Path: csiph.com!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail From: phoenix Newsgroups: comp.theory,sci.logic,sci.math,comp.ai.philosophy,alt.messianic Subject: Re: Simplifying the Church / Turing thesis Date: Sat, 16 May 2026 11:38:50 -0600 Lines: 334 Message-ID: References: <10qml9j$1e38l$1@dont-email.me> <10thkat$1t10f$2@dont-email.me> <10tk2pe$2mr0m$1@dont-email.me> <10tl1l9$306rb$2@dont-email.me> <10tl4n0$31lpp$1@dont-email.me> <10tmrbj$3grcc$2@dont-email.me> <10tn8dr$3khtu$1@dont-email.me> <10tpb14$74fa$1@dont-email.me> <10tqkvu$jlu4$1@dont-email.me> <10ts08a$ufcs$1@dont-email.me> <10tsffi$12v9u$1@dont-email.me> <10tujfj$1oqdj$1@dont-email.me> <10tva5c$2019m$1@dont-email.me> <10u0pku$2dj1o$1@dont-email.me> <10u1mm7$2l5cn$1@dont-email.me> <10u1ote$2losr$1@dont-email.me> <10u21cc$2oeht$1@dont-email.me> <10u22e1$2oc3l$1@dont-email.me> <10u25bk$2po56$1@dont-email.me> <10u2quv$302jv$1@dont-email.me> <10u324t$32ibn$1@dont-email.me> <10u33ob$32mss$1@dont-email.me> <10u3fdq$35fr1$1@dont-email.me> <10u3gi4$376c6$1@dont-email.me> <10u93r6$pc64$1@dont-email.me> Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: individual.net 4k8tA+jJD6uLsxUMkT48TgynxIF1aPnONROxjLbZupPibrk16T Cancel-Lock: sha1:ml677YPrTEcLjmOL5NSLpdJDUo4= sha256:U+SroWAa/OLHIXHDjkLze6XhfqBjYPSn/u9iz6siHPU= User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:128.0) Gecko/20100101 Firefox/128.0 SeaMonkey/2.53.23 In-Reply-To: Xref: csiph.com comp.theory:141242 sci.logic:345970 sci.math:645139 comp.ai.philosophy:34560 alt.messianic:321328 Ross Finlayson wrote: > On 05/16/2026 08:37 AM, phoenix wrote: >> Ross Finlayson wrote: >>> On 05/16/2026 07:58 AM, Ross Finlayson wrote: >>>> On 05/15/2026 11:45 PM, dart200 wrote: >>>>> On 5/13/26 8:46 PM, olcott wrote: >>>>>> On 5/13/2026 10:26 PM, dart200 wrote: >>>>>>> On 5/13/26 5:07 PM, André G. Isaak wrote: >>>>>>>> On 2026-05-13 17:40, olcott wrote: >>>>>>>>> On 5/13/2026 4:37 PM, André G. Isaak wrote: >>>>>>>>>> On 2026-05-13 09:28, olcott wrote: >>>>>>>> >>>>>>>>>>> *The entire body of knowledge that can be expressed in language* >>>>>>>>>> >>>>>>>>>> ... is an ill-defined set which only exists in your mind. There's >>>>>>>>>> over 8 billion people on earth, all of whom believe different, >>>>>>>>>> often contradictory things. And, with the exception of >>>>>>>>>> theorems of >>>>>>>>>> formal systems, there is nothing that we know with absolute >>>>>>>>>> certainty. Only varying degrees of certainty, but for every given >>>>>>>>>> fact you won't get a universal consensus on exactly how >>>>>>>>>> certain we >>>>>>>>>> are of that fact. >>>>>>>>>> >>>>>>>>> >>>>>>>>> So maybe cats were never animals and this "belief" >>>>>>>>> has always been mass psychosis? In actual reality >>>>>>>>> cats were always a kind of snake? >>>>>>>>> >>>>>>>>> I propose that a finite set of "atomic facts" of general >>>>>>>>> knowledge inherently exists and that no 100% concrete >>>>>>>>> counter-example can ever be found. >>>>>>>> >>>>>>>> Until you can produce this finite set of atomic facts you're all >>>>>>>> just bluster. Here's a few statements. Which would you consider >>>>>>>> atomic facts: >>>>>>>> >>>>>>>> – The Universe is 14 billion years old. >>>>>>>> >>>>>>>> – The Ungulates and the Carnivores form a clade. >>>>>>>> >>>>>>>> – Jesus Christ died for our sins. >>>>>>>> >>>>>>>> – Nearly 70% of the mass-energy of the universe consists of dark >>>>>>>> energy. >>>>>>>> >>>>>>>> – Anthropogenic climate change is currently occurring. >>>>>>>> >>>>>>>> – The Earth is 6000 years old. >>>>>>>> >>>>>>>> – Argentinosaurus is the largest land animal to ever have lived. >>>>>>>> >>>>>>>> – Measles vaccine causes autism. >>>>>>>> >>>>>>>> – There exists an "island of stability" where extraheavy elements >>>>>>>> with approximately 184 neutrons will have a considerably longer >>>>>>>> half- life than that of the heaviest elements currently know. >>>>>>>> >>>>>>>> – Turing showed that halting cannot be computed. >>>>>>> >>>>>>> actually his proof was in regards to circle-free vs circular >>>>>>> machines, not specifically halting ones. please do read p246 and >>>>>>> p247 >>>>>>> of his paper /on computable numbers/ more carefully. >>>>>>> >>>>>> >>>>>> As with Gödel, I don't give a rat's ass about the convoluted >>>>>> mess of his paper. Unless we boil these things down to their >>>>>> barest possible essence they greatly exceed the capacity of >>>>>> any human mind. >>>>>> >>>>>>> and what he showed was that it cannot be computed by a single turing >>>>>>> machine. >>>>>>> >>>>>> >>>>>> Only because he used a fucking dishonest trick that >>>>>> proof theoretic semantics would toss out on its ass. >>>>>> >>>>>>> no one has demonstrated any _actual_ turing machine with a halting >>>>>>> behavior that provably cannot be computed by _any_ machine, as >>>>>>> such a >>>>>>> machine would have under-specified, non-determinable