the ratio of one to n, where n is the largest logically possible number of universes that can appear.”

As I remarked in the previous parts, probability is an intelligible concept only if one first assumes the existence of an observer who is able to form an enumerated (or denumerated) ratio of what are believed to be logical contingencies. That is, probability presupposes the existence of a self-aware observer cognitively sophisticated enough to express information in terms of Laplace's classical probability quotient. For example, in proposition 8 we really haven't got a clue as what this mysterious object or entity called Nothing is likely to create, if anything at all. Therefore Richard is right in suggesting that in the absence of any further information “every possible number of universes that can appear has an equal probability of occurring,” Well, as I know Richard himself realizes it's going to be quite an intellectual challenge denumerating all the possible universes in order to return a Laplacian probability ratio here, but the principle entailed is apparently coherent and comprehensible; for as far is our quantified ignorance is concerned we are left with a ratio of 1 to n where n is clearly some huge number. 

But between the two propositions 8 & 9 there is a serious logical fallacy. The probability ratio of 1 to n pertains to an observer's subjective information level and not some potential creation dynamic which pertains to Nothing. Moreover, this probability is conditioned on our complete lack of knowledge as to which logical contingency of the n possibilities which Nothing, so called, will "choose" to create. Those apparent possibilities includes any number of n universes where n actually includes the "null" universe; that is, the universe with nothing in it. On this basis Nothing, so called, sounds like a pretty sophisticated object; don't you think Richard? (Arguing that with Nothing there is nothing to stop it creating something can be turned on its head: Viz: There is nothing to stop Nothing remaining as Nothing; this kind of polemic is just informal verbal sophistry!)

Well, we know that Nothing didn't create the null universe so on the basis of these informational conditions the probability of the creation of a particular universe,  which I shall call U_p, can be symbolized by:

Prob(U_p/E) = 1/(n-1)

....where E is the information condition that a universe is known to exist, although at this stage we don't know which particular universe exists. Now, assuming we know which universe of the n-1 possible universes has been created (because we can look out and observe it) then n = 1. Therefore on these updated informational conditions... 

Prob(P_u/E) = 1/1 = 1 !!!

...which only goes illustrate just how conditional probabilities are upon observer information. For the very reason that probability is a measure of observer ignorance it is an entirely incoherent move to then try to use it to impute a creative dynamic to an object such as Nothing of which we know very little.  Probability in and of itself is not a creative dynamic; rather it concerns our knowledge or lack of knowledge about the object in question. 

What is very clear is that whatever Prob(P_u/E) works out at we have no logical right to infer that Nothing will consequently generate universes at random....along such lines, I suspect, Richard is thinking. A quantified probability does not imply randomness, although the reverse is not true ....the patterns of randomness often entail probability because these patterns are so algorithmically complex that they are from a human angle, practically unknowable in succinct algorithmic terms. Therefore random outcomes can usually only be expressed in terms of probabilities (Unless we've got a book of randomly generated numbers which we've memorised!).

***

RICHARD: Assume that only the numbers 0 to 100 exist, and therefore 100 is the largest logically possible number of universes that can appear. In that event, the probability that Nothing would remain Nothing (the probability of ex nihilo nihil) is 100 to 1 against. There being 101 numbers, including the zero, i.e. the continuation of nothing being the condition of there arising zero universes, and only one of those numbers constitutes remaining nothing, then there are 100 times more ways for Nothing to become something, than to remain nothing. And when there is Nothing, there is nothing to stop any of those other ways from materializing, nor does anything exist to cause any one of those ways to be more likely than any of the others.

It is therefore logically necessarily the case that, if we assume there was ever Nothing, the probability of ex nihilo nihil is less than 1%.

Of course, 100 is not the highest number. Go looking, you won’t find a highest number. It is in fact logically necessarily the case that no highest number exists. So really, the probability of ex nihilo nihil is literally infinitesimal—infinity to one against. One might complain that we don’t really know what that means. But it doesn’t matter, because we can graph the probability of ex nihilo nihil by method of exhaustion, and thus see that the probability vanishes to some value unimaginably close to zero.

