Various Musings of Simon James Kissane

Universals

noreply@blogger.com (Simon James Kissane) — Sat, 06 Sep 2008 08:51:00 +0000

Consider all chairs. They seem to all have some property in common, that of being a chair. How do we explain this property? A universalist might say, there exists a concept, form, idea, of chairness, which exists independently of any individual chair, which all the individual chairs participate in. A nominalist, by contrast, would claim that "chairness" has no real existence; "chair" is nothing more than a label, which we choose to apply to certain things; ultimately, all they have in common is the fact that we choose the same label to refer to them.

Let us suppose we agree with the nominalist. But then let us turn to an individual chair. Much as chairs are individuals, which are claimed to participate in a universal, so we might observe that each individual chair is in fact a compound object - it is compounded temporally of temporal parts; it is compounded spatially of different physical subcomponents; as an experience, it is compounded of different qualia. And it is claimed that these various subcomponents, these various qualia, participate in the individual. How is this relationship of participation of the subcomponents or qualia in the individual different from the participation of the individual in the universal? So, if we agree with the nominalist that the later participation is merely nominal, should we not also hold that the former participation is equally nominal? So it seems, that when we believe in the existence of a chair, we are as deluded as when we believe in the existence of a universal of chairness.

An argument that a Q-space account is more fundamental than a P-space account: Consider a chair. Does the chair have a clear boundary with the air? Experientally it seems it does. And, in terms of a Q-space account, it certainly does, since Q-space is no finer than the limits of our perception. And yet, P-space is far finer than the limits of our perception; thus, we can ask, what is the boundary of the chair, in terms of molecules, or atoms, subatomic particles, etc? And it seems, that later question is impossible to answer with exact certainty at the boundary. Which suggests, that a Q-space description of a chair is more natural, and hence more fundamental, than a P-space description, which suggests that Q-space is more fundamental than P-space.

Buddhistic musings

noreply@blogger.com (Simon James Kissane) — Thu, 04 Sep 2008 11:48:00 +0000

Derek Parfit writes (p.281 of Reasons and Persons):

Is this truth [of reductionism] depressing? Some may find it so. But I find it liberating, and consoling. When I believed that my existence was a such a further fact, I seemed imprisoned in myself. My life seemed like a glass tunnel, through which I was moving faster every year, and at the end of which there was darkness. When I changed my view, the walls of my glass tunnel disappeared. I now live in the open air. There is still a difference between my life and the lives of other people. But the difference is less. Other people are closer. I am less concerned about the rest of my own life, and more concerned about the lives of others.

Even though, I do not share Parfit’s reductionism, I think this passage is intriguing because it acknowledges that the question of personal identity, even when approached from the most abstract, rational, secular perspective, is always an issue of great personal, psychological, even spiritual import, whatever conclusions we may draw. I suppose it should not be surprising that personal identity is personal.

To what extent can Parfit’s views be seen to parallel the Buddhist doctrine of anatta / anatman? Has Parfit attained nirvana?

Questions about Buddhism:

— Suppose there is karma and samsara. Now, let us suppose atman was true. I should be concerned about my next life, because it will be me who suffers or benefits in it. Then, suppose atman is false. Then, why should I be concerned about the next life, since if there is no common self which exists across lives, then it is not me who suffers or benefits, but some other person whom my deeds or cravings caused to exist — why should I care for them?

— Suppose there is karma and samsara. Now, let us suppose atman is true, and furthermore the atman incapable of any merger or division, and can occupy but one body at a time. Hence, after each death, there can only be one immediately subsequent rebirth, and before each birth, there can only be one immediately subsequent death. But, suppose on the contrary, anatman, and the bundle theory (of skandhas) often associated with it are true. Now, in the later case, why should I assume that one bundle gives rise to only one immediately subsequent bundle, or that one bundle is only given rise to by one immediately preceding bundle? Would it not be equally possible, for I to have multiple immediately subsequent lives, or for I to have multiple immediately preceding lives? Might not the bundle elements simply return to the All, only to be taken out of it again, in some essentially random configuration, such that I could have no reason to think I am the successor of any preceding person any more than any other, or that any future person will be any more or less my successor than any other? But if this is the case, I should not be concerned by karma.