semantics that >>>>>>> then could not actually exist as a real machine, that any actual >>>>>>> decider would actually have to decide upon... >>>>>>> >>>>>>> the theory of computing has predicated itself on a limitation that >>>>>>> fundamentally resolves to a catch-22 type paradox that has existed >>>>>>> since turing wrote his first paper /on computable numbers/ >>>>>>> >>>>>> >>>>>> Its essentially the same damn thing as the Liar Paradox >>>>>> that mindless robot humans still have not agreed on. The >>>>>> brains of most humans are hard-wired to short-circuit. To >>>>>> woefully fallible humans textbooks are the word of God. >>>>>> Proof theoretic semantics sees right through this crap. >>>>>> >>>>> >>>>> it just isn't polcott... >>>>> >>>>> the liar's paradox is a sentence that is false, in regards to nothing. >>>>> what is it false about? who the fuck knows 🤷 >>>>> >>>>> godel's sentence is a truth, about nothing, that has no proof. what is >>>>> that truth?? again, who the fuck knows 🤷🤷 >>>>> >>>>> turing's diagonal, however, is computing an explicitly defined object. >>>>> it is trying to take the n-th digit from the n-th circle-free machine, >>>>> and constructing it into the n-th digit of a "diagonal" ... and >>>>> stumbling on the fact it never defined a digit for itself on that >>>>> diagonal >>>>> >>>>> turing's diagonal isn't a "dishonest" trick. he legitimately got >>>>> stumped >>>>> by trying to compute an explicitly defined object, and figured it >>>>> supported godel's result >>>>> >>>> >>>> Ever heard of Yaroslav Sergeyev? >>>> >>>> How about Simon Stevin? >>>> >>>> You must have heard of Zeno. >>>> >>>> Then, I imagine you remember geometry and the compass and edge, >>>> and about classical constructions. >>>> >>>> So, if you add an Archimedean spiral to compass and edge, >>>> all of a sudden the "angle-trisection" and "squaring the >>>> circle" and "doubling the cube" are constructible, since >>>> it's a new elementary object that happens to fulfill >>>> making it so that these otherwise "impossible" constructions >>>> are not impossible any-more. >>>> >>>> Have you heard of Ruffini-Abel and the insolvability of >>>> the quintic? It presumes a limited set of elementary >>>> functions, it doesn't say the quintic doesn't have >>>> solutions, only as among some usual elementary functions. >>>> >>>> So, Turing didn't have a "Zeno machine" architecture, >>>> while it's figured that nature in its continuity >>>> solves Turing problems all the time. >>>> >>>> >>>> Then, mathematical idea of the infinite make for that >>>> number theorists like Erdos make constructions that >>>> disagree, about the laws of large numbers and limits >>>> and the inductive limit (beyond classical constructions), >>>> the "infinite" limit and the "continuum" limit, make >>>> for things in mathematics that are called "emergence" >>>> after "convergence" since "convergence" would never arrive. >>>> >>>> >>>> Anyways people can look to Mirimanoff who points out >>>> that an infinitely-many would have an infinitely-grand, >>>> and then take Goedel's theorem and point out that >>>> that's the first obvious thing to Goedel's missing >>>> sentence to be, "extra-ordinary". >>>> >>>> It's obvious, or "duh". >>>> >>>> >>> >>> And, "The Liar" is false about _nothing_ yet itself. >>> >>> It's like, in a world where there is no 'but', only 'yet', >>> that "the Liar", is the only "but". >>> >>> That "there is no but: only yet", is the idea that instead >>> of excluded-middle being universal, since it isn't and >>> instead only defines a class of propositions that happen >>> to be binary predicates, instead that the temporal modal >>> relevance logic keeps "yet" as proper. >>> >>> "There are IFs, there are ANDs, ..., >>> don't really need any BUTs, ..., yet". >>> >>> 'Yet': it's kind of like 'that', and is implicit anywhere. >>> >>> Yet that yet that yet that yet that yet that it is so: >>> that that that that that it is so. >>> >>> >> I find that 'except' paired with 'yet' covers every instance of 'but.' >> If you can find an exception to this, please show me. >> > > Perhaps most striking is that "yet" and "but" often could stand > in for each other in the simple posing or positing of contraries, > similarly "but not" and "yet not", > yet "not but" and "not yet" make for entirely opposite sorts > of suppositions (or suppositiones since Occam), then as with > regards to, "yet but" as alike "not but" and "but yet" as > alike either "yet" or "but". > > > So, for introducing terms like "multi-valued" or "multi-valent" > logic, or, the temporal, for time-series data, has it that > "yet" is overall stronger, more expressive and not less un-ambiguous. > > Then, for an account where a truly classical logic is > _not_ the quasi-modal, and that "there is no material implication, > only direct implication", then there is that "yet" instead of > "but" also makes