MY COMMENT: Here we go again. Richard has projected his otherwise coherent probability examples onto the cosmos as if they entail a creation dynamic. This is very apparent in these sentences.....

In that event, the probability that Nothing would remain Nothing (the probability of ex nihilo nihil) is 100 to 1 against.

It is therefore logically necessarily the case that, if we assume there was ever Nothing, the probability of ex nihilo nihil is less than 1%.

So, according to Richard he can project what is in fact a purely subjective measure of information (i.e. probability) onto this mysterious big deal he calls Nothing and then come up with the conclusion that Nothing will very likely create a universe! This does not follow because those probabilities reside in his observer's head; those Laplacian ratios don't reside "out there". 

***

RICHARD: We therefore do not need God to explain why there is something rather than nothing. There may also be something rather than nothing simply “because there just is.” There isn’t any actual basis for assuming “nothing” is the natural state of anything, or that there has ever really been nothing. We could honestly just as fairly ask why should there be nothing rather than something. No God is needed here. But even if we are to presume that there ever once was Nothing, we still need no further explanation of why then there is something. Because that there would be something is then as certain an outcome as makes all odds.

Formally:

·         If Proposition 1, then Proposition 2

·         If Proposition 2, then Proposition 3

·         If Proposition 3, then Proposition 4

·         If Proposition 4 and Proposition 1, then Propositions 5 and 7

·         If Proposition 5 and Proposition 1, then Proposition 6

·         If Propositions 5, 6, and 7, then Proposition 8

·         If Proposition 8, then Proposition 9

·         If Proposition 9 and Proposition 1, then the probability that Nothing would produce something is incalculably close to 100% and therefore effectively certain to occur.

   MY COMMENT:  Well OK let's run with the idea that "We do not need God to explain why there is something rather than nothing", whatever Richard means by "God" in this context. But according to Richard we do need two other things:

    Firstly, of course, we need this enigmatic entity called "Nothing". But all we know about Nothing is that it is the irreducible logical truism left when all logical contingencies/possibilities have been eliminated; according to this account trying conceive absolutely nothing is in fact a contradiction (I suspect that's true). That word "Nothing" however, is a place holder for what may well be a very exotic truism capable of creating who knows what.  Fair enough Richard, this point of yours has a good feel about it as far as I'm concerned.

    But secondly, Richard is asking us to accept his very logically dodgy maneuver involving the projection of subjective probabilities onto Nothing and then assuming that this is sufficient to give Nothing a dynamic with creative potential. Well yes, Nothing may well be sophisticated enough to be creative (in fact as a Christian I believe this entity is creative) but to suppose that human ignorance somehow projects that creative potential onto Nothing is not the way to argue the case! It's a bogus argument. And I say it yet again; probabilities pertain to a measure of observer ignorance and don't create anything.

  But if I'm understanding him aright Richard does have a fallback position which I can respect: He says above "There may also be something rather than nothing simply “because there just is.”. That is very reminiscent of this post of mine on Galen Strawson where I quote Strawson suggesting that the universe "just is"; that is, it's just brute fact and to hell with abductive mythologies like Christianity which bring sense, purpose and meaning. If you simply find it impossible to believe that some kind of personal God has created our kind of universe with its all too off-putting human predicaments and suffering, then I have sympathy with that response. But I'm not sympathetic with Richard's cack-handed logic pushed through with self-recommending claims about his intellectual authority. Self-praise is no recommendation.

****

    As we've seen in the previous parts of this series the logic of Richard's list of connected propositions is OK up until about proposition 5 when his analysis really goes off the rails as he hits the question of probability and randomness. In the above Richard talks about not needing God. But whatever he means by God in this context, the creative potential he allocates to Nothing is startling to say the least and it looks suspiciously god-like. In particular if Nothing's creative powers extend to the capability of generating patterns of randomness that in itself is a pretty god-like trait: First and foremost random patterns are contingent - they have no logical obligation and there is no known logical contradiction entailed by their non-existence. Secondly, if we are talking algorithmic generation, randomness of varying degrees entails either very long and complex  algorithms or very large generation times or a combination of both.  In the ideal mathematical limit of pure randomness one or both of these two features extend to infinity.

