gilbert@cs.glasgow.ac.uk (Gilbert Cockton) (08/23/88)
In reply to two separate comments from Marvin Minsky in comp.ai.digest >Yes, enough to justify what those who "knew" that they were right did >to Bruno, Galileo, Joan, and countless other such victims. >More generally, let's see more learning from the past. Take care when there are trained historians on the net :-) It is not beliefs that kill, but the power to act on them. Where "scientists" have had power, notably in Nazi Germany and Stalinist Russia, they have killed to suppress heresy, just as the religious leaders of pre-modern Europe killed the early scientists to put down particularly annoying heresies. Of course, you will say, these people in Germany and Russia were not scientists. As a trained historian, it is enough for me that they called themselves scientists, just as the Inquisition were undoubtedly Christian. But as a historian, I would exercise great caution in extending the facts of a previous time into the present. One thing one can learn from the past is that this went out of fashion years ago :-) The way to analyse what a scientist or Christian would do now, given the absolute power enjoyed by the Inquisition, is to examine their beliefs. Neither group are democrats, nor would they respect many existing freedoms. Note that I am talking of roles of science and religion. As these people live in democracies, the chances are that the values of the wider society will repress the totalitarian instincts of their role-specific formal belief systems. Do not take this analysis personally. The way to attack my argument is to demonstrate that scientific or christian AUTHORITY are compatible with a liberal democracy. Any scientist who believes in a society regulated by scientific reason (which would rule out the need for consultative subjective democracy) would, given the power, introduce gulags, mental hospitals and other devices for the control of the irrational and the heretical. If anyone finds this unreasonable, consider how scientists wield power when they do have it in academic organisations and funding bodies. Admittedly they only murder rival research rather than rival researchers. Stakes don't have to be made from wood :-< P.S. Sure, move this discussion somewhere else :-) -- Gilbert Cockton, Department of Computing Science, The University, Glasgow gilbert@uk.ac.glasgow.cs <europe>!ukc!glasgow!gilbert
smryan@garth.UUCP (Steven Ryan) (08/27/88)
>The way to analyse what a scientist or Christian would do now, given >the absolute power enjoyed by the Inquisition, is to examine their >beliefs. Neither group are democrats, nor would they respect many >existing freedoms. Note that I am talking of roles of science and >religion. As these people live in democracies, the chances are that >the values of the wider society will repress the totalitarian >instincts of their role-specific formal belief systems. Do not take >this analysis personally. The way to attack my argument is to >demonstrate that scientific or christian AUTHORITY are compatible with a >liberal democracy. I feel you have made the distinction between Christians and Christianity implicitly, and I wish to make it explicit. The ideals of Christianity, tolerance, mercy, and love, would make an excellent system. Western Christians, on the other hand, still tend toward out German (cultural) ancestors. (I don't know about Eastern Christians.) I do take issue that Christians are held in checked by the wider society. In this country Christians are the majority: it is eternal internal conflicts between the sects that holds things in checks.
lag@cseg.uucp (L. Adrian Griffis) (08/30/88)
In article <1311@garth.UUCP>, smryan@garth.UUCP (Steven Ryan) writes: > I feel you have made the distinction between Christians and Christianity > implicitly, and I wish to make it explicit. > > The ideals of Christianity, tolerance, mercy, and love, would make an > excellent system. Western Christians, on the other hand, still tend toward > out German (cultural) ancestors. (I don't know about Eastern Christians.) Another "ideal" of Christianity is the notion that part of what make one a good person is believing the right things. In other words, A great deal of unpleasentness awaits one who does not believe in the right things. It's not clear to me who tolerance, mercy, and love (Compassion) can ever be meaningful when they are something that one must do to please others. It strikes me that this is likely to lead to profound confusion over what as individuals beliefs really are. This is not to say that Science never indulges in this sort of intolerance of beliefs. But at least Science as a whole does not state as part of its fundamental platform that you must accept such and such a belief as fact, without evidence and without question (regardless of what individual scientist may do). It's not clear to me at all that any system based on the notion of belief-as- a-performance can be as the root of an "excellent" system of government. > > I do take issue that Christians are held in checked by the wider society. In > this country Christians are the majority: it is eternal internal conflicts > between the sects that holds things in checks. > And am I ever grateful for that. ---L. Adrian Griffis -- UseNet: lag@cseg L. Adrian Griffis BITNET: AG27107@UAFSYSB
ok@quintus.uucp (Richard A. O'Keefe) (09/02/88)
In article <545@cseg.uucp> lag@cseg.uucp (L. Adrian Griffis) writes: >This is not to say that Science never indulges in this sort of intolerance >of beliefs. But at least Science as a whole does not state as part of its >fundamental platform that you must accept such and such a belief as fact, >without evidence and without question (regardless of what individual scientist >may do). Straw man! Straw man! Neither does Christianity state any such thing. A major theme of the Bible is "here is the evidence". Biblical Archaeology (which tests the historical claims to the extent that they *can* be tested by present archaeological methods) is regarded as a PRO-religious activity. Thomas *is* one of the Apostles, after all... >Another "ideal" of Christianity is the notion that part of what make one >a good person is believing the right things. Again, not so. To quote the Bible (paraphrased, because my memory's not that reliable): "You believe in God? So do the devils!" An analogy: you cannot enter into an effective marriage with a particular woman as long as you continue to believe that she is a fossilized whale. Criticims of any religion are more effective when they are well-informed. I'm a little bothered by this reification of "Science" as if it were an agent capable of "indulging in" behaviours and "stating" things. Perhaps Gilbert Cockton could clarify the ontological status of "Science" for us (:-). What's the relevance of all of this to AI, anyway? Are AI people unusually sensitive to "Science" issues because we want to be part of it, or what? The study of English literature is not normally regarded as part of "Science", but it's a decent intellectual field for all that.
