Uncommon Descent Serving The Intelligent Design Community

Coyne Believes a Version of “Turtles all the Way Down”

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As our News Desk has noted, over at Mind Matters Michael Egnor engages with Jerry Coyne on whether, as a matter of logic, the cosmos can be self-existent. Egnor says no, and one reason he gives is the logical principle that any causal chain points to a first cause. He writes:

Imagine a chain hanging from the sky supporting a weight suspended in the air. Each link in the chain is a cause for the continued suspension of the links and the weight they hold up. However, the chain could not hold itself up alone. It can’t be “links all the way up.” Something at the beginning must be holding the chain up. And whatever holds the whole causal series up cannot just be another link in the chain. To be a “first cause,” whatever is holding up the chain must be something different from the chain itself.

Most of us are familiar with the amusing “turtles all the way down” story:

The following anecdote is told of William James. […] After a lecture on cosmology and the structure of the solar system, James was accosted by a little old lady.

“Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it’s wrong. I’ve got a better theory,” said the little old lady.

“And what is that, madam?” inquired James politely.

“That we live on a crust of earth which is on the back of a giant turtle.”

Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position.

“If your theory is correct, madam,” he asked, “what does this turtle stand on?”

“You’re a very clever man, Mr. James, and that’s a very good question,” replied the little old lady, “but I have an answer to it. And it’s this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under him.”

“But what does this second turtle stand on?” persisted James patiently.

To this, the little old lady crowed triumphantly,

“It’s no use, Mr. James—it’s turtles all the way down.”— J. R. Ross, Constraints on Variables in Syntax, 1967

Coyne would certainly howl in disdain and ridicule at the rube who believed in turtles all the way down. Isn’t it ironic, then, that he himself believes in a similar story except instead of “turtles all the way down” he believes in “links all the way up.”

