Gödel’s proof of the existence of God

_{News
May 10, 2020

Intelligent Design, Mathematics, Philosophy, theism

2}_{Categories
Intelligent Design
Mathematics
Philosophy
theism}

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You didn’t know, possibly, that when he thought we was dying, he showed the notebook to one of his colleagues, who copied out the proof:

In an unsanitized, politically incorrect (but factual) history, Selmer Bringsjord talks about how the tormented genius Kurt Gödel took up a quest that dated back a thousand years to prove the existence of God by formal logic. His original version didn’t quite work but his editor’s version passed an important logic test:
“When we go to Gödel, we skip over the modern advocates of this argument. It’s harsh—I’m just going to say it—from the standpoint of someone who’s reasonably well-versed in formal logic, I think it’s a bit of a doldrums, despite some of the attention, until Gödel does his thing.
Gödel does it formally and then some folks in Germany, doing automated reasoning, verified it a few years back. They verified the version that Dana Scott copied out of the notebook. That is, what they verify is that there is no doubt; it’s machine-verified proof. So now we’re left with just the truth of the premises and how we judge them.”
News, “Gödel and God: A surprising history” at Mind Matters News

Further reading:

Faith is the most fundamental of the mathematical tools: An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions. (Daniel Andrés Díaz-Pachón)

and

God’s existence is proven by science. Arguments for God’s existence can be demonstrated by the ordinary method of scientific inference. (Michael Egnor)

Comments

In the physical realm, infinity is an absurdity. You aren't anywhere (not a place or time or anything) in an infinity. Andrewasauber_{May 15, 2020
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ET: You don’t have to get to infinity. You have to get to the now from an infinite past. No, you can't be at an infinite past. You can only be at some point along the way. Infinity is not a place.JVL_{May 15, 2020
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JVL:
But not being able to ‘get to’ infinity doesn’t mean there isn’t an infinite past.
You don't have to get to infinity. You have to get to the now from an infinite past.ET_{May 15, 2020
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DS, so, kindly define a metric or model of duration of actual time lapsed that does not require actual past points in the span to now. Do so, without violence to what time lapsed is generally understood to mean. Do so, without implying what you do not wish to allow. My model is, the past has stages that were once present but were incrementally succeeded to now. So for a past stage p and now n, duration p to n = n - p on some reasonable scale, e.g. years etc. From this, I argue that a transfinite past requires actual past points beyond any finite past point. Further, ellipses, arrows, open ended inf intervals give a pointer to the transfinite, they don't actually express it. A set can be without finite limit, a duration requires at least representive end points. I find we keep shunting off the infinite into, already traversed by any given p. KFkairosfocus_{May 15, 2020
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KF, As far as I can tell, none of the IPPs who work earnestly on this stuff propose the existence of pairs of time coordinates separated by an infinite interval. Apparently that's just too far-out even for them. I don't see any point in discussing a proposal that no one thinks is plausible in the first place.daveS_{May 15, 2020
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DS, there is likely an incommensurateness gap of paradigms here, where I am saying limitless continuation points to definitively transfinite numbers and to the challenge of spanning what the ellipses are indicating or round braces on an inf, in finite stage steps. Notice, R and R* are mileposted with integers, broad sense. KFkairosfocus_{May 15, 2020
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DS, I gave a particular, specific reason for that, starting with addressing Zeno then showing why we need to set reals in wider context in a unified space of quantities. That included drawing out what open interval notation with infinite sides points to. Potential vs actual infinities are central, please address the substance. The ellipses and simple round brace glyphs, pointing arrow tips on number lines etc are highly significant. You can see what else is specifically on my mind just now. Maybe, that will help to show why I can be so particular and even insistent. KF PS: Kindly, observe:
Far more relevant is that our past comes in successive, cumulative finite stages, we commonly use years and seconds. Uniformity and duration are irrelevant, the key issue is successive cumulative effect of the actual past to now. Any ACTUAL past stage was once the present and has been succeeded in sequence to now by further stages. These can be counted and such a count is a metric. Where, clearly from p n, duration d = n – p, on some reasonable metric; where, it is also well known that the continuum is mileposted with the whole numbers. THERE IS NO DURATION SINCE THE PAST THAT IS NOT A DURATION SINCE SPECIFIC PAST EVENTS. In that connexion, we can readily see that if duration since p is finite,past since p is finite. It is my contention, here, that appeals to the infinitude of Z or R have in them a pointing arrow or two or ellipses for a reason: they do not have defined borders within the set, once any given z in Z or r in R are given, they can be exceeded, so we do not have a definable limit. However w is order type of the natural counting numbers and the continuum number attaches to any extended span in R^n, including R^1. The pointing arrows on axes or ellipses in set builder notation count.
