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Physics and the contemplation of nothing

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In a review of Void: The Strange Physics of Nothing by James Owen Weatherall, Steven Poole writes at Spectator (UK):

In an action-packed epilogue, the author describes how the contested field of string theory posits a bogglingly large number of possible kinds of nothingness, and impresses upon the reader how much of physics still depends on intuition and battling ‘interpretations’. The book is not an exhaustive typology of scientific nothings: not directly addressed, for example, is the nothingness that supposedly obtained before the Big Bang. But to regret this is just to emphasise the success of this stylishly written and admirably concise book, at the end of which you will be inclined to agree, along with the author and Freddie Mercury both, that ‘Nothing really matters.’More.

String theory leads physics down the bramble patch of unacknowledged metaphysics.

See also: Multiverse explains why progress in fundamental physics is slow?

and

Must we understand “nothing” to understand physics?

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94 Replies to “Physics and the contemplation of nothing

  1. 1
    harry says:

    The thing to understand about material and temporal nothingness is that it is just that: nothing.

    So any discussion of “kinds” of material and temporal nothingness is absurd, at least when by nothingness we mean the absence of space, time, matter and energy.

    The absence of material and temporal realities, i.e., natural realities, is a situation from which nothing can ever come by natural means. Only some kind of supernatural reality can bring natural realities into existence from material and temporal nothingness. That is why it took decades for atheistic science to accept the Big Bang theory in spite of ever increasing corroborating evidence for the theory.

    The same kind of thing will eventually happen with ID theory due to the ever increasing corroborating evidence for it. See, for example:

    The Designed Body, Continued: Coherence Wins, Gradualism Fails

    on the Evolution News web site.

  2. 2
    kairosfocus says:

    Harry, you are right, nothing properly denotes non-being. Not matter, not energy, not waves, not space, not mind etc., non-being. Literally, NO-thing. Where, non-being can have no causal capacity so were there ever utter nothing (= nothing but nothing!) such would forever obtain. Logic of being — as opposed to physics, a science that studies matter, energy, space-time and interactions — then implies that as a world manifestly is, something always was, something is a necessary being. And as contingent beings are not necessary, such are in the end rooted in this necessary being. Onward, that points to framework reality at the root of possible worlds. As in, the proper discussion is, what is the NB at root of this and other possible worlds. A couple of clues lie in how we are morally governed (even in how we reason), and that both the world of life and the observed cosmos show copious signs of intelligent design. However, this cuts across entrenched ideological interests and so we see the huge controversy at the core of the focus for this blog. Understanding the ideological agenda also helps us understand the mindset of many objectors. KF

  3. 3
    harry says:

    KF @2,

    That was good. From nothing, nothing can ever come, so if there is something, something necessarily always was, an utterly non-contingent reality the essence of which is “to be,” upon which all else is contingent.

    It has always struck me how superior in philosophical sophistication the Hebrew Scriptures were regarding the accounts of origins compared to the texts of other ancient religions. The God of the Hebrews creates ex nihilo and identifies Himself as “I AM WHO AM.”

    Amazing.

  4. 4
    Armand Jacks says:

    KF:

    Understanding the ideological agenda also helps us understand the mindset of many objectors. KF

    This, of course presupposes an ideological agenda exists with your objectors. And, if one does not exists, some feel it necessary to fabricate one so that they can argue against it. Pretty standard strawman tactic.

    We all have ideologies, in a broad and literal interpretation of the word. In that we all act based on the assemblage of ideas that we have developed for ourselves based on evidence, experience and teaching (in some cases, indoctrination). Most Christians had Christian parents. Most Muslims had Muslim parents, and most Hindus had Hindu parents. This is a prime example of the teaching/indoctrination aspect of ideology.

    Many people convert, become atheist/agnostic or adopt a faith. This is an example of the influence of evidence and experience.