Comments
I’m using/applying what I learned on the OP that Kf wrote on common sense. Knowledge is justified true belief (JTB.) But what is JTB? Is there JTB that a creator exists? That a creator exists, knowledge of this is defined as the following 1) a creator actually exists for our universe 2) the person believes that a creator exists is true and 3) the person is justified that believing in a creator is true It is 3) that then becomes the point of discussion as to whether the person has justification. I personally believe that 3) will never be absolutely certain by design but is extremely likely. Science supports this justification. But for others they will be absolutely certain that it is justified while for others there will nothing close to certainty Anyone who says they have certainly that 3) is not justified is probably lying. Their assertion for this is probably more of an emotional statement based on something for which I will not speculate. It is definitely not based on any science we know Turtles or links all the way have no basis in anything we have observed except in wishful thinking that it be so. Those who make this or similar arguments seem desperately wishing a creator not be true for some reason. All this ignores the nature of the creator and the reasons for the creation. Which since time began has been a basis for much conflict. For this one has to go further into different types of justification.jerry
April 22, 2021
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I agree. It was never intended to be about the real world.
No one gives a flying **** about non-real or imaginary worlds. Sorry for the implied crudity. But the issue is Jerry Coyne believes he is describing a real world. That is what the OP is about.jerry
April 22, 2021
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BA writes, "Your argument is mathematically meaningless as far as the real world is concerned." I agree. It was never intended to be about the real world.Viola Lee
April 22, 2021
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This quote from Mark Twain should be the basis of most comments here.
“Mark Twain once ended a long letter to a friend by writing, “If I’d had more time I would have written you a shorter letter.”
There are infrequent occasions when something long is necessary but not very often. Once something long has been posted, it can be referred to thereafter with a simple link and a short explanation for linking to it.jerry
April 22, 2021
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I suggest in the name of sanity that the words “infinite” and “finite” and their various forms be banished from UD. It will limit (allowed word) seemingly endless (allowed expression) discussions over nonsense, of worlds that do not exist except in our imagination.jerry
April 22, 2021
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BA77, further to that, any specific finite value is bounded by onward values. You will note I have specifically identified finite duration stages that can be assigned values along the number line, like successive years. In that context, we can assert the constraint that any actual past stage p must once have been the present but gave rise to the next stage p+1 and so forth to now, n. As a transfinite span cannot be traversed completely in successive finite stage steps, we are therefore only warranted to speak of a past that is finite in two senses. First, that p can complete a stepwise succession to now. Second, that counting the number of steps to now from p will be strictly finite and bounded by steps to n+1 etc, the immediate prospective future. Were p's to extend such that every member of Z- could be assigned to some p, the overall span would take up the property of being beyond ability to exhaustively traverse by counting, i.e. it would be implicitly infinite. We have very good reason to infer that the actual past has not traversed through a set of stages that would exhaust Z-. That is, the past is strictly finite once stages that were once the present, p, must cumulatively succeed one thermodynamically controlled step at a time, p+1, p+2 etc onward to n, now; even going beyond the singularity, the big bang. Which, recall, I set as 0. Mathematical imagined pasts such as D spanning Z- as VL raised in 75 are not physically real. KFkairosfocus
April 22, 2021
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VL's own words, “There is no mathematical problem in stating that every moment had a prior moment, and therefore there was no first moment”. I observed that "Others disagree." VL responds that, "There is a considerable difference in saying “There is no mathematical problem (in stating that every moment had a prior moment, and therefore there was no first moment). ” and “time must be infinite into the past.” That is obvious. Hmm "that is obvious"???,,, Really? But anyways, VL continues, (to quote her in full lest I be accused of misrepresenting VL's words.)
Also above I wrote (and this is something I have said every time this subject has come up, “I don’t think we know at all what the nature of time might be outside our universe. I’m just discussing this from a mathematical point of view.” I am making no arguments about what real time might be: I am just discussing the notion of time as modelled by the negative integers. My argument is (but I am absolutely sure you will not represent this accurately) is outlined in post 43: it is mathematically consistent to say that time, as modelled by the negative integers, could have no beginning–no first moment– and yet not involve an infinite traverse to now. That’s all. I am certainly in no way saying that real time, whatever that may be, must be infinite.
