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.

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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. 

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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. 

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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. 

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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.  

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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