• Dot, Dot, Dot: Infinity Plus God Equals Folly

    Here is a post from James A. Lindsay’s blog, reposted here because I have just edited and published his book through Onus Books. it has had really good reviews and we managed to get Victor Stenger to write a foreword for it. Please support our work by buying the Kindle version from the voer image below. The paperback version will follow in about a week:

     Dot, Dot, Dot

    The Kindle edition of Dot, Dot, Dot: Infinity Plus God Equals Folly, my second book, has been released (and is available here). The paperback should be on its heels and will probably be accessible via the same link. Here, I want to take a moment to say a few things about the book and to let you all know what other people have been saying about it already.

    First, let me note that I’m pretty excited about this, less than 24 hours in, in fact–with a Friday afternoon release and everything:

    Dot, Dot, Dot is already a best-selling book about infinity!

    Now, I don’t want to bore anyone with the long, winding story of how this book came to be, but I will address what it is a little.

    About Dot, Dot, Dot in my words

    The book is pretty short, as I had always intended it to be, and as you’ll see from some of the commentary it’s already received, I aimed to keep it interesting, generally accessible, and readable despite being about mathematical topics. I also tried to avoid using equations essentially entirely.

    The title refers to the ellipsis, the three dots that we use to denote the elements of many infinite collections, for example {1, 2, 3, …}. The reasoning behind that choice is that really all of what makes up infinity is hidden within those three dots. Of course, we also use “…” as a written response when trying to indicate incredulous silence, which is what many arguments regarding God, especially when involving the infinite, deserve.

    The primary themes of the book aim to reveal that “existence” in the abstract sense doesn’t mean the same kind of thing that it means in the real sense, which is to say it makes an attempt to undermine mathematical and philosophical Platonic realism. Indeed, I make the analogy of a “map” (abstractions, mental objects) and the “terrain” it attempts to describe (reality) and repeatedly thrust the idea that we must be careful not to confuse the two. Infinity and God, so far as we can tell, both are abstract, mental stuff used to attempt to understand reality, and the line should be drawn there. This implies, of course, that God, as the being so widely believed-in, simply doesn’t exist. All there is in its place is an idea, or really a philosophical ideal.

    I also sought to clear up how easily infinity can end up being misused, particularly in philosophical arguments and even more especially in theological ones. It’s not just a penchant of theologians to invoke infinity when talking about God, though. As I show, it’s an inextricable part of theology and an element of official religious dogmas. Of course, this leads apologists to have to scramble to defend their use of the concept of the infinite, and upon that–their own petard–I hope to hoist them.

    What others have had to say about Dot, Dot, Dot

    Jonathan MS Pearce, author of The Little Book of Unholy Questions and blogger at the Skeptic Ink Network, has described it as “an easy-to digest mathematical treatise on infinity and its application to the concept of God, which, given the nature of infinity, becomes more and more abstract to the point of non-existence.” He goes on to say, “I am really enjoying the book … James has done a great job on making it a greatly readable and fascinating book.”

    Most exciting for me about the book is that it has a foreword by New York Times Bestselling author and noted physicist Vic Stenger. I’m utterly touched that in the foreword he calls Dot, Dot, Dot a “unique and fascinating book” (p. 2).

    The book received some nice advance praise as well, something immeasurably exciting for me as a writer that started off via self-publishing–a hard road for getting read if ever there was one.

    Peter Boghossian, philosopher and author of the new and eminently useful book A Manual for Creating Atheists (do get it!) writes,

    A short and engaging read on the meeting of two huge ideas, infinity and God, that leaves us seeing both as abstract notions that may have nothing to do with reality. Honest and accessible, Dot, Dot, Dot is a great little book to stretch your thinking.

    Aaron Adair, PhD, physicist and author of The Star of Bethlehem: A Skeptical View had this to say about it,

    Infinity is not only unbounded in bigness, it is unbounded in weirdness, destroying our intuitions, driving mathematicians to madness, and creating theological nonsense. Fortunately for us, James Lindsay can show the amazing features of the infinite without that many words, and staying very light on the equations. Along the way, he shows how the concept can be misunderstood and abused. Read this to avoid making any more cardinal sins and learn how much math is an amazing human endeavor.

    “Tippling” philosopher Jonathan MS Pearce, author of The Little Book of Unholy Questions, also had more kind words about Dot, Dot, Dot. He wrote,

    God and infinity have much in common, most notably that they are abstractions conceptually devised by man in order to try to make sense of reality. They are a kind of map. And, as James Lindsay so adeptly points out, we must not confuse the map with reality. For too long (mathematical) Platonic realism has been allowed to underwrite belief in God. With excellent books, like the eminently readable Dot, Dot, Dot, that rug is being firmly pulled from under believers’ feet.

