Is it right to believe things by faith, rather than reason? There is a downside to faith. Some people will believe by faith things that I consider wrongheaded; if they believed those things by reason, I might be able to reason them out of them; but if they believe them by faith, there is nothing I can obviously do to dissuade them. Even worse, some people will believe horrendous and reprehensible things by faith (e.g. the faith that God exists and wants them to kill the infidels.)
And yet, I want to believe, and do believe:
In the long-run, if my desires are good, then the universe will be favourable to them.
I know this claim is incapable of rational proof or disproof. And yet, I do believe it, by something I cannot clearly distinguish from religious faith, even though, it is a much broader and vaguer statement than most things religious people hold by faith.
Other statements which are articles of faith for me:
—In the long-run, everyone will come to believe the truth, whatever the truth may be.
—In the long-run, people will always desire what is good. The apparent desire for evil, is ultimately caused either by holding false beliefs about the world, or insufficient trust in the truthfulness of true beliefs held.
I cannot prove any of these statements. But I do believe them to be true.
I think faith is defensible, as follows: Reason proceeds either by logic (deductive reasoning), or by observation (empirical reasoning). Now, logic cannot ultimately prove anything, without making assumptions, other than ultimately empty truisms. So, with logic one can know abstract statements like “If A implies B, and B implies C, then A implies C”, without needing to make any assumptions. And yet, that is not knowledge of the what is and is not; it is knowledge that is essentially empty. Empirical reasoning can only derive truth from experience, if we accept certain assumptions — such as the regularity of nature. Those assumptions themselves cannot themselves be demonstrated by either logic or empirical reasoning. So, the use of reason is only possible if one accepts extra-rational assumptions, in other things, through believing things by faith. And, I think the fact that reason requires a foundation of faith, shows that the operations of reason and faith cannot be clearly distinguished anyway.
Why do people believe wrongheaded or reprehensible things by faith? Due to the social reality in which they exist. I think the claim that “my religion is right and yours is wrong”, is often, but not necessarily always, reducible to “you are not part of my social group and so you make me feel uneasy”. If that is true, then, if they actually form stronger personal relations with members of that other group, then they will end up giving up their faith that their group’s religion is right and the other group’s religion is wrong.
By contrast, improving personal relationships with others, will not result in us giving up our faith that “In the long-run, everyone will come to believe the truth, whatever the truth may be” — on the contrary, it can only serve to strengthen that faith.
And, this I think is the answer to my original concern “if they believed those things by reason, I might be able to reason them out of them; but if they believe them by faith, there is nothing I can obviously do to dissuade them” — let us consider an anti-Semite. No amount of rational reasons as to why anti-Semitism is wrong, is likely to convince them to give up their anti-Semitism. On the other hand, getting to know and form relationships with Jewish people almost certainly will help, and I’m sure in the long run will succeed.
I disapprove of racism. But is my disapproval due to racism’s obvious irrationality? Or is it due to the fact that I grew up in a multicultural society, from an early age forming personal relationships with people of a variety of different races/ethnicities, and someone who grows up under such circumstances is likely to end up disapproving of racism? If someone says “group X is inferior”, and people of group X are my friends, then they are insulting my friends. And, people don’t take kindly to their friends being insulted. Then again, if I had have been born in a different time or place, which was much more ethnically homogenous, I would have been much less likely to form personal relationships with people of diverse backgrounds, and thus much more likely to hold racist views, or at least, to not look upon racism so disfavourably.
And this is why I think a universalist faith is more justifiable than one rooted in religious parochialism.
If we accept the existence of multiple universes, and adopt a criterion of transworld identity such that our existence is not necessarily confined to one single universe but rather spread out across all the many existent universes in which we are identical (at least in some temporal part), then it could follow that certain statements might be true in some universes and false in others, and yet all those universes being equally this universe for me, then for me they would be equally true and false. Whereas for others, who only exist in some of the universes in which I exist, those very same statements might be entirely true or entirely false. However, we can eliminate this issue by rewriting all statements from X to “X in every universe U”, where U is some phrase which identifies universes. Then, those rewritten forms of the original statement are no longer capable of being simultaneously true and false in the way that the original statement was. And yet, every ordinary statement we make, is not in the form “in every universe U”, but rather in the form “in some universe that I exist in”.
A criterion of transworld identity which identifies persons across universes takes away the boundaries between universes. And I think, with Q-space, we can dispose of the boundaries entirely. The claim that you and I are identical in some temporal part, is simply the claim that within that temporal region we wholly overlap in Q-space. The claim that you and I, while being non-identical, both exist in the same universe, is simply a claim about the geometrical similarity of the Q-space regions we occupy. Thus, once we introduce Q-space, we can dispense with parallel universes (a bit like Schopenhauer’s proverbial hired cab).