smryan@garth.UUCP (Steven Ryan) (09/05/88)
>This is not to say that Science never indulges in this sort of intolerance >of beliefs. But at least Science as a whole does not state as part of its >fundamental platform that you must accept such and such a belief as fact, >without evidence and without question (regardless of what individual scientist >may do). Frequent mistake--to do science you have to accept the scientific method on faith. Essentially science states that the universe is rational and objective. Ultimately, any way of viewing the universe is based on assumptions taken on faith. A similar subject is the Church-Turing hypothesis (after all, this is comp.ai). Minsky-style people assert it is true and justifies their most ambitious scheme. >> I do take issue that Christians are held in checked by the wider society. In >> this country Christians are the majority: it is eternal internal conflicts >> between the sects that holds things in checks. > >And am I ever grateful for that. I once heard that in English Civil War Protestant Anglicans and Puritans fought each other with the hatred normally reserved for Catholics. I suppose the battle between pro-ai and anit-ai programmers is similar.
francis@proxftl.UUCP (Francis H. Yu) (09/06/88)
Christian Bible is a piece of junk. Let's forget it.
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (09/06/88)
From article <1369@garth.UUCP>, by smryan@garth.UUCP (Steven Ryan): " ... " Frequent mistake--to do science you have to accept the scientific method on " faith. Why do I have to do that? I don't think anyone has to do that. It's just as well people don't have to know that the method will work before they will use it, since theories and experiments sometimes fail, don't they? If you want to treat the failures as discrediting the theories and experiments always, rather than the scientific method, you are confusing science and magic -- when the magic doesn't work, the magician says: "Well, I didn't do it right this time." " Essentially science states that the universe is rational and " objective. No, it doesn't. In those instances where theories have worked well, we can reasonably conclude that in the relevant domains the universe was to a certain extent lawful. If you want to take a leap of faith and go beyond this to adopt science as a religion, of course you may. You and Mr. Wells. " Ultimately, any way of viewing the universe is based on assumptions " taken on faith. Maybe, but why view the universe? We need to adopt provisional assumptions to get on, but there's no need to have faith in them. That's as harmful in ordinary life as it is in science. Greg, lee@uhccux.uhcc.hawaii.edu
robinson@pravda.gatech.edu (Steve Robinson) (09/07/88)
In article <707@proxftl.UUCP> francis@proxftl.UUCP (Francis H. Yu) writes: >Christian Bible is a piece of junk. Let's forget it. Anything, if abused, taken out of context, etc, etc can be said to be a piece of junk. I doubt that you have read the Bible with any open mindedness at all or you would at least have to give it credit for being a dissemination of some excellent wisdom and advice. Those that attempt to make the Bible a yardstick of science or make it fit into a one or another philosophical mold always come up short and either have to admit they can't do it or make up something that sounds plausible to them to cover the gap. Just because you've seen these efforts fail does not mean that the Bible fails in its purpose or is junk. Do you even know what the Bible claims as its purpose (not what others say it claims)? Of course, to find that out you will have to read it because if I tell you then I've made a claim for it. I have other strong personal opinions and beliefs that I defer writing at this time but will share if contacted via email. Regards, Stephen P.S. The relevance to ai here is that anything in ai, if abused, taken out of context........
josh@klaatu.rutgers.edu (J Storrs Hall) (09/07/88)
>Christian Bible is a piece of junk. Let's forget it.
If nothing else, the C.B. is one of the most successful and infectious
meme complexes in our intellectual history, and deserves careful
meta-study.
--JoSH
Relevance: I suspect that a study of memetic ecology would prove
quite profitable to AI.
Reference: "The Ecology of Computation", B.A.Huberman, ed.,
North-Holland, 1988.u-dmfloy%sunset.utah.edu@utah-cs.UUCP (Daniel M Floyd) (09/07/88)
In article <707@proxftl.UUCP> francis@proxftl.UUCP (Francis H. Yu) writes: >Christian Bible is a piece of junk. Let's forget it. What? I missed the premise and supporting evidence for this conclusion. I think I understand 'Christian Bible' and 'Let's forget it'; however, the construct 'piece of junk' is too ambiguous to agree with. Is this literary, historical, scientific, theological, sociological, or some other junk class refered to? Furthermore, what is this doing in comp.ai? *Personal* replies or flames welcome. Let's let comp.ai do it's thing while we do ours elsewhere. Keep in mind, I have candle snuffers and a flame thrower of my own. (;<)=
smryan@garth.UUCP (Steven Ryan) (09/08/88)
Seems I made I mistake. When I referred to scientific method I was referring to a philosophy: - Nobody plays games with universe. Entities interact in fixed manner; that is, the planets go around the sun because the sun's mass has distorted the local continuum, not because Ares and Jove and ... are having a chariot race. It is assumed the universe plays by a fixed set of rules--the challenge is to determine the rules. - Only public knowledge is necessary to understand the universe. In order to convince you I know what a rule is, I have to be to demonstrate it in repeatable fashion. Private revelations are not sufficient to demonstrate I understand the universe. It would seem what I mean by science differs from other people. >" Frequent mistake--to do science you have to accept the scientific method on >" faith. > >Why do I have to do that? I don't think anyone has to do that. It's >just as well people don't have to know that the method will work before >they will use it, since theories and experiments sometimes fail, don't >they? If you are referring to a specific theories, they should never be accepted as more than convenient explanations given the current facts. Otherwise it becomes dogma. I was not referring to this theory or that--I was referring to the philosophy on which these theories are demonstrated. >" Essentially science states that the universe is rational and >" objective. > >No, it doesn't. Assuming the law of the excluded middle law, `No, it doesn't,' means either science doesn't state this--in which case we are at cross definitions and nothing further of value can be said--or the universe is irrational--there is something transcendental which can never be captured by our theories--or the universe is subjective--and it can only be explained by private revelation. >No, it doesn't. In those instances where theories have worked well, >we can reasonably conclude that in the relevant domains the universe was to >a certain extent lawful. If you want to take a leap of faith and go beyond >this to adopt science