    In all, Dot, Dot, Dot, has been extraordinarily fun to research, write, and share, and it is my hope that those of you who read it find it equally fun and intriguing to read. Infinity really is a neat thing to think about, and the Platonism that ties it to God is one of theism’s deeper, less obvious, and thornier roots, one well worth pulling up. Reading Dot, Dot, Dot will help you be sure about how to do so.

    Again, you can get Dot, Dot, Dot on Amazon.com here. And I do hope you enjoy it!

    Category: BooksPhilosophical Argument Against God

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    Article by: Jonathan MS Pearce

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    • If I understand you correctly, then this sort of highlights the problem with infinity. We always have to jumps there, as if that is logically acceptable. Hence the dot, dot, dot and then bam, infinity. There is no other way to actually get to infinity other than a conceptual jumps. and this is because it doesn’t really exist.

      • labreuer

        The problem doesn’t seem to be with infinity so much as thinking we know what it’s like. Consider this: looking toward the point at infinity while driving is a good way to stay between the lines. Or consider trying to make a society more just: this treats ‘justice’ as a kind of infinity. Viewed this way, the reality or nonreality of infinity gets pushed to the background: trying to head towards it seems beneficial. Thinking that way seems beneficial. Or am I missing something?

        It seems dangerous to say that something we cannot epistemically reach “doesn’t really exist”. It seems more prudent to put it on the shelf of things to investigate if we seem to be running into ‘boundaries’, of the Gödel sentence variety.

        • James Lindsay

          To jump in here:
          1. We don’t look toward the point at infinity while driving. We look at a point sufficiently far on the horizon to where it appears that something the width of the road has converged roughly to a single point. This is less than the distance to the horizon in almost all interesting cases, which is to say less than seven miles away, unless I have my facts off on how far away the horizon is. That we call it a “point at infinity” to mean “some arbitrarily or sufficiently far enough away point so that our perspective lines cross or very nearly do” doesn’t justify it as a “point at infinity” nor does it make “infinity” real in this context.

          2.Your justice example actually posits no more than a hypothetical maximum degree of justice, where every relevant entity within the society is behaving as justly as possible. When you reach the north pole, you simply cannot go north any longer because “more north” doesn’t exist.

          “Doesn’t exist” is a bit strong, though, I agree. “Have no good reason to believe exists” is plenty in this case, perhaps along with “is an abstract notion that gives us something to model certain ideas with,” as you’ve actually presented some examples of.

          • labreuer

            1. Your correction is well-taken (looking somewhere ‘close enough’ to the point at infinity suffices), but I’m not sure it really impinges on my argument. It is still the case that aiming somewhere you will never get to can be useful. Whether or not something is an actual infinity becomes irrelevant, because the important thing is to get closer to it than we currently are.

            2. You have no guarantee that justice is finitely describable. Indeed, I think much damage has done by people who assumed they had reached the north pole of justice. The fact that we can imagine a system we’d call perfectly just is no guarantee that what we imagined is realistic.

            “Have no good reason to believe exists” is plenty in this case, perhaps along with “is an abstract notion that gives us something to model certain ideas with,” as you’ve actually presented some examples of.

            Whether or not we ought to believe that something exists in this category seems unclear. How do we determine what ought to believed? We aren’t talking about what is here—we’re not doing science. If some belief leads to moral progress, it seems that it is just as ‘true’ as a scientific hypothesis which leads to an advance in science.

            • James Lindsay

              Never did I say that I think we have reached or that anyone has reached a zenith on something like justice, but it strikes me as not only likely but plain that it is finitely describable. There will only be finitely many interactions between humans and other sentient beings, and thus there are only finitely many opportunities to be just. It is unlikely that there are meaningfully an infinite number of potential actions/responses in any given interaction, and it is therefore unlikely that even something so complex and nuanced as justice can be measured on a continuum (itself a useful approximation for something very, very fine-grained). That yields justice as being finitely describable.

              This is very important, though: if there is a potential finite maximum of justice, that has literally nothing to do with someone claiming that they are at that point (and being wrong about it).

              As for determining what we ought to believe, I wonder if you’ve read Sam Harris’s The Moral Landscape closely? I found it convincing the first time I read it, and the second time I read it, I found it an absolute tour de force. Indeed, I was thinking about it earlier today, wondering if it is finally Hume’s defeater. The value problem seems to be able to be decided according to a matter of consequence, but I don’t mean straight philosophical consequentialism here with its weird dilemma games and unrealistic corner cases, among its flaws.

              In terms of beliefs, we should, I think, agree that we should believe that which seems to give us the best fit to the data, given some assumptions about simplicity and elegance of models–which we should value because repeatedly it has been shown that simpler explanations have a greater chance of being accurate, according to Einstein’s maxim that “everything should be made as simple as possible but not simpler.”