I have previously thought that the true model of the universe consists of these components: qualia; minds; relationships between qualia and minds; relationships between qualia; relationships between minds. The first relationship is that of binding; the second relationship is the geometry of Q-space; I’m starting to think the third relationship is a relationship of geometrical similarity between bound Q-space regions (Some days, I will add universals to the mix; other days, I’m not so sure if they exist.)
When I speak to myself, in the quietitude of my own thoughts, my thoughts lack pitch or timbre; even though when I speak aloud, my voice has these properties. I think that is part of why I have always been disturbed by the sound of my own voice, having pitch, having timbre, it sounds so alien to how I normally speak to myself, in pitchlessness, in timbrelessness.
And yet, when I sing to myself in my own private thoughts, my thoughts then have at least some pitch, although they still struggle to attain timbre. Maybe, my struggles in conception, are related to my own limits of musical ability? (Then again, if only I had practiced as much as I might have, my musical ability might be much, much, greater than it is now.)
a Cartesian soul. So named, because: (A) it refers to the phenomenon of first person perspective identity (subjective identity), as opposed to third person perspective identity (objective identity); and (B) it is atomic, in the sense that it is indivisible, and has no inherent properties, other than its binding. (Any property it has, other than: (1) being the token it is, (2) being of the type it is of, and (3) being bound as it is bound, is a derivative property of properties (1)-(3).)
experience stream
a region of Q-space. Note that qualia does not only include our external senses, but also our internal ones. Our private thoughts, our dreams, our emotions, are as much qualia as any external sense is.
binding
the fact that every Cartesian soul corresponds to a Q-space region
consistency criteria
the fact that, in order for a Cartesian soul to be bound to a Q-space region, the Q-space region must possess particular properties. These are both the basic geometric constraints of Q-space, as previously discussed; and also, certain further constraints, best demonstrated through (1) the pasting argument, (2) the random selection argument, and (3) the excessive order argument.
Pasting arguments
Suppose Alice and Bob are two distinct persons, who in no way overlap. (Suppose Alice walks into an exact matter duplication machine, which then produces Alice-1 and Alice-2. Alice-1, Alice-2, and original Alice are all persons who in some way overlap, and the question of their distinction or identity is complex. Whereas, for Alice and Bob, there are no such complexities in their distinction, thus we say they in no way overlap.)
Now, let us consider universe 1. In universe 1, Alice and Bob exist. And, in universe 1, Alice and Bob each have an experience stream (= region in Q-space), and let us call these streams Alice-stream and Bob-stream, respectively. Now, these streams are distinct, in such a way that there is no time t such that at time t, the two streams are totally overlapping in non-temporal dimensions.
Now, let us construct universe 2 as follows: choose an arbitrary time t, such that both Alice-stream and Bob-stream exist at time t. Now, let us construct two new streams, Alice-prime-stream and Bob-prime-stream, as follows:
Before time t:
Alice-prime-stream = Alice-stream
Bob-prime-stream = Bob-stream
After time t:
Alice-prime-stream = Bob-stream
Bob-prime-stream = Alice-stream
Let us refer to universe 2 as a pasting of universe 1. In other words, to get universe 2, we have cut the experience streams of universe 1, and then pasted them together again, in some improper manner, to produce universe 2.
Thesis:
A Cartesian soul can be bound to Alice-stream, and a Cartesian soul can be bound to Bob-stream. But no Cartesian soul can be bound to Alice-prime-stream, and nor can any Cartesian soul be bound to Bob-prime-stream.
Intuitively, this thesis appears to be true. Why would it be true? It would be true, if, in order to be bound to a Cartesian soul (= subjective identity atom), a region of Q-space must obey certain criteria, connected to its internal consistency, or equivalent continuity (= it must exhibit macroscale continuity, even if that is reducible to microscale discreteness).
The random selection argument
Consider the set of all possible Q-space regions. Now, select a random region. It seems, with extraordinarily high probability (if not even, almost surely), that the region has no discernable structure; that it is utterly random; that it is indistinguishable from white noise. Now, the following thesis seems intuitively true:
Thesis:
A Cartesian soul cannot be bound to a Q-space region of excessive noise.
Suppose, we could devise some metric n, which measures the noise of a region of Q-space. We might equivalently state, that there is some upper bound to n, such that no Cartesian soul can be bound to a region whose noise is above that bound.
The excessive order argument
The random selection argument, seeks to show that an atom cannot bind to a Q-space with excessive noise. But, consider instead a Q-space which has almost no noise. Consider, for instance, the region of an n-plane in Q-space. As much as a soul cannot bind to noise, it seems that a soul cannot bind to an n-plane either. For in the first case, there is too much noise; in the second, too little.