as a religion, of course you may. You and Mr. Wells. Science is philosophy on how the universe can be understood. If some aspect if the universe cannot be understood in this way, then science is incomplete. Christianity asserts this is true: that there exists transcendental forces which science cannot explain. That is an assumption. >" Ultimately, any way of viewing the universe is based on assumptions >" taken on faith. > >Maybe, but why view the universe? We need to adopt provisional assumptions >to get on, but there's no need to have faith in them. That's as >harmful in ordinary life as it is in science. You need to view the universe, in part, just to get on with ordinary life. Isn't adopting provisional assumptions an act of faith? I don't recall saying once assumptions are made, they cannot be changed. If faith says faith can't be changed, fine, those are your assumptions, but don't expect me to agree. I define faith as adopting assumptions without proof. That's it. Any formal system requires such assumptions. I get the feeling many people like to think of themselves as rational creatures. I don't know why. I can't think of an rational behaviour which is enjoyable because rational behaviour is devoid of joy or sorrow or any emotion. It's the irrational parts of me that have all the fun: watching the setting sun, feeling the cool breeze, sitting on the lawns watching the geese on Vasona. I have no problem saying I take these assumptions because it make me feel good (irrational) or because they are convenient (rational). I really don't understand anti-religion people. I understand objecting to the actions of people in the name of their religions, and I understand people disagreeing and choosing to reject religion, but I don't understand condemning religion out of hand. Religion is an act of faith. Saying the sun will rise (or rather the earth will descend) tomorrow is ultimately an act of faith.
u-dmfloy%sunset.utah.edu@utah-cs.UUCP (Daniel M Floyd) (09/08/88)
In article <1383@garth.UUCP> smryan@garth.UUCP (Steven Ryan) writes: >...[No it doesn't and more]... >Science is philosophy on how the universe can be understood. If some aspect >if the universe cannot be understood in this way, then science is incomplete. >Christianity asserts this is true: that there exists transcendental forces ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >which science cannot explain. That is an assumption. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >...[more blah blah that we read]... I agree with the argument (mostly). However, this point I've under-pointed needs clarification. No it doesn't. (Here we go again). No, Christianity doesn't make that assertion. Some sects may. Not all do. Some are more moderate and assert: that there exists transcendental forces which science cannot explain *today*. This allows the concept of God as a being the understands 'science' so well that he not only understands the universe, but controls it using scientific laws. A being like that might even be able to make some artificial intelligence that isn't so artificial. (This is comp.ai, or are we changing it to comp.theology.vs.sci?). ;-)
ceb@edai.ed.ac.uk (Colin Bridgewater) (09/08/88)
In article <707@proxftl.UUCP> francis@proxftl.UUCP (Francis H. Yu) writes: >Christian Bible is a piece of junk. Let's forget it. This is truly an ignorant assumption.....ignoring evidence in a supposedly scientific endeavour makes the whole enterprise futile. If you write the Bible off so easily, what else doesn't get by you ?
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (09/09/88)
From article <1383@garth.UUCP>, by smryan@garth.UUCP (Steven Ryan): " ... " Isn't adopting provisional assumptions an act of faith? Not really. Consider the provisional assumption of a reductio ad absurdum argument. " ... I define faith as adopting assumptions without proof. It's an odd definition -- if we adopt it, we are led to the conclusion that all of us have faith and are therefore religious. " That's it. Any formal system requires such assumptions. Well, I would say that some natural deduction systems of logic have no assumptions -- only rules of derivation. But you can probably find a definition of 'assumption' that makes what you say true. " I get the feeling many people like to think of themselves as rational creatures. If so, that's foolish of them. I don't think it's foolish to try to distinguish the rational from the irrational, and sometimes, for certain purposes, to try to be rational. You've proposed definitions of science and faith that prevent one from distinguishing them. Greg, lee@uhccux.uhcc.hawaii.edu
spector@brillig.umd.edu (Lee Spector) (09/09/88)
In article <2362@uhccux.uhcc.hawaii.edu> lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes: >From article <1383@garth.UUCP>, by smryan@garth.UUCP (Steven Ryan): >" I get the feeling many people like to think of themselves as rational > creatures. " > >If so, that's foolish of them. I don't think it's foolish to try to >distinguish the rational from the irrational, and sometimes, for >certain purposes, to try to be rational. Rationality is not an all or nothing phenomenon. I highly recommend a book by Christopher Cherniak (a U of MD Philosopher) called MINIMUM RATIONALITY. Humans do not, and in fact can not, meet what Cherniak calls the "ideal rationality condition." However, there are levels of rationality between ideal rationality and no rationality. Cherniak characterizes various levels and discusses the possibility of cognitive systems with various capabilities attaining the given levels. - Lee Spector, U. of MD Computer Science Dept. (spector@brillig.umd.edu)
afo@s.cc.purdue.edu (Neil Rhodes) (09/09/88)
In article <2362@uhccux.uhcc.hawaii.edu> lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes: >From article <1383@garth.UUCP>, by smryan@garth.UUCP (Steven Ryan): >" That's it. Any formal system requires such assumptions. > >Well, I would say that some natural deduction systems of logic have >no assumptions -- only rules of derivation. But you can probably >find a definition of 'assumption' that makes what you say true. > I have a problem with Mr. Lee's reasoning in the above statement, and it seems to be the foundation of most of his recent arguments. If a formal system were to contain "only rules of derivation," what would these rules act upon to form statements (theorems) about the system? Rules alone in a formal system give you nothing. For this reason, you need a given set of statements (axioms) from which these rules can derive other statements (theorems). Since these axioms are not derived and are necessary to the formal system, then you must "believe" them to be true while working within the system. Since many scientific statements are derived within formal systems, to believe these statements you must also believe other statements which cannot be proved. If Mr. Lee still believes that science asks us to take nothing on "faith," then I am curious to know what flaws he finds in *my* reasoning. -- Neil Rhodes afo@s.cc.purdue.edu
ok@quintus.uucp (Richard A. O'Keefe) (09/09/88)