              Since you raised this directly in the context of moral beliefs, though, and moral progress, again, I urge you to read Sam Harris, or to do so again if need be. To talk about moral progress is to talk about what is, as Harris identified it with the bedrock moral value of achieving well-beingness while avoiding suffering. The connection is sentience: everything moral has to be moral in terms of someone or something that can experience it, and the bottom-line understanding of that experience comes to whether it causes suffering or promotes well-being.

            • labreuer

              There will only be finitely many interactions between humans and other sentient beings, and thus there are only finitely many opportunities to be just. It is unlikely that there are meaningfully an infinite number of potential actions/responses in any given interaction, and it is therefore unlikely that even something so complex and nuanced as justice can be measured on a continuum (itself a useful approximation for something very, very fine-grained). That yields justice as being finitely describable.

              You offer a plausible scenario. How can we discern between the two? Let’s say we keep finding out that justice is more complicated than we previously thought. You can keep pushing off the supremum and I can keep saying it’s infinite. Our two models would then be forever indistinguishable. Can you make a case for why I ought to prefer your model over mine?

              As for determining what we ought to believe, I wonder if you’ve read Sam Harris’s The Moral Landscape closely?

              I have not read it. I have some sympathy with the idea that we should actually gather data when trying to develop a good moral system. I ask questions such as Are there laws which govern minds? But does Sam Harris have testable models for how we actually get to a better future? The reviews of Harris I read indicate that Harris tends to give extreme examples of obvious goodness and obvious badness, but extremes are easy; dealing with the day-to-day fuzziness and grayness of reality is where the rubber meets the road.

              Christianity suggests that it’s people without moral backbones that’s the real problem, people who would prefer to follow authorities and let their authorities determine right and wrong. The Milgram experiment, Stanford prison experiment, and The Third Wave are favorite experiments of mine which demonstrate this, at least among white American college students. According to Christianity, the problem with the world is not ‘out there’, it’s inside me. Jesus’ solution is a life of self-sacrifice, of service to others, doing what I can to make their lives better. The answer is not new social programs, but changed hearts.

              I imagine that my interpretation of the Bible the plan it provides for moral progress is… quite different from Harris’. My interpretation has volunteers being the key to moral change, while I’ll bet Harris’ is more of a top-down approach. But feel free to correct me! You might even convince me to buy his book. :-)

              In terms of beliefs, we should, I think, agree that we should believe that which seems to give us the best fit to the data

              I’m just not sure this is how we operate when we think of creating better futures. We do base some of our future-thinking upon now-knowledge, but there seems something distinctly different between working toward better futures and understanding what reality is like. Maybe I’m making this up, but at this point, there seems to be a critical difference that I can’t quite nail down and describe eloquently.

              the bottom-line understanding of that experience comes to whether it causes suffering or promotes well-being.

              You do know that there are problems with utilitarianism, right?

            • James Lindsay

              Since we have no evidence for infinite anything, presuming finitism, if the two are indeed indistinguishable and doing so presents no additional challenges, is the simpler of the assumptions as it involves assuming nothing of infinite complexity. That’s what would distinguish the two, although as I said, I don’t think that’s likely to be how it is. Indeed, even apologists like William Lane Craig defend a definition of “infinite” that really means “comprising all possible positiveness;” I would guess for this same reason.

              As for your questions about Harris, since you haven’t read the book, which is not long, I feel it’s a bit out of my sphere to explain it to you when he’s already done such a fine job of it. Just read his book for yourself. You’ll find that he doesn’t claim to offer moral prescriptions or any explanation of what to do where the “rubber meets the road,” as that would be committing exactly the error you were warning about earlier. Instead, he makes an impassioned case that we can determine moral values–we can determine what ought by considering what is, i.e. by examining evidence pertaining to the bedrock moral value of well-being versus suffering.

              As I mentioned, I feel at this point, after having read the book twice a couple of years apart and thought about it considerably after both readings, that the only salient way we can determine moral values is by a consideration like what Harris suggests, and I don’t give a hoot about moral values that do not possess real-world salience any more than I care about physics that does not possess real-world salience (which could bring us back to infinity and it’s proper and improper uses).

              As to your interpretation for the Bible–now we’re talking about how you might know whether or not you’re right. Ha! Seriously? I’m afraid I’m going to have a hard time taking you seriously at this point, since you’ve forwarded your interpretation of the Bible as something salient and meaningful, and worse, you’ve done so in exactly the way I feel is the proof that the ideology is bad: it requires people, lots of them, to fundamentally change how they are.