Then as directly follows:
We can, however capture Z and R in context and that makes a difference, through the hyperreals, R* mileposted by Z*. We then see that there are transfinite spans extending these numbers into the specifically infinite ranges. Mathematically, these transfinite spans cannot be traversed in finite stage successive steps, which is why step builder notation points to the completion of a potential infinity by using ellipses or the equivalent. Where also, the 1/x catapult say prof Carol Wood used allows us to see that from 0 to transfinites, we have a unified space and structure of quantities. Where, infinitesimals and transfinite hyperreals have as much claim to “reality” as Complex numbers, negative numbers, zero, real but irrational numbers such as pi or e etc. We may freely model: . . . . K’ –> K’+1 . . . . -2, -1, 0, 1, 2 . . . n . . . . w . . . . K-1. K, K+1 . . . ., where 4-dot ellipses denote specifically transfinite ellipses and the continuum is mileposted by numbers in Z* as shown. Now, let us consider your: The infinite past proponents hypothesize that the past can be modeled using the real numbers. Here are a couple of obviously true statements. Let x be any real number. Then the set (?inf, x) has the following properties: 1) It is unbounded. Given any positive integer M, there is a number p in (?inf, x) such that |x ? p| > M. 2) If p is in (?inf, x), then |x ? p| < inf. Certainly I can say that without begging the question, correct? Do you see what comes in in interval indications with (- inf … or . . . +inf)? The ordinary curved brace indicates an OPEN ended interval with no definable terminal element. Here, as there is endless onward continuation L-ward or R-ward respectively. In short the continuum line goes on implicitly to transfinite hypereal spans which cannot be represented within R mileposted by Z explicitly, but we know that any specific given value we can write down or specifically represent can be exceeded, most easily seen with z in Z. This is actually the issue I found in 2nd form Algebra and 4th form Calculus. It is why on accessing Surreals and hyperreals, I could see that my Math teachers were struggling with the inadequacies of R mileposted by Z as models of the full span of relevant quantity, which became acute with integrals spanning to infinity and with the use of infinitesimals that had been tamed less than a decade before. There was that handwaving struggle with the clumsy epsilon-delta limits approach that while it carefully distinguishes potential from actualised infinity, hides more than it reveals.
Note, I clip and respond.kairosfocus_{May 15, 2020
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KF,
The real numbers are irrelevant.