Nick Bostrom writes (in Are you living in a computer simulation?):

Further rumination on these themes could climax in a naturalistic theogony that would study the structure of this hierarchy, and the constraints imposed on its inhabitants by the possibility that their actions on their own level may affect the treatment they receive from dwellers of deeper levels. For example, if nobody can be sure that they are at the basement-level, then everybody would have to consider the possibility that their actions will be rewarded or punished, based perhaps on moral criteria, by their simulators. An afterlife would be a real possibility. Because of this fundamental uncertainty, even the basement civilization may have a reason to behave ethically. The fact that it has such a reason for moral behavior would of course add to everybody else’s reason for behaving morally, and so on, in truly virtuous circle. One might get a kind of universal ethical imperative, which it would be in everybody’s self-interest to obey, as it were “from nowhere”.

Let us suppose that we are living in a computer simulation. Let us furthermore suppose, that our simulators have simulated us to fulfil some petty desire of theirs (e.g. I want to be a Hollywood movie star), and that all the horrors of human history (wars, holocausts, etc.) have been accurately simulated, so that the authenticity of the fulfilment of the petty desire can be better guaranteed. Having done so, let us say our simulators feel some twang of guilt (And all time past, was it all for this?, to quote Swinburne), and wish to justify to themselves their behaviour by saying: “Well, let us at the end give them the same opportunity that we have; let us even assume, the same opportunity as we had, for as surely as there are those beneath us, there must also be others above us, who have treated us in the very same way; we cannot give up our desires — for without desire fulfilment, what is the point of existence? — but, if there is no ”

One day you are walking down the street, and you see a man hitting his girlfriend. You try to intervene, and he pulls out a gun and shoots you dead. The media lauds you as a noble good Samaritan, innocent victim, etc.; but, nevertheless, you are dead.

You awake from after the bullet wound. A being appears before you and says: I am a representative of the beings who created your world; you have lived your life, in order that their desires might be fulfilled through the existence of your world and all that is within it; how your life fulfilled those desires, however large or small a role it had in their fulfilment, is irrelevant. But, having so been used, it is only right that we atone by giving you the power to use others as we ourselves have used you. What, then, do you wish for?

What might you answer? Maybe, for a world in which you were not gunned down trying to save a total stranger. And, maybe, you might wish: I want a world in which the man who shot me has the worst life he possibly could.

So it seems, that some variation of Bostrom’s naturalistic theogony can result in a phenomenon not dissimilar to Karma.

Another question:

— If Karma is a theory of causation, must we assume that it is temporal? Suppose the universe is temporally finite and unbounded, and thus that time is cyclic. Then every world line is a closed time-like curve. If that was so, there would be no reason to assume that only the past can cause the future; so long as we allow indirect causation, there is seemingly no reason why the future cannot cause the past, and thus the Karmic consequences of an action might not be reaped before or after or simultaneously with the action itself. And, if every world-line is a CTC, might it be the case that not every such world-line has maximal circumference? In which case, we can make time-reversed causation as direct as we’d like, by making the circumference as small as we’d like.

The branch line case is seen by many as terminal for Cartesianism. If we assume that there is, at any one time, a one-to-one correspondence between bodies and souls, then either one, the other, or neither of the succeeding lines can still possess the same soul as the anterior line. And yet, neither of these three choices seems satisfactory. Thus, it is argued, Cartesianism must fail. But, suppose we deny the claim of one-to-one-correspondence. I might then analyse a branch-line case in my future as follows. Right now, I have two souls, which are absolutely identical, except that, when the branch-line occurs in my future, one soul will follow one line the other the other; the point of branching is the time at which they become distinct.

As much as I might branch, might I not also come together? At the moment, we experience our first-hand experiences first-hand; whereas we experience the first-hand experiences of others only third-hand. But suppose you and I were joined in such a way, that whatever you saw I saw, whatever you felt I felt, whatever you thought I thought, etc. Would we not, quickly, become unable to tell ourselves apart? Would we not then, cease to be two different persons, but have merged together as one? Or, to give a more Cartesian reading, just as in the branch-line case two previously identical souls have become distinct, so in the merger case two previously distinct souls have become identical.

Parfit feels liberated from the glass tunnel by his reductionism. And yet suppose the glass was real, not merely illusory — am I then condemned to live within it, as long as I live, or else forever? What if the branch line, and the merger line, were not merely philosophical gedanken, or rare actual occurrence, but the reality in the lives of all of us? What if we had one single predecessor, of which we are all branch lines? What if we have one single successor, which is of us all a merger? Indeed, if we had one single ultimate predecessor and one single ultimate successor, might it not be that the two were in fact one and the same, in one great cycle of time? And if we were to give a Cartesian reading to such a chain of events, might we not conclude that the glass wall is but a temporary phenomenon; the wall is broken in branching and merging; and, in the beginning and the end, then many walls reduce to one wall, which encompasses all that is. Thus, to be liberated from our glass walls, we do not have to pretend not to see them.