              Harris doesn’t give any such top-down formulation, for what it’s worth–again you show your ignorance of a book you haven’t read. You should read it. He says that we possess the tools to start investigating a science of morality, a way to try to craft a best-possible moral situation with what is.

              As for problems with utilitarianism (or pragmatism, which I prefer in this context), yes. Further, I know there are issues with every philosophical position. That’s why I try not to waste much of my time with philosophers that seem to want to wallow in those problems, missing entirely that things are actually really working, and often working quite well, in the world outside. Indeed, this is part of the clarion call for a science of morality that works with what is instead of trying to create these overarching, consistent philosophical frameworks that are meant to apply in most or all cases.

            • labreuer

              Since we have no evidence for infinite anything, presuming finitism, if the two are indeed indistinguishable and doing so presents no additional challenges, is the simpler of the assumptions as it involves assuming nothing of infinite complexity.

              When I come across Ockham’s razor, it’s usually in a context where applying it leads to something the brain can more easily manipulate. It’s like trying to deal with a matrix that is linearly dependent, where all your vectors are likewise linearly dependent, which means you can properly invert the matrix, but at greater mental cost. In the situation we’re talking about, I see no improvement in mental processing by assuming e.g. that ultimate justice has finite definition instead of infinite. Furthermore, I see infinitude as mentally preferable if indeed we’ll never reach an actually-extant finitude. That is, assuming we’ll never achieve perfect justice, assuming it is infinite in description may be mentally more efficient. This is contra Ockham’s razor in letter, but with it in spirit.

              You’ll find that he doesn’t claim to offer moral prescriptions or any explanation of what to do where the “rubber meets the road,” as that would be committing exactly the error you were warning about earlier.

              How is a morality that doesn’t deal with where the rubber meets the road a useful morality? Later on in your comment you indicate that your interest is in “things [which] are actually really working”, things “which possess real-world salience”; if there is no way to practically apply a given theory, what is the use of the theory? But perhaps, as you said, I just need to read the book. If you’d be willing to discuss the book, I’ll be much more likely to read it.

              […] I try not to waste much of my time with philosophers that seem to want to wallow in those problems, missing entirely that things are actually really working, and often working quite well, in the world outside. Indeed, this is part of the clarion call for a science of morality that works

              You say that this ‘science of morality’ works; are there peer-reviewed papers I can read on the topic?

              As to your interpretation for the Bible–now we’re talking about how you might know whether or not you’re right. Ha! Seriously? I’m afraid I’m going to have a hard time taking you seriously at this point, since you’ve forwarded your interpretation of the Bible as something salient and meaningful, and worse, you’ve done so in exactly the way I feel is the proof that the ideology is bad: it requires people, lots of them, to fundamentally change how they are.

              The is-ought gap can only be bridged by positing something in addition to what is; that you think it’s fine for Harris to do this and unacceptable for me to do this reveals an asymmetry in your thought. You disparage my belief that people must fundamentally change, not realizing that to the extent that people think measuring themselves by how they compare to other people and to the extent that people think it’s ok to benefit from forcing others to sacrifice, there will be no well-being for massive numbers of people. If you think this world can be an excellent place without a lot of people fundamentally changing what they want, I think you’re delusional. That’s tantamount to saying that if everyone were just greedy together, things would work out alright.

            • James Lindsay

              “Furthermore, I see infinitude as mentally preferable if indeed we’ll never reach an actually-extant finitude.”

              It doesn’t matter how you see it. Finiteness is less complex and thus more parsimonious than infinite complexity. If the two approaches are otherwise indistinguishable, as you posited, then the additional assumption of infiniteness falls on the wrong side of this.

              If we want to analyze it more cautiously, we should assign epistemic plausibilities to each of the two cases, and as complexity increases, plausibility decreases. Thus, absent any way to choose between an infinite and an indefinitely large unknown, we should always chose the finite, leaving open the possibility of an infinitely complex understanding as a plausibility measure-zero possibility.

              “How is a morality that doesn’t deal with where the rubber meets the road a useful morality?”

              It isn’t, but defining such a thing isn’t Harris’s goal. Harris’s goal is to make a case for a science of morality that starts working on such a thing, not to define one. He’s essentially making a case for breaking the philosophical taboo on scientific investigations of morality, not defining what a science of morality necessarily is or what its findings should be.

              “if there is no way to practically apply a given theory, what is the use of the theory?”

              No practical way today implies nothing about no practical way tomorrow, but in this case, that’s not even the case. A great deal of our morality has already been determined by imprecise attempts to understand the world around us and to make value judgments according to various metrics according to what we see. At least one of the axes therein is well-being (vague or not) versus suffering, and thus we’re already doing and have already done work in this vein. I’m not a moral philosopher, though, so I don’t know what peer-reviewed articles have been written on this topic. Do your homework if you’re interested.