Heh. Sometimes I wonder if this whole interaction is just a crazy hallucination. Anyway, this is where my "strawman" accusation comes in. You immediately dismiss the claims the infinite-past proponents (IPPs) actually put forth, and start talking about what you interpret "infinite past" to mean. Predictably, it's very different from what the IPPs mean. At that point, you're talking about something else entirely.daveS_{May 15, 2020
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JVL, run away is exactly what I cannot do. This is my "dayjob" stuff. I doubt the regulators spot the issues I am highlighting. And Rev 13 is directly relevant. The ECCB Governor went on radio with a parson -- cherry-picked I think -- to allay the 7th floor FBI concerns of pushing for cashless. When I wanted to pay a phone bill by cheque in one bank here, I was told not possible, I went to the other . . . which just bought the first [another LONG story] . . . and oh just deposit to A/c xyz. Did. Then now, the local credit union is stepping up near bank operations that leverage that it has different reserve requirements [20% in absolute terms of that for banks proper] though it faces board requirements written in by a previous administration over protest of "a relevant client" on coops based on research including cases such as Kenya. Board members are by implication responsible for any wrong done by any officer, in law, as opposed to there being a negligence or worse standard. Lesson 0, clever glib cutting rhetoric can make sense and caution sound silly, esp when backed by a partisan, morally numb parliamentary majority. Then, to go back and fix unless things visibly go over the cliff is next to impossible given onward firehose flood of new things. I have not been alarmist in pointing to lemmings heading over a cliff, that is a daily observation. KFkairosfocus_{May 15, 2020
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Kairosfocus: >>Subject to subsections (4) and (5), a licensed financial institution or licensed financial holding company shall not, except with prior written approval of the [Eastern Caribbean] Central Bank, declare, credit or pay any dividend or make any other transfer from profits if the licensed financial institution or licensed financial holding company realises a net loss for that financial year. >> In the words of the Monty Pythons: RUN AWAY! RUN AWAY!! Anyway: good for you for trying to improve the status of your fellow citizens and guests by slogging away at such bureaucracy. I don't think I'd have the stomach for it but it certainly needs to be done! Fight the good fight!JVL_{May 15, 2020
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How is this issue for you >>Subject to subsections (4) and (5), a licensed financial institution or licensed financial holding company shall not, except with prior written approval of the [Eastern Caribbean] Central Bank, declare, credit or pay any dividend or make any other transfer from profits if the licensed financial institution or licensed financial holding company realises a net loss for that financial year. >> As Divs, stock splits, buy backs etc in loss making years send signals to investment markets, and as profit/loss is up for debate and for revision even post auditor's statement, plus taxes are often in negotiation for years on end, that means, unless Fed Jr approves IN WRITING, no gravy for investors. I am going to suggest, divs that materially affect required reserves. Banks and shareholders have a legitimate interest in using prudent reserves to damp down instability of share prices and bond values. Also, stock buybacks are implicit dividends and Banks have legitimate interests in stabilising share prices by holding and buying/selling their own shares, contradictory as that may seem. Let's not get into mutually owning cartels like Canada's big six. Then there is this one: >>in the definition of “affiliate” by deleting paragraph (e) and substituting the following— “(e) a company which— (i) has the same beneficial owner; or (ii) shares common management, and has any interlinked business with F,”>> It is wider context why I let that one pass. Then try: >>in the definition of “banking business”, in paragraph (a)(ii), by deleting the word “frequent”; >> PLUS, in princ amd to Jan 2019: >>“banking business” means— (a) the business of receiving funds through— (i) the acceptance of monetary deposits which are repayable on demand or after notice or any similar operation; (ii) the frequent sale or placement of bonds, certificates, notes or other securities, and the use of such funds either in whole or in part for extensions of credit or investment for the account and at the risk of the person doing such business; (b) any other activity recognised by the Central Bank as banking practice and which a licensed financial institution may additionally be authorised to do>> [--> this required fiddling with alleged pdf protective schemes, thankfully I did not need to snapshot, OCR and work from text. Lawyers are annoying that way. What logic operator implicitly connects a i and ii? I will suggest an AND operator so the deposit business in some form must be there for the investment side to be part of a bank] So, is a lawyer or a CFO or realtor who occasionally does such now a banker carrying on a banking business? If so, a whole new order of de facto licencing of fit and proper persons, beneficial ownership, disclosures, reporting and oversight by Fed Jr now obtains. And you betcha that some officious regulator would one day make that case. Then there's the push: we gotta get rid of those dirty bills carrying germs. Do you want a time stamped data shadow of every transaction you do, where, when, in the hands of the ilk of 7th floor FBI bldg and their media slander trumpeters? (KGB, Gestapo, Stasi, hold my three beers . . .) And more of such order. Rev 13:
16 It [beast from the land, or The Land] also forced all people, great and small, rich and poor, free and slave, to receive a mark on their right hands or on their foreheads, 17 so that they could not buy or sell unless they had the mark, which is the name of the beast or the number of its name. 18 This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man.[e] That number is 666 [Code for Nero].