If a soul was bound to an n-plane, it only have one single experience, repeated continuously throughout the totality of its existence. And yet, it seems, that a single repeated experience, is identical to there being a single unit of time, which is identical to the utter absence of any temporality.
Thesis:
A Cartesian soul cannot be bound to a Q-space region of insufficient noise.
Can the consistency criteria be known exactly?
I would suggest, that any attempt to discover the consistency criteria with exactitude, will fall victim to some parallel to Gödel’s theorems. If the universe is finite, then I would suggest that the information contained in the consistency criteria is greater than or equal to the total information content of the universe. Thus, in its precise form, it is in essence unknowable, or if knowable at all, only through some ineffable, mystical, Zen-like form of knowledge.
If this is true, then there are two possibilities:
The precise form of the consistency criteria exists, but is unknowable.
There is no precise form of the consistency criteria.
It would seem, that these two possibilities are in fact indistinguishable and absolutely equivalent and identical.
Let us refer to the notion of property space which I have defined earlier as P-space (P = property; or equally, P = physical). Now, I want to define another space, which I shall christen Q-space (Q is for qualia.)
Essentially, P-space models a physical universe as a set of point particles, spatiotemporally arranged, each having various numerical physical properties. Q-space, by contrast, models a universe of experience, a stream of qualia which may be experienced by an individual.
Let us consider a simple example. Imagine that sight was our only sense. Let us assume furthermore that we are trichromats, and capable of depth perception. So, at every temporal moment t, we are perceiving a certain visual field, which is organized two-dimensionally. Each point in that visual field can be described by four numbers: three dimensions in colour space, and one dimension of depth. The colour space might be, for instance, CIE L*a*b*. As in the case of P-space, there are certain geometric constraints — for any given combination of x, y, t, there can only be one possible value of L*, a*, b* or z.
An observer, then, can be identified with a region of Q-space.
We can define two different observers, being identical in their temporal parts, as regions of Q-space which in some temporal subregion are fully overlapping. Whereas, cases of non-identical observers having the same experiences, the regions are only partially overlapping, or non-overlapping yet transformable.
An objection: Some people are dichromats; possibly, some people are also tetrachromats. Can we define this Q-space in a way which does not depend on chromatacy? Well: we define colour spaces in terms of differing spectral power distributions which all produce the same qualia (or, equally, are reported to produce the same qualia). Obviously, dichromats and trichromats report differently. But what is the relationship between dichromatic qualia and trichromatic qualia? Since, invariably, an individual will be one or the other for their whole life, or, if they were to change between them, it would likely be either a gradual process, or even if an abrupt process, a non-repeatable one, so it would be difficult for an individual which was to so change to make a judgement as to the identity or non-identity of qualia of different chromatacy. But, suppose through some advanced technology, one had the ability to reconfigure one’s retina at will. (Suppose, due to blindness, one has been given an artificial retina, which, due to technological advances, is identical in behaviour to a natural one; but, even better than a natural one, is adjustable at will, so that one can change the effective number of cone cells, or their response curves, as one wishes.) One might then experiment, by switching frequently between different levels of chromatacy, and even different response curves within a single chromatacy, while keeping constant the spectral power distribution to which one was exposed. One would then be able to form a judgement, as to the relationship between the qualia spaces constructed by different chromatacies. Thus, we could potentially move beyond a Q-space linked to a single vision system, to a generic Q-space which encompasses vision systems with a multitude of different parameters.
Three questions:
—Is the Q-space of generic vision bounded?
—Is the Q-space of generic vision finite-dimensional?
—Is the Q-space of generic vision discrete?
I feel, the answer to all these questions must be “Yes”, up to humanoid beings. For, any humanoid being has an intelligence less than some finite upper bound. And yet, if any of these three questions was false, then the a being capable of such vision would need to perform a potentially infinite amount of computation within its visual systems. Thus, even if, at our present level of knowledge of cognitive science, we do not understand the properties of the Q-space of generic vision, we can conclude that, up to humanoid beings, it is bounded, discrete and finite-dimensional.