In article <1383@garth.UUCP> smryan@garth.UUCP (Steven Ryan) writes: >Seems I made I mistake. When I referred to scientific method I was referring >to a philosophy: [lots of stuff deleted] >Science is philosophy on how the universe can be understood. If some aspect >if the universe cannot be understood in this way, then science is incomplete. >Christianity asserts this is true: that there exists transcendental forces >which science cannot explain. That is an assumption. This seems to be saying that "science" _ought_ to be able to explain everything. If this is so, then I think we just have to put up with science being "incomplete". - in logic, we keep finding unprovable/undecidable things - in computing, we keep finding things which are infeasible in principle - in biology, neo-Darwinism distinguishes between "selection" (which can be explained by reference to phsyical/chemical/mathematic laws) and "mutation" (which "just happens"). We may try to explain how a mutant survives, but should not look for an explanation of why _that_ mutation. - in physics, the Copenhagen interpretation says that events "just happen" and rejects as wrong-headed "hidden variables" schemes. There is a tenuous connection with AI here. I suggested in an earlier message that it may be rational for an agent _NOT_ to test its beliefs, if the expected risk is high enough. Now we find that some explanations may not exist, or may not be computationally tractable if they do. So, when designing a learning system, how do we deal with this? How should it "decide" when to look for an explanation of something, and when to change the subject? Is there a connection with the "noisy data" problem?
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (09/09/88)
From article <3546@s.cc.purdue.edu>, by afo@s.cc.purdue.edu (Neil Rhodes): " ... " I have a problem with Mr. Lee's reasoning in the above statement, and it " seems to be the foundation of most of his recent arguments. " " If a formal system were to contain "only rules of derivation," what would " these rules act upon to form statements (theorems) about the system? " Rules alone in a formal system give you nothing. For this reason, you They give you nothing but tautologies, at least. " need a given set of statements (axioms) from which these rules can derive " other statements (theorems). Since these axioms are not derived and are " necessary to the formal system, then you must "believe" them to be true " while working within the system. There are formalizations of logic that require axioms, but not all do. Gerhard Gentzen created systems that have no axioms. For instance: Suppose p (one can introduce provisional assumptions freely) Conclude p (one can repeat an assumption as a conclusion) So, p implies p (since p was concluded on the basis of the provisional assumption p, one can derive the implication) " Since many scientific statements are derived within formal systems, to " believe these statements you must also believe other statements which " cannot be proved. Perhaps that's so. My example does not concern "scientific statements". I was reacting to a statement that "formal systems" require assumptions. They don't -- maybe formalized scientific systems do, in a sense, but even there assumptions can be treated as provisional rather than as axioms. This is not to disagree with what Neil Rhodes said just above. As you will observe, a Gentzen system does involve assumptions, but no specific assumption is given as part of the system. That is, there are no axioms. " If Mr. Lee still believes that science asks us to take nothing on ""faith," then I am curious to know what flaws he finds in *my* " reasoning. I find no flaws. If you are to have faith in scientific conclusions, you must have faith in scientific assumptions. But why have faith in anything? Why does "science ask us" to do this? If you have a need to believe in things, other than tautologies, I think you ought not to lay this at the door of science. It's a personal problem, which I think you should try to get over. Greg, lee@uhccux.uhcc.hawaii.edu
cik@l.cc.purdue.edu (Herman Rubin) (09/10/88)
In article <2365@uhccux.uhcc.hawaii.edu>, lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes: > From article <3546@s.cc.purdue.edu>, by afo@s.cc.purdue.edu (Neil Rhodes): .................... < " Rules alone in a formal system give you nothing. For this reason, you > They give you nothing but tautologies, at least. < " need a given set of statements (axioms) from which these rules can derive < " other statements (theorems). Since these axioms are not derived and are < " necessary to the formal system, then you must "believe" them to be true < " while working within the system. > There are formalizations of logic that require axioms, but not all > do. Gerhard Gentzen created systems that have no axioms. For > instance: > Suppose p (one can introduce provisional assumptions freely) > Conclude p (one can repeat an assumption as a conclusion) > So, p implies p (since p was concluded on the basis of the provisional > assumption p, one can derive the implication) In a treatment of natural deduction mentioned above, one shows that The customary axioms and axiom schemes are derivable. The customary rules of derivation are valid. Any theorem provable by natural deduction can be proved by using the customary axioms, axiom schemes, and rules of derivation. However, starting with a set of axioms and no rules, nothing more can be derived. Thus we see that rules are stronger than axioms. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)
bill@proxftl.UUCP (T. William Wells) (09/10/88)
In article <5699@utah-cs.UUCP> u-dmfloy%sunset.utah.edu.UUCP@utah-cs.UUCP (Daniel M Floyd) writes: : In article <707@proxftl.UUCP> francis@proxftl.UUCP (Francis H. Yu) writes: : >Christian Bible is a piece of junk. Let's forget it. : : What? I missed the premise and supporting evidence for this conclusion. : I think I understand 'Christian Bible' and 'Let's forget it'; however, : the construct 'piece of junk' is too ambiguous to agree with. Is this : literary, historical, scientific, theological, sociological, or some : other junk class refered to? : : Furthermore, what is this doing in comp.ai? : : *Personal* replies or flames welcome. Let's let comp.ai do it's thing : while we do ours elsewhere. Keep in mind, I have candle snuffers and : a flame thrower of my own. (;<)= My apologies. I introduced a new employee to the net without making sure he understood netiquette. Unfortunately, the cancellation didn't get out soon enough (or maybe just didn't get out.) This has been corrected. --- Bill novavax!proxftl!bill
smryan@garth.UUCP (Steven Ryan) (09/11/88)
>There are formalizations of logic that require axioms, but not all >do. Gerhard Gentzen created systems that have no axioms. For >instance: > Suppose p (one can introduce provisional assumptions freely) > Conclude p (one can repeat an assumption as a conclusion) > So, p implies p (since p was concluded on the basis of the provisional > assumption p, one can derive the implication) Well, I see an assumption--it assumes the existence of a formal system.