Now, back to mere branes and hyperreals with transfinite durations. KFkairosfocus_{May 15, 2020
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Kairosfocus: Right now banking definitions unpleasantly remind me of working around pathologies of math. Nicely put!!JVL_{May 15, 2020
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JVL, advisor-analyst. Mr T-F is current premier. BTW, 9 elected reps, others are ex officio, in a unicameral. HM is designated head. Right now banking definitions unpleasantly remind me of working around pathologies of math. KFkairosfocus_{May 15, 2020
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Kairosfocus: RW RW . . . RW . . . OH! Real World! Whew! That took me far too long! Are you part of the Legislative Assembly? According to Wikipedia there are only nine members of that body. Is Mr Taylor-Farrell part of the debate as Premier? It seems like he'd still be part of the LA correct?JVL_{May 15, 2020
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JVL, while too busy to further go into further points in detail just now [forced prioritisation], the remote past of origins is specifically not observable. It is inferred from traces and the logic of temporal-causal succession. Where as I noted long since, the beyond the singularity is commonly raised and must be addressed. Yes phil dressed up in mathematical apparatus and while wearing lab coats is still phil not empirically controlled science. Hence grumblings about strings and vibrating colliding branes, quantum fluctuation sub cosmi and the like. We know that the logic of structure and quantity is a clear guide on what is possible or not and one thing that is not is to have a succession of stages that is a completed actual infinity. That is what needs to be faced, even before thermodynamic considerations are on the table. Back to bills for debate in RW. KFkairosfocus_{May 15, 2020
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DS, I wont' bother on the continued projection. here, "motivated" reasoning. The pivotal issue is simple enough: what does DURATION since the past mean? Esp. when claimed, infinite. The real numbers are irrelevant. As is well known, first, Zeno paradox sequences converge as infinite successions in finite time as causally linked increments of space and time form a cumulative, convergent succession. This is tied to foundations of Calculus. Far more relevant is that our past comes in successive, cumulative finite stages, we commonly use years and seconds. Uniformity and duration are irrelevant, the key issue is successive cumulative effect of the actual past to now. Any ACTUAL past stage was once the present and has been succeeded in sequence to now by further stages. These can be counted and such a count is a metric. Where, clearly from p n, duration d = n - p, on some reasonable metric; where, it is also well known that the continuum is mileposted with the whole numbers. THERE IS NO DURATION SINCE THE PAST THAT IS NOT A DURATION SINCE SPECIFIC PAST EVENTS. In that connexion, we can readily see that if duration since p is finite,past since p is finite. It is my contention, here, that appeals to the infinitude of Z or R have in them a pointing arrow or two or ellipses for a reason: they do not have defined borders within the set, once any given z in Z or r in R are given, they can be exceeded, so we do not have a definable limit. However w is order type of the natural counting numbers and the continuum number attaches to any extended span in R^n, including R^1. The pointing arrows on axes or ellipses in set builder notation count. We can, however capture Z and R in context and that makes a difference, through the hyperreals, R* mileposted by Z*. We then see that there are transfinite spans extending these numbers into the specifically infinite ranges. Mathematically, these transfinite spans cannot be traversed in finite stage successive steps, which is why step builder notation points to the completion of a potential infinity by using ellipses or the equivalent. Where also, the 1/x catapult say prof Carol Wood used allows us to see that from 0 to transfinites, we have a unified space and structure of quantities. Where, infinitesimals and transfinite hyperreals have as much claim to "reality" as Complex numbers, negative numbers, zero, real but irrational numbers such as pi or e etc. We may freely model: . . . . K' --> K'+1 . . . . -2, -1, 0, 1, 2 . . . n . . . . w . . . . K-1. K, K+1 . . . ., where 4-dot ellipses denote specifically transfinite ellipses and the continuum is mileposted by numbers in Z* as shown. Now, let us consider your:
The infinite past proponents hypothesize that the past can be modeled using the real numbers. Here are a couple of obviously true statements. Let x be any real number. Then the set (?inf, x) has the following properties: 1) It is unbounded. Given any positive integer M, there is a number p in (?inf, x) such that |x ? p| > M. 2) If p is in (?inf, x), then |x ? p| < inf. Certainly I can say that without begging the question, correct?