So VL, since you admit that you are making no mathematical argument as to what 'real time' might be, what in blue blazes makes you think that you have "no mathematical problem in stating that every moment had a prior moment, and therefore there was no first moment”? Your infinite series of negative integers, by your own admission, does not represent 'real time'. And if it does not represent, by your own admission, 'real time', it must, of necessity be talking about some 'imaginary time' But then why are talking as if your mathematical model of counting backwards from 'now'' had any relevance to time whatsoever? You could have just as well stuck any imaginary entity into your infinite series of negative integers instead of your 'imaginary time' that has no connection to the real world. i.e. you could have used widgets, pink unicorns, cosmic turtles, etc.. etc.., it does not matter, because you, by your own admission, are not talking about anything that has to do with the real world. But you are instead talking about something that is, for all practical purposes, totally disconnected from the real world. As Karen observed at post 131, “All the way down” isn’t meaningful, because it isn’t isomorphic to anything in our universe including turtles or units of time." Your argument is mathematically meaningless as far as the real world is concerned.bornagain77
April 22, 2021
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VL, every integer p [- direction] or k [+ direction] we actually count to or represent as counted to is finite and bounded by onward remote cases, p-1 etc l-ward and k+1 etc r-ward. But this means that onward succession WITHOUT FINITE LIMIT is part of the definition of Z and of R which it mileposts. So, it is material to note that onward succession feature. As in: . . . p, p+1, p+2 . . . -2, -1, 0, 1, 2, 3 . . . k, k+1, k+2, . . . Taking in *0* as there being a cloud of infinitesimals near 0 and closer than 1/n for any finite n in N, we can take one such h and go 1/h --> H, a transfinite hyperreal beyond any finite n in N, thus onward H+1, H+2 etc. . . . - H . . . p, p+1, p+2 . . . -2, -1, *0*, 1, 2, 3 . . . k, k+1, k+2, . . . --> H [= 1/h, in *0*], H+1, H+2 . . . Having so opened up our understanding of the intuitive number line we can now see that in R* we can and do have any number of transfinite integers, some even, some odd, and that R is the span that embraces numbers mileposted by counting numbers from 0, N, and their mirror image, Z-; with the property of limitless onward extension beyond any specific p or k as already discussed. It is artificial to constrict discussion to finite values, once the set R* is available. KFkairosfocus
April 22, 2021
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JVL, 68:
IF we think we can model the passage of time mathematically and NOW is time zero and we pick our units to be years then t = -1 is a year ago, t = -2 is 2019, etc. You can keep doing that a long as you like and when you stop at a particular t = -something you will still be a finite number of years away. Cosmologists think the Big Bang happened at something like t = -13.8 billion years. If there is a creator God who exists outside of our limited view of space and time then it seems plausible that God would recognise t = – 14 billion years and t = -20 billion years and t = -200 billion years, etc. BUT all of those points are a finite number of steps away from t = 0 which is today. That’s all we’re saying. Just because there is a mathematical -infinity doesn’t mean we think that time extends backwards forever and ever.
The challenge here is that the structure of N and Z builds in onward limitless extension, . . . p, p+1, p+2 . . . -2, -1, 0, 1, 2, 3 . . . k, k+1, k+2, . . . That is, for any specific finitely remote p or k, there is limitless onward succession L-ward or R-ward respectively. Where, the order type of the ordinals that can be matched to N is w, first transfinite ordinal. Where, we count duration or separation, etc, -- span if you will -- as number of steps between. 0-->1, 1 step, 1 --> 3, 3 steps from 0 less 1 step from 0 or 2 steps, 0 -->k, k steps. p --> 0 p steps. It follows that p --> k, p + k steps, more readily seen as for -r to + k, k - [-r] steps, i.e. k + r. So, the span metric between any two members we count to or represent as countable to from 0 will be finite BUT always there is a continuation beyond. The problem arises when we take past to present time and map it against this structured set, Z, especially Z-. The span count, for such a range is of scale aleph null, i.e. transfinite, recognisable as not just without beginning but infinitely remote in the past. Further to which, there are cosmological models put on the table, that while they are in fact speculative, purport to have a past that is limitless like that. Hence, why in my discussions for years, I set now, n as some positive value beyond 0 as singularity with onward modelled past beyond that. This puts the issue of an infinite, quasi-physical past on the table. Hence the relevance of pointing out that the nature of time viewed as successive finite duration stages, is that of causal-temporal succession as the now gives rise to the next now. Our succession of years gives an idea. However, that causal flow is thermodynamically connected, so that every actual past stage p -- deliberately, well beyond the singularity -- must be able to chain cumulatively from the once now that has become the past to the current now. That is, stepwise succession of stages p -->p+1 --> p+2 . . . 