    If Richard is trying to tell us that the creative source he calls Nothing is in fact a generator of genuinely random patterns then I think we are clear what Richard Carrier's god looks like. 

 

****

.....to be continued...? 

    There are still some remaining paragraphs to consider in Richard Carrier's post but as far as the thrust of my criticism is concerned his closing passages will entail just more of the same kind of critique; that is, criticism of his fallacies revolving round his misconceptions about probability and randomness. So, I may or may not finish the series depending on how I feel and whether I consider it to be time well spent....I'll see.

   CAVEAT

   Disagreeing with Richard Carrier on the above issues should not be taken as a sign that I identify as being a member of some polar opposite tribe. For example, it is likely that I agree with him on many issues particularly when he is criticizing the hard-right. 

Let's Carry on Carriering Part IV

In this post I continue analyzing a web post by self-recommending professional atheist Richard Carrier. 

The other parts of this series can be seen in the links below:

Quantum Non-Linearity: Let's Carry on Carriering Part I

Quantum Non-Linearity: Let's Carry on Carriering Part II

Quantum Non-Linearity: Let's Carry on Carriering Part III

Before going on with the rest of Richard's post, below I recap Richard's proposition 8 and comment on it again.

***

RICHARD: Proposition 8: If every logically possible thing that can happen to Nothing has an equal probability of occurring, then every logically possible number of universes that can appear has an equal probability of occurring.

This is logically entailed by the conjunction of Propositions 6 and 7. So again it cannot be denied without denying, again, Proposition 1.

MY COMMENT: In the above quote Richard is telling us that given this entity he calls Nothing we can infer that every logically possible universe that can arise from Nothing has an equal probability of occurring. As I have said in the previous parts, probability isn't a property of the object we are taking cognizance of (in this case the object is Nothing) but a function of the observer's level of knowledge about an object; the negated way of saying the same thing is that probability is a measure of the observer's ignorance. In the above, therefore, Richard is merely telling us that he has no idea what Nothing is capable of generating and that all logically feasible bets are therefore of equal probability; this equality correctly follows from the principle of equal a priori probabilities, a principle which applies to any observer who has no information which leads him/her to expect one bet over another. In this instance one of those bets includes whether or not Nothing will generate the high contingencies and complexities of random patterns. Because Richard is admitting that he knows 0.0% of nowt about Nothing these observer-based betting odds say nothing at all about what Nothing will actually generate. 

I will now continue analyzing Richard's post from where I left off in the last part (Part III).  From this point on his work is a teetering tower of endeavor with its foundations resting upon the implicit assumption that probability is a physical property which he also assumes must logically entail a totally random process; that is, a process which generates random patterns. 

***

RICHARD: And this is true regardless of the measure problem. There are lots of different ways you can slice up the “outcome” of a totally random process that’s unlimited in how much can happen—how much “stuff,” and in how many configurations, that can arise. But insofar as the “stuff” that pops out is connected to other stuff, it necessarily causally interacts with it, and that logically entails a single causally interacting “system,” which we can call a “universe” in a relevant sense. But when there is Nothing, nothing exists to make it even likely, much less ensure, that only one such “universe” will randomly materialize.

Of course, even within a single causally interacting “system,” (= a "universe") and thus within a single “universe,” it is not necessarily the case that every part of it will have the same contents and properties. Eternal inflation, for example, entails an initial chaotic universe will continue splitting off different bubble universes forever, and everyone will have different laws, contents, and properties, insofar as it’s possible to. And this is actually what we usually mean by “universe” now: one of those regions of the whole metaverse that shares a common fundamental physics (the same dimensionality of spacetime, the same fundamental constants, and the same causal history). Other regions may differ, e.g. if we fly far enough in space, maybe a trillion lightyears, we might start to enter a region of the universe where the laws and constants and shape and contents start to change.