    This being said, to infer that your objectors have some sort of nefarious agenda is simply a fallacy. I can only speak for myself, but my only agenda, is to assist in the development of the best explanatory models of what we perceive around us. Admittedly, neither you nor I, nor most of the people who post here, really contribute anything of significance to this effort. Our efforts, at best, are nothing more than entertaining distractions. We really shouldn’t take ourselves so seriously.

  5. 5
    daveS says:

    AJ,

    In the same vein, as a sometime objector, I can affirm that some posters here apparently believe they understand our/my “mindset” when they in fact are actually way off. I know I could fall into this trap just as easily, so I try not to assume I have access to anyone else’s thoughts or motives unless they have stated them explicitly here.

  6. 6
    Armand Jacks says:

    DaveS:

    In the same vein, as a sometime objector, I can affirm that some posters here apparently believe they understand our/my “mindset” when they in fact are actually way off.

    Sadly, I think this is a tactic more than it is an actual belief. Some here even go as far as quoting an objector’s comment and then start their response with “Translation:…”. An obvious attempt to ascribe words or intention to the objector that any rational person could see are not justified by what the objector actually said.

  7. 7
    daveS says:

    AJ,

    That could be, of course.

    Reading my previous post, I actually should amend it:

    I can affirm that some posters here apparently believe they understand our/my “mindset”

    What I should have said is that other posters have told me directly what my thoughts/motives are, incorrectly as it happens.

  8. 8
    Armand Jacks says:

    DaveS:

    What I should have said is that other posters have told me directly what my thoughts/motives are, incorrectly as it happened.

    You must have been talking about subjective morality.

  9. 9
    kairosfocus says:

    AJ:

    Agendas?

    Try this, first, as summarised by Richard Lewontin (now that we have power back for 1/2 hr or so, so far):

    . . . to put a correct view of the universe into people’s heads [==> as in, “we” have cornered the market on truth, warrant and knowledge] we must first get an incorrect view out [–> as in, if you disagree with “us” of the secularist elite you are wrong, irrational and so dangerous you must be stopped, even at the price of manipulative indoctrination of hoi polloi] . . . the problem is to get them [= hoi polloi] to reject irrational and supernatural explanations of the world, the demons that exist only in their imaginations,

    [ –> as in, to think in terms of ethical theism is to be delusional, justifying “our” elitist and establishment-controlling interventions of power to “fix” the widespread mental disease]

    and to accept a social and intellectual apparatus, Science, as the only begetter of truth

    [–> NB: this is a knowledge claim about knowledge and its possible sources, i.e. it is a claim in philosophy not science; it is thus self-refuting]

    . . . . To Sagan, as to all but a few other scientists [–> “we” are the dominant elites], it is self-evident

    [–> actually, science and its knowledge claims are plainly not immediately and necessarily true on pain of absurdity, to one who understands them; this is another logical error, begging the question , confused for real self-evidence; whereby a claim shows itself not just true but true on pain of patent absurdity if one tries to deny it . . . and in fact it is evolutionary materialism that is readily shown to be self-refuting]

    that the practices of science provide the surest method of putting us in contact with physical reality [–> = all of reality to the evolutionary materialist], and that, in contrast, the demon-haunted world rests on a set of beliefs and behaviors that fail every reasonable test [–> i.e. an assertion that tellingly reveals a hostile mindset, not a warranted claim] . . . .

    It is not that the methods and institutions of science somehow compel us [= the evo-mat establishment] to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes [–> another major begging of the question . . . ] to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute [–> i.e. here we see the fallacious, indoctrinated, ideological, closed mind . . . ], for we cannot allow a Divine Foot in the door . . . [–> irreconcilable hostility to ethical theism, already caricatured as believing delusionally in imaginary demons]. [Lewontin, Billions and billions of Demons, NYRB Jan 1997,cf. here. And, if you imagine this is “quote-mined” I invite you to read the fuller annotated citation here.]

    And, should that seem idiosyncratic to you, here — as a formal case in point, duly passed and met with no significant repudiation (but used, e.g. to impose an ideologically loaded and historically unwarranted redefinition of science in education, one hailed by the major media and talking heads) is the board of the US National Science Teachers:

    The principal product of science is knowledge in the form of naturalistic concepts and the laws and theories related to those concepts [–> ideological imposition of a priori evolutionary materialistic scientism, aka natural-ISM; this is of course self-falsifying at the outset] . . . .