0 --> n, now, rules. Yes, onward we may well have a potential infinite succession [ignoring heat death] n --> n+1 --> n+2 . . . but at no stage is the span implicit in the ellipsis traversed to completion. Finite, growing without limit onward. But that inability to fully traverse the suggested onward possible future of scale aleph null, is the very same issue as to why such a traverse in the past could not have been completed. In that context, the logic of structure and quantity poses a problem. Namely, only specifically finite cumulative traverse is feasible. We only can COMPLETE a traverse for a specifically finite span. As noted, we can label stages from Z, including Z- but we cannot exhaust Z- with actual past stages once causal-temporal succession to n is a constraint. The actual past, by logic of being and by the thermodynamic succession constraint, is strictly finite. That is, if there is a quasi-physical sub-verse underlying our observed cosmos, it too only extends a finite duration -- quantified as above -- into the causally-temporally connected past. There was a finitely remote specific beginning, even for such a subverse. KFkairosfocus
April 22, 2021
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BA77, time is bound up in thermodynamically driven change. This sets time's arrow as having degradation of energy as the forward direction; which also ties to degradation of information-rich organisation. We can therefore see a physical cosmos level process that ultimately looks toward a dead cosmos, at perhaps 10^25 s beyond the singularity. Where, origin is ~10^17s past, on the usual timelines. I have already dealt with the issue of finite stage scale, stepwise succession to now. There is no good reason, on structure and quantity aspects of logic of being, to pose any model of the past, say D, where the collection of actual past days is in correspondence with Z-, which we saw in 75 above. That sort of model of the past should be recognised as failing in the starting gates as the implied transfinite traverse of scale aleph null, is infeasible for structure-quantity reasons. There just are no turtles all the way down without beginning. We have to face the logic of being import, that causal-temporal arrow of time reality is finite in the past. Connect to, necessary, so eternal being at root of reality and we are in a much different position for onward thought. KFkairosfocus
April 22, 2021
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VL, pardon, but the evidence is that you tried to set up transfinite traverse across the past at the outset. I therefore highlighted something from logic of being's structural and quantitative aspect [what sort of sets can be traversed stepwise in finite stages] and something from physics, that a given stage of the actual past is thermodynamically connected to its immediate successor, chaining to the present]. In that context, any actual past stage p must be connected to now by a chain of actual, thermodynamically controlled causal-temporal succession, stage to next stage. As a direct result, your D-model of the past (of a past comprising days countable but corresponding to Z-, i.e. an infinite set) fails. That is the balance on merits, how I am allegedly lecturing you on mathematics you know notwithstanding. So, if that relatively simple issue is deadlocked, that there can be a more fruitful wider analysis of logic of being, thence why necessary being is required at root of reality does not seem likely just now. As for onward issues on how the eternality implied in necessary being cashes out on topics like the theistic vision of the eternal God and his relationship to time, absent working through the logic of being, there is no general, worldviews analysis basis for discussion. I will note, that were there ever utter non-being such would forever obtain, that infinite past models fail to resolve stage by stage traverse to the present, that circular causation is trying to pull a world out of not yet being, leaving finitely remote necessary [so, eternal in some sense] being as required root of reality and source as key framework for any possible world to be or to begin and be sustained. That this world has in it inescapably morally governed creatures is a further constraint, we need a reality root adequate to ground goodness. As for philosophical or systematic or biblical theology, there is no reason for me to think such a tangential matter would do anything more than open up onward tangents. The key takeaway is, that turtles all the way down, infinite, thermodynamically connected stages models of the past fail. KFkairosfocus
April 21, 2021
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WJM- What do I mean by" real"?, Exactly my point.Marfin
April 21, 2021
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EDTA @ 135 -
I can’t believe this discussion has continued this long.