MY COMMENT: Probabilities are defined in terms of ratios of sets of possibilities: The measure problem concerns the difficulty observers have in defining probabilities when trying to form ratios from ill-defined sets of possibilities, particularly potentially infinite sets of possibilities. If one is faced with sets of possibilities for which it is not easy to define clearcut size comparisons, then calculating probabilities (which are based on ratios of possibilities) becomes problematic. In this instance Richard is discussing the question of what class of possibilities constitutes what we would like to call a "universe" and how we measure the probability of a "universe" against the immense set of "all" possible universes. The comparison of these spectacularly vague and huge sets and the accompanying calculation of the relevant probabilities are sensitive to the methods of comparison.  (See here). 

At the start of the above quote Richard is telling us that his proposition 8 isn't affected by the measure problem; well, that may be true: For his purposes it is often enough to show that one set is  clearly much, much larger than another thus implying that the probability in question is all but zero and therefore its negated probability is all but unity. But for Richard to take us any further one first has to swallow his two seemingly unconscious assumptions: Viz:

1. That probabilities are an intrinsic property of an object when in fact they are an observer relative extrinsic property in so far as being a function of an observer's knowledge about an object. 

2. That the existence of a probability necessarily implies something capable of generating random patterns (certainly not true!).

Regarding assumption 1: Going over the point I have repeatedly made: The one-on-one element-by-element comparison between two sets needed to create ratios of possibilities and underwrite the calculation of the probability of a universe is only intelligible if we first assume, a priori, the existence of highly sophisticated third person observers for whom probability ratios (which are a measure of observer information level) are meaningful and interesting. Without the assumed existence of sufficiently cognitively sophisticated observers, probability is an unintelligible notion. Probability is not a property of something "out there" whether of universes or other; it is a measure of an observer's information about the object in question.

Regarding assumption 2:  That this seems to be some kind of habit of mind is more than hinted at when Richard says in the above quote about “the stuff” that pops out which presumably is the “outcome” of a totally random process. However, to be fair to Richard it is true that the term "probability" is often used as a metonym for randomness because the algorithmic intractability of random patterns makes them difficult to know and therefore random patterns very often entail a probability.  One of Richard's pratfalls is that I think he's conflated the use of the term "probability" as a metonym with the object it is frequently associated with (i.e. random patterns). As we will see, given a probability he wrongly infers that he has in his hands a random generator of universes; a non sequitur if there ever was one. 

***

RICHARD: However, we needn’t account for this in what follows. If it is the case—in other words, if universes in the broad sense (causally interacting systems) can themselves contain even more universes in the narrow sense (regions of a shared fundamental physics), then what follows, follows with even more certainty. Because then there are even more “universes” to make the point with. You will notice eventually how this simply makes the math even stronger, and gets us to the same conclusion with even greater force. Because all adding this does to the math, is increase how many universes a Nothing will inevitably randomly produce.

MY COMMENT:  If for the sake of argument we allow Richard's two assumptions above to slip past us then it's true that the measure problem doesn't affect his conclusion: Although we may be unable to come up with the rigorously correct ratios of possibilities it is often clear that the sets of possibilities Richard is comparing are obviously vastly different in size and so it is clear that the probabilities concerned are as near as can be to either 100% or 0%.

But the conclusions Richards draws from this exercise of probability calculation are based, once again on the falsehood I've emboldened at the end of the above quote: Viz: Richard thinks he's proved to himself that the logical truism he calls Nothing will inevitably randomly produce...“stuff” that pops out.

Richard's argument is that if we do at least know we are dealing with huge numbers of possible universes this is only going to add more grist to his mill by feeding his gluttony for immense numbers of possible outcomes. But unfortunately for Richard there is no wind or water to drive his mill: As we can see from his last sentence above, he's assuming that observer-defined probabilities necessarily entail a random pattern generator which he is hoping will drive his system of universe creation. Well, whatever complex logical necessities Nothing contains one thing is clear; the generation of random patterns is not known to logically follow from the Unknown and Mysterious logical necessity Richard calls "Nothing" and about which Richard can tell us very little. And again: The generation of random patterns doesn't follow as a logical necessity from observer defined probabilities whether those probabilities are calculated correctly of not.