    [S]cience, along with its methods, explanations and generalizations, must be the sole focus of instruction in science classes to the exclusion of all non-scientific or pseudoscientific [–> loaded word that cannot be properly backed up due to failure of demarcation arguments] methods, explanations, generalizations and products [–> declaration of intent to ideologically censor education materials] . . . .

    Although no single universal step-by-step scientific method captures the complexity of doing science, a number of shared values and perspectives characterize a scientific approach to understanding nature. Among these are a demand for naturalistic explanations supported by empirical evidence that are, at least in principle, testable against the natural world. Other shared elements include observations, rational argument, inference, skepticism, peer review and replicability of work [–> undermined by the question-begging ideological imposition and associated censorship] . . . .

    Science, by definition, is limited to naturalistic methods and explanations and, as such, is precluded from using supernatural elements [–> question-begging false dichotomy, the proper contrast for empirical investigations is the natural (chance and/or necessity) vs the ART-ificial, through design . . . cf UD’s weak argument correctives 17 – 19, here] in the production of scientific knowledge.

    That there is a new magisterium imposing an a priori, ruthlessly determined agenda of evolutionary materialism wherever it can, is beyond reasonable doubt.

    KF

  10. 10
    kairosfocus says:

    DS, the issue is not whether an agenda of evolutionary materialistic scientism exists, despite its utterly irretrievable self-refutation and its indefensible amorality, the issue is whether we deal with knowing principals with great influence, or fellow travellers, or enablers, activists and unknowing foot-soldiers in front groups every inch comparable to Lenin’s useful idiots. I leave categorisation to you, as to which group(s) you belong to. In the end, given the locus of power and civilisationally ruinous force of the agenda [long since pointed out by Heine in the 1830’s and too often manifested ever since], it makes little difference to the outcome. KF

  11. 11
    kairosfocus says:

    PS: let me cite Pearcey on the self-referential incoherence of epistemologies tied to evolutionary materialism:

    A major way to test a philosophy or worldview is to ask: Is it logically consistent? Internal contradictions are fatal to any worldview because contradictory statements are necessarily false. “This circle is square” is contradictory, so it has to be false. An especially damaging form of contradiction is self-referential absurdity — which means a theory sets up a definition of truth that it itself fails to meet. Therefore it refutes itself . . . . An example of self-referential absurdity is a theory called evolutionary epistemology, a naturalistic approach that applies evolution to the process of knowing. The theory proposes that the human mind is a product of natural selection. The implication is that the ideas in our minds were selected for their survival value, not for their truth-value.

    But what if we apply that theory to itself? Then it, too, was selected for survival, not truth — which discredits its own claim to truth. Evolutionary epistemology commits suicide.

    Astonishingly, many prominent thinkers have embraced the theory without detecting the logical contradiction. Philosopher John Gray writes, “If Darwin’s theory of natural selection is true,… the human mind serves evolutionary success, not truth.” What is the contradiction in that statement?

    Gray has essentially said, if Darwin’s theory is true, then it “serves evolutionary success, not truth.” In other words, if Darwin’s theory is true, then it is not true.

    Self-referential absurdity is akin to the well-known liar’s paradox: “This statement is a lie.” If the statement is true, then (as it says) it is not true, but a lie.

    Another example comes from Francis Crick. In The Astonishing Hypothesis, he writes, “Our highly developed brains, after all, were not evolved under the pressure of discovering scientific truths but only to enable us to be clever enough to survive.” But that means Crick’s own theory is not a “scientific truth.” Applied to itself, the theory commits suicide.

