Re: KIM 2.3 (was Re: Time)
Le 11-janv.-09, à 17:55, Brent Meeker a écrit : Stathis Papaioannou wrote: 2009/1/11 Brent Meeker meeke...@dslextreme.com: I'm suggesting that running a state is incoherent. A machine running a program goes through a sequence of states. Consider 20 consecutive states, s1 to s20, which give rise to several moments of consciousness. Would you say that running the sequence s1 to s20 on a single machine m1 will give a different conscious experience to running s1 to s10 on m1 and separately s11 to s20 on m2? I'm suggesting that there has to be something that makes the states a sequence instead of just a set or an aggregate. I agree. What you need is a Universal system/machine/language/whatever. To say that something is a state in a computation, or that something is a computation, you need a universal machine capable of producing that computation. Now, assuming the yes doctor entails that the universal system does not need to be physical, and that the very term physical will have to be explained in term of purely combinatorial or arithmetical universal system. The explanatory gain is fabulous, then. Bruno Brent http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: KIM 2.3 (was Re: Time)
2009/1/12 Brent Meeker meeke...@dslextreme.com: A machine running a program goes through a sequence of states. Consider 20 consecutive states, s1 to s20, which give rise to several moments of consciousness. Would you say that running the sequence s1 to s20 on a single machine m1 will give a different conscious experience to running s1 to s10 on m1 and separately s11 to s20 on m2? I'm suggesting that there has to be something that makes the states a sequence instead of just a set or an aggregate. In that case, there would be a difference between the two cases I described above, perhaps a gap in consciousness when the sequence is separated into two parts on two machines. But this presents conceptual problems. For a start, the observer notices no gap, and his external behaviour is also unchanged. If there is nevertheless a gap, would it be of infinitesimal duration or would its duration perhaps be that of the period of consciousness s10 and s11 would have given rise to had they occurred in the usual causally connected way in the one machine? What would happen to the gap if there were communication between the two machines, say by sneakernet? And what if the information transfer between the two machines was unreliable, so that the right state was transferred only half the time? -- Stathis Papaioannou --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Exact Theology was:Re: Kim 2.4 - 2.5
Bruno, sorry for taking it jokingly (ref: Steinhart): Latest research revealed that Shakespeare's oeuvre was not written by William Shakespeare, but by quite another man named William Shakespeare. John From: Bruno Marchal marc...@ulb.ac.be To: everything-l...@googlegroups.com Sent: Monday, January 12, 2009 4:57:17 AM Subject: Re: Exact Theology was:Re: Kim 2.4 - 2.5 Ah bravo Günther, now I am depressing :( I don't succeed in finding my Steinhart book. I don't either find the book on the net, and I begin to doubt it is a book by the same Steinhart. I have some doubt that my Steinhart has Eric as first name. I remember only that the book was taking Pythagorus very seriously, which is rare in the literature. Once I find the information, I will let you know. Your Steinhart seems interesting too (and open to Pythagorus), like Leslie is interesting too, btw. Of course those people seems not to be aware of all the progress in the field ... Have a good day, Bruno Le 11-janv.-09, à 16:54, Günther Greindl a écrit : Which one did you have? Was it good? (I only know his papers) Cheers, Günther Bruno Marchal wrote: Gosh, you make me realize that I have lost my book by Steinhart. . I did appreciated it some time ago. Thanks for the references. Best, Bruno On 09 Jan 2009, at 21:26, Günther Greindl wrote: Hello, My domain is theology. scientific and thus agnostic theology. I specialized my self in Machine's theology. Or Human's theology once assuming comp. The UDA shows (or should show) that physics is a branch of theology, so that the AUDA makes Machine's theology experimentally refutable. Will machines go to paradise? Some related work: http://www.ericsteinhart.com/abstracts.html Especially: Steinhart, E. (2004) Pantheism and current ontology. Religious Studies 40 (1), 1 - 18. ABSTRACT: Pantheism claims: (1) there exists an all-inclusive unity; and (2) that unity is divine. I review three current and scientifically viable ontologies to see how pantheism can be developed in each. They are: (1) materialism; (2) platonism; and (3) class-theoretic pythagoreanism. I show how each ontology has an all-inclusive unity. I check the degree to which that unity is: eternal; infinite; complex; necessary; plentiful; self-representative; holy. I show how each ontology solves the problem of evil (its theodicy) and provides for salvation (its