What is the point of anatta? To escape the glass wall?

We can consider two models of the Cartesian soul. One, a fuller model, in which the soul is the person, and it has all the properties which can be ascribed to a person — likes, dislikes, loves, hates, desires, beliefs, a name, a history; etc. — and a simple model, in which the souls has no properties other than being exposed to a particular qualia stream; anything we might ascribe to a person is reducible to certain qualia in the qualia stream, either of that person or of some other; a reductionism, not of psychological states to physical states, but rather a reductionism of both psychological and physical states to qualia. Is the point of anatta, to deny the fuller model, to deny the permanence of these myriad attributes? For if that is the intention, then the simpler model equal denies the myriad attributes; they are but the ephemera of qualia; they come and go as the qualia change. And, if the branching and merging of all be true, then they change from and to something which cannot be identified with the person of the fuller model, even if it remains the atom of subjective identity, bound to a Q-space region, which the simpler model assumes.

Sorites and humanoid intelligences

noreply@blogger.com (Simon James Kissane) — Wed, 03 Sep 2008 08:48:00 +0000

In my various musings, I have made significant use of the notions of "humanoid being" and "Earth-like planet", which I have argued are essentially connected notions. (Humanoid beings can only exist on Earth-like planets -- it may be objected that they can also exist on spaceships or space colonies; but, the essence of the idea of Earth-like planet is that involves certain types of sensations and a certain order of magnitude of volume of sensation -- thus, the term "Earth-like planets" should be taken to include human settlements in space or on non-Earth-like planets.)

Now, I realise this falls victim to Sorites paradox. For example, I claim that humanoid beings can only have a finite and bounded intelligence. And yet, I cannot name any such bound, and it would seem, by Sorites paradox, no such bound exists.

Consider the case, in which beings exist with ever increasing intelligence, without limit. This is a scenario which falls victim Sorites paradox -- suppose I try to fix some limit b, such that a being is humanoid if its intelligence is less than b. But if there exist beings with both slightly more and slightly less intelligence than b, one could claim my choice of limit is arbitrary. And if the intelligence distribution was sufficiently smooth, one could claim that any such choice I might make would be arbitrary.

Suppose, on the contrary, that only a finite number of beings exist, have ever existed and ever will exist. Then, there must be (or have been) a being such that no being has, ever has had or ever will have a greater intelligence. Now, is this being humanoid? Suppose the answer is yes -- is then the notion of humanoid being precisely definable? One should say, that a humanoid being is any being with intelligence no greater than that of the greatest ever intelligence. One might object, that a purely hypothetical being with even greater intelligence might still, if it existed, be justifiably called humanoid; and yet, it would seem, that to entertain such an objection would be rather pointless; it is one thing to ask whether our concepts can be applied to beings whom we do not know to exist, but then again we do not know that they do not or might not either; but, when it has been established as a matter of fact (in this case, by assumption) that no such being ever has or ever will exist, the question then seems pointless to answer or entertain.

I would assert that either (1) every being which exists is humanoid; or (2) there exist a finite number of beings, some of which are humanoid and some of which are not. Now, in the latter case, we may still encounter Sorites around humanoid beings; but since, the main point of invoking the notion of humanoid beings was to prove their finitude, if that was established then the continued maintenance of the concept might not be so necessary.

Rationality in Parallel Universes

noreply@blogger.com (Simon James Kissane) — Tue, 02 Sep 2008 11:53:00 +0000

As I understand it, one of the points of Derek Parfit's Reasons and Persons is that questions of rationality and personality identity are intimately connected.

People will frequently give up immediate benefits for their present self in favour of a greater benefit for some future self, whereas they might not give up the same benefit for their present self in favour of a greater benefit for a present or future other. They treat their future selves with some special consideration which they do not extend to the present selves of others. This special consideration is considered rational, on the grounds that their future self is the same person as their present self. So, this concept of the rationality of self-interest, assumes a concept of personal identity across time.

The problem is — if I have multiple future selves, not temporally subsequent from each other, but rather temporally simultaneous with each other, how do I make sense of the concept of "giving up immediate benefits for my present self in favour of a future benefit for some future self"? What if, a certain course of action, will produce a better outcome for future self A, and a worse outcome for future self B? If I knew that one was such self was uniquely I in a way in which other such selves was not, I would be rationally justified in giving that future self special consideration above the others. But, in the absence of such knowledge, it seems that I am rationally obliged to extend to them all equal consideration.