    Of course, the sheer pressure to survive is likely to produce some correct ideas. A zebra that thinks lions are friendly will not live long. But false ideas may be useful for survival. Evolutionists admit as much: Eric Baum says, “Sometimes you are more likely to survive and propagate if you believe a falsehood than if you believe the truth.” Steven Pinker writes, “Our brains were shaped for fitness, not for truth. Sometimes the truth is adaptive, but sometimes it is not.” The upshot is that survival is no guarantee of truth. If survival is the only standard, we can never know which ideas are true and which are adaptive but false.

    To make the dilemma even more puzzling, evolutionists tell us that natural selection has produced all sorts of false concepts in the human mind. Many evolutionary materialists maintain that free will is an illusion, consciousness is an illusion, even our sense of self is an illusion — and that all these false ideas were selected for their survival value.

    [–> that is, responsible, rational freedom is undermined. Cf here William Provine in his 1998 U Tenn Darwin Day keynote:

    Naturalistic evolution has clear consequences that Charles Darwin understood perfectly. 1) No gods worth having exist; 2) no life after death exists; 3) no ultimate foundation for ethics exists; 4) no ultimate meaning in life exists; and 5) human free will is nonexistent . . . .

    The first 4 implications are so obvious to modern naturalistic evolutionists that I will spend little time defending them. Human free will, however, is another matter. Even evolutionists have trouble swallowing that implication. I will argue that humans are locally determined systems that make choices. They have, however, no free will [–> without responsible freedom, mind, reason and morality alike disintegrate into grand delusion, hence self-referential incoherence and self-refutation. But that does not make such fallacies any less effective in the hands of clever manipulators] . . . [1998 Darwin Day Keynote Address, U of Tenn — and yes, that is significant i/l/o the Scopes Trial, 1925]

    So how can we know whether the theory of evolution itself is one of those false ideas? The theory undercuts itself.

    A few thinkers, to their credit, recognize the problem. Literary critic Leon Wieseltier writes, “If reason is a product of natural selection, then how much confidence can we have in a rational argument for natural selection? … Evolutionary biology cannot invoke the power of reason even as it destroys it.”

    On a similar note, philosopher Thomas Nagel asks, “Is the [evolutionary] hypothesis really compatible with the continued confidence in reason as a source of knowledge?” His answer is no: “I have to be able to believe … that I follow the rules of logic because they are correct — not merely because I am biologically programmed to do so.” Hence, “insofar as the evolutionary hypothesis itself depends on reason, it would be self-undermining.” [ENV excerpt, Finding Truth (David C. Cook, 2015) by Nancy Pearcey.]

  12. 12
    kairosfocus says:

    PPS: Plato long ago pointed to the amorality and radical relativism that invite nihilism:

    Ath [in The Laws, Bk X 2,350+ ya]. . . .[The avant garde philosophers and poets, c. 360 BC] say that fire and water, and earth and air [i.e the classical “material” elements of the cosmos], all exist by nature and chance, and none of them by art . . . [such that] all that is in the heaven, as well as animals and all plants, and all the seasons come from these elements, not by the action of mind, as they say, or of any God, or from art, but as I was saying, by nature and chance only [ –> that is, evolutionary materialism is ancient and would trace all things to blind chance and mechanical necessity] . . . .

    [Thus, they hold] that the principles of justice have no existence at all in nature, but that mankind are always disputing about them and altering them; and that the alterations which are made by art and by law have no basis in nature, but are of authority for the moment and at the time at which they are made.-

    [ –> Relativism, too, is not new; complete with its radical amorality rooted in a worldview that has no foundational IS that can ground OUGHT, leading to an effectively arbitrary foundation only for morality, ethics and law: accident of personal preference, the ebbs and flows of power politics, accidents of history and and the shifting sands of manipulated community opinion driven by “winds and waves of doctrine and the cunning craftiness of men in their deceitful scheming . . . ” cf a video on Plato’s parable of the cave; from the perspective of pondering who set up the manipulative shadow-shows, why.]