              “You say that this ‘science of morality’ works; are there peer-reviewed papers I can read on the topic?”

              This, in the context, is a bit like asking for peer-reviewed papers on nuclear energy that were written in the 17th century and then concluding, on the absence of such things, that a science of nuclear energy doesn’t work. I encounter this all the time with moral philosophers who doubt the possibility of a science of morality: “we don’t have one today, therefore there’s not one,” to paraphrase. These people need more imagination and hope.

              “The is-ought gap can only be bridged by positing something in addition to what is”

              This is the value-judgment problem. I think Harris makes a rock-solid case that promoting well-being and avoiding suffereing for sentient beings constitutes the only meaningful value, at bottom, which gives us a starting place for bridging the is-ought gap. Again, read Harris.

              The rest of what you said after that point is mostly nonsense. I have neither said nor implied any such thing as what you indicate. I shouldn’t respond to it at all because it spawns more tangents upon which you will try to pick a nit in something I’ve said, but I’m often too willing to discuss things.

              I have said that it is an error to base an ideology on something that entails a widespread change in human psychology. It very well may be the case that wide swaths of people are not psychologically capable of becoming “volunteers” in the sense you describe, and then what? And you call me delusional? Sure, people will have to have different wants, but we do not need to see any radical changes for this to occur. We need only appeal to the reality that most people want what’s best for some set of others while managing those who fall outside this general social framework.

              All I have advocated looking at what is without biases, the real state of human psychology and sociology, and crafting psycho-socio-cultural norms around that reality in a way that minimizes suffering to the best extent possible while also aiming to increase well-beingness. This requires no fundamental change of human psychology, only cultural values, which we know can change. It need only be done by open and honest inquiry and then the free dissemination of accurate information, in all likelihood–well, that and sufficient time.

              It need not be any kind of top-down, forced plan. Such a thing need only be information that is clearly demonstrated becoming publicly known. If we find out that certain behaviors engender suffering upon our children, for instance, sharing such information widely will typically lead to people choosing different behaviors of their own accord, which has neither the mark of being forced in a top-down fasion nor the fantastic hope that people will voluntarily revolutionize themselves (esp. if such hope depends upon a very dubious ancient book of fairy tales, horror, and nonsense). Social pressure and cultural practice will eventually fill in the gaps among those who do not value honest facts, though this may take generations. And so what if it does?

            • labreuer

              If we want to analyze it more cautiously, we should assign epistemic plausibilities to each of the two cases, and as complexity increases, plausibility decreases.

              How do you know “as complexity increases, plausibility decreases”? Ockham’s razor/parsimony are about modeling systems with successive approximation, not talking about what is. Their very point is that if you ‘multiply entities unnecessarily’, you make the system harder for the brain to do useful things with it. Ockham’s razor is not applicable when we want to talk about the actual nature of systems.

              Thus, absent any way to choose between an infinite and an indefinitely large unknown, we should always chose the finite, leaving open the possibility of an infinitely complex understanding as a plausibility measure-zero possibility.

              Unless you can establish that it is harder for our brains to use ‘infinite’ over ‘an indefinitely large unknown’, I question your ‘should’. At least, I say that your ‘should’ ought to be pragmatic, not based on some unjustified axiom.

              It isn’t, but defining such a thing isn’t Harris’s goal. Harris’s goal is to make a case for a science of morality that starts working on such a thing, not to define one. He’s essentially making a case for breaking the philosophical taboo on scientific investigations of morality, not defining what a science of morality necessarily is or what its findings should be.

              Ahh, ok. I’m not sure I should read TML then, because I believe science can help us with morality. I would want to be careful about trying some sort of verificationism—trusting someone about his/her measurement of the well-being of others—but I would be very much in favor of falsificationism, which in this case would put value on people’s self-reported pain and suffering. People are very good at undervaluing others’ suffering, and claiming that others are thriving when they aren’t.

              This is the value-judgment problem. I think Harris makes a rock-solid case that promoting well-being and avoiding suffereing for sentient beings constitutes the only meaningful value, at bottom, which gives us a starting place for bridging the is-ought gap. Again, read Harris.

              Virtually nobody disagrees with your (and Harris’) stated level of abstraction. Less suffering and more wellbeing is an excellent goal. You understand this, right? The complexity lies in how you define the terms, how you weight various people’s suffering/wellbeing (see the problems with utilitarianism, which are not just abstract philosophical problems), and what means you use to improve things. It sounds like Harris hasn’t tackled the difficult issues; please correct me if I’m wrong. If he does, please let me know; that would make TML attractive reading.

              I have said that it is an error to base an ideology on something that entails a widespread change in human psychology.