An objection: At best, all you have modelled is vision. Indeed, that is true. There are some number of senses (I am not sure, at present knowledge, if we can precisely enumerate them.) They all share a common dimension of time. Although, we may not be able to devise Q-spaces for all of them, with our current knowledge, I feel confident in claiming that they all have Q-spaces, which are bounded, finite-dimensional and discrete, waiting to be discovered. At least some of them, have spatial dimensions; if the Q-spaces of two senses both have spatial dimensions, should we treat the spatial dimensions of each as identical or equivalent (i.e. common), or as distinct? It seems, that the answer to that question is most likely to be an arbitrary choice of modelling, as opposed to an actual question of fact. We can then construct a model, of some number of Q-spaces, with a common dimension of time, and some subset of those Q-spaces also sharing common spatial dimensions. Now, we can construct an overarching combination Q-space, incorporating all those separate Q-spaces. Let us have dimensions of time, of qualia type, of space, and of property. For non-spatial qualia types, we fix the spatial dimensions at an arbitrary value, say origin. The various qualia types have differing applicable properties; for a point at a given qualia type, we can fix the value of the non-applicable property dimensions at an arbitrary point. Thus, as well as the geometrical constraints of the individual Q-spaces, we also have geometrical constraints deriving from their combination into a single overarching combination Q-space. And, if the individual Q-spaces be bounded, finite-dimensional and discrete, and if the number of qualia types be finite, then the combination Q-space must be bounded, finite-dimensional and discrete.
A soul can be bound to a region of combination Q-space, which (1) obeys the inherent geometrical constraints of Q-space; (2) obeys the consistency criteria. Every region of Q-space, which meets both sets of criteria, can potentially be bound to a soul; and yet, it seems, not every such candidate region is so bound. Indeed, I would argue, that the proportion of regions so bound must be greater than none but less than all. We might call this last requirement a third requirement, but it applies over the set of all actual bindings, not over any individual one.
A fourth requirement, again one ranging over all bindings, is anti-solipsism; in other words, the bindings must be as such that there exist the qualia of a belief in the falsehood of solipsism; and the bindings must be as such as there to be other associate qualia which would justify the belief constituted by the former qualia.
P-Space and Q-Space
P-Space is an essentially observer independent notion. Q-Space is essentially observer dependent. However, in constructing subregions of P-Space, I have appealed to observer dependent criteria, which I feel ultimately justifies us in preferring the concept of Q-space. I feel that, Q-space is a better model of the ultimate nature of reality; whereas, P-space, represents a class of models, which while not as good at explaining ultimate reality, are still pragmatically useful. Physical laws, expressed in terms of constraints on the shape of P-space, are ultimately constraints on the shape of the atom-bindings in Q-space; but, it is easier to reason about them in terms of P-space than Q-space. But, I don’t think we should accept the scientist idea that ease of notation = truth. Ease of notation is simply that, ease of notation.
Let us construct a model of a physical universe. I am going to assume a quasi-classical picture of reality. I think, even though the technical detail might not entirely work with relativity or quantum theory, the philosophical intent would still be salvageable. My intentions here are philosophical, rather than physical.
Points exist in spacetime. These points have various properties, such as mass or electrical charge. Now, we can convert this model into one in which points have no property other than location, by treating the properties such as mass or electrical charge as additional dimensions. Vacuous points, not occupied by any particle, would lie upon the origin of the property dimensions. We also need to introduce some geometrical restrictions, since a single point can only have one possible mass or one possible electrical charge. We can divide the dimensions of this model into two subsets:
—positional dimensions: x, y, z, t
—property dimensions: m, q, etc.
For each possible value of x, y, z, t, there is only one possible value of m, q. This is a geometrical constraint.
This new space (I might christen it property-space) I have defined is somewhat similar to the concept of phase space. However, in phase space, each point of the space represents a different possible state of the system as a whole. Whereas, in this space, each point of the space represents a possible state of a single individual particle, so a possible state of the system is not a single point (as in phase space), but rather a collection of points. Thus, in phase space the number of dimensions is a multiple of the number of particles, whereas in this space it is constant irrespective of the number of particles.
Now, our spacetime is finite dimensional (at least, up to the limits of observation), and specifically 4-dimensional. Let us assume that every particle only has a finite number of properties. Then, our property space is also finite dimensional.
We are familiar with the notion of spatial volume. This is possible because the dimensions of space are commensurable, and indeed naturally so. Can we extend this notion to one of spatiotemporal volume? Well, relativity provides a natural relationship between space and time. But, even supposing relativity was false, and there was no natural relationship, for the purpose at hand we could equally well choose an arbitrary, conventional, relationship. So, for any region of spacetime, we can consider its spatiotemporal volume.
Now, let us consider property space. We can also define a notion of property space volume. There may be some natural relationship between the spatiotemporal dimensions and the non-spatiotemporal dimensions of property space. Planck units, for instance, may provide such natural units. But again, if there are no natural units, then arbitrary ones will do just as well. Whatever the choice of units, the resulting units of volume will differ only by a constant factor.