    These, my friends, are the sayings of wise men, poets and prose writers, which find a way into the minds of youth. They are told by them that the highest right is might,

    [ –> Evolutionary materialism — having no IS that can properly ground OUGHT — leads to the promotion of amorality on which the only basis for “OUGHT” is seen to be might (and manipulation: might in “spin”) . . . ]

    and in this way the young fall into impieties, under the idea that the Gods are not such as the law bids them imagine; and hence arise factions [ –> Evolutionary materialism-motivated amorality “naturally” leads to continual contentions and power struggles influenced by that amorality at the hands of ruthless power hungry nihilistic agendas], these philosophers inviting them to lead a true life according to nature, that is,to live in real dominion over others [ –> such amoral and/or nihilistic factions, if they gain power, “naturally” tend towards ruthless abuse and arbitrariness . . . they have not learned the habits nor accepted the principles of mutual respect, justice, fairness and keeping the civil peace of justice, so they will want to deceive, manipulate and crush — as the consistent history of radical revolutions over the past 250 years so plainly shows again and again], and not in legal subjection to them [–> nihilistic will to power not the spirit of justice and lawfulness].

  13. 13
    kairosfocus says:

    harry, pardon the sidebar above. The focal issue of non-being is in fact the core of where the worldviews of evolutionary materialism etc break apart in utter incoherence as worldview platforms. Predictably, we will see implications of actually completed infinite successive, stepwise causal chains to date, backed up by distractions such as that at every point we identify a past infinity would already exist and attempts to deny or dismiss that implying such an infinite actual past requires that there be real world times that are endlessly separated and yet succeeded from the one to the other in finite stage successive steps, and more. When, it is readily seen that no such finite stage process can actually complete an endless span as beyond any kth step, there is a k+1, k+2, etc. onward, i.e. we can just as well call k = 0 and begin again, never able to span endlessness in steps. To ground temporal reality we need a root of being of a different, eternal, necessary order. Mix in that we are morally governed and we see that such needs to also be an IS capable of grounding OUGHT, requiring some pretty strong characteristics. That’s why the only serious candidate has been the inherently good creator God, a necessary and maximally great being, worthy of loyalty and the responsible, reasonable service of doing the good in accord with our manifest nature. If one challenges this, simply put forward another candidate that does not at once collapse in absurdity: _________ . The ancient Hebrews, unknowingly, were way ahead of their time in worldviews, logical, physical and mathematical terms when they reported that God spoke to Moshe and said I AM THAT I AM. KF

  14. 14
    daveS says:

    KF,

    DS, the issue is not whether an agenda of evolutionary materialistic scientism exists, despite its utterly irretrievable self-refutation and its indefensible amorality, the issue is whether we deal with knowing principals with great influence, or fellow travellers, or enablers, activists and unknowing foot-soldiers in front groups every inch comparable to Lenin’s useful idiots. I leave categorisation to you, as to which group(s) you belong to.

    If only 🙂

    The issue for me is simply that it is an error to ascribe motives or beliefs to someone who does not hold them. And it does happen from time to time here.

  15. 15
    daveS says:

    KF,

    Predictably, we will see implications of actually completed infinite successive, stepwise causal chains to date, backed up by distractions such as that at every point we identify a past infinity would already exist and attempts to deny or dismiss that implying such an infinite actual past requires that there be real world times that are endlessly separated and yet succeeded from the one to the other in finite stage successive steps, and more. When, it is readily seen that no such finite stage process can actually complete an endless span as beyond any kth step, there is a k+1, k+2, etc. onward, i.e. we can just as well call k = 0 and begin again, never able to span endlessness in steps.

    If you want to revisit that topic, you could start a dedicated thread. (Or maybe right here? This thread is vaguely related).

    Oddly enough, this very issue was what I had in mind in my first post in this thread. I simply believe that your argument involving the tapes is unsound. That’s it. No further agenda or motive.