              Note that profound changes in psyche is observed by some converts to religion, as well as in other circumstances as well. So radical change is indeed possible—I’m not talking about fairy-tale stuff. I’m not sure this constitutes “a widespread change in human psychology”; would you say it does?

              It very well may be the case that wide swaths of people are not psychologically capable of becoming “volunteers” in the sense you describe, and then what? And you call me delusional?

              I predicated my ‘delusional’ statement on an if—a very important if. You may be happy to accept the world being an alright place instead of an excellent one. Personally, I would prefer to be in a community where self-sacrifice is routinely practiced but not compelled. This would be a community where people who merely want to feed off of others’ self-sacrifice will need to be somehow prevented from doing this more than a certain amount. I think such a community would be a much better place to live in than one that doesn’t require a radical change of what e.g. people in America generally desire.

              One thing that concerns me is if an implementation of TML/scientific morality prohibits people from trying a community like the one I just outlined. Would it?

              All I have advocated looking at what is without biases, the real state of human psychology and sociology, and crafting psycho-socio-cultural norms around that reality in a way that minimizes suffering to the best extent possible while also aiming to increase well-beingness.

              There’s simply nothing to disagree with at this level of generality. The devil is in the details.

            • James Lindsay

              I’m going to have to thank you for the conversation here. I simply do not have time to keep this up the way it continues to go. Forgive me.

            • labreuer

              With regarded to scientific morality, you might like Jonathan’s recent post, Can an ‘is’ be an ‘ought’? Mike D on the science of morality.

    • James Lindsay

      Thanks for your comment, labreuer.

      I’d say we’re not epistemically equipped to know whether or not a physical infinity exists, but if it does, it necessarily does so in a rather mundane way like an infinite extent of space or an infinite timeline for the universe. The link you provided highlights why this is. To my understanding, though I’m not a cosmologist, the question of whether or not the universe is infinite in scope physically (or temporally) is not solved, but it certainly lies on the other side of an epistemic wall for thinking beings.

      Here we run smack into a problem for God, do we not? If God is to be posited as a thinking being, Lord of an infinite universe, that entails that God must know and be able to manage an infinite quantity of information. That starts running into coherency problems immediately. So maybe God isn’t Lord of an infinite universe or of all of it (note: we have already left the fundamental claims of mainline theology in order to accommodate a possibility as if it is a probable thing). Omniscience and omnipotence still present problems with infinity.

      Ultimately, though, all of these “people are bad at thinking about this or that about God” and “this or that could be the case about God” is the usual rather pointless apologetics exercise in trying to leave room for something that seems less and less plausible the more we look at it or think about it, i.e. generally a waste of time, particularly given the kinds of Gods that this sort of gerrymandering defends (increasingly vague, increasingly pointless philosophical abstractions).

      This problem is especially pronounced when we start looking at the damands of what amount to overwhelmingly silly religions designed to worship that God and all of the problems that arise from them. In fact, those problems are so rife and serious that unless God is as disturbingly petty as the religions say he is, we still have a very weak justification to be religious in any religion while having strong motivations not to be so. You can say I changed the subject here from theism to religion, but isn’t that the point of the whole discussion? Does anyone on earth really care whether or not God exists outside of the context of whether or not she should worship/attend to/communicate with said God, and how?

      • labreuer

        :-)

        I’d say we’re not epistemically equipped to know whether or not a physical infinity exists, but if it does, it necessarily does so in a rather mundane way like an infinite extent of space or an infinite timeline for the universe.

        I don’t understand how you know the bolded part.

        That starts running into coherency problems immediately.

        I’m not particularly well-versed in the alleged incoherence in an omni-* deity, but I get the sense that people who find said incoherences tend to assume that an omni-* deity can be defined in finite space. That is, certain infinities can be reformulated so that they have finite description—like a non-halting Turing machine [of finite size] which just keeps on producing output. But what if an omni-* deity has infinite, non-compressible description? Then, any philosophical discussion will necessarily have to use approximations, which means that inconsistencies may be artifacts of the model and not the thing being modeled—kind of how particle/wave duality was a paradox until we realized that a thing can propagate as a wave and interact as a particle: paradox eliminated.

        something that seems less and less plausible the more we look at it or think about it

        Given the data at hand, I’m not sure I disagree with you. This begs the question of whether all ways to come up with an omni-* deity consonant with observed reality have this property, or merely the vast majority of the attempts so far. I don’t blame those who give up the search, but it’d be nice to see a well-defined ‘test’ for formulations which would ‘seem more and more plausible’. My own answer would be along the lines of something that advances the state of the art in understanding either the external world (what science does) or our internal worlds (that is, our inner lives). I would contrast true understanding with ‘just-so stories’ which lead nowhere.

        Does anyone on earth really care whether or not God exists outside of the context of whether or not she should worship/attend to/communicate with said God, and how?