This is nothing (yet). I suspect these infinity thread are attempts to make a thread that is infinitely long.Bob O'H
April 21, 2021
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In fact, BA, here are two simple pure mathematics questions. Do you think these are true, or not? Explain briefly if you like. 1. There are an infinite number of negative integers. Agree, or not? 2. Every negative integer is finite. Agree or not?Viola Lee
April 21, 2021
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There is a considerable difference in saying "There is no mathematical problem ... " and "time must be infinite into the past." That is obvious. Also above I wrote (and this is something I have said every time this subject has come up, "I don’t think we know at all what the nature of time might be outside our universe. I’m just discussing this from a mathematical point of view." I am making no arguments about what real time might be: I am just discussing the notion of time as modelled by the negative integers. My argument is (but I am absolutely sure you will not represent this accurately) is outlined in post 43: it is mathematically consistent to say that time, as modelled by the negative integers, could have no beginning–no first moment– and yet not involve an infinite traverse to now. That's all. I am certainly in no way saying that real time, whatever that may be, must be infinite.Viola Lee
April 21, 2021
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VL's own words, “There is no mathematical problem in stating that every moment had a prior moment, and therefore there was no first moment”. Others disagree! :)bornagain77
April 21, 2021
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BA writes, "VL’s contention that time must be infinite into the past." VL absolutely never said that. It is pitiful the way you misrepresent things.Viola Lee
April 21, 2021
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Since we are discussing time itself and whether it is infinite or not, I guess it would be fair for us to ask the question, "What is Time?" First off, I think it is important to note that time does not have an independent physical existence of its own, but that time has a contingent existence that is always based on some regularity of nature that we measure. And indeed, what we base our measurement of time on has changed drastically throughout history: (although the orbit of the earth around the sun has always been the 'master regularity' that we ultimately base our measure of time on)
1 Timekeeping devices of early civilizations 1.1 Ancient Egypt 1.2 Ancient Greece and Rome 1.3 Ancient and medieval Persia 1.4 Ancient and medieval China 2 Timekeeping innovations in medieval and pre-modern periods 2.1 Candle clocks 2.2 Incense clocks 2.3 Sundials 2.4 Hourglass 2.5 Clocks with gears and escapements 2.6 Clock towers 2.7 Astronomical clocks 2.8 Early mechanical clocks and watches 2.8.1 Wristwatch 2.8.2 Equation clock 3 Era of precision timekeeping 3.1 Pendulum clock 3.2 Spiral-hairspring watch 3.3 Pocket watch 3.4 Marine chronometer 3.5 Electric clock 3.6 Quartz clock and watch 3.7 Atomic clock https://en.wikipedia.org/wiki/History_of_timekeeping_devices
As well, I think it is also important to point out that time is immaterial in its foundational essence, in that it involves us counting numbers. Yet, Numbers, like time itself, has no physical existence on its own that we can measure. As Berlinski noted, "The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious."
An Interview with David Berlinski - Jonathan Witt Berlinski: There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time…. Interviewer:… Come again(?) … Berlinski: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with elementary particles or accelerating forces. But these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects. http://tofspot.blogspot.com/2013/10/found-upon-web-and-reprinted-here.html ?
Thus it follows that time is an abstract concept of the immaterial mind that has a contingent existence, (not a necessary existence), that is based on some regularity of nature that we measure and count with immaterial numbers, via, and ultimately, count with our immaterial minds. To drive this point further home, the fact that time does not have an independent physical existence of its own is hinted at in the following article which states, "many scientists question whether time even exists."
The Arrow of Time? It’s All in Our Heads - Robert Lanza - September 26, 2016 Excerpt: For years physicists have known that Newton’s laws, Einstein’s equations, and even those of the quantum theory, are all time-symmetrical. Time plays absolutely no role. There is no forward movement of time. Thus, many scientists question whether time even exists. Indeed, Einstein’s theories of relativity suggest not only that there is no single special present but that all moments are equally real.,,, Thus, a “brainless” observer — that is, an observer without the ability to store observed events — does not experience time or a world in which we age. http://blogs.discovermagazine.com/crux/2016/09/26/the-arrow-of-time-its-all-in-our-heads/ of related note: “Imagine that you do something as simple as throwing a ball. At any instant in time, if you tell me where it is (its position) and how it’s moving (its velocity), I can predict for you exactly where and when it will hit the ground. Except, if you simply write down and solve the equations governed by Newton’s laws of motion, you won’t get a single, correct answer. Instead, you’ll get two answers: one that corresponds to the ball hitting the ground in the future, and one that corresponds to where the ball would have hit the ground in the past. The mathematics of the equations doesn’t tell you which answer, the positive or the negative one, is physically correct." per Forbes
