Re: A mathematical description of the level IV Multiverse
On 6/19/2015 8:41 AM, Bruno Marchal wrote: On 16 Jun 2015, at 01:41, meekerdb wrote: On 6/15/2015 8:15 AM, Brian Tenneson wrote: Therefore, perhaps proof of truth is an unattainable goal in math. Perhaps proof of truth is an unattainable goal anywhere. Math isn't concerned with true, it's only concerned with what theorems follow from given axioms. I disagree a lot with this. I'm afarid you confuse the tools, like a theory, formal or informal, with the subject matter. I'm afraid you do the same. You assume that the tools constitute a subject matter. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A (somewhat) different angle on the reversal
On Thu, Jun 18, 2015 Bruno Marchal marc...@ulb.ac.be wrote: Bruno Marchal got the feeling that John Clark develops an allergy to pronouns. From Bruno Marchal's long time experience, the roots of the allergy is guessed to come from the inability to keep the 1-3 person view distinction all along the thought experience If Bruno Marchal abandoned personal pronouns then Bruno Marchal would be FORCED to keep those 1-3 person view distinction straight all along the thought experience, and that is precisely why Bruno Marchal refuses to do it, Bruno Marchal's entire theory would evaporate away in a puff of ridiculousness. Personal pronouns in philosophical proofs are like dividing by zero in mathematical proofs, both are great places to hide sloppy thinking. I need John Clark still answering this: does JC agree that in step 3 protocol, John Clark doesn't remember what the step 3 protocol is but is quite certain it, like everything else in the proof, is not important. + the promise of giving coffee to both reconstitutions, the probability of the experience drinking coffee is one? Both? That's sounds rather dull, why not give give it to one but not the other? I ask John Clark in Helsinki, who already agreed that John Clark will survive (with comp and the default hypotheses), and I ask John Clark's expectation of drinking soon a cup of coffee. John Clark is 100% certain that John Clark will drink that coffee and John Clark is 100% certain that John Clark will not drink that coffee. And after the experiment is carried out the outcome will prove that John Clark was not only certain but correct too. Bruno Marchal just said all of them are you therefore it doesn't take a professional logician to figure out that you will see Moscow AND Washington. Brilliantly correct, for the 3p description of the experience attributed to 3p bodies. But as Kim pointed out, it does not take long to a child to understand that this was not what the question was about. If that is not the question you wanted answered then rephrase the question so it makes logical sense and ask it; you're a logician so you should know how to do that, and if not then get that child you were talking about to help you. I can't give an answer, not even a incorrect answer, to a incoherent question. The question is about the first person experience The? There is no such thing are THE first person experience! expected What on earth do expectations about the future have to do with the nature of personal identity? If things don't turn out as you expected does that make you feel like you've lost your identity? The question was what city will you see ?, to answer that question it is necessary to know what the word you We need only to agree on the approximate meaning which is enough to pursue the reasoning. And we have agreed to define the 3p you by your body ^^^ Hmm.. you has the body owned by you and it's true I do agree that You is you regardless of the definition of you. And this is a fine example of a tautology that like all tautologies is true but unlike some this one is silly and useless too. If Bruno Marchal dislikes that conclusion and wants to say you will see only one city then it would be necessary to change the definition of you from the guy who remembers being in Helsinki to something else. On the contrary, we can just keep that definition. Computationalism predicts that both will remember to be the guy in Helsinki Good, so Bruno Marchal is conceding that according to that definition of the pronoun you will see Moscow AND Washington. So both who have the memory of Helsinki understand what I meant by you (John Clark) will be in one city. What the hell?! If you has been duplicated then it would be IMPOSSIBLE for you to see only one city. Despite what your third grade teacher may have said if matter duplicating machines exist then the the word you is plural not singular. the question is about the future 1p experience Then the question is gibberish because there is no such thing as THE future 1p experience. and by comp, we know that I know nothing from comp. as each of them cannot feel to see both W and M simultaneously, So what? Suzzy had 2 apples and gave one to Tommy and one to Johnny, so who received an apple from Suzzy? Hmm... let me think. Tommy and Johnny? But there was 2 apples and yet both Tommy and Johnny agree they have only one apple! I believe this thought experiment is just as paradoxical as your thought experiment. Not very. That's enough to understand that in helsinki, knowing that you will survive and ^^^ Yep, personal pronouns can cover up a huge amount of sloppy thinking. Comp gives a precise answer That's cute, but to tell the truth I don't care what comp gives because I'm not interested in your baby-talk. In AUDA [...] And I''m not interested in your alphabet soup