        Perhaps; I’ve run across many atheists and skeptics who merely want to know “what is true”, but I’d say it’s hard to gain knowledge without it being either mathematical/logical, or falsifiable—whether scientifically or by common sense.

        Something which many be unique to the Christian God—I don’t know enough about all religions to say this for sure—is that Yahweh is primarily interested in the well-being of his creation; “If I were hungry I would not tell you”. Martin Luther famously quipped, “God does not need your good works, but your neighbor does.” Things done ‘for God’ are identical to things done for benefit in a sort of ‘fractal’ pattern: for a proper balance of oneself, one’s family, one’s tribe, one’s nation, the world, and the future of humanity.

        An idea I’ve been playing with is the concept of the Holy Spirit as being a ‘coordinator’ for those interested in building a true utopia—a heaven on earth. He would be ‘most present’ to those who want the right things and are employing the right means of achieving those things. Such people would routinely need to take ‘sabbaths’ to ask, “Is there a better (more God-like) way of going about this?” If God’s will is the thriving of all the humans who want to thrive but not at the expense of other humans (‘slaves’), then he will be most present to those who are most closely following his will. Anyhow, I don’t know if this gives you a different way of thinking about this than you have before. I just thought you might find it to be a change of pace from the usual.

        • James Lindsay

          As to why we should think that infinity only exists in mundane ways, like as a scale, did you not read your own link talking about the physical issues if it exists in more interesting ones, like infinitely massive objects (which therefore would also include objects of infinite size)? If we know we run into serious issues with these more exotic infinities, it seems pretty reasonable to rule them out. Perhaps I overstepped my boundaries there, but then, if I did, I’m requiring hard evidence to believe it and don’t care about the musings of philosophers on the matter.

          Note that a non-halting finite Turing machine requires a non-compressible infinite timeline to create an infinite output, so such a description, even recursive, doesn’t produce an infinite actuality without assuming one first. I don’t think either situation requires us to model using approximations, though. We have a well-developed theory of the infinite from which we can, hypothetically, pull any particular individual value or entity from for closer examination. Even so, this is why counterapologetics is nearly as big a waste of time as apologetics: we’ve already had to assume some kind of deity maybe kind of exists and are grasping at straws for why we should maybe think so (even if only to defeat those arguments). It’s a very clever way to get people to keep talking about dragons for as long as dragons could conceivably be talked about, but it doesn’t do anything with regard to establishing that a dragon is a legitimate thing that should be feared.

          Not to sound Chopra on you, but our “inner lives” are simply part of the external world doing its thing, so far as any of us have any reason to believe. This is why investigating the subjective as if it implies more than brain activity is a dangerous thing. Look at what it did to Chopra, for instance.

          As to things done “for God” being identical to things done for the self, family, etc. etc., this is identical to God being a metaphor for those various layers of understanding society and the self. I’ve never tried to argue that God is anything other than a psychosocial abstraction, so yeah, okay. That’s not what people believe in, and it’s not what people worship, and it’s not what people who talk about God think they mean. That distinction is important and easily lost when talking philosophy.

          I don’t have such a favorable view of what the “holy spirit” is as a metaphor. I’d say it’s more of an animating ethos of believing oneself to be righteous along a particular idealized moral agenda, those differing from individual to individual and unlikely to admit a universal standard (unless Sam Harris is right and our science gets a LOT better at figuring out a science of morality).

          Again, thanks for your input. I do appreciate the conversation.

          • labreuer

            I haven’t interpreted anything you’ve said as hostility; really the only way to offend me is to claim I’m being intentionally dishonest (yes, people do this all the time online); it is a claim which is almost always unfalsifiable, making it a tar baby. I’d rather such people just stop talking to me! :-|

            If we know we run into serious issues with these more exotic infinities, it seems pretty reasonable to rule them out. Perhaps I overstepped my boundaries there, but then, if I did, I’m requiring hard evidence to believe it and don’t care about the musings of philosophers on the matter.

            The word that tripped me up was “it necessarily does so in a rather mundane way”. I’m happy to accept that if we can’t seem to do anything productive with a non-mundane ‘real infinity’, then there is no imperative to predicate beliefs and actions on it, and because we tend to only be able to make incremental improvements upon ideas, trying to venture far beyond what we have so far is very unlikely to yield helpful results.

            Note that a non-halting finite Turing machine requires a non-compressible infinite timeline to create an infinite output, so such a description, even recursive, doesn’t produce an infinite actuality without assuming one first.

            I think you missed my point; what I meant to talk about was something infinite in description; Turing machines are the best way we know to compress descriptions of things. So saying that there is no finite Turing machine which can generate the kind of ‘infinite description’ I’m talking about was a way to be technically accurate.