Richard's misconceptions around probability and randomness are continuing to run through his thinking.  He needs to revisit his bad habits of mind about probability and randomness. 

***

RICHARD: The converse is also true. If it is somehow the case that there can’t be disconnected systems, that somehow it is logically impossible for Nothing to produce multiple “universes” in the broad sense, then it must necessarily be the case that it will produce, to the same probability, multiple universes in the narrow sense. Because there is only one possible way left that it could be logically impossible for both (a) Nothing to produce more than one causal system and (b) that system be entirely governed by only one physics, is if this universe we find ourselves in is the only logically possible universe. And if that’s the case, then we don’t need any explanation for it. All fine-tuning arguments sink immediately. The probability of any universe existing but this one (given that any universe exists at all) is then zero. And the probability of fine tuning without God is then exactly and fully 100%.

MY COMMENT:  A largely Valid point here: Richard is admitting that Nothing is such a big Unknown that it is conceivable that by some logic we don't yet understand Nothing entails that only one causally connected universe can exist and that this is the universe we observe (if perhaps only a small part of a much broader causally connected universe). But I doubt he'll bite this bullet: His concept of Nothing is his subliminal stand in for "The Unknown God" in so far as this mysterious Nothing somehow implies the highly organized universe we see around us. 

***

RICHARD: I doubt any theist will bite that bullet. I’m pretty sure all will insist that other universes are logically possible. 

MY COMMENT:   Theist or not I think we can be agnostic about whether or not other universes are logically possible. After all we know so little about this mysterious entity which Richard keeps calling "Nothing"; we don't even know if the logic of Nothing rules out cosmic configurations that otherwise to us seem logically possible. 

***

RICHARD: And if other universes are logically possible, it must necessarily be the case that it is logically possible either for different regions of a universe to exhibit different physics or different universes as closed causal systems to exist (with, ergo, different physics). Therefore, by disjunctive logic, if the second disjunct is ruled impossible (“different universes as closed causal systems can exist”), the first disjunct becomes a logically necessary truth (“different regions of a universe can have different physics”). Even if one were to say “there are infinitely many outcomes logically equivalent to a single universe with a single uniform physics” and “therefore” there are as many such outcomes as any version of multiverse and so “it’s fifty fifty” or “the measurement problem gets you” or whatever, Cantor strikes: as all the infinite such possible universes are already contained in possible multiverses and yet there are infinitely many more multiverses possible which cannot be included in the previous infinite set, the cardinality relation of possible multiverses to possible singleverses is still infinitely more; ergo, the probability of getting “a singleverse” rather than “a multiverse” is infinity to one against.

MY COMMENT:    Yes, I agree the number of possible multiverses, if compared against the number of possible singleverses, will be infinitely greater.  But if this relationship is to be transformed into a probability as per the last sentence (Viz the probability of a singleverse against a multiverse) Richard once again must assume the pre-existence of a sufficiently sophisticated observer to make the calculation of his probability meaningful. But Richard's logic here although valid is irrelevant; these observer relative probabilities imply nothing about what Richard's "Nothing" will in actual fact generate. 

***

RICHARD: Therefore, when there are no rules governing how many “universes” can randomly arise from Nothing, there must necessarily be either a random number of universes in the broad sense (causally separated systems) or a random number of universes in the narrow sense (regions of different physics within a single causal system), or both. Including, of course, the possibility that that number, either way, will be zero. Which is what it would mean for Nothing to produce nothing, to remain eternally nothing. Ex nihilo nihil, in other words, is simply describing one possible outcome of a true Nothing: the outcome of there being zero things arising.

But as we just confirmed, there is no rule or law that entails the number of things that will arise uncaused from Nothing is zero. In fact, zero is just one possibility out of countless other possibilities: countless other numbers of things, and thus universes, that can arise. And Proposition 6 entails each possible outcome has the same probability as each other possible outcome. Which means no outcome (such as “zero”) is more likely than any other (such as “one” or “ten billion” or “ten to the power of twenty trillion”). Hence, Proposition 9....