soteriology). I conclude that platonism and pythagoreanism have the most divine all-inclusive unities. They support sophisticated contemporary pantheisms. and Steinhart, E. (2003) Supermachines and superminds. Minds and Machines 13 (1), 155 - 186. ABSTRACT: If the computational theory of mind is right, then minds are realized by computers. There is an ordered complexity hierarchy of computers. Some finite state machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible computers whose powers exceed the Church-Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. They have infinitely complex bodies. Transfinite games anchor their social relations. Especially the first paper (concerning Pythagorenaism) is interesting. Best Wishes, Günther http://iridia.ulb.ac.be/~marchal/ -- Günther Greindl Department of Philosophy of Science University of Vienna guenther.grei...@univie.ac.at Blog: http://www.complexitystudies.org/ Thesis: http://www.complexitystudies.org/proposal/ http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: MGA 2
Hello Bruno, I think you are correct, but allowing the observer to be mechanically described as obeying the wave equation (which solutions obeys to comp), Hmm well if you have a basis, yes; - but naked infinite-dimensional Hilbert Space (the everything in QM)? You put the finger on a problem I have with QM. I ill make a confession: I don't believe QM is really turing universal. The universal quantum rotation does not generate any interesting computations! Could you please elaborate a bit on the two above sentences. I am missing a more context to understand where really points to. And with the second sentence, I simply don't understand it. I am open, say, to the idea that quantum universality needs measurement, and this could only exists internally. So the naked infinidimensional Hilbert space + the universal wave (rotation, unitary transformation) is a simpler ontology than arithmetical truth. Yet, even on the vaccum, from inside its gives all the non linearities you need to build arithmetic ... and consciousness. Cheers, mirek --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: MGA 2
Hi Mirek, On 12 Jan 2009, at 15:36, Mirek Dobsicek wrote: Hello Bruno, I think you are correct, but allowing the observer to be mechanically described as obeying the wave equation (which solutions obeys to comp), Hmm well if you have a basis, yes; - but naked infinite- dimensional Hilbert Space (the everything in QM)? You put the finger on a problem I have with QM. I ill make a confession: I don't believe QM is really turing universal. The universal quantum rotation does not generate any interesting computations! Could you please elaborate a bit on the two above sentences. I am missing a more context to understand where really points to. really was just some emphases. Also I should have said instead: I don't understand how QM can be really Turing Universal. This could be, and probably is, due to my incompetence. It is due to the fact that I have never succeed in programming a clear precise quantum Universal dovetailer in a purely unitary way. The classical universal dovetailer generates easily all the quantum computations, but I find hard to just define *one* unitary transformation, without measurement, capable of generating forever greater computational memory space. Other problems are more technical, and are related to the very notion of universality and are rather well discussed in the 2007 paper: Deutsch's Universal Quantum Turing Machine revisited. http://arxiv.org/pdf/quant-ph/0701108v1 And with the second sentence, I simply don't understand it. Me too. Forget it. Let me try to remember what I did have in the mind. I guess I did have wanted to say that a universal unitary transformation (what I meant by Universal Quantum rotation) cannot generate infinite complexity, although I have a good idea why a sufficiently big or rich unitary transformation can generate any long (but finite) simulation of any universal Turing machine. This is again related to my lack of success in just programming the Universal quantum Dovetailer. If you have any idea how to do that, let me know. I am not sure I am saying deep things (here :), just that I have not enough practice in quantum computing to make all this clear, and when I consult the literature on quantum universality it makes things worse (see the paper above). I could relate this with technical problem with the BCI combinator algebra, that is those structure in which every process are reversible, and no cloning are possible (cf the No Kestrel, No Starling summary of physics(*)). Those algebra are easily shown being non turing universal, and pure unitarity seems to me to lead to such algebra. This leads to the prospect that a sort of Everything-structure could exist, yet not be Turing universal. Computers would just not exist, in the sense that the universe, in that case, would not been able to provide the extendable memory space without which universality