Now, consider a finite spatiotemporal volume. Is the corresponding property space volume finite? Equivalent statements: Is there a greatest possible mass? Is there a greatest possible electrical charge (of either sign)? etc. If yes, then for every finite spatiotemporal volume, the property space volume is also finite.
Now, property space may be continuous or discrete. If it is continuous, then even a finite property space volume will contain an infinite number of points. But if it is discrete, then the number of points in a region of property space will be infinite only if the volume of the property space is infinite.
So, we can derive the following:
—If property dimensions are bounded, and property space is discrete, then a finite spatiotemporal volume can only be in a finite number of possible states.
Let us consider “Earth-like planets”. Clearly, there is an upper-bound to planetary size after which a planet should no longer be considered Earth-like, set by the laws of physics. Even if, through some miraculous violation of physical laws, there existed a terrestrial planet the size of the Milky Way, supporting Earth-like lifeforms, one would still say such an entity is too large for the term Earth-like. Thus, there is an upper bound on the spatial volume of Earth-like planets.
Is there a limit on the temporal volume of Earth-like planets? Science implies so — the Earth has only existed for a finiteperiod of time, and after a finite period of time will likely cease to exist; and, long before its existence ceases, it will have become inhospitable to life, and thus no longer able to be called Earth-like. But, let us suppose that the Earth is in fact infinitely old; even if that were true, we are unaware of that fact, and thus we should say that a later finite temporal part Earth-like.
The point is, that Earth-like planets are important because they constitute the life-worlds of humanoid beings, at least up to current levels of technology. Thus, they are the entities whose possible or actual existence we as humanoid beings should be most interested in. “Earth-likeness” is not predominantly a scientific concept defined purely in terms of physical characteristics; rather, it is defined in terms of humanoid characteristics. Now, given known physical laws, the humanoid definition implies a physical definition; but, potentially, there may be other (actual or possible) universes with different physical laws, in which there exist planets which are not Earth-like by a scientific definition inspired by the physical laws of this universe, and yet we might still recognize as Earth-like in a humanoid sense.
So, let us say that the spatiotemporal volume of Earth-like planets is bounded. Are the associated property dimensions bounded?
—Physics suggests there may well be limits, e.g. a maximum possible temperature, maybe Planck temperature.
—But, even if there is, for instance, no maximum possible temperature, it would seem that, for instance, there is a maximum temperature T, achievable on an Earth-like planet, without threatening that planet’s status of Earth-like, in the generic case. By the “generic case”, I mean to exclude, for example, temperatures achieved in contexts such as nuclear weapons, fusion reactors, particle accelerators, etc.
—Let us suppose there is an upper limit T, to the temperature achievable in the general case on an Earth-like planet. But, suppose, there is no upper limit to the temperature achievable on an Earth-like planet in particle accelerators, etc. Imagine that we took such a planet, on which the maximum temperature in particle accelerators exceeds T, and created a duplicate, in which, by some supernatural means, it was ensured that every experience ever had by any observer on that planet was exactly the same as in the original planet, even though the temperature inside particle accelerators was limited to exceed T. So, for instance, even though the temperature inside the particle accelerator was limited to T, our hypothetical supernatural force would intervene to cause all experimental readings of the temperature inside the particle accelerator to be greater than T, precisely the same reading as in the original planet, even though the actual temperature was in fact limited to T. Thus, even though, the two planets would physically differ, all observations ever made by any humanoid being would be identical, between the two planets. Let us use this as a criterion of identity for Earth-like planets; therefore, we can define a maximum property space volume for Earth-like planets, such that, if any Earth-like planet has a greater property space volume, there is any identical Earth-like planet with no greater property space volume.
The above uses the example of temperature; but, we could reason the same for any property dimension.
So, an Earth-like planet has a finite property space volume. Is its property space volume discrete or continuous? Quantum theory would suggest that it is discrete. But, consider a hypothetical universe in which quantum theory is false. Even then, if we do not have quantum theory to discretize reality, we can appeal to our criterion of identity instead. For, it seems, that in any humanoid being, experiences are ultimately discrete rather than continuous. For all senses, there would be some finite amount, such that if the sensory input differed by less than this amount, the conscious experience would be indistinguishable. Any being, whose sensory system did not obey this principle, would not be a humanoid being. Now, let us consider, not direct sensory perceptions, but measurements taken through scientific instruments. In a quantum universe, these are inevitably discretized. But, what about non-quantum universes, in which measurement is possible to arbitrary accuracy? Let us suppose we have a planet in a continuous universe; let us transpose it to a discrete universe,using the same supernatural force as earlier to ensure the scientific measurements are identical. Thus, the property space volume of Earth-like planets is discrete, such that, if there is any Earth-like planet in a continuous property space, there is an identical Earth-like planet in a discrete property space.