smryan@garth.UUCP (Steven Ryan) (09/11/88)
>>Science is philosophy on how the universe can be understood. If some aspect >>if the universe cannot be understood in this way, then science is incomplete. > >This seems to be saying that "science" _ought_ to be able to explain >everything. If this is so, then I think we just have to put up with >science being "incomplete". Shades of Goedel. If the universe is one big Turing Machine, unprovable/undecidable things do not exist in reality. Since science only deals with realities (are thoughts real?), it would be complete and still not have to explain transcendental phenomon.
smryan@garth.UUCP (Steven Ryan) (09/11/88)
>" Isn't adopting provisional assumptions an act of faith? > >Not really. Consider the provisional assumption of a reductio ad >absurdum argument. > >" ... I define faith as adopting assumptions without proof. > >It's an odd definition -- if we adopt it, we are led to the conclusion >that all of us have faith and are therefore religious. > >" That's it. Any formal system requires such assumptions. > >Well, I would say that some natural deduction systems of logic have >no assumptions -- only rules of derivation. But you can probably >find a definition of 'assumption' that makes what you say true. I really was hoping people would be content with an intentionally imprecise and informal discussion. If we want to be rigourous, I think it is important to define a process. I will propose: A process P is an orderred triple (S,M,Q). S is a undefined set (of states). M is a set of pdfs m:S->[0,1]. Q is a relation on MxM called transistions, denoted m->n. P is probablistic if for any m,s, 0<m(s)<1. P is not probablistics if for all m,s, m(s)=0 or m(s)=1. P is deterministic if Q is a function. P is nondeterministic if Q is not a function. P is a formal system if S is denumerable and Q is effectively computable. I think science and religion and CT could be explained as different constraints on S, M, and Q. If the consensus is to move the discussion into a cryptoformal notations, that's fine by me, since my education was in math anyway rather than philosophy.
smryan@garth.UUCP (Steven Ryan) (09/13/88)
>My apologies. I introduced a new employee to the net without >making sure he understood netiquette. Unfortunately, the >cancellation didn't get out soon enough (or maybe just didn't get >out.) > >This has been corrected. I hope nobody was decapitated, as in Monty Python.
ok@quintus.uucp (Richard A. O'Keefe) (09/13/88)
In article <1390@garth.UUCP> smryan@garth.UUCP (Steven Ryan) writes: >>>Science is philosophy on how the universe can be understood. If some aspect >>>if the universe cannot be understood in this way, then science is incomplete. [in a message with reference deleted, I wrote] >>This seems to be saying that "science" _ought_ to be able to explain >>everything. If this is so, then I think we just have to put up with >>science being "incomplete". >Shades of Goedel. Hardly "shades"; my allusion [not quoted] was pretty explicit. >If the universe is one big Turing Machine, unprovable/undecidable things >do not exist in reality. Since science only deals with realities (are thoughts >real?), it would be complete and still not have to explain transcendental >phenomon. But is there any reason to suppose that the universe _is_ a Turing machine? (*please* make it a neural net, they're *much* more fashionable :-) Note that there is a big difference between "unprovable ``things'' do not exist in ``reality''" and "it is provable that unprovable things do not exist in ``reality''" The second is a more "science-like" statement than the first; only the second offers an explanation. It isn't really true that science deals with ``realities''. I strongly suggest that people who would like to know what science is *actually* like read "Unfinished synthesis", Niles Eldredge, ISBN 0-19-505574-8 "Genes, Organisms, Populations", Brandon & Burian, ISBN 0-262-52115-6 I reckon this is exciting stuff. Ryan seems to have missed the point of my examples from physics and biology: there are *known* classes of events (mutations, electrons passing through slits) where the question "why *THIS* event rather than another in the same class" is said not to have or require any explanation. If this is true, the Universe cannot be a Turing machine. If the Universe is a Turing machine, the "hidden variables" view of Quantum Mechanics is right.
smryan@garth.UUCP (Steven Ryan) (09/14/88)
>>If the universe is one big Turing Machine, unprovable/undecidable things >>do not exist in reality. Since science only deals with realities (are thoughts >>real?), it would be complete and still not have to explain transcendental >>phenomon. > >But is there any reason to suppose that the universe _is_ a Turing machine? I have many reasons not to believe. (I can't believe I said that on comp.ai. Oh-oh, I can smell the tar bubbling.) >Ryan seems to have missed the point of my examples from physics and >biology: there are *known* classes of events (mutations, electrons >passing through slits) where the question "why *THIS* event rather than >another in the same class" is said not to have or require any I didn't miss the point, I thought my answer was implicit. WHY an event occurs is an observation from without the system. If the universe is a TM, reasons are irrelevant. If the universe transcends formal methods, it might be interesting. -------------------------------------------------------------------------- Talking about ignorant assumptions, some people were presented axiom-free logics as assumption-free method of understanding life, the universe, and everything. Assumptions still exist, but they are pushed down to a lower level: it assumes logic is effective. We share this planet with people who reject logic as an inherently limited and ineffective technique. We all know (I hope) formal systems are either incomplete or inconsistent. Perhaps by using incomplete methods, we have an incomplete view of world, with the incompleteness folding back on itself so that we are unable to realise it? Maybe? Maybe not? Pop quiz: Prove your response.