does not exist. This would not make the UDA (AUDA) reasoning false, but it would make the ultimate physics still much more constrained. Physical reality would be essentially finite. I was pointing on place where I am a bit lost myself, which means that I am the one who would like a bit more explanation. Could you implement with a quantum computer the really infinite counting algorithm by a purely unitary transformation? The one which generates without stopping 0, 1, 2, 3, ... That would already be a big help. Bruno (*) Marchal B., 2005, Theoretical computer science and the natural sciences, Physics of Life Reviews, Vol. 2 Issue 4 December 2005, pp. 251-289. I am open, say, to the idea that quantum universality needs measurement, and this could only exists internally. So the naked infinidimensional Hilbert space + the universal wave (rotation, unitary transformation) is a simpler ontology than arithmetical truth. Yet, even on the vaccum, from inside its gives all the non linearities you need to build arithmetic ... and consciousness. Cheers, mirek http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: KIM 2.3 (was Re: Time)
Stathis, thinking about this way (which I did when reading Egan's Permutation City) is indeed problematic - because then you would also have to let consciousness supervene on Lucky Alice (the one from MGA), right down to Super Lucky Alice (Alice which is made anew for every state through random events). In a materialist view, you can associate consciousness with states directly (which leads to strange consequences, see MGA for instance); or some part of the running is responsible - in which case you can't leave out the causal dynamics or maybe the material substrate - but that isn't computationalism anymore, because you must assume that the substrate is not turing-emulable (otherwise you would just have to choose a different, correct, substitution level). That is why I agree with Bruno - IF you assume COMP - and you are assuming it, I gather - then forget matter, and forget running, and forget isolated states - you will find your OMs in UD* - and as such, the states s1 through s20 etc will only contribute to the measure of histories for an OM, but will not constitute the OM _by themselves_. In one sentence: The states s1 through s20 (or any others) will contribute to the measure of a certain OM and the ingoing/outgoing histories, independent of order, if they can be attributed to a computation of an UD. Cheers, Günther Stathis Papaioannou wrote: 2009/1/11 Brent Meeker meeke...@dslextreme.com: I'm suggesting that running a state is incoherent. A machine running a program goes through a sequence of states. Consider 20 consecutive states, s1 to s20, which give rise to several moments of consciousness. Would you say that running the sequence s1 to s20 on a single machine m1 will give a different conscious experience to running s1 to s10 on m1 and separately s11 to s20 on m2? -- Günther Greindl Department of Philosophy of Science University of Vienna guenther.grei...@univie.ac.at Blog: http://www.complexitystudies.org/ Thesis: http://www.complexitystudies.org/proposal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: QM Turing Universality (was: MGA 2)
Thank you for a quick answer! I'll take a look at it, my curiosity approves additional items on my TODO list :-) Best, mirek The classical universal dovetailer generates easily all the quantum computations, but I find hard to just define *one* unitary transformation, without measurement, capable of generating forever greater computational memory space. Other problems are more technical, and are related to the very notion of universality and are rather well discussed in the 2007 paper: Deutsch's Universal Quantum Turing Machine revisited. http://arxiv.org/pdf/quant-ph/0701108v1 I could relate this with technical problem with the BCI combinator algebra, that is those structure in which every process are reversible, and no cloning are possible (cf the No Kestrel, No Starling summary of physics(*)). Those algebra are easily shown being non turing universal, and pure unitarity seems to me to lead to such algebra. Could you implement with a quantum computer the really infinite counting algorithm by a purely unitary transformation? The one which generates without stopping 0, 1, 2, 3, ... That would already be a big help. Bruno (*) Marchal B., 2005, Theoretical computer science and the natural sciences http://www.sciencedirect.com/science?_ob=ArticleURL_udi=B75DC-4GX6J45-1_user=532047_coverDate=12%2F31%2F2005_rdoc=1_fmt=_orig=search_sort=dview=c_acct=C26678_version=1_urlVersion=0_userid=532047md5=e087a268f1a31acd7cd9ef629e6dc543, Physics of Life Reviews, Vol. 2 Issue 4 December 2005, pp. 251-289. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Binary logic is insufficient
*The universe is not just black and white...*
Or another way to state that is that two truth values (true and false)
are insufficient to describe all propositions.