Thus, we can conclude that:
—All Earth-like planets exist in a discrete, finite-dimensional, property space
—There is a finite upper bound on property space volume, such that every Earth-like planet has a property space volume less than or equal to that bound.
Therefore, there are only a finite number of possible Earth-like planets.
Hence, these are three possibilties with respect to the universe as a whole (let us also assume that spacetime is Archimedean):
1.The universe is spatiotemporally finite
2.The universe is spatiotemporally infinite, but Earth-like planets only exist within a finite, contiguous, sub-region of spacetime [we need the Archimedean property to prove that the sub-region is finite and contiguous]
3.The universe is spatiotemporally infinite, and an infinite number of Earth-like planets exist, but there are only a finite number of distinct Earth-like planets, but the universe contains an infinite number of identical copies of at least one of those planets
So, above is a sketched argument that there are only a finite number of Earth-like planets. I believe, one could sketch a similar argument, that there are only a finite number of humanoid observers. These two arguments are essentially related, in that one concerns the type of entities in whom we are interested (entities fundamentally like ourselves), and the other concerns the domain of their existence.
This should not be taken to mean that a space-faring civilization could not be humanoid. Clearly, it could be. Then, it would seem, that “Earth-like planet” is an insufficiently small domain. And yet, I think the point remains, that to be a humanoid, a being must be both finite, and also, finite beyond some upper limit. For example, a species with twice the average intelligence of homo sapiens would still be humanoid; however, a species with a billion times the average intelligence of homo sapiens would post-humanoid or non-humanoid. And, if there is a finite bound on the size of humanoid entities, then there is also a finite bound on the size of their domain, even if that domain could be interplanetary or interstellar. Indeed, what matters here is not the domain of the civilization as a whole, but the domain of the individuals. A single human being, in the space of one lifetime, could in principle visit every country on earth; every city on earth; every town on earth; etc. Thus, the actual domain of our civilization is more or less identical to the potential domain of each individual. But, conceivably, for a vast interstellar civilization, it might be far too vast for any single individual to visit all of it in one lifetime, even in principle, even if individuals in that civilization had lifetimes vastly exceeding our own.
Suppose the civilization was actually infinite. An infinite civilization could only contain a finite number of distinct humanoid individuals, so it must either contain an infinite number of identical copies of at least one humanoid individual, or a finite number of copies of humanoid individuals and an infinite number of non-humanoid individuals. Supposing the civilization contained only humanoid individuals, I think one might even be able to show that it must consist of an infinite number of disconnected finite segments, all absolutely identical, and thus be finite. For, how could two subregions that were absolutely identical (up to the identity of humanoid beings) sensibly interact? I suppose this issue is a bit like closed time-like curves.
Now, back to the three cases:
1.The universe is spatiotemporally finite
2.The universe is spatiotemporally infinite, but Earth-like planets only exist within a finite, contiguous, sub-region of spacetime [we need the Archimedean property to prove that the sub-region is finite and contiguous]
3.The universe is spatiotemporally infinite, and an infinite number of Earth-like planets exist, but there are only a finite number of distinct Earth-like planets, but the universe contains an infinite number of identical copies of at least one of those planets
Cases (1) and (2) differ only in inobservables, with respect to humanoid beings. So, we might say that, up to the identity of humanoid beings, they are the very same universe. And likewise, case (3) is, identical to (1) / (2), up to the identity of humanoid beings as well. Furthermore, why should we assume that there are an infinite number of absolutely identical copies, rather than a single copy, possibly with some complex topology? I mean, an infinite spacetime with an infinite number of repeating subregions is indistinguishable from a finite but unbounded spacetime, such as the surface of a hypersphere.
So, it seems, that in any case, the universe is spatiotemporally finite.
Many physicists would undoubtedly rejoice if an omniscient genie appeared at their death bed, and as a reward for life-long curiosity granted them the answer to a physics question of their choice. But would they be as happy if the genie forbade them from telling anybody else? Perhaps the greatest irony of quantum mechanics is that if the MWI is correct, then the situation is quite analogous if once you feel ready to die, you repeatedly attempt quantum suicide: you will experimentally convince yourself that the MWI is correct, but you can never convince anyone else!
Could you convince other people? Suppose you set up the quantum suicide experiment. You might do it in a public place, before a large crowd, and do everything possible to convince people that it is correctly configured (i.e. not faked in any possible way.) Assuming MWI is true, then in the vast majority of universes, they would see you die. But in a very small minority of universes, they would see you miraculously not die. What should those in the minority who see you live think of you? That you were some kind of divine being, invincible against even the most stupendous odds? Of course, your invincibility would be a one time affair, for if you were to repeat the experiment, in the vast majority of universes in which the you lived the first time you would die the second; still, there would always be that, ever smaller minority, of universes, which continue to be wowed by your divine invincibility, every single time. And, if such a divine being were to open its lips and speak to us, ought we not believe its wisdom?