MY COMMENT:   And again, the bulk of the deliberations above are irrelevant. Richard's attempt to make numerical comparisons between classes of possible universes and thus arrive at one or other end of the probability spectrum is futile without building in his two hidden prior assumptions: To repeat: 1. The a priori existence of a sufficiently sophisticated cognitive perspective to make the probability calculations meaningful 2. In this particular connection, the a priori existence of the super contingency of random pattern generators to a give meaningful hook to the observer's probability calculations.

That Richard's "Nothing" is a huge Unknown to him is evidenced by the fact that above we find him considering the case where, for all he knows, Nothing has no known rules to limit the classes from which probabilities can be calculated. He then, yet again, wrongly thinks that from these probabilities he can logically infer a random pattern generator.  Moreover, random pattern generation is a rule in itself which contradicts any notion that Nothing has no rules. 

***

RICHARD: Proposition 9: If when there is Nothing every possible number of universes has an equal probability of occurring, the probability of Nothing remaining nothing equals the ratio of one to n, where n is the largest logically possible number of universes that can occur.

MY COMMENT:  Given that our Richard is admittedly working completely in the dark as to what the logic of Nothing entails then given such an advanced state of ignorance it is true that every possible universe has an equal probability of being generated by Nothing; and this includes the possibility of literally nothing being generated by Nothing. Well, there is only one way to generate absolutely nothing, so therefore Richard is right in telling us that the probability of nothing is 1/n, where n is the largest logically possible number universes that can occur. But yet again: We can't move from this state of hyper ignorance, expressed as a probability, to the conclusion that from this ignorance we can then infer a random generator of universes is at work. The quantified ignorance expressed by a probability evaluation tells us nothing about what Nothing will actually generate, least of all whether it will generate the hyper-complexities of random patterns.

***

RICHARD: But Proposition 6 entails n is transfinite. There is no maximum possible universes that can arise. This creates difficulties for continuing mathematically here, because no one has fully worked out a mathematics of transfinite probability. We can bypass that problem, however, the same way Archimedes originally did, by adapting the Method of Exhaustion. We’ll get there in a moment.

MY COMMENT:  No dispute that n is transfinite. But you bet there's going to be huge difficulties in defining intelligible probabilities here because measure problems make the definition of coherent ratios of possible universes highly problematic. But let's wait see what Richard's method of exhaustion entails. Something to look forward to in Part V.  

***

RICHARD: Proposition 10: If Nothing produces a random number of universes, nothing exists to prevent the contents of each of those universes from being equally random.

In other words, if it is logically possible for any universe, upon coming into existence, to have a different set of attributes than another, then each possible collection of attributes is as likely as every other. This follows by logical necessity from the absence of anything that would make it otherwise. And Nothing lacks everything, including anything that would make it otherwise. To deny this Proposition therefore requires producing a logical proof that some logical necessity makes it otherwise. Good luck.

MY COMMENT: Richard has not established that Nothing generates universes at random. All we've seen is that from the carefully measured human ignorance expressed as probabilities he's then assumed that this mysterious object he's called Nothing at least has the possibility of generating the high contingencies & complexities of randomness.  In fact in the above he does venture to assert something about Nothing; that is, that Nothing lacks everything, including anything that would make it otherwise. And yet he's somehow inferred that if Nothing produces a random number of universes, nothing exists to prevent the contents of each of those universes from being equally random. That is, he's allowing Nothing the possibility of generating the highly sophisticated complexes of random patterns. He has inferred that a lack of logical restriction logically entails the possibility of random patterns being generated. So, Richard where's the logical proof that there is some logical necessity which allows Nothing the possibility of generating these high contingencies? Good luck with that one Richard!

...to be continued

Let's Carry on Carriering Part III

In this post I continue analyzing a blog post by super-duper, self-recommending professional atheist Richard Carrier. 