I propose the following:
If the universe exists and if for all things X and Y, the utterance X
contains Y is proposition, then the universe must operate with more
than the two usual truth values, true and false.
Consequently, since the universe does exist, and if we assume that X
contains Y is decidable, then at least three truth values are necessary
to describe the state of all propositions.
First the definitions and then the argument for the above proposition.
IMHO, the only room you might have for disagreement is in the
definitions, as the argument is valid.
*Definitions*
/Proposition/
Define a proposition to be something that can be decided, given enough
resources (such as computational power), and mapped to a single truth
value. An example of a proposition is I perceive the sky to be blue as
that is decidedly true (in good weather). Another is I perceive the sky
to be green, which is decidedly false. A proposition is a statement
that is decidable, meaning there is a best truth value to assign to
that statement. If there are only two truth values then an example of a
non-proposition is this statement is false, the liar's paradox. Later,
we will see that If the universe exists then it operates on more than
two truth values is a proposition as well because it will be decidedly
true.
/TV/
Let TV be a set, to be determined, consisting of truth values, possibly
such as TV = {true, false}, that represents all truth values
-sufficient- to allow for -all- propositions to have a unique,
assignable truth value, i.e., sufficient to decide all propositions.
/The universe/
For the purposes of this argument, the universe is the totality of all
that exists. Remark: what exists isn't completely clear and people
disagree on what exists; some, for example, believe that nothing exists
save themselves; this is called solipsism. Nevertheless, the definition
of universe stands as whatever that totality of all that exists is.
/Thing/
X is a thing if, and only if, X is or can be an object of thought.
(Slightly modified version of definition 3 from dictionary.com.)
/Containment/
One thing /contains/ another thing (where the 'another thing' is allowed
to be the first thing) if and only if the first thing has all of the
second thing's contents or constituent parts. In other words, all
content and/or constituent parts within the second thing is also content
of the first thing. (Slightly modified version of definition 3 from
dictionary.com.) Examples: the solar system contains the planet earth
and water molecules contain hydrogen. The primary example is the
universe: the universe contains -all- things.
*Argument*
/Overview/
The argument is an augmented form of Russell's theorem, sometimes
referred to as Russell's paradox, which proves that in Zermelo Frankel
set theory there is no set which contains every other set. The twist is,
this time, when talking about the universe, we know it exists. However,
we'll use the fact that a particular statement is a proposition except
it is neither true nor false. Recall that a proposition must have a
decidable truth value in order to be a proposition; so since this
statement is a proposition, there must be at least one extra truth value
that this proposition is most accurately mapped to in TV.
/The case for the universe operating on more than two truth values./
/Premise 1/
The universe as defined exists.
/Premise 2/
For all things X and Y, the utterance X contains Y is a proposition.
(Intuitively, I think the proposition X contains Y is 'usually' false.)
Suppose the universe exists and for all things X and Y, the utterance X
contains Y is a proposition. Consider the thing that contains all
things that don't contain themselves. Let's denote this thing by the
letter D. D is a thing because it is now an object of thought. The
universe, which contains all things, and itself exists by assumption,
contains D in particular as D is a thing.
Now consider the utterance D contains D. By assumption, D contains D
is a proposition. (X and Y are both D in this particular case.)