Do you see what comes in in interval indications with (- inf ... or . . . +inf)? The ordinary curved brace indicates an OPEN ended interval with no definable terminal element. Here, as there is endless onward continuation L-ward or R-ward respectively. In short the continuum line goes on implicitly to transfinite hypereal spans which cannot be represented within R mileposted by Z explicitly, but we know that any specific given value we can write down or specifically represent can be exceeded, most easily seen with z in Z. This is actually the issue I found in 2nd form Algebra and 4th form Calculus. It is why on accessing Surreals and hyperreals, I could see that my Math teachers were struggling with the inadequacies of R mileposted by Z as models of the full span of relevant quantity, which became acute with integrals spanning to infinity and with the use of infinitesimals that had been tamed less than a decade before. There was that handwaving struggle with the clumsy epsilon-delta limits approach that while it carefully distinguishes potential from actualised infinity, hides more than it reveals. Blow the lot up and use the hyperreals and surreals to set context, say I! I yet further contend that playing within the trainer-wheels of R and Z glides by the lurking hyperreals by using unacknowledged potential, pointing infinities and thus implicit hyperreals. Combine that with the requirement of actuality of the past and definition that duration since is not between an implicit potential infinity and now, but must only be between definite events/stages that were once the actual present and now. From this, the claim of an infinite past -- stripped of its potential, pointing infinities and made explicit -- requires actual past events K' that are specifically transfinitely remote. Which is where the breakdown happens as trying to span a transfinite in steps of finite size is a patent supertask. Hence, again from 30:
In that light you cannot count up from a transfinite negative hyperreal K’ s.t. K + K’ = 0 and attain to a finite range of 0: . . . . K’ –> K’+1, K’+2 . . . K’+p –> K’+p+1, K’+p+2 . . . . -2, -1, 0, 1, 2, 3 . . . n, n being “now” and 0 conveniently the singularity. I use four dot ellipsis for a specifically transfinite span. Notice, at K’+p, at some finite remove from K’, we are in effect starting the finite count over again, which can repeat any finite number of times. We cannot traverse a cumulative, transfinite span in finite stage steps. So, the logic of structure and quantity plus the concept that any actual past stage had to have once been the actual present, leads to the problem. Namely, a supposed past point K’ cannot succeed in finite stage steps to 0 much less now, usually estimated at 13 – 14 BY beyond singularity. There was no transfinite remote actual past that was explicitly or implicitly transfinite. World from nothing –> X World from infinite past –> X Circular cause is just as bad: the not yet reaches back and sets in motion the chain of stages that causally, temporally succeed to itself. Circular cause –> X. Last man standing: a finitely remote, world source or root that is not causally dependent. That is, a necessary being. We can call it an ultimate cause or THE first cause.
There is motivation in my reasoning: to get the matter clear. I find it appalling to hear talk of how a collection of only finite values {0,1,2 . . .} is collectively infinite as beyond any z in N we may go onward z+1 etc. All that says to me is that any number we may successively count up to will be finite but exceed-able with a three dot ellipsis here pointing to the potential but not exhaustively counted infinity. Put it in the broader context and pop, things are clearer. The difference between normal and transfinite induction is of similar order, especially noting the significance of limit ordinals with no identifiable immediate predecessor, e.g. there is no definable, particular z in N so z+1 = w. In such a context, it seems to me rather to beg the question to suggest for every L-ward finite z in a succession of stages in a causal-temporal order that reaches now, one asserts or implies that the transfinite succession has already happened. Mathematically we can define the onward L-ward or imply it, but causal temporal succession has to have an effective means and duration has to be anchored to real world actual stages on either end. As we know all too well from the little dash on a tomb stone between two dates now commonly called sunrise and sunset in my neck of the woods. I think there is need for some rethinking. KFkairosfocus_{May 15, 2020
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Kairosfocus: I'm perfectly happy with there being a finite past; that's pretty much how I think about things for everyday purposes: the observable universe began between 13.5 and 14 billion years ago. Discussing the possibility of there being an infinite past outside of that is just philosophy at this point and I thought it was interesting to pursue for a bit. We've both had our say and are starting to repeat ourselves so it seems to me it's a good time to let it rest. We'll just stick to our observable universe from now on. We haven't agreed on the existence of a necessary being though! I don't think we will but that's okay.JVL_{May 14, 2020
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ET: As for an infinite past, how do we get to the now from an infinite past? Do tell. You can't, everyone knows that; I said as much already! But not being able to 'get to' infinity doesn't mean there isn't an infinite past. Anyway, I think we've beat this topic to death already.JVL_{May 14, 2020
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KF, There is one thing that might be useful to address:
DS, it is not a strawman. The suggestion you formerly made kept putting the transfinite traverse as already accomplished at any particular past time; repeatedly begging the key question which is that a transfinite past — whether implicitly or explicitly — will mean the duration from certain particular actual past stages to now would be itself transfinite.