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (09/15/88)
From article <1411@garth.UUCP>, by smryan@garth.UUCP (Steven Ryan): " ... " Talking about ignorant assumptions, some people were presented axiom-free " logics as assumption-free method of understanding life, the universe, and " everything. No one said that. " ... We all know (I hope) formal systems are either " incomplete or inconsistent. I don't know that. Can you show this for predicate logic? Greg, lee@uhccux.uhcc.hawaii.edu
andru@rhialto.SGI.COM (Andrew Myers) (09/15/88)
> From article <1411@garth.UUCP>, by smryan@garth.UUCP (Steven Ryan): > > ... We all know (I hope) formal systems are either > incomplete or inconsistent. Only formal systems which include number theory as a subset. Andrew
smryan@garth.UUCP (Steven Ryan) (09/16/88)
>" ... We all know (I hope) formal systems are either >" incomplete or inconsistent. > >I don't know that. Can you show this for predicate logic? Either a system is too simple (like propositional calculus) to do number theory (which is equivalent to everything else) or it's powerful enough in which Godel's theorem come into play: any system powerful enough for number theory is either incomplete or omega-inconsistent. Simple systems like propositional calculus are complete within their domain, but their domain is incomplete with respect to number theory and all other formal system. (Predicate calculus includes quantifiers; propositional calculus does not.)
firth@sei.cmu.edu (Robert Firth) (09/20/88)
In article <388@quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe) writes: >But is there any reason to suppose that the universe _is_ a Turing machine? None whatever. The conjecture is almost instantly disprovable: no Turing machine can output a true random number, but a physical system can. Since a function is surely "computable" if a physical system can be constructed that computes it, the existence of true random-number generators directly disproves the Church-Turing conjecture.
ok@quintus.uucp (Richard A. O'Keefe) (09/20/88)
In article <7059@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) writes: >In article <388@quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe) writes: >>But is there any reason to suppose that the universe _is_ a Turing machine? If you will inspect the original posting, you will see that it was a rhetorical question directed at a posting which said "if we assume that the universe is a Turing machine ...". My question was a polite way of saying "I _won't_ assume that, so there". >None whatever. The conjecture is almost instantly disprovable: no Turing >machine can output a true random number, but a physical system can. Reference please! This is a _staggering_ result! I can believe that it is true, but it is astonishing to learn that it has been _shown_. (I strongly suspect that Robert Firth has assumed here what he set out to prove.) How do you tell when "a true random number" has been output, anyway?
jwm@stdc.jhuapl.edu (Jim Meritt) (09/22/88)
In article <7059@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) writes: }In article <388@quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe) writes: } }>But is there any reason to suppose that the universe _is_ a Turing machine? } }None whatever. The conjecture is almost instantly disprovable: no Turing }machine can output a true random number, but a physical system can. Since }a function is surely "computable" if a physical system can be constructed }that computes it, the existence of true random-number generators directly }disproves the Church-Turing conjecture. Love it! If the universe is random, you can have uncaused events. If the universe is not random, it is (a type of) Church-Turing machine... Disclaimer: Individuals have opinions, organizations have policy. Therefore, these opinions are mine and not any organizations! Q.E.D. jwm@aplvax.jhuapl.edu 128.244.65.5 (James W. Meritt)
nlt@grad3.cs.duke.edu (Nancy L. Tinkham) (09/27/88)
Robert Firth offers the following proposed refutation of the Church-Turing thesis: > The conjecture is almost instantly disprovable: no Turing > machine can output a true random number, but a physical system can. Since > a function is surely "computable" if a physical system can be constructed > that computes it, the existence of true random-number generators directly > disproves the Church-Turing conjecture. The claim of the Church-Turing thesis is that the class of functions computable by a Turing machine corresponds exactly to the class of functions which can be computed by some algorithm. The notion of an algorithm is a somewhat informal one, but it includes the requirement that the computation be "carried forward deterministically, without resort to random methods or devices, e.g., dice" (Rogers, _Theory of Recursive Functions and Effective Computability_, p.2). If it is demonstrated that a physical system, by using randomness, can generate the input-output pairs of a function which cannot be computed by a Turing machine, we have merely shown that there exists a non-Turing-computable function whose output can be generated by non-algorithmic means -- hardly surprising, and not relevant to the Church-Turing thesis. Nancy Tinkham {decvax,rutgers}!mcnc!duke!nlt nlt@cs.duke.edu
firth@sei.cmu.edu (Robert Firth) (09/27/88)
In article <12512@duke.cs.duke.edu> nlt@grad3.cs.duke.edu (Nancy L. Tinkham) writes: > The claim of the Church-Turing thesis is that the class of functions >computable by a Turing machine corresponds exactly to the class of functions >which can be computed by some algorithm. No it isn't. The claim is that every function "which would naturally be regarded as computable" can be computed by a Turing machine. At least, that's what Turing claimed, and he should know. [A M Turing, Proc London Math Soc 2, vol 442 p 230]
kilroy@mimsy.UUCP (Darren F. Provine) (09/28/88)