For most of the last two parts of this series (See Part I and Part II) I was actually getting on quite well with Richard's post titled The Problem with Nothing: Why The Indefensibility of Ex Nihilo Nihil Goes Wrong for Theists • Richard Carrier Blogs

I probably agree with Richard in so far as agreeing that many theists have muffed their arguments re. the existence of God. For example: The cosmological argument, the ontological argument, the fine-tuning argument, the Kalem argument, the first cause argument, the moral argument etc are for the most part polemical bodges.  In fact, we can drop all those arguments in this particular connection as my terms of reference are restricted to a critique of Richard's post; in my opinion his arguments as to the ultimate source of the cosmos are no less bodged than those arguments for God I've listed. (And I say that as Christian myself; for me theism is a retrospective sense making abduction)

As we saw in Part II crucial to Richard's argument is his concept of "Nothing", that is "Nothing" spelt with a capital N. "Nothing" is the hard kernel of irreducible logical truisms that you are left with when you've subtracted all logical contingencies; that is mere logical possibilities. It's unfortunate terminology that he's called it "Nothing" because as we saw in Part II it is clear that Nothing is in fact Something and a very sophisticated Something at that! This is clear because to create Richard's much desired randomness a very sophisticated source of creation is required. Other than that, however, Richard doesn't and probably can't give us much detail about just what constitutes Nothing (= Something). I can go along with Richard's identification of this mysterious irreducible Nothing (= Something). Moreover, it seems that this Something is the origin of our apparently highly contingent universe with all its ordered and random complexities. Wow!

But in the second half of Part II, it became very clear to me that as he developed his reasoning our Richard, in his enthusiasm to debunk theism, is utterly unaware that he goes completely off the logical rails. The consequences of the resulting train cash are then felt throughout the rest of his post. As we get to his Proposition 7 he continues to consolidate his error....

***

Richard: Proposition 7: If nothing (except logical necessity) prevents anything from happening to Nothing, then every logically possible thing that can happen to Nothing has an equal probability of occurring.

Every logically possible thing that can happen to Nothing is as likely to happen as every other possible thing that can happen. This is a logically necessary truth. So it again cannot be denied without denying Proposition 1. Or, again, Proposition 4, if you want to desperately wrestle again with what it means for Nothing to be ungoverned by any rules about what happens—but you’ll lose every time; because that’s what Nothing logically entails. So the only way out left is to go all the way back to becoming one of those whackadoos who deny Proposition 1. Good luck with that.

My Comment: Well, as I said in Part II, I would want to enthusiastically embrace Proposition 1 and Proposition 4, but as I also said in Part II, I certainly wouldn't accept Richard's interpretations which he goes on to construct upon these propositions. 

As we've seen Nothing (= Something) is a very mysterious object, and Richard isn't elaborating it. That's fair enough though; we are all a bit in the dark about the Unknown God Something that is the origin of the universe. Richard acknowledges the existence of this Big Unknown in his entirely acceptable Proposition 3 where he says If there was ever Nothing, then nothing governs or dictates what will become of that Nothing, other than what is logically necessary.  Whatever the Big Unknown is it must be logically necessary.

But, and here's the kicker, in the above courier font quote Richard also tells us: 

if you want to desperately wrestle again with what it means for Nothing to be ungoverned by any rules about what happens—but you’ll lose every time; because that’s what Nothing logically entails.

Now compare that statement with Proposition 3 where we read If there was ever Nothing, then nothing governs or dictates what will become of that Nothing, other than what is logically necessary. Notice the difference? Richard has suppressed that Big Unknown; namely, "what is logically necessary". Clearly Nothing is governed by rules; that is the rules of logical necessity, whatever they may be. He also tells us above what he thinks one of those logical rules governing Nothing might be: Viz: 

Every logically possible thing that can happen to Nothing is as likely to happen as every other possible thing that can happen. This is a logically necessary truth.

That is, Richard is trying to get past us the very questionable notion that equal a priori probabilities is a truism from which he can then deduce a dynamic which leads to every possible happenstance that can happen (presumably at random) at some point or other. But as I said in Part II, probability only coherently pertains to observer information about possible happenings. It is therefore contingent upon the existence of an observer whose information may vary from other observers; that is, equal a priori probabilities is an observer relative feature. Moreover, observers able to compute ratios of possibilities (which is how probability is defined) are necessarily very sophisticated entities, entities about which it is unclear whether they are logical necessities or not; certainly, when it comes to individual human observers it seems we are not talking logical necessity.