Re: A (somewhat) different angle on the reversal
On 6/19/2015 10:57 AM, Bruno Marchal wrote: On 19 Jun 2015, at 02:36, meekerdb wrote: On 6/18/2015 4:11 PM, Bruce Kellett wrote: meekerdb wrote: On 6/18/2015 1:10 PM, John Clark wrote: On Thu, Jun 18, 2015 at 1:51 PM, meekerdb meeke...@verizon.net This is gitting muddled. '2+2=4' is a tautology if the symbols are given their meaning by Peano's axioms or similar axiom set and rules of inference. If the symbols are interpreted as the size of specific physical sets, e.g. my example of fathers and sons, it's not a tautology. In an equation, ant equation, isn't a tautology then it isn't true. An equation is just a sentence. A tautology is a declarative sentence that's true in all possible worlds. 2+11=1 in worlds where addition is defined mod 12. That's why an equation alone can't be judged to be a tautology without the context of its interpretation. But your counterexamples are simply changing the meaning of the terms in the equation. I agree that a tautology is true in all possible worlds, because its truth depends only on the meaning of the terms involved. If the meaning is invariant, the truth value does not change. But this is not invariant under changes in meaning. 2+2=4 is a theorem in simple arithmetic, and a tautology because of the way we define the terms. In a successor definition of the integers: 1=s(0), 2=s(s(0)), 3=s(s(s(0))), 4=s(s(s(s(0, 2+2=4 can be proved as a theorem. But that relies on the above definitions of 2, 4 etc. In modular arithmetic, and with non-additive sets, these definitions do not apply. Note, however, that this interpretation of 'tautology' differs from the logical interpretation that Bruno refers to. Bruce I don't think it's different if you include the context. Then it becomes Given Peano's axioms 2+2=4. Isn't that the kind of logical tautology Bruno talks about? Within that meaning of terms it's a logical truism. I don't think it's necessary to restrict logic to just manipulating and, or, and not. Bruno introduces modalities and manipulates them as though they are true in all possible worlds. But is it logic that a world is not accessible from itself? As you say, it depends of the context. Yet, the arithmetical reality kicks backs and imposed a well defined modal logic when the modality is machine's believability(or assertability), for simple reasoning machine capable of reasoning on themselves, as is the case for PA and all its consistent effective extensions. But why should we think of modal logic and the measure of true? I still haven't heard why a world should not be accessible from itself. Logic is intended to formalize and thus avoid errors in inference, but it can't replace all reasoning. Arithmetical truth is a well defined notion in (second order) mathematics. It does not ask more than what is asked in analysis. But all first order or second order *theories*, effective enough that we can check the proofs, can only scratch that arithmetical reality, which is yet intuitively well defined. It is not Given Peano axioms 2+2=4. It is because we believe since Pythagorus, and probably before, that 2+2=4, that later we came up with axiomatic theories capturing a drop in the ocean of truth. I didn't say that's why we believe 2+2=4; I said that's what makes it a tautology, i.e. when you include a context within which is provable. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
A riddle for John Clark
You find yourself in a sealed room. There is only one exit, a door. The next person to open the door will be killed, at which point the door will be disarmed. Fortunately for you, there is a duplication machine in the room that makes an exact replica of whatever is placed inside. How do you get out of the room? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A (somewhat) different angle on the reversal
On 18 Jun 2015, at 19:07, John Clark wrote: Before responding to Bruno Marchal's post John Clark would like to say that it's amazing how much sloppy thinking and elementary logical errors can be swept under the rug by the simplest shortest words like you and I; Promising introduction. I am not quite sure why suddenly you avoid the pronouns. You might develop a pronophobia. therefore John Clark requests that when Bruno Marchal rebuts this post Bruno Marchal does not use these personal pronouns. Bruno Marchal got the feeling that John Clark develops an allergy to pronouns. From Bruno Marchal's long time experience, the roots of the allergy is guessed to come from the inability to keep the 1-3 person view distinction all along the thought experience. Let us see. I mean let Bruno Marchal and any other possible reader of this list see. John Clark understands that this can lead to prose that sounds a bit awkward because the English language was never designed for this sort of thing, but making the effort can really clarify ones thinking. And no cheating by talking about THE future 1p as if it were singular and not plural. I need John Clark still answering this: does JC agree that in step 3 protocol, + the promise of giving coffee to both reconstitutions, the probability of the experience drinking coffee is one? I gave the criteria of confirmation, which are the statements written in the personal diaries, which are duplicated in the 3p view. I ask John Clark in Helsinki, who already agreed that John Clark will survive (with comp and the default hypotheses), and I ask John Clark's expectation of drinking soon a cup of coffee. On Thu, Jun 18, 2015 Bruno Marchal marc...