Let us assume that MWI is true. Then, it seems, that I have an innumerable number of future selves, and that, whatever course of action I might take in the present, there will be future worlds, and hence future selves, in which that course of action has resulted in a positive outcome, and other future worlds in which that course of action has resulted in a negative outcome. So, there does not seem to be any course of action in the present, which can be said to benefit myself in the future; since, whatever I do, there are some future selves who are better, and other future selves that are worse. So, it seems, that rational behaviour is impossible.

The obvious objection is as follows: Act such that the future self whose world has the greatest probability amplitude experiences the most benefit. The problem I see here is, as I have earlier discussed, can we really claim to know the probability amplitudes of other universes? The only way we could know them, is by observation of this world, combined with an assumption that our world is an “average” world — and yet, there are no grounds to justify the assumption that our world is average. (We could say that, average worlds have the highest probability amplitudes; and yet, if we were in a non-average world, by this argument we would still think our world was average — thus, it seems equally epistemically likely that our world is average as it is not.) We should also ask, even if the concept of probability amplitudes can be justified, whether

Now, many minds might not have this problem, since many minds would hold that there are many present selves, which are exactly identical in every way, other than having as their successors differing future selves, those future selves themselves differing from each other in ways other than succession. (Which is not to say that many minds may not have other, different, problems.)

Does modal realism have this problem? Suppose there exists two universes, which are right now exactly identical, and one of which is our universe, but which begin to diverge in a thousand years time. Let us assume both universes are equally real; let us also assume that I only live for a normal human lifespan (thus I will be dead before the universes begin to differ), and let us assume there is no pre-mortal nor post-mortal existence. Therefore, for the entire duration of my life then there is an I in this world, and there is another person in that other world which is exactly like me in every possible way. Now, if we adopt Lewis’ approach to trans-world identity, which states that if two entities belong to different universes they are non-identical, even if their universe membership is the sole property by which they differ, then it follows that there actually exist two people, one of which who is me, and another one who is not me, but is exactly like me, in every possible way, and has always been exactly like me and always will be exactly like me. But, there seems to be no rational reason to claim two entities who are absolutely identical in content are nonetheless distinct, simply because each is distantly related to two distinct future events. It seems more intuitive to claim that there is one single entity, which is doubly related, once each to each of the distinct future different events. Therefore, I would say, we should reject Lewis’ approach to trans-world identity.

But, if we do so, then modal realism does fall victim to this very same issue? Any theory

I think, that for rational behaviour to be possible, the set of our actual futures must be sufficiently smaller than the set of all possible futures. It may be that there is a single actual future from the present; it may be there are several. But so long as there are only a few, it seems we do not have this problem.

Hypothetical scenario: I am homeless, and have been living on the streets for the last twenty years. An extraordinarily rich man appears, who has is famous for giving immense gifts to randomly selected homeless people. He offers me the following choice: $1 million today, or $1 billion in 2 weeks time. Which is it rational for me to accept? Almost everyone would say, all things being equal, that the $1 billion in 2 weeks is better than the $1 million today, and that I would be irrational to prefer the $1 million today. Suppose the world from today has a single unique future. Then, although because I don’t know the future, it could perchance turn out that the $1 million today is the best option (e.g. maybe (an epistemic maybe), whatever I do, the famous rich man will go mad and murder me in one weeks time — better then 1 week of living the good life on $1 million followed by death, then 1 week of continued poverty and homelessness followed by death, all the while waiting patiently to receive $1 billion which in the end will never come), I still feel justified in saying that the $100 million is the better choice.

Now, suppose it is true that every logically conceivable future is an actual future, and there is no reason to consider one future more “real” than another, and I know these facts. Then, it seems, that if I choose A, there exist futures in which C or D follows; and if choose B, there also exist universes in which C or D follows. So, it seems, that based on the universes which actually exist, I have no reason to believe that A causes C over D (or vis-à-vis), or that B causes C over D (or vis-à-vis). Therefore, it seems, preferring D over C, but being neutral in and of themselves as to A and B, that I have no reason therefore to choose one of A or B over the other. Thus, it seems, whatever I desire, that any course of action is as rational as any other, and thus, rational behaviour is impossible.