Richard then jumps from that error to another error: Viz: That of assuming that once one has a probability, it implies a dynamic about what then actually happens: I suspect he is thinking "randomness" here; randomness is a configurational object which does in fact display a highly complex form of contingency rather than being a logical necessity. Moreover, as we saw in Part II randomness does not necessarily follow from an observer relative probability. 

In noting these logical errors there is no need to deny Proposition 1 as Richard's whackdoos do. 

***

Richard: In case it’s not obvious, here is why Proposition 7 is logically necessarily the case:

1. For any one possible thing that can happen to Nothing to be more probable than another, some rule, property, or power would have to exist to make it so.

2. By definition Nothing contains no rules, properties, or powers.

3. Therefore, no rule, property, or power would exist to make any one possible thing that can happen to Nothing more probable than another.

4. Therefore, no possible thing that can happen to Nothing can be more probable than another.

So accepting Proposition 1, and thus Proposition 2, you must accept Proposition 7. As Proposition 7 merely states what is logically necessarily the case when 1 and 2. And 1 and 2 entail that that which is logically necessarily the case must always obtain whenever there is Nothing.

My Comment: The foregoing is utterly incoherent. Richard is trying to tell us that Nothing has no rules and yet he has admitted that it is constrained by what is logically true (fair enough) and then goes on to identify what he thinks to be one of those logical truths : Viz equal a priori probabilities (which isn't a logical truth and is observer relative) and then wrongly logically connects this with a dynamic with the ability to generate contingencies (at random?). So again, whilst we can enthusiastically embrace propositions 1 and 2, I must reject proposition 7 which is a fanciful invention of Richard's imagination and is certainly not a logical truism. 

In his proposition 8  Richard continues to build his house of cards.....

***

Richard: Proposition 8: If every logically possible thing that can happen to Nothing has an equal probability of occurring, then every logically possible number of universes that can appear has an equal probability of occurring.

This is logically entailed by the conjunction of Propositions 6 and 7. So again it cannot be denied without denying, again, Proposition 1.

My Comment: That's Richard's continued abuse of probability for you! As I've said probability is not logically fundamental or axiomatic.  For probability to be an intelligible concept one must first posit observers sophisticated enough to construct and understand ratios of possibilities. And again, Richard wrongly assumes that probability logically entails the dynamics of random happenstance. So, as with proposition 7, in his botched enunciation of proposition 8 Richard finds himself up a creek without a paddle. He tries to pressure our acquiescence to this nonsense by the intimidating suggesting that if we don't accept it then we commit the cardinal logical sin of not accepting proposition 1. And I thought it was only cult leaders like Ken Ham who try to intimidate! 

***

Richard's suggestion as to the potential source of the cosmos is beginning to look suspiciously like the passe notion of a random generator as the source of the cosmos and that we necessarily exist in what by chance is a very ordered part of that immense maximally disordered cosmos. I'm not going to be too hard on him here because this common fanciful invention of the imagination, which conjures up the specter of a meaningless random universe, is a nightmare which confronts us all at some time or other as it did for example Conan-Doyle's hero Sherlock Holmes in the short story, The Cardboard Box:

“What is the meaning of it, Watson?” said Holmes, solemnly, as he laid down the paper. “What object is served by this circle of misery and violence and fear? It must tend to some end, or else our universe is ruled by chance, which is unthinkable. But to what end? There is the great standing perennial problem to which human reason is as far from an answer as ever.”

So, I'm in no position to be judgmental of genuine boarder-line atheists (like for example Mr. mice guy Brian Cox and that should also include Don Cupitt) who are an understandably having a struggle giving meaning to the cosmos.  But in Richard's case we must factor in that he is a professional atheist whose income depends on him fervently, vehemently and vociferously defending his brand of atheism just as theme park manager Ken Ham defends his lucrative brand of young earthism at all costs using the most insulting of spiritual terms about those who disagree with him, as we have seen.

...to be continued

INTERESTING LINKS

1. Sir Richard Attenborough's comments are worthy of applause in my view: 

Quantum Non-Linearity: David Attenborough on God