No. Surely, even if we observed such a feat, the logical conclusion would be that in some way, unknown to us, you have faked the experiment. Assuming MWI, universes in which you lived by faking the experiment would be more likely than those in which you lived by carrying out the experiment correctly. Assuming the negation of MWI, the epistemic probability of undetectable fakery will be greater than the probability of miraculous survival. So, it seems, whether MWI is true or not, no one would ever be justified in believing MWI based on a third person observation of the quantum suicide experiment, even if they were in one of the vast minority of universes in which the experimental subject lives.
Indeed, even in the first person case: suppose there is conspiracy with arbitrary resources, whose mission, deriving from some peculiar sense of mischievousness, is to deceive you into believing that you have successfully carried out the quantum suicide experiment, thus causing you to believe that you have thereby proven to yourself the truth of MWI. Now, conspiracy theories inherently have a very remote probability of being true. And yet, how does that probability compare to the probability of survival in a quantum suicide experiment? Now, an interesting observation: the probability of the conspiracy existing and being successful, however small it is, is largely constant in terms of experimental duration. If your resources are sufficient to successfully deceive me for five minutes, surely they are also sufficient to deceive me for ten or fifteen minutes; thus the probability of a fifteen minute deception is not substantially less than the probability of a five minute deception. Whereas, the probability of a survival universe exponentially decays in terms of experimental duration. So, however small the probability of the conspiracy theory, we can easily make the experiment long enough that its probability will be greater than the probability of survival. So, it would seem, even if you carried out quantum suicide and lived, you would not be justified in believing the truth of MWI; the more reasonable conclusion is the existence of a conspiracy to make you believe in the truth of MWI.
So, it would seem, that the quantum suicide experiment can never justify us in believing in the truth of MWI, irrespective of the outcome of the experiment.
Now, I’ve attempted to show that quantum suicide cannot even convince us first person of the truth of MWI, contra Tegmark. But, let us suppose that Tegmark’s original point is in fact correct – that quantum suicide can be convincing first person but not third person. The question is — is an experiment whose very nature means that no one who successfully performs it could ever convince anyone else thereby a valid experiment? From a philosophy of science perspective, science is inherently a social activity, and thus it seems that such an inherently anti-social experiment could never be a scientific experiment, and, whatever knowledge about the world it might give us, such knowledge would not belong to science.
A religious believer is discussing the afterlife with a positivist. The positivist says:
If the existence of an afterlife would lead to paranormal activity, such as communication with ghosts or memories of past lives, as some have claimed, then it is a theory unsupported by the evidence. But, the idea as espoused by more sober religionists such as yourself, with no necessary paranormal implications, is not even a theory, because it does not even make unsupported predictions, it makes no predictions at all.
The religious believer (well, in this case a believer in one particular religion) replies:
On the contrary, my theory does make experimental predictions. I predict that after you die, you will reawaken before the judgement seat, as per Romans 14:10-12.
Now, both the MWI theorist’s quantum suicide experiment, and the Christian’s death experiment, are actually quite similar. They are both experiments that involve the death of the experimenter. Now, one has to ask, is it really valid to call an experiment that requires the death of the experimenter an “experiment”? Again, science is a social reality, and death is a separation from that reality. So an experiment which requires the investigator’s death (as opposed to the death of a mere subject) seems not to be an experiment. I suppose, the positivist needs to ask, whether their devotion to experimentalism is to a specifically scientific experimentalism, or a more broadly construed, even extra-scientific, experimentalism?
The Christian has one advantage which the MWI theorist does not; religious accounts of the afterlife, whatever their specific detail, tend to be inevitably social. If you wake up after death in some shape or form of afterlife, you may be unable to inform the living of your momentous discovery, but at least you will be able to share your Eureka moment with your fellow dead. So, the Christian’s experiment, is more scientific than the MWI theorist’s — it shares science’s inherent sociability, albeit in the context of a different society.
Sketch of an argument against the many worlds interpretation
—Essentially, as I understand it, the many worlds interpretation seeks to reduce probability distributions in observation to probability distributions among parallel universes.
—So, if quantum theory predicts, and experiments observe, that some quantum event occurs with 25% probability, then many worlds explains this as saying that in 25% of universes it occurs, and in the other 75% it does not.
—Now, first of all, the number of universes predicted by many worlds is unimaginably vast, if not actually infinite. Thus, it would seem, that almost every conceivable universe does by many worlds actually exist.