@ulb.ac.be wrote: We're talking about multiple (probably infinite) copying and branching, so who the hell is you? All of them are you, I agree, and so the conclusion is logically inescapable, you will see Moscow AND Washington. In the 3-1 view. In any view! The question was what city will you see ?, to answer that question it is necessary to know what the word you We need only to agree on the approximate meaning which is enough to pursue the reasoning. And we have agreed to define the 3p you by your body, or its 3p description/implementation, and the 1p view by the guy who got the memories corresponding on its accessible and memorized sequence of experience, itself approximated, for the purpose of this reasoning, to the content of the diary, that the tele-travelers take with him in the reading-destruction boxes. means and Bruno Marchal just said all of them are you therefore it doesn't take a professional logician to figure out that you will see Moscow AND Washington. Brilliantly correct, for the 3p description of the experience attributed to 3p bodies. But as Kim pointed out, it does not take long to a child to understand that this was not what the question was about. The question is about the first person experience expected as a being doing some experience and surviving it. In that case, BOTH will agree that, indeed, although in the 3-1 view they have been reconstitituted in both city, they do feel to be in only one city. In the diary, the reconstituters wrote W (resp. M), not W M which is the 3_1 view, and not the 1-view. As I said, you sto the thought experience (which asks you to describes the 1-view) in the middle of the experience. But computationalism provides the simplest explanation of the difference between the 1p discourse, and its undeterminacies, and the 3p determinist description. If Bruno Marchal dislikes that conclusion and wants to say you will see only one city then it would be necessary to change the definition of you from the guy who remembers being in Helsinki to something else. On the contrary, we can just keep that definition. Computationalism predicts that both will remember to be the guy in Helsinki and both will agree to be in front of a unique city. So both who have the memory of Helsinki understand what I meant by you (John Clark) will be in one city. Both John Clark (the guy who remember Helsinki) agree that they are in front of one city. That prediction on the 1p experience if correct, for both of them. John Clark can't imagine what that new definition of you that would be but is willing to listen. So we did not need to change it. We need only to listen to all John Clarks relevant for the problem. But, of course, it is obvious that after the duplication, each reconstitution will feel to be only one of the reconstitutions That is irrelevant to answering the question what city will you see? . Yes, it is, given that the question is about the future 1p experience, and by comp, we know that from the 1p experience view the person does not feel being splitted at all. She feels to be a particular person with an history (WWMWMMMWW...M)
Re: A mathematical description of the level IV Multiverse
On 16 Jun 2015, at 01:41, meekerdb wrote: On 6/15/2015 8:15 AM, Brian Tenneson wrote: Therefore, perhaps proof of truth is an unattainable goal in math. Perhaps proof of truth is an unattainable goal anywhere. Math isn't concerned with true, it's only concerned with what theorems follow from given axioms. I disagree a lot with this. I'm afarid you confuse the tools, like a theory, formal or informal, with the subject matter. Traditionally the axioms are assumed to be true, but this concept of true is no more than a marker like #t which marks a property preserved under logical inference rules. For a logician, we can roughly say that truth means satisfied by a reality. But then logicians have studied the notion of reality mathematically through semantic or model theory. The other kind of true, as when we say It's true that the Earth is round. is a rough or approximate relation between a statement, The Earth is round. and some facts in the world which can in principle be tested empirically. It's like truth in jury trials, we may believe it beyond reasonable doubt, but we're never sure. Same in math. We might say that arithmetical truth, and computer science elementary basic truth, are, contrary to all other notion of truth, very well understood and accepted. So when you say truth is unattainable you need to distinguish the different uses of the concept. I think it is possible to determine that some things are true beyond a reasonable doubt. Yes, like most if not all theorem in arithmetic. But even more when we have an elementary proof (not making detour in analysis, like the use of complex number in natural number theory). Bruno Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A (somewhat) different angle on the reversal