In article <7167@aw.sei.cmu.edu>, firth@sei.cmu.edu (Robert Firth) writes: /* * In article <12512@duke.cs.duke.edu> nlt@grad3.cs.duke.edu (Nancy L. Tinkham) * writes: * * > The claim of the Church-Turing thesis is that the class of functions * >computable by a Turing machine corresponds exactly to the class of * >functions which can be computed by some algorithm. * * No it isn't. The claim is that every function "which would naturally * be regarded as computable" can be computed by a Turing machine. At * least, that's what Turing claimed, and he should know. */ I do not see any point to this reply. You have merely restated the definition she provided and did nothing to answer her objection. You see, ``every function "which would naturally be regarded as computable"'' and ``the class of functions which can be computed by some algorithm'' are pretty much the same thing. Do you have some way of computing a function without an algorithm that nobody else in the entire world knows about? If so, do go and get your Turing Award & your Ph.D., and then tell us how it works. If not, go reread the requirement that the algorithm used for computation must be deterministic, and tell us how a random process is relevant to the discussion. And you'll also need a definition of "random function" -- if it is random, then how can it be a function, or even a mapping? [ All of this ignores, of course, the fact that some people believe that physical processes cannot act randomly (and that quantum randomness is a misperception). Sadly, we cannot prove this either way. ] Darren ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Darren F. Provine UUCP: uunet!mimsy!kilroy University of Maryland ARPA/CSNET: kilroy@mimsy.umd.edu
firth@sei.cmu.edu (Robert Firth) (09/29/88)
Somehow, I get the feeling that our machines are better at forward chaining than we are. Please let me run this Turing machine stuff by you once again. (Translation: this post says nothing new, merely recapitulates.) ---- The question that originally prompted me to speak was this one [ <388@quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe)] >But is there any reason to suppose that the universe _is_ a Turing machine? As I understood it, the question referred to the physical world, as imperfectly revealed to us by science, and so I replied [ <7059@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) ] >None whatever. The conjecture is almost instantly disprovable: no Turing >machine can output a true random number, but a physical system can. To elaborate: I can build a box, whose main constituents are a supply of photons and a half-silvered mirrir, that, when triggered, will emit at random either the value "0" or the value "1". This can be thought of as a mapping {0,1} => 0|1 where I introduce "|" to designate the operator that arbitrarily selects one of its operands. The obvious generalisation of this - the function that selects an arbitrary member of an input set - is surely not unfamiliar. Nobody has denied that a Turing machine can't do this. The assertion that a physical system can do it rests on the quantum theory; in particular on the proposition that the indeterminacy this theory ascribes to the physical world is irreducible. Since every attempt to build an alternative deterministic theory has foundered, and no prediction of the quantum theory has yet been falsified, this rests on pretty strong ground. Now, it is not my job to supply an "algorithm" for this function: as the physicist I have given you a specification and a model implementation; as the computer scientist it is your job to give me an equivelent program. However, being a kind-hearted soul, I shall point you to an algorithm; it is given as equation (3.1) in the paper [Deutsch: Proc Roy Soc A vol 400 pp 97-117] Naturally, it uses primitive operations that you won't find in a classical computing engine, which is why the title reads "Quantum theory, the Church-Turing principle, and the universal quantum computer". Turning now to that "principle": The formulation I learned was, briefly, that any function that would naturally be regarded as computible can be computed by a universal Turing machine. Once again, I made my opinion on this absolutely clear [art. cit.]: Since a function is surely "computable" if a physical system can be constructed that computes it, ... from which, I submit, the conclusion follows: ... the existence of true random-number generators directly disproves the Church-Turing conjecture. Granted, one can readily evade this conclusion. It is necessary merely to redefine "natural", "computable", "function", or some other key term. For example, one could stipulate A function is to be regarded as computable only if it can be described by an algorithm written in a programming language implementable on a universal Turing machine. In which case, the conjecture becomes vacuously true, and the discipline of AI becomes vacuously futile. For the point of "artificial intelligence", surely, is accurately to reproduce, in some computing engine, the behaviour of certain physical systems, especially those that show goal- directed behaviour, judgement, creativity, or whatever else one means by "intelligence". If this is to be remotely feasible, then the model of the computation process must be at least general enough to embrace the known basic operational features of physical systems. After all, if your programming tools cannot reproduce so simple a physical system as my random Boolean generator, the chance of their being able to reproduce a complicated physical system - the brain of a flatworm, for instance - must be very close to zero. Robert Firth
nau@mimsy.UUCP (Dana S. Nau) (09/30/88)
In article <7202@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) writes: < ... I can build a box, whose main constituents are a supply < of photons and a half-silvered mirrir, that, when triggered, will emit < at random either the value "0" or the value "1". This can be thought < of as a mapping < < {0,1} => 0|1 < < where I introduce "|" to designate the operator that arbitrarily selects < one of its operands. The obvious generalisation of this - the function < that selects an arbitrary member of an input set - is surely not unfamiliar. As far as I can see, what you have defined is not a function. A function is normally defined to be a set F of ordered pairs (x,y) such that for each x, there is at most one y such that (x,y) is in F (and this y we normally call F(x)). Until all of the ordered pairs that comprise F have been unambiguously determined, you have not defined a function. Note that this does NOT mean that you have to tell us what all of the ordered pairs are or how to compute them, or that you know what they are, or that it is even possible to compute them (for some interesting examples, see page 9 of Hartley Rogers' book, "Theory of Recursive Functions and Effective Computability). It just means that it must be unambiguous what they are. If your mapping "|" is a function, then it must be one of the following: | = {(0.0), (1,0)} | = {(0.0), (1,1)} | = {(0.1), (1,0)} | = {(0.1), (1,1)} If it were unambiguous WHICH function "|" was, then "|" WOULD be Turing-computable. In fact, it would even be primitive recursive. But if we assume that the output of your box is truly random, then your definition leaves