This alleged "question begging" strikes me as very odd. If you're sincerely proposing this, I have to conclude it's an extreme case of motivated reasoning. The infinite past proponents hypothesize that the past can be modeled using the real numbers. Here are a couple of obviously true statements. Let x be any real number. Then the set (−∞, x) has the following properties: 1) It is unbounded. Given any positive integer M, there is a number p in (−∞, x) such that |x − p| > M. 2) If p is in (−∞, x), then |x − p| < ∞. Certainly I can say that without begging the question, correct?daveS_{May 14, 2020
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KF, I don't mean to be especially quarrelsome, rather I'm just making some observations. My jimmies are not the least bit rustled. I've had my say on the subject. PS: I see your post #131 above, and will read it a bit later once I get some work done.daveS_{May 14, 2020
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DS, it seems you wish to go off into the weeds on a quarrel, which is a classic context from which master manipulators derived the turnabout projection strategy and cross-complaint strategy; which are proven ways to cloud, confuse, poison and polarise an issue. I will note, when I have pointed to turnabout projection tactics, it has been for cause AS YOU FULL WELL KNOW. Right now you are coming across as how dare you call specific, known, observable tactics all too commonly seen in these dark days of a waning civilisation by their names. Sorry, it does not work that way, especially when you are obviously distracting from going over the line gratuitously. Those we simply do not need, given that from 30 I put up a clear enough reason why I hold for cause as I have again outlined. We may have a disagreement, but in no way can it be reasonably held that it is because of "disingenuous debate tactics" on my part. And, you need to explain to us all, if you object to the conclusion, how we can have a transfinte past duration to now in a causal temporal world without actual, specifically transfinitely removed past points, whether implied or explicitly acknowledged. Duration, p to n is n - p on some metric. The ellipsis is not a past event but an indicator of such. Duration is event to event. KFkairosfocus_{May 14, 2020
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DS, I took some time to do a search on your papers, I can find the reply but not the original. The reply responds to something I have not argued (assuming this is an accurate summary) so I find it tangential. I am not arguing about Tristam Shandy writing down his daily activities and being slower than his activities but both accumulating to the transfinite. Nor do I merely assume or assert that one cannot span a transfinite succession in finite stage, cumulative sequences. I SHOWED why. A big part of our exchanges in the past pivoted on confinement to the reals (with Z interpolated), and I eventually went to Dr Wood on that subject, cf https://uncommondescent.com/mathematics/logic-first-principles-17-pondering-the-hyperreals-r-with-prof-carol-thomas-including-infinitesimals/ . I have concluded, for reason, that R* is a more reasonable model and context for number issues that originally came up with number line, infinitesimal and transfinite discussions that first came up in second to fourth form for me. First in Algebra then in Calculus [when I first carried home 4th form Calculus homework, my Dad said, that at my then age he didn't know it existed when he was a boy]. I was delighted to find out that Abraham Robinson tamed infinitesimals and thus we can see Calculus foundations as extending Algebra on R*. It was you who pointed me to the Surreals, and I thank you. The hyperreals allow us to connect naturals, reals, infinitesimals and transfinites in one common number space. The j* operator rotation, vector view extends this to my 6th form experience: Complex numbers. And I recall being in an Astronomy club meeting in QC on St Michaels Row in Bridgetown and having a student ahead of us go through the derivation of the Euler Identity. Over the years since, Y, it has been a wonderful acquaintance. Now, coming back, it is clear that the ACTUAL, cumulative to present past has to be that, actual. Duration of the past is time [however accounted for] lapsed since definite past stages that were actual. Duration since p to now, n is n - p, on some metric. You know why I speak of stages and sequence counts across such. Call this a common sense stipulation, however you may disagree or agree. In that context, for cause of question begging, I reject any approach that for any past p accessible to now in a finite number of finite stage steps, infers that the transfinite is beyond p and that we cannot reasonably discuss a past point K' as I discussed above. I care not that one may say that every number we can count to c, will be at finite remove and so as we may then go c+1 etc we conclude the set {0,1,2 . . . c . . .} is transfinite as a whole defines a transfinite set. What I point out is that the ellipsis is material and that we can better address the matter in R* mileposted with Z* which sets up, again clipping 30 above:
you cannot count up from a transfinite negative hyperreal K’ s.t. K + K’ = 0 and attain to a finite range of 0: . . . . K’ –> K’+1, K’+2 . . . K’+p –> K’+p+1, K’+p+2 . . . . -2, -1, 0, 1, 2, 3 . . . n, n being “now” and 0 conveniently the singularity. I use four dot ellipsis for a specifically transfinite span. Notice, at K’+p, at some finite remove from K’, we are in effect starting the finite count over again, which can repeat any finite number of times. We cannot traverse a cumulative, transfinite span in finite stage steps. So, the logic of structure and quantity plus the concept that any actual past stage had to have once been the actual present, leads to the problem. Namely, a supposed past point K’ cannot succeed in finite stage steps to 0 much less now, usually estimated at 13 – 14 BY beyond singularity. There was no transfinite remote actual past that was explicitly or implicitly transfinite. World from nothing –> X World from infinite past –> X Circular cause is just as bad: the not yet reaches back and sets in motion the chain of stages that causally, temporally succeed to itself. Circular cause –> X. Last man standing: a finitely remote, world source or root that is not causally dependent. That is, a necessary being. We can call it an ultimate cause or THE first cause.
Notice, I have found a way to model an explicitly transfinite span and to show how a stepwise incremental process will not span it, which should be familiar too from the exercises of moving around a given transfinite hyperreal as Dr Wood does in an onward linked video. You can use 1/x to catapult across the span between transfinites and infinitesimals but that is different. In short, the infinity lurks in the ellipses. In that context, you will observe how carefully I distinguish numbers in finite step counting range from 0 from those lurking beyond transfinite ellipses. In that context putting a preceding further transfinite ellipsis beyond K' does not affect that duration from K' to now would span a transfinite range. The above shows that it cannot be done in finite stage cumulative steps. If one dismisses K' and points to some c' on the negative side with a transfinite beyond it that is always given as already traversed, the duration from c' to now is finite and the transfinite spanning has been question beggingly assumed. It is thus always implicit that a transfinite duration has to be spanned so let's put it up explicitly. R* lets us do so and brings out the trouble. KFkairosfocus_{May 14, 2020
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KF, In this very thread you have claimed that we made objections to certain points simply because we found the alternatives "unpalatable" or "obviously unwelcome" (reading our minds in the process, no doubt). Not that such behavior is a capital offense---and this is UD, not a tea party. Edit: It seems you often a form of the word "turnabout" when someone challenges you on a point, as if it's somehow invalid to do so. Again, not of great moment, and we're all used to it, but perhaps suboptimal.daveS_{May 14, 2020
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DS, turnabout, given immediate and uncalled for context. I will note, that the cases where I have spoken of Agit Prop and Rhetorical tactics, have been cases where there is specific warrant for the view. Unfortunately this is an era of manipulation and when major supporters of a view characterise those who question on terms like: "ignorant, stupid, insane or wicked" there is little choice on the point. Of course, the penumbra of attack sites speaks for itself, down to on the ground stalking. I am rather surprised to see you use such language as you did above. For cause, I object. KFkairosfocus_{May 14, 2020
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KF, PS: I'm a little surprised at your reaction. You call our intellectual honesty into question routinely. You even have tags for your posts involving "Darwinist Rhetorical Tactics", "Agit-Prop", etc.daveS_{May 14, 2020
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KF, I'm sorry, but we were not born yesterday. An argument essentially identical to yours already appears in: Whitrow, G. J. “On the Impossibility of an Infinite Past.” The British Journal for the Philosophy of Science, vol. 29, no. 1, 1978, pp. 39–45. The philosopher John Bell points out the fatal flaw in: Bell, John. “The Infinite Past Regained: A Reply to Whitrow.” The British Journal for the Philosophy of Science, vol. 30, no. 2, 1979, pp. 161–165.daveS_{May 14, 2020