On 18 Jun 2015, at 22:45, John Mikes wrote: Bruno wrote: Do you assume a physical reality, or are you agnostic on this question? I do believe in a natural or physical reality, but I am agnostic if it needs to be assume and thus involved primitive element, or if what we take as a physical universe is a (collective) experience of numbers that we can derive from arithmetic (as it seems to be necessarily the case once we bet that brains are Turing emulable (I am agnostic on this, but not on the fact that if the brain is Turing emulable then the physical is an emergent pattern in the mind of the (relative) numbers). Hard to follow the summersaults of your concepts. I was waiting for some 'mathematical' reality as well. To LIVE in this universe I have to accept some scientific conclusions of the little info we so far absorbed (observed?) from a wider infinite Nature. That does not mean I ASSUME. I may use it. Turing - as I think - was a human person so T-emulable is human conclusion. It is a human theory. That does not make it necessarily wrong. That's why we can be agnostic on this, and try to derive the consequence and compare with the rest of our beliefs. Again you seem to have circumwent the 'physical experience that we can derive from arithmetic vs. arithmetic, for which we learned a lot from Nature. I don't think arithmetic just jumped out from the human mind as Pallas Athene from the head of Zeuss. In full armor. Integers, Primes or else. We know a nice history how zero was invented and so on after the Romans with their decimal(pentagonal?) system. Invented or discovered? I don't think human can invent zero. They can learn it from nature, but I doubt that nature would even exist without the number zero making some sense. Our agnosticism may be different (I stress the so far unknown and maybe even unknowable infinite complexity of the Entirety as potentially influencing our (known/knowable) world as the basis of MY agnosticism. Beyond that I try to comply with the World as we humans may know it by now). We never know as such, except opur consciousness, which is not on the public domain. But it happens that some belief can be true. Today, we accumalate evidence that nature is not fundamentally real, and that the nature that we see arise from dreams statistics. That might be false, or true, but that is enough to remain agnostic on naturalism and physicalism. The least I try to do is to illustrate that we don't know what is the case. Bruno JM On Thu, Jun 18, 2015 at 3:59 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 17 Jun 2015, at 22:11, John Mikes wrote: Bruno: to describe what OTHERS did does not mean (in my vocabulary) that I KNOW (agree?) the same domain as it was handled. I 'know' (or may know) the efforts to derive science by human scientists. Does NATURE have regularities indeed? or our scientific observation assigns returning facets and calls them regularities as long as they are not contradicted? OK, maybe I should use EVENTS instead of regularities. And please do not make me a Straw-Man by repeating what I wrote. Your sentence: Humans *might have learned a lot in mathematics by looking at nature, but this does not prove that nature precedes logically mathematics. I have not included logically and may write: Q.e.D. Do you assume a physical reality, or are you agnostic on this question? I do believe in a natural or physical reality, but I am agnostic if it needs to be assume and thus involved primitive element, or if what we take as a physical universe is a (collective) experience of numbers that we can derive from arithmetic (as it seems to be necessarily the case once we bet that brains are Turing emulable (I am agnostic on this, but not on the fact that if the brain is Turing emulable then the physical is an emergent pattern in the mind of the (relative) numbers). Bruno On Wed, Jun 17, 2015 at 10:45 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 15 Jun 2015, at 21:53, John Mikes wrote: Brent concluded ingeniously: They have a theory for why THIS might be so no matter what THIS is. You just have to find the right mathematics to describe it and miracle of miracles the mathematics is obeyed! Brent May I step a bit further: by careful observations humanity (or some 'higher' cooperating intellect maybe?) derived the connotions we call 'theories', math, even axioms to make them fit. Then we fall on our backside by admiration that they fit. Don't forget the historic buildup of our 'science' etc, stepwise, as we increased the observational treasure-chest of Nature. So Nature does not obey mathematics, mathematics has been derived in ways to follow the observed regularities of Nature. I thought that you were agnostic, but here you talk like if you *knew* something, which I don't. Even assuming Nature, the question remains: why does
Re: Reconciling Random Neuron Firings and Fading Qualia