/D contains D can't be true/
Suppose that D contains D is a true proposition. Then, by the
definition of D, D does not contain D. Therefore, D contains D is
false. Since D contains D can't be both true and false, our original
assumption that D contains D is a true proposition is incorrect.
Consequently, D contains D is not a true proposition.
/D contains D can't be false/
A similar argument shows that D contains D can't be false. If we
suppose D contains D is false, then D does does not contain D is
true. However, by the definition of D, D contains D is then true since
D contains all things that don't contain themselves. This
Re: QM Turing Universality (was: MGA 2)
On 12 Jan 2009, at 17:24, Mirek Dobsicek wrote: Thank you for a quick answer! I'll take a look at it, my curiosity approves additional items on my TODO list :-) Manage keeping finite your todo list :) I have finished the reading of the paper I mentioned (Deutsch's Universal Quantum Turing Machine revisited) and I see they have very similar problems, probably better described. The paper mentions (but does not tackle) an old problem already described by Shi 2002, which made me think at the time that the notion of Universality is a bit dubious in the quantum realm. To sum up: is there a (never stopping) quantum counting algorithm? I think I can build a Quantum UD from it, well in case the Shi problem is not too much devastating. But here, and now, I got a feeling there is just no quantum counting algorithm ... Cheers, Bruno PS Note that AUDA (the arithmetical UDA) is in principle already able to solve completely that problem. It is still possible that the material hypostases of the self-observing *classical* universal machine lacks both the kestrels and the starlings, and their descendant combinators in which case comp predicts that physics is NOT Turing Universal. Comp would predict that not all natural numbers are in any possible nature or physics! in principle only because the translation in arithmetic leads to very complex arithmetical formula (bounded by PI_1 IN Arithmetical Truth, if you know a bit of degrees of unsolvability. I will perhaps explain a bit of this, but take it easy for not making explode the todo list :). Note the beauty of comp: even if there are no physical universal machine in the physical universe (including the physical universe(s)), *you* (and other persons) are and remains universal machine. We do not live in physical universes, we just traverse them to be able to chat some bits, perhaps. The first persons would be spiraling through an infinite sequence of rotations, if said through an image. http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: KIM 2.3 (was Re: Time)
Stathis Papaioannou wrote: 2009/1/12 Brent Meeker meeke...@dslextreme.com: A machine running a program goes through a sequence of states. Consider 20 consecutive states, s1 to s20, which give rise to several moments of consciousness. Would you say that running the sequence s1 to s20 on a single machine m1 will give a different conscious experience to running s1 to s10 on m1 and separately s11 to s20 on m2? I'm suggesting that there has to be something that makes the states a sequence instead of just a set or an aggregate. In that case, there would be a difference between the two cases I described above, perhaps a gap in consciousness when the sequence is separated into two parts on two machines. But this presents conceptual problems. For a start, the observer notices no gap, You are assuming the set of states is a sufficient simulation to instantiate an observer, which is what I doubt. and his external behaviour is also unchanged. If there is nevertheless a gap, would it be of infinitesimal duration or would its duration perhaps be that of the period of consciousness s10 and s11 would have given rise to had they occurred in the usual causally connected way in the one machine? In human consciousness, as instantiated by brains, there is a process in which signal/information is not local, it is distributed in spacetime and is connected causally which means, per relativity, that you cannot make any unique spacelike snapshot and label it the state. I don't go so far as to claim that consciousness *must be* instantiated in this way, but I think there must be something that makes the states part of a process - not just snapshots. Bruno gets around the problem of defining states by assuming a digital Turing like process, but then he has to provide something besides spacetime to make the set of states a sequence; which is he does by invoking the requirement that they be a computation. I have some doubts as to whether this is enough, but at least it is something. Brent What would happen to the gap if there were communication between the two machines, say by sneakernet? And what if the information transfer between the two machines was unreliable, so that the right state was transferred only half the time? --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Binary Logic is Insufficient
The universe is not just black and white...