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DS, it is not a strawman. The suggestion you formerly made kept putting the transfinite traverse as already accomplished at any particular past time; repeatedly begging the key question which is that a transfinite past -- whether implicitly or explicitly -- will mean the duration from certain particular actual past stages to now would be itself transfinite. That transfinite span is the issue and it cannot be traversed in stages of finite steps. And as someone who has put LIFE repeatedly on the line not merely career, on matters of pivotal truth, I take strong exception to your accusation of "a disingenuous debating tactic." You are out of order, sir and should withdraw such. KF PS: Just to be clear as to the objectionable tactic on your part,
disingenuous Also found in: Thesaurus. dis·in·gen·u·ous (d?s??n-j?n?yo?o-?s) adj. 1. Not straightforward or candid; insincere or calculating: "Increasingly, the question of immigration has become a disingenuous stalking-horse for race and racial hostility" (Tyler Stovall). 2. Pretending to be unaware or unsophisticated; faux-naïf. 3. Usage Problem Unaware or uninformed; naive. dis?in·gen?u·ous·ly adv. dis?in·gen?u·ous·ness n. Usage Note: Disingenuous means "not ingenuous," that is, not innocent, naive, or guileless. As such it can refer to someone who is insincere or calculating, as in It is both insensitive and disingenuous for the White House to describe its aid package and the proposal to eliminate the federal payment as "tough love," or to someone who is pretending to be unsophisticated, as in "I don't have a clue about late Beethoven!" he said. The remark seemed disingenuous, coming from one of the world's foremost concert pianists. Both of these examples were accepted by 90 percent of the Usage Panel in our 2016 survey. As with many words containing prefixes that negate (dis-) or seem to negate (in-), speakers sometimes lose track of exactly what is being negated, and sometimes use disingenuous when ingenuous would be more appropriate, namely as a synonym for naive. This usage is considered an error by careful writers: in our 2016 survey, 87 percent of the Usage Panel disapproved of the phrase the disingenuous tourist who falls prey to stereotypical con artists. American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
For cause, this word as used by you is unacceptable. Kindly withdraw it.kairosfocus_{May 14, 2020
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KF, I can't speak for JVL, but it's not that your conclusions are "unwelcome". Rather, it's that you are knocking over a strawman but refuse to acknowledge it. It's obviously a disingenuous debating tactic.daveS_{May 14, 2020
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JVL, since I am here, I note that length of past timeline is irrelevant; though you will note 0 to now would be 13 - 14 BY on the last values I looked for. The irregular cluster HR patterns with branching from main sequence to Giants bands set that, as would incidence of white dwarfs. The beyond I have addressed is on suggested multiverse models. My basic point is, once we have finite duration stages in succession, the ACTUAL past cannot be transfinite on logic of structure and quantity . . . note the application of mathematics to the criterion that the real past must have been actual. Time, strictly is a within a going concern phenomenon. We have that temporal sequence cannot extend to past infinity and a cosmos does not come from non being. This puts necessary being as the last man standing. Where as from utter non being nothing can come, as a world is, something that is causally independent and adequate to source a cosmos always was. KF PS: I note, the balance on merits of an issue obviously unwelcome to you is distinct from our opinions. Sorry, once we are dealing with unobservable past of origins and the like we are looking at philosophy strictly, not Science. Doing phil while dressed in a lab coat and using mathematical apparatus does not cut off what it opens up or that the full range of world root consideratins become applicable under comparative difficulties. Besides onlookers now and future will draw their own evaluation and need to do so on a subject where information is hard to find.kairosfocus_{May 14, 2020
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JVL- Don't try to change the subject. Just answer the question I asked. As for an infinite past, how do we get to the now from an infinite past? Do tell.ET_{May 14, 2020
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