On Mon, Jun 15, 2015 at 3:23 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 15 Jun 2015, at 15:32, Terren Suydam wrote: On Sun, Jun 14, 2015 at 10:27 AM, Bruno Marchal marc...@ulb.ac.be wrote: We can, as nobody could pretend to have the right intepretation of Plotinus. In fact that very question has been addressed to Plotinus's interpretation of Plato. Now, it would be necessary to quote large passage of Plotinus to explain why indeed, even without comp, the two matters (the intelligible et the sensible one) are arguably sort of hypostases, even in the mind of Plotionus, but as a platonist, he is forced to consider them degenerate and belonging to the realm where God loses control, making matter a quasi synonym of evil (!). The primary hypostase are the three one on the top right of this diagram (T, for truth, G* and S4Grz) T G G* S4Grz Z Z* X X* Making Z, Z*, X, X* into hypostases homogenizes nicely Plotinus presentation, and put a lot of pieces of the platonist puzzle into place. It makes other passage of Plotinus completely natural. Note that for getting the material aspect of the (degenerate, secondary) hypostases, we still need to make comp explicit, by restricting the arithmetical intepretation of the modal logics on the sigma- (UD-accessible) propositions (leading to the logic (below G1 and G1*) S4Grz1, Z1*, X1*, where the quantum quantization appears. The plain language rational is that both in Plotinus, (according to some passagethis is accepted by many scholars too) and in the universal machine mind, UDA show that psychology, theology, even biology, are obtained by intensional (modal) variant of the intellect and the ONE. By incompleteness, provability is of the type belief. We lost knowledge here, we don't have []p - p in G. This makes knowledge emulable, and meta-definable, in the language of the machine, by the Theaetetus method: [1]p = []p p. UDA justifies for matter: []p t (cf the coffee modification of the step 3: a physical certainty remains true in all consistent continuations ([]p), and such continuation exist (t). It is the Timaeus bastard calculus, referred to by Plotinus in his two-matters chapter (ennead II-6). Sensible matter is just a reapplication of the theaetetus, on intelligible matter. I hope this helps, ask anything. Bruno I'm not conversant in modal logic, so a lot of that went over my head. Maybe the problem is here. Modal logic, or even just modal notation are supposed to make things more easy. For example, I am used to explain the difference between agnosticism and beliefs, by using the modality []p, that you can in this context read as I believe p. If ~ represents the negation, the old definition of atheism was []~g (the belief that God does not exist), and agnosticism is ~[]g (and perhaps ~[]~g too). The language of modal logic, is the usual language of logic (p q, p v q, p - q, ~p, etc.) + the symbol [], usually read as it is necessary (in the alethic context), or it is obligatory (in the deontic context), or forever (in some temporal context), or It is known that (in some epistemic context), or it is asserted by a machine (in the computer science context), etc... p abbreviates ~[] ~(possible p = Non necessary that non p). All good here. Thus my request for plain language justifications. In spite of that language barrier I'd like to understand what I can about this model because it is the basis for your formal argument AUDA and much of what you've created seems to depend on it. In AUDA, the theory is elementary arithmetic (Robinson Arithmetic). I define in that theory the statement PA asserts F, with F an arithmetical formula. Then RA is used only as the universal system emulating the conversation that I have with PA. Everything is derived from the axioms of elementary arithmetic (but I could have used the combinators, the game of life, etc.). So I don't create anything. I interview a machine which proves proposition about itself, and by construction, I limit myself to consistent, arithmetically sound (lost of the time) machine. This determined all the hypostases. It is many years years of work and the hard work has been done by Gödel, Löb, Grzegorczyck, Boolos, Goldblatt, Solovay. I think it's debatable that you didn't create anything. I think reasonable people could disagree on whether the 8 hypostases you've put forward as the basis for your AUDA argument are created vs discovered. I'm coming from an open-minded position here - but trying to assert that you're not creating anything strikes me as a move to grant unearned legitimacy to it. I still am not clear on why you invent three new hypostases, granting the five from Plotinus (by creating G/G*, X/X*, and Z/Z* instead
Re: super intelligence and self-sampling
On 16 Jun 2015, at 00:50, meekerdb wrote: On 6/15/2015 9:59 AM, Bruno Marchal wrote: On 11 Jun 2015, at 01:21, meekerdb wrote: On 6/10/2015 4:06 PM, LizR wrote: On 11 June 2015 at 06:26, meekerdb meeke...@verizon.net wrote: A human is an ape which torture other apes. Not just torture but also eliminate, e.g. homo erectus, homo neaderthalis,... It's called evolution. You sound like you're in favour. When they're winners and losers I'm in favor of being a winner. To win you need to master the art of losing. The future belongs to the good losers :) Is that an extrapolation from the past? It is more an interpolation on the futures :) It is a principle in the Art of the War. It is also a principle of many martial art, with the many ways to fall down, in judo, and technic to transform defeat into victory. Good losers are better than bad winners, if you mind this quasi- tautology (as the good is always better than the bad, by definition). Bruno Bruno Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A (somewhat) different angle on the reversal