Or another way to state that is that two truth values (true and false)
are insufficient to describe all propositions.
I propose the following:
If the universe exists and if for all things X and Y, the utterance X
contains Y is proposition, then the universe must operate with
more than the two usual truth values, true and false.
Consequently, since the universe does exist, and if we assume that X
contains Y is decidable, then at least three truth values are
necessary to describe the state of all propositions.
First the definitions and then the argument for the above proposition.
IMHO, the only room you might have for disagreement is in the
definitions, as the argument is valid.
Definitions
Proposition
Define a proposition to be something that can be decided, given enough
resources (such as computational power), and mapped to a single truth
value. An example of a proposition is I perceive the sky to be blue
as that is decidedly true (in good weather). Another is I perceive
the sky to be green, which is decidedly false. A proposition is a
statement that is decidable, meaning there is a best truth value to
assign to that statement. If there are only two truth values then an
example of a non-proposition is this statement is false, the liar's
paradox. Later, we will see that If the universe exists then it
operates on more than two truth values is a proposition as well
because it will be decidedly true.
TV
Let TV be a set, to be determined, consisting of truth values,
possibly such as TV = {true, false}, that represents all truth values -
sufficient- to allow for -all- propositions to have a unique,
assignable truth value, i.e., sufficient to decide all propositions.
The universe
For the purposes of this argument, the universe is the totality of all
that exists. Remark: what exists isn't completely clear and people
disagree on what exists; some, for example, believe that nothing
exists save themselves; this is called solipsism. Nevertheless, the
definition of universe stands as whatever that totality of all that
exists is.
Thing
X is a thing if, and only if, X is or can be an object of thought.
(Slightly modified version of definition 3 from dictionary.com.)
Containment
One thing contains another thing (where the 'another thing' is allowed
to be the first thing) if and only if the first thing has all of the
second thing's contents or constituent parts. In other words, all
content and/or constituent parts within the second thing is also
content of the first thing. (Slightly modified version of definition 3
from dictionary.com.) Examples: the solar system contains the planet
earth and water molecules contain hydrogen. The primary example is the
universe: the universe contains -all- things.
Argument
Overview
The argument is an augmented form of Russell's theorem, sometimes
referred to as Russell's paradox, which proves that in Zermelo Frankel
set theory there is no set which contains every other set. The twist
is, this time, when talking about the universe, we know it exists.
However, we'll use the fact that a particular statement is a
proposition except it is neither true nor false. Recall that a
proposition must have a decidable truth value in order to be a
proposition; so since this statement is a proposition, there must be
at least one extra truth value that this proposition is most
accurately mapped to in TV.
The case for the universe operating on more than two truth values.
Premise 1
The universe as defined exists.
Premise 2
For all things X and Y, the utterance X contains Y is a proposition.
(Intuitively, I think the proposition X contains Y is 'usually'
false.)
Suppose the universe exists and for all things X and Y, the utterance
X contains Y is a proposition. Consider the thing that contains all
things that don't contain themselves. Let's denote this thing by the
letter D. D is a thing because it is now an object of thought. The
universe, which contains all things, and itself exists by assumption,
contains D in particular as D is a thing.
Now consider the utterance D contains D. By assumption, D contains
D is a proposition. (X and Y are both D in this particular case.)
D contains D can't be true
Suppose that D contains D is a true proposition. Then, by the
definition of D, D does not contain D. Therefore, D contains D is
false. Since D contains D can't be both true and false, our original
assumption that D contains D is a true proposition is incorrect.
Consequently, D contains D is not a true proposition.
D contains D can't be false
A similar argument shows that D contains D can't be false. If we
suppose D contains D is false, then D does does not contain D is
true. However, by the definition of D, D contains D is then true
since D contains all things that don't contain themselves. This
contradiction implies that D contains D is not false.
Conclusion
So we've established that D contains D is neither true nor false. By
premise 2, D contains