            A possible example of this type of infinite description is how reality works, itself. That is, science may never stop and it may never slow down. Ideas such as ‘justice’ may also be infinite in description, especially if they need to be balanced by things like ‘mercy’, ‘liberty’, etc. Positing that these things are infinite in description has the function of dissuading people from claiming, “I have it all figured out.”—as many have claimed in the past, concerning both nature and morality. Furthermore, induction does provide reason to believe infinite description. If we keep finding out more and more and more, at some point you just expect that ‘more and more’ to continue.

            we’ve already had to assume some kind of deity maybe kind of exists and are grasping at straws for why we should maybe think so

            But you have an arsenal of ways to respond. Examples:

            1. How does belief in your deity help you understand how the world works, other than by providing ‘just-so’ stories?
            2. How is your belief in that deity just a delusion that provides false comfort?
            3. How does belief in your deity make you a better person?
            4. How do you know you’re not just imagining your deity in your own image?

            You can always refuse to ‘do anything’ with your interlocutor’s idea of a deity if it doesn’t pass any of the above tests. And if somehow your interlocutor does pass one of the above tests, he/she will have a model of God which would be compelling. Or have I erred?

            Not to sound Chopra on you, but our “inner lives” are simply part of the external world doing its thing, so far as any of us have any reason to believe. This is why investigating the subjective as if it implies more than brain activity is a dangerous thing. Look at what it did to Chopra, for instance.

            Merely shying away from things because they’re “dangerous” seems shortsighted. Shortchanging what a person’s inner life could be like—see BF Skinner and all like him—seems like about the worst thing you could do to a fellow human. Were it to be shortchanging, you’d be constructing the most evil kind of prison: one that is virtually invisible. The solution to stuff like Chopra is to continually monitor the results of believing various things, and stopping the experiment if it ends up being more than what people were willing to risk.

            I think you’re going to have a hard time defining what is “reason[able] to believe” when it comes to people’s inner lives. Reasonable as defined by whom, on what basis? I doubt you’ll get a single answer, because I think what constitutes ‘reasonable’ at least depends on what risks a person is willing to take.

      • labreuer

        Whoops, I forgot to include a plug for the simulation argument, which has caused quite a stir:

        This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.

        This, I think, heightens the stakes in terms of thinking about “what an omni-* deity would do”. Unless there are restrictions we don’t know about, anyone who runs a simulation of sentient beings has omni-* powers, because the simulation can always be stopped, inspected, altered, etc. Many of the discussions about the problem of evil would become extremely poignant if we were to, say, try and simulate the evolutionary history of the Earth in a sufficiently ‘real’ way. The Star Trek episode, Measure of a Man, is utterly fascinating: it explores whether androids would have the same rights as humans. If they do, then does a sufficiently sophisticated digital sentient being also have the same rights as humans?

    • mikespeir

      I can’t get a handle on whether God’s infinite or not. Pascal seemed to think so. (Otherwise, why the “infinite abyss” if he didn’t have a Peg in mind to fill the hole?) William Lane Craig, on the other hand, has a problem with calling anything–to include God, presumably–infinite.

      • James Lindsay

        One of the more interesting things that I found while doing some of the research that led to writing this book is that God being infinite “in every sense” is actually Catholic dogma. Also, Georg Cantor (the mathematician who blew open the topic of infinity) thought that there were different kinds of infinity with God being the Absolute Infinite that’s more infinite than any of the infinite cardinals. This, though, is probably the bit that drove him mad in the end, trying to square what he did with sets and infinite cardinals with his view of an unsurpassibly excellent God.

        I suspect that Craig shies away from it, though, because I think he realizes two things, although he does call God infinite by using a lot of squirrelly language. Firstly, he realizes that if God is infinite, then there are some pretty serious coherence problems that are difficult to apologize around, apparently difficult enough to where he’s taken a tack of denying the infinite as it is usually understood. Second, he wants to make the Kalam argument, which requires a finite timeline (at least into the past) to support one of its premises, and the easiest way to do that is to categorically deny the existence of the “actual” infinite. (NB: The Kalam fails even if we let it get off the ground with a finite timeline, but that’s an aside.)

        Craig, ultimately, is a finitist, which is fringe among mathematicians but interesting. I’m not sure if he realizes he’s a finitist or not. Apparently, or so I’m told by finitists, all of useful mathematics can be reformulated as-is in a finitist (no infinities) system, although doing things becomes considerably more cumbersome as a result (think needing a master’s degree in math or computer science to do the calculus we teach to high school students). For me, then, infinity is a useful enough abstraction to justify using, whether it corresponds to anything physical or not.

        Incidentally, finitists use the word “indefinite” to replace “infinite,” meaning “indefinitely large.”

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