it indeterminate which of the above functions "|" actually is. Thus, as a function, "|" is ill-defined. < ... The formulation I learned was, briefly, < that any function that would naturally be regarded as computible can be < computed by a universal Turing machine. Once again, I made my opinion < on this absolutely clear [art. cit.]: < < Since a function is surely "computable" if a physical < system can be constructed that computes it, ... < < from which, I submit, the conclusion follows: < < ... the existence of true random-number generators directly < disproves the Church-Turing conjecture. I disagree. The point of my above argument is that true random-number generators do not satisfy the definition of a function, so the theory of Turing computability does not apply to them. Just one other point, to avoid possible confusion: A random variable IS normally defined as a function. However, it is not a function such as "|", but is instead the function which maps the sample space of a random experiment into the set of real numbers. In your example, the sample space is the set {0,1}, so to map this into the set of real numbers you can simply use the identity function. -- Dana S. Nau ARPA & CSNet: nau@mimsy.umd.edu Computer Sci. Dept., U. of Maryland UUCP: ...!{allegra,uunet}!mimsy!nau College Park, MD 20742 Telephone: (301) 454-7932
ok@quintus.uucp (Richard A. O'Keefe) (09/30/88)
In article <7202@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) writes: > Since a function is surely "computable" if a physical ******** > system can be constructed that computes it, ... >from which, I submit, the conclusion follows: > ... the existence of true random-number generators directly > disproves the Church-Turing conjecture. >Granted, one can readily evade this conclusion. It is necessary merely >to redefine "natural", "computable", "function", or some other key term. It is not necessary to REdefine "function", only to use the usual meaning. Given the same inputs, a function must always yield the same output(s). The kind of physical system Firth has described is a realisation of a(n indexed) random variable, and it has been held for many years that "true random numbers" are not computable. (See section 3.5 ("What is a random sequence") of Knuth's "The Art of Computer Programming, Vol 2", this statement is implicit in definition R6. The original question was a purely rhetorical one (I _don't_ believe that the universe is a Turing machine), but it's worth pointing out that we only have a finite set of imprecise observations, so that a sufficiently good simulation of a quantum-mechanical system (with top-notch pseudo- random number generation!) *might* be fooling us. You can only appeal to phsyical random number generators to disprove the Church-Turing hypothesis if you assume that the quantum-mechanical laws a really true, which is to say if you already assume that the universe is not running on a Turing machine. I believe it, but a circular "proof" like that is no proof!
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (09/30/88)
From article <13791@mimsy.UUCP>, by nau@mimsy.UUCP (Dana S. Nau):
" In article <7202@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) writes:
" ...
" < of as a mapping
" <
" < {0,1} => 0|1
" ...
" As far as I can see, what you have defined is not a function. A function is
There are a couple (>=2) of things I don't understand about this discussion:
Why does it matter whether Turing machines compute functions? If one
wants to compute non-functional relations, why not just define the
machines accordingly? If there's a terminological problem, then call
the machines something else.
What does it matter to Church's thesis whether what is computed is
a function? Sometimes the thesis is phrased using the word function,
but is that essential to the thesis?
And anyhow, why can't `0|1' be considered a single value?
Greg, lee@uhccux.uhcc.hawaii.edusmryan@garth.UUCP (Steven Ryan) (10/01/88)
>random number generation!) *might* be fooling us. You can only appeal to >phsyical random number generators to disprove the Church-Turing hypothesis >if you assume that the quantum-mechanical laws a really true, which is to >say if you already assume that the universe is not running on a Turing machine. >I believe it, but a circular "proof" like that is no proof! Well, just to keep things straight, I'm the one who mentionned TM and CT. I used them as a conditionals, `If the universe was a TM, then such and such would follow.' It wasn't intended to assert, prove, or disprove CT, but just engage in withywanderring philosophical speculation. To me, the Ignorant Assumption is not any particular theory or religion, but the meta-assumption that assumptions are unnecessary.
nlt@romeo.cs.duke.edu (N. L. Tinkham) (10/01/88)
I have no objection to the formulation "any function that would naturally
be regarded as computable can be computed by a universal Turing machine", as
long as it is clear that being "naturally...regarded as computable" includes
the list of conditions associated with algorithms. Setting aside those
conditions would introduce a broader definition of "computable" than is in
common use; such a definition may well be interesting to consider, but it might
reduce confusion to use a different term (say, "q-computable").
The claim that "a function is surely 'computable' if a physical system
can be constructed that computes it" is the disputed point. In order to
believe that a function f is computable, I will require that I be shown that
there is an algorithm by which f may be computed. This algorithm need not be
a Turing-machine program (if that were the case, the thesis would indeed be
trivial), but it should conform to the general requirements of an algorithm:
ability to be specified in a description of finite length, computation in
discrete steps, and so forth. And one of these requirements is that the
computation should not use random methods. (Reference, again, is to chapter 1
of Rogers' text.
Falsifying the Church-Turing thesis would require presenting a function f
for which such an algorithm exists, and then showing that f cannot be computed
on a Turing machine.
[We have drifted quite far from religion here. Followups are directed to
comp.ai.]
Nancy Tinkham
{decvax,rutgers}!mcnc!duke!nlt
nlt@cs.duke.eduw25y@vax5.CCS.CORNELL.EDU (10/03/88)
The Church-Turing thesis deals with relations that always give the same
output value for a given input value. Any quantum-generated random function
would not have this property.
-- Paul Ciszek
W25Y@CRNLVAX5 Bitnet
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