As well, on Einsteins 70th birthday, Gödel presented Einstein with a paper on time travel being possible within relativity which Godel held, "demonstrated,,, that time itself,,,, is but an illusion.”
THE GOD OF THE MATHEMATICIANS: THE RELIGIOUS BELIEFS THAT GUIDED KURT GÖDEL’S REVOLUTIONARY IDEAS by David P. Goldman - August 2010 Excerpt: In a Festschrift for Einstein’s seventieth birthday in 1949, Gödel demonstrated the possibility of a special case in which, as Palle Yourgrau described the result, “the large-scale geometry of the world is so warped that there exist space-time curves that bend back on themselves so far that they close; that is, they return to their starting point.” This means that “a highly accelerated spaceship journey along such a closed path, or world line, could only be described as time travel.” In fact, “Gödel worked out the length and time for the journey, as well as the exact speed and fuel requirements.” Gödel, of course, did not actually believe in time travel, but he understood his paper to undermine the Einsteinian worldview from within. Yourgrau observes, “The very fact that this inconceivably fast spaceship would return its passengers to the past demonstrated, by Gödel’s lights, that time itself—hence speed and motion—is but an illusion.” Stephen Hawking so abhorred the implications of Gödel’s demonstration that he proposed an ad hoc bylaw for general relativity, the “chronology protection conjecture,” simply to exclude it. https://www.firstthings.com/article/2010/08/the-god-of-the-mathematicians
Moreover, the following study confirmed Gödel's contention to Einstein that "time is not a physical dimension of space through which one could travel into the past or future.”
Physicists continue work to abolish time as fourth dimension of space - April 2012 Excerpt: “The rate of photon clocks in faster inertial systems will not slow down with regard to the photon clocks in a rest inertial system because the speed of light is constant in all inertial systems,” he said. “The rate of atom clocks will slow down because the 'relativity' of physical phenomena starts at the scale of pi mesons.” He also explained that, without length contraction, time dilation exists but in a different way than usually thought. “Time dilatation exists not in the sense that time as a fourth dimension of space dilates and as a result the clock rate is slower,” he explained. “Time dilatation simply means that, in a faster inertial system, the velocity of change slows down and this is valid for all observers.,, Our research confirms Gödel's vision: time is not a physical dimension of space through which one could travel into the past or future.” http://phys.org/news/2012-04-physicists-abolish-fourth-dimension-space.html
Moreover, as we have built more and more accurate clocks to measure time with, we have conducted experiments that now show us that time passes differently for the clocks depending on how fast the clocks are traveling (Special Relativity) and/or where the clocks are positioned in relation to a gravitational field (General Relativity). This is referred to as time dilation. And indeed, the fact that time is not constant everywhere in the universe is of practical concern for satellite navigation systems (Global Positioning System, GPS), in that complex calculations have to made in order to keep the clocks synchronized with one another in order that they may give accurate positioning information to their customers.
Time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them (special relativistic "kinetic" time dilation) or to a difference in gravitational potential between their locations (general relativistic gravitational time dilation).,,, These predictions of the theory of relativity have been repeatedly confirmed by experiment, and they are of practical concern, for instance in the operation of satellite navigation systems such as GPS and Galileo.[1] https://en.wikipedia.org/wiki/Time_dilation
The important thing for us to know about time dilation is that time itself, as we understand it, comes to a complete stop in both General Relativity and Special Relativity. In General Relativity time, as we understand it, comes to a complete stop at the event horizon of a black hole when the gravitational acceleration equals the speed of light,, Whereas in Special Relativity time, as we understand it, comes to a complete stop at the speed of light. (see post 29 for a more detailed discussion about the time dilation of special relativity) https://uncommondescent.com/intelligent-design/118649/#comment-728764 Thus in conclusion, and in regards to VL's contention that time must be infinite into the past, we have every right to ask him or her, "Can you even prove that time physically exists outside of your imagination, much less that it physically exists infinitely into the past?" :) Verse:
Genesis 1:1 In the beginning God created the heavens and the earth.
bornagain77
April 21, 2021