  16. 16
    kairosfocus says:

    DS, with all due respect evasive and inviting of dismissive projections. There is a kulturkampf in progress, it is now leading to riotous assemblies in the streets. The worldview engine that drives what is happening is the utterly destructive and pervasive, entrenched, powerful influence of radically secularist evolutionary materialist scientism and its fellow traveller ideologies and agendas [–> note this emphasis on a key distinction] that feed on its self-referential incoherence, its amorality and radical relativism, leading to a long rising tide of nihilisms that operate on the premise that might and manipulation make ‘truth,’ ‘knowledge,’ ‘right,’ ‘rights,’ ‘news,’ ‘education,’ ‘justice,’ ‘law,’ ‘history,’ etc etc. The impacts are so direct, so dominant and so utterly ruinous — starting with the ongoing holocaust of posterity of 800+ millions in 40+ years, mounting up at a million more per week — that we no longer have the luxury of ignoring or imagining we are neutral bystanders etc: s/he who does not stand up to fight against the onrushing destructive tide is now a part of the problem, regardless of what s/he may wish. Just as in the 1930’s and 40’s with Nazism. This pattern drives much of what happens in and around UD. KF

  17. 17
    Armand Jacks says:

    KF@9, 10 and 11.

    That is a lot of words and links, but it is a tangent and distraction to what was actually being responded to. To remind you:

    Understanding the ideological agenda also helps us understand the mindset of many objectors. KF

    I can probably be classified as an objector to ID. So, how do you presume to understand what my idiological agenda is? I don’t presume to claim to understand what your idiological agenda is, let alone comment on it. I may have my own opinions about it but it would be pure speculation. I prefer not to deal in speculation.

  18. 18
    kairosfocus says:

    DS, the world unfolds in causally linked, temporally successive stages. If there was an infinite actual past, it necessarily requires that there were times/stages I and P such that I causally led to I + 1, I + 2 etc, which are endlessly — transfinitely — remote from P, the present, and such that the increments onward +1, +2, etc past I are an actually completed infinite succession. Otherwise, you contradict in terms so that you mean in the end there was no real-world, actually infinite causally successive temporal past. I am quite content to state the implication and draw out the absurdity, as no successive sequence of cumulative, finite stage steps can actually complete, step by step, an endless span. KF

  19. 19
    daveS says:

    KF,

    If there was an infinite actual past, it necessarily requires that there were times/stages I and P such that I causally led to I + 1, I + 2 etc, which are endlessly — transfinitely — remote from P, the present, and such that the increments onward +1, +2, etc past I are an actually completed infinite succession. Otherwise, you contradict in terms so that you mean in the end there was no real-world, actually infinite causally successive temporal past.

    Well, that’s certainly not true by definition. Virtually all those who write on this subject do not take “an infinite past” to mean a past in which there must exist a point infinitely remote in the past.

    For example, see this web page owned by philosopher Ezio Vailati (some formatting changed):

    2. The past is infinite iff (if and only if) there is an infinite number of same length intervals, e.g., years, before the present one, e.g.: 0 (present year), −1, −2, −3 (year),… .

    NOTE: in order to avoid confusion, it’s important to keep in mind the following points:

    * The qualification “of same length” is somewhat more restrictive than necessary. What must be ruled out are intervals which became small fast enough to prevent going back to infinity. For example, if the first interval is 1/2 year, the second 1/4 year, etc., one cannot go back past one year ago.

    * Since there’s no negative infinite number, there’s no infinitely past year or earliest year.

    * Each year is separated from any other by a finite number of years (remember that there’s no first year).

    * There never was a time when the past became infinite because no set can become infinite by adding any finite number of members. So, if the past is infinite, then it has always been infinite.

  20. 20
    LocalMinimum says:

    daveS,

    If there isn’t an infinitely remote point in the past, then all points are finitely accessible? But then it wouldn’t be infinite?

    You highlighted no infinite negative number implying there’s no infinitely past year. Note that if I subtract any finite number from infinity, it remains infinite; otherwise it would be the sum of what I subtracted and the difference, which would be finite.

    If the meaning is that infinities are reducible to finite intervals…well, sure, but then you’re dealing with infinite intervals between.

    If it’s to make an absurdity out of an infinite history…well, the absurdity would lie on imposing the limits of human cognition on reality, not in reality’s “failure” to yield to human cognition.