for the usual account of "assume" that instead > of "this but that (but this but that ..., fail)" is for along > the lines of "this yet that: these". > > > Anyways I've been using always 'yet' and never 'but' > for quite some years, and, not missing anything. > > "... but but but but ..." -> contradiction > "... yet yet yet yet ..." -> contingency > > > So, usual accounts of proof-by-contradiction are > by themselves merely partial and half of accounts, > of truly classical Chrysippean Aristotlean logic, > that today is called "modal temporal relevance logic", > and may include the multi-valent, and has _all_ the > expressive and decisive power of logic, where, > for example, that 'but' has not. > > > > > "The "inductive" is very much like the "empirical", > and "deduction" isn't only about "elimination". > > > "There is no but: only yet", reflects that the > modal and temporally modal relevance logic is > not about contradictions, instead change. > > > The very idea of a Principle of Contradiction > instead of a Principle of Inversion leads to > a very simple obstinacy and fallacies like > those of, "material implication", that aren't so. > > Then a principle of inversion can help arrive > at a Principle of Sufficient Reason: yet a > more "Principle of Sufficient, and Thorough, Reason". > > > > The analytical bridges for abduction about the > deduction about the impasses of induction, help > make for the "classical superclassical" reason > usually attributes to Zeno with the most, "paradoxes", > that there are none or that there is one a paradox, > make for a, "wider, fuller dialectic", what makes > for why "axiomless natural deduction" arrives at > being the only true theory of Truth, capital Truth. > > > Then, that requires a bit of a complete ontological > commitment, yet at least it's true so won't be wrong. " - 5/31/2025 > > > > > "Well, the "paradoxes" of mathematical logic have kind of > been "decided" one way, the existence of an ordinary inductive > set, yet, that doesn't always make sense, since, it's stipulated > that that's so, and there's no right to do that, except in a theory. > > Induction then carries out into the limit, yet it results being > entirely timid about, after an "inductive limit", some, > "infinite limit", about some, "continuum limit". > > Now, everybody knows cases for induction, what's so and > so for the next is so for any iteration. Yet, in the limit, there > are cases where induction fails. Besides things like convergence > laws of mathematics, that sometimes don't hold, like Stirling's > formula for factorial and various laws of convergence, then > a graphical example is the yin-yang ad infinitum. A circle has > a constant coefficient relating its cirumference and diameter, > it's pi. So, two half circles whose diameter are the radii of > the outer diameter, have the same sum diameter, so they > have the same sum circumference. Yet, in the limit, those > go to zero, and the sum of the flat line in the limit, is only > 1, or 2, and not pi. So, induction fails, as an example. Then > the most usual classical example is the Heap or Sorites, > how many grains is a heap and this sort thing, and how many > grains less than a heap is no longer a heap and this sort of thing. > Then, the most direct example about the discrete and continuous > is about points and lines, that dividing lines doesn't make a point > and combining points doesn't make a line, yet it's another axiom > in today's usual axiomatic descriptive set theory that after making > models of integers and rationals it's axiomatized the least-upper-bound > property thusly that lines are point-sets, then that uncountability > sits right there and that's said to be "The foundations of mathematics". > > > > So anyways: sometimes induction fails. > > Then, it takes a wider, fuller, dialectical account of the > deductive, than what is a one-side partial account of > the inductive, to make thorough sense. > > So, things like the branching or halting problems, > well, these have the baggage of having ordinals and > cardinals together, about an inductive set, which is > about ordinals (i.e., that inductive cases are serial, > besides the fact that a separate apparatus, may > count them). > > It's not even necessarily a fact that there's a standard > model of integers at all, only bounded if unbounded fragments > and actually infinite extensions. > > > Some have P(halts) around zero, > some have P(halts) around one, > some have P(halts) as about .85, > some have P(halts) as 1/2." > > > Except that this is English, and we don't necessarily apply 1/2 to 'except' and 1/2 to 'yet'. I contend that in some cases either would be applicable, amounting to a modicum of overlap, which means that the sum of 'except' and 'yet' is likely to be greater than 1. Speaking figuratively, of course. -- War in the east War in the west War up north War down south War War