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KF you write, "VL, kindly notice what you started out with in 75 above to EDTA and then effectively asked me to respond to:" No, I wasn't effectively, or otherwise, asking you to respond. I was just asking if you were aware that ETDA and I were discussing a paper.Viola Lee
April 21, 2021
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KF, instead of lecturing us on math we all know, you should try instead to follow a conversation with the intent of understanding it. I was trying to understand the paper EDTA recommended, and was trying to compare my understanding with EDTA's. You know, we were having a cooperative discussion where we were trying to understand each other. You should try it sometime. See EDTA's response at 81.Viola Lee
April 21, 2021
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I can't believe this discussion has continued this long. JVL, We have no idea if God has anything analogous to our concept of time. I doubt we could conceive what it was even if it did exist.EDTA
April 21, 2021
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WJM @ 112, >So, you see the problem here. Undermining one’s reality program is no small task and it has very uncomfortable experiential consequences... An interesting way to put it, "undermining one's reality program". I'm going to have to drop the inquiry. Thanks for the explanations, though.EDTA
April 21, 2021
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You guys are taking these turtles awfully seriously! :-) Turtles all the way down, almostViola Lee
April 21, 2021
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VL, kindly notice what you started out with in 75 above to EDTA and then effectively asked me to respond to:
[VL, 75:] 1. “Let t represent today, D the collection of all days prior to t”. D represents all the days in the past. If we assume, for convenience, that t = 0 represents now, D represents the set of negative integers. I assume collection is the same as set. Do you agree with these statements?
As Wiki correctly acknowledges, "a finite set is a set which one could in principle count and finish counting. For example, { 2 , 4 , 6 , 8 , 10 } is a finite set with five elements. The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: { 1 , 2 , 3 , … } ." As an almost trivial point, Z-, the mirror image of Z+ in 0, has the same cardinality, aleph null, i.e. is infinite. So, you directly imply the claim that D, "the collection of all days prior to t," is infinite. Thus, counting out 0,-1,-2 . . . will fail to exhaust it, and one cannot count in the direction from left to 0, . . . -2,-1,0 either. That is effectively the points I have made for several years and in your presence. A transfinite span cannot be completely traversed in finite stage steps, and so once every actual past time p was once the present and has been succeeded p+1, p+2 . . . t to use your symbol, the completed span -- so, the DURATION since any such p will be finite. Furthermore, if we leave the implicit transfinite D = Z- so to speak, it cannot have been completely traversed to t. By the meaning of the transfinite scale of Z-. That is, the actual past was finite. There are not infinitely many turtles all the way down. And were there somehow, the span of turtles to t cannot be traversed completely in steps. KFkairosfocus
April 21, 2021
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Viola: Summary of the issue: It’s not turtles all the way down, because you can’t ever get to “all the way down”. "All the way down" isn't meaningful, because it isn't isomorphic to anything in our universe including turtles or units of time. But there is always another turtle. A conclusion not supported by any facts in evidence.Karen McMannus
April 21, 2021
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Viola Lee:
Summary of the issue: It’s not turtles all the way down, because you can’t ever get to “all the way down”. But there is always another turtle.
That is the summary of the issue from someone looking at it backwards. And there aren't any turtles. Just an intelligently designed space-time fabric of a universe.ET
April 21, 2021
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KF, are you aware that post 75 is about trying to understand the paper that EDTA linked to at #34?Viola Lee
April 21, 2021
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JVL, there we go again. I set up my points of response step by step [such as understanding different possibilities for being which shows why necessary being is eternal and part of the fabric for any world to exist with two as a case in point], showing what was needed and I let the record stand as it is adequate for purpose. KFkairosfocus
April 21, 2021
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VL, D is assumed in in 75 as having aleph null cardinality, i.e. you begged the question of infinite stepwise traverse. Notice, that finite sets can be exhausted by such a traverse but those that cannot are not-finite, i.e. infinite. Your argument in 75 fails at outset. KFkairosfocus
April 21, 2021
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Summary of the issue: It's not turtles all the way down, because you can't ever get to "all the way down". But there is always another turtle. :-)Viola Lee
April 21, 2021
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