On Thu, Jun 18, 2015 at 4:45 PM, meekerdb meeke...@verizon.net wrote: An equation is just a sentence. Yes, and in the sentence 2+2=4 let's list what the symbols mean: The symbol 2 means the successor of 1. The symbol + means and The symbol = means is. The symbol 4 means the successor of 3 A tautology is a declarative sentence that's true in all possible worlds. All tautologies are true but not all are useful. Tautologies say that something is something else expressed in a different way; if the difference in expression is very small or zero then the tautology is silly and useless, but if the difference in expression is enormous then the tautology can be profound and very useful indeed in advancing our understanding of how the world works. 2+11=1 in worlds where addition is defined mod 12. That's why an equation alone can't be judged to be a tautology without the context of its interpretation. That's still a tautology, all you've done is change the meaning of the + symbol. Tautologies have a bad reputation and I'm not sure why, yes some of them are trivial but others can be revolutionary allowing us to look at things in a different way, but silly or profound there is one virtue all tautologies have, they're all true. John K Clark Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: A (somewhat) different angle on the reversal
On 19 Jun 2015, at 02:36, meekerdb wrote: On 6/18/2015 4:11 PM, Bruce Kellett wrote: meekerdb wrote: On 6/18/2015 1:10 PM, John Clark wrote: On Thu, Jun 18, 2015 at 1:51 PM, meekerdb meeke...@verizon.net This is gitting muddled. '2+2=4' is a tautology if the symbols are given their meaning by Peano's axioms or similar axiom set and rules of inference. If the symbols are interpreted as the size of specific physical sets, e.g. my example of fathers and sons, it's not a tautology. In an equation, ant equation, isn't a tautology then it isn't true. An equation is just a sentence. A tautology is a declarative sentence that's true in all possible worlds. 2+11=1 in worlds where addition is defined mod 12. That's why an equation alone can't be judged to be a tautology without the context of its interpretation. But your counterexamples are simply changing the meaning of the terms in the equation. I agree that a tautology is true in all possible worlds, because its truth depends only on the meaning of the terms involved. If the meaning is invariant, the truth value does not change. But this is not invariant under changes in meaning. 2+2=4 is a theorem in simple arithmetic, and a tautology because of the way we define the terms. In a successor definition of the integers: 1=s(0), 2=s(s(0)), 3=s(s(s(0))), 4=s(s(s(s(0, 2+2=4 can be proved as a theorem. But that relies on the above definitions of 2, 4 etc. In modular arithmetic, and with non- additive sets, these definitions do not apply. Note, however, that this interpretation of 'tautology' differs from the logical interpretation that Bruno refers to. Bruce I don't think it's different if you include the context. Then it becomes Given Peano's axioms 2+2=4. Isn't that the kind of logical tautology Bruno talks about? Within that meaning of terms it's a logical truism. I don't think it's necessary to restrict logic to just manipulating and, or, and not. Bruno introduces modalities and manipulates them as though they are true in all possible worlds. But is it logic that a world is not accessible from itself? As you say, it depends of the context. Yet, the arithmetical reality kicks backs and imposed a well defined modal logic when the modality is machine's believability(or assertability), for simple reasoning machine capable of reasoning on themselves, as is the case for PA and all its consistent effective extensions. Arithmetical truth is a well defined notion in (second order) mathematics. It does not ask more than what is asked in analysis. But all first order or second order *theories*, effective enough that we can check the proofs, can only scratch that arithmetical reality, which is yet intuitively well defined. It is not Given Peano axioms 2+2=4. It is because we believe since Pythagorus, and probably before, that 2+2=4, that later we came up with axiomatic theories capturing a drop in the ocean of truth. Peano arithmetic here is only an example of sound and correct Löbian machine. The truth of 2+2=4 does not depend of the truth of if this or that machine believes it or not. Yet with comp, the proposition the machine x believes y becomes theorem of sigma_1 complete machine. It is an ideal case, amenable, by comp, to mathematics. That ideal case leads to an already very subtle theology, with some canonical struggle between the different views the self can take. The machine's soul is bipolar at the start, well octopolar. Although PA only scratches the arithmetical reality, PA is already quite clever and self-aware about its own abilities. Bruno Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