Suppose I know there are a limited number of actual futures (less than every possible, but more than only one). Would rationality be possible in these circumstances? It would depend, on what assumptions I could make about the choice function which chooses which worlds are actual and which are merely possible.

Let us suppose that Bostrom’s simulation hypothesis is true — suppose that, at a certain point in human history, technology develops to the point that human beings can create highly accurate computer simulations, and that we, rather than being “real” humans, are actually part of one of those computer simulations. Suppose we can assume that the simulators have reasonably similar goals, motivations, desires, etc., to us, and that they have created us to fulfil some desires on their part (e.g. desires for drama, for excitement, for sex, for role-playing, to explore historical what-if scenarios, etc.; the kind of reasons for which we today would create highly accurate computer simulations, if we had the power.) So, we know there are likely multiple future histories, and we don’t know which possible future histories are actual, but we do have at least some idea of the kind of factors which determine which possible future histories are actual and which are not. Our judgement of a certain course of action being rational is based on our holding certain causal theories, and our past observations support those theories. (e.g. (1) this rich man’s behaviour is well known, he has been on TV and in the newspaper, everyone talks about him, etc.; (2) a person, having established a pattern of behaviour, is likely to continue in it.) Our question is, are simulators having these motivations likely to create simulations in which these judgements are valid, or invalid? Or in other words, are simulators having these motivations likely to create simulations in which basic principles of inductive reasoning and reasoning from authority hold, or are so frequently violated as to be impossible to rationally adhere to? It seems, if the simulators are motivated by the factors aforementioned, they are likely to leave the causal structure of the world largely as we would expect, and only violate it on rare occasions, as necessary to achieve their goals; and given that these principles are only expressed as generalities, an occasional violation of a general principle is no violation at all, and thus, it seems the simulators will uphold them. Suppose, by contrast, that modal realism is true instead. Then, we have no reason to believe that the choice of universes which exist, would tend to support belief in inductive principles, since it seems every possible violation of those principles would occur in some future history, and every possible combination of those violations. So it seems, if we know there are multiple actual futures, then rationality is only possible if we can rationally assume that the selection of actual futures out of possible futures occurs in such a way as to encourage rationality.

Now, I have argued that under MWI, it is impossible to derive the probabilities of universes in the multiverse from the probabilities observed within any particular universe, since every possible particular set of probabilities will be observed by someone, and if it justified for any of them to derive multiverse-level probabilities from universe-level probabilities, then it is justified for everyone to make the very same derivation. Thus, we have no reason, based on observation of the probabilities in this universe, to believe that any particular assignment of probabilities in the multiverse is true.

Is the simulation scenario self-defeating in the same way? No. This is because, we have no reason to believe every possible particular set of probabilities will be observed by someone. Since only some possible universes exist, and the choice of which is based on certain motivations, we thus determine the multiverse-level structure. Since the universe-level structure of every universe would be driven by the same motivations, we have good reason to believe that one is a good cue to the other. In other words — if the actual universe determining principle is based on humanoid motivations, we have good reason to believe “as above so below” — i.e. intra-universe distributions are similar to inter-universe distributions. If, on the other hand, the determining principle is based on everything logically possible is, then we have no reason to believe there is any parallel between inter-universe and intra-universe distributions.

[Also relevant here is Bostrom’s general work on observer-dependence, as seen in both the simulation and doomsday arguments. I suppose, with MWI — if X observers actually exist, do we consider it equally likely for us to be any of them, or can we somehow claim that we are more likely to be some of those observers than others (e.g. more likely to be those observers having higher probability amplitudes?)? We might say, well, we observe p. But, all we can conclude from that, is 100% we are in the group of observers who observe p, and 0% that we are in the group of observers who do not. It still doesn’t justify the belief that we are an ‘average’ observer, i.e. one whose local probability measurements give an accurate measure of global probability measurements.]

Faith

noreply@blogger.com (Simon James Kissane) — Sun, 31 Aug 2008 08:36:00 +0000

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.

Objective truth in multiple universes

noreply@blogger.com (Simon James Kissane) — Sun, 31 Aug 2008 08:18:00 +0000

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.)

The pitchlessness of thought

noreply@blogger.com (Simon James Kissane) — Sun, 31 Aug 2008 07:15:00 +0000

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 model of humanoid beings

noreply@blogger.com (Simon James Kissane) — Sun, 31 Aug 2008 05:09:00 +0000

Definitions:

atom of subjective identity	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.

Q-space

noreply@blogger.com (Simon James Kissane) — Sun, 31 Aug 2008 05:02:00 +0000

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.