—Many worlds does place some constraints on the set of actual universes — it is not the same as modal realism or ultimate ensemble theory, in that there are actual physical laws which all universes must obey. But, let us distinguish two different types of potential parallel universes:
othose which a physicist or mathematician might be interested in, say those with radically different physical laws from our own
othose of maybe more quotidian interest – those which in broad concerns, such as physical laws, are largely identical to our own, and yet in numerous specific details are different; say, in which your favourite TV show is actually real, or in which that special someone you had a crush on in high school ends up being the love of your life, rather than someone you never ever see again
—Clearly, many worlds rules out at least some of the first group. It may well be the case that, even by many worlds, there is no universe supporting sentient life having at a macroscopic level a 174-dimensional spacetime. And yet, it seems unlikely that it rules out every, or even most or all, possible universes in which observed physical laws are identical to our own, but nonetheless certain events which in this universe some wish would occur and yet do not, actually do.
—More to the point, however; it seems there must be at least some universes in which, even if purely by the remotest chance, intelligent life exists despite radically different laws of physics being observed. For any finite probability, however small, if there are a sufficiently large number of universes, then the probability that at least one of them contains the desired state of affairs is as close to certain as we would like; and if there be an infinity of universes, almost surely such a universe exists.
—Now, the underlying assumption behind the many worlds theory is that the observed probability distribution within this universe can be extrapolated to the distribution of universes within the ensemble. But let us suppose, we are in an extremely unlikely yet nonetheless actual universe — we may observe within our own universe an extremely rare probability distribution, and thus by this assumption we would assume that this distribution is the norm for the universe ensemble.
—It might be objected that the aforementioned scenario is extremely unlikely; and yet, to so object is to engage in circular argumentation: for our judgement that it is unlikely is dependent on our judgement that it is false.
—And, going back to the point about many worlds, having certain pan-multiverse physical laws, thereby excluding certain mathematically / logically possible universes from those it claims to exist — it would seem, even if no such universes are actual, that there would be universes in which rational agents would be justified in believing they were in such a universe. But, by the same argument as earlier, that we can have no knowledge of the distribution of universes, thereby we have no reason to believe we are not in such a universe, thus we have no reason to believe in any pan-multiverse laws.
—What I am essentially trying to prove here, is that many worlds, as distinguished from modal realism, is self-defeating. Taking into account the existence of observers, and that if many worlds is true, then we are one of those observers (and, our belief in many worlds is itself subject to many worlds), it follows that we have no reason to believe in any version of many-worlds which is non-identical to Lewisian modal realism, or Tegmark’s ultimate ensemble theory.
—Thus it follows that many worlds is not a scientific theory, since modal realism certainly is not a scientific theory.
I have been working on a taxonomy of parallel universe theories. I think I can distinguish five primary types:
1) Physical Theories
Under this type I would include any theory of parallel universes which takes its inspiration from physics. I think the progenitor of this type must be the many worlds interpretation of quantum theory, as developed by Hugh Everett III and his various successors; but equally, other ensemble theories such as the string landscape, or the theory associated with cosmic inflation that different areas of the cosmos may represent different choices with respect to values for fundamental constants. I would also include in here the observation that, in an infinite non-deterministic universe, every possible event almost surely occurs.
2) Ultimate Ensemble theory
As per Max Tegmark. In other words, the universe of mathematics is identical to the universe of physics. I would say that this theory differs radically from the theories above, in that it no longer has a connection to any particular physical theory; it has definitely crossed over (far over) the boundary between physics and philosophy. And, it is an interesting question, how much it actually differs from Lewisian modal realism — certainly it does in inspiration: one, an attempt to explain the existence of the universe; the other, an attempt to explain the meaning of modal statements — but does it differ in substance?
3) Modal realism
As per David K. Lewis.
4) Simulation cases
As per Nick Bostrom’s Simulation Argument; parallel universes achieved through computer simulations.
5) Theistic theories
If one accepts the claims of classical theism, that there exists a deity who created the physical universe — might not that deity have created not merely one universe, but rather many? If the deity is omnipotent, surely it could do so if it wanted to; and even if it was not omnipotent, if it is powerful enough to create one universe, surely it is powerful enough to create many? And, this applies not only to classical theism, but equally to stronger (e.g. trinitarian theism) or weaker (e.g. deism or limited theism) positions. Now, unlike the previously mentioned viewpoints, I’m not aware of anyone who has ever actually defended this position, and yet, if one accepts the necessary theistic presumptions, which rightly or wrongly have been prevalent enough in history to be worth at least momentary consideration, it seems logically defensible. (Surah 1:2 is interesting in this context.)