    If it’s none of the above, I await your correction.

  21. 21
    daveS says:

    LocalMinimum,

    This is the definition we used in a previous thread:

    infinite: extending beyond, lying beyond, or being greater than any preassigned finite value however large – infinite number of positive numbers

    which is consistent with the usage on the philosopher’s page.

    The condition requires only that given any finite value (say any positive integer n), there exist points in the past separated by more than n years, seconds, whatever your favorite unit of time.

    We also referred to the illustration of an infinite tape, such as that using in Turing machines.

    The question became: Does such an infinite tape necessarily have two cells separated by an infinite distance (i.e., by an infinite number of cells)? Before I give my answer, what do you think?

  22. 22
    kairosfocus says:

    DS, it seems we are going back to the exchanges of a bit over a year past (this is after another blackout, BTW). I should point out that to say that any arbitrarily remote past time A, will have an onward earlier limitless span of even earlier times in the causal chain first implies that we can only give finite values of the past time, which itself is a clue. That is, we can only ever specify a finite past time, even when we give an arbitrary symbol A. Further, that there is an onward infinite further past [for argument] beyond A, or — more relevantly — I as used above does not eliminate the challenge of spanning I to P in finite stage, successive steps I + 1, I + 2 etc to reach P. Where the “etc” hides a requirement of traversing the transfinite — the endless — in steps. Where, please recall, that on your view I was once the present, with the world in some sort of quasi-physical causally and temporally successive order that gives rise to a successor stage I + 1 that CAUSALLY emerges from I and succeeds it as the next present, and so forth down to our time and world today, P. And yes, this imposes the challenge of advancing from some definite value I to the transfinite beyond I, a POSITIVE transfinite, where such an advance is inherently of character starting and going upwards in the positive integer chain, as can be labelled. It is patent that such a spanning cannot occur, as any I + k will be such that we go I + (k+1), I + (k+2) etc, where we could as well just start at k, then go on up, or we could just as well start at 0 again and go on up. Spanning the transfinite or endless in finite successive steps is a doomed exercise. The logic of structure and quantity is telling us that where quantities here speak of past times to the present, the causal, successive nature of the past so constrains the circumstance that we are not warranted to assert an infinite actualised past for the world. Where, of course such a past could stretch beyond the big bang and still be finite. There is no warrant for asserting an actually infinite quasi-physical, causally connected, temporally successive past that advances in finite stage steps to the present. KF

  23. 23
    daveS says:

    KF,

    Sorry, my parser threw a rod about halfway through your post. I will say I’m not claiming there is “warrant for asserting an actually infinite quasi-physical, causally connected, temporally successive past that advances in finite stage steps to the present”. I simply maintain that these anti-infinite-past arguments being discussed fail.

    Here is the issue which I believe is the crux of the matter, referring to the image of the Turing machine tape I posted above.

    Consider the following two properties that the tape could conceivably satisfy. The first is literally the dictionary definition of “infinite”, applied to the present situation.

    P: Given any positive integer n, there exist two cells in the tape separated by a distance greater than n steps.

    P’: There exists a particular cell C in the tape that is at infinite distance from the first (leftmost) cell.

    My question is: If the tape satisfies P, must it then satisfy P’?

  24. 24
    Latemarch says:

    DS,
    P: Given any positive integer n, there exist two cells in the tape separated by a distance greater than n steps.

    P’: There exists a particular cell C in the tape that is at infinite distance from the first (leftmost) cell.

    It was obvious that P’ was false. Any two particular cells are a finite distance apart. As soon as you identify the cells you no longer have an infinite series.
    I was more interested in how you smuggled that in. That is why I bolded the word two in P. While P is within the bounds of English as true the word two implies particularity thus connecting it in the mind to the two particular cells in P’.
    As for Ezio Vailati who seems to declare that the past has always been infinite (because you cannot become infinte). That neatly avoids the fact that time has a direction.
    I will not ascribe possible motivations to you. You either knew of the category error in the P,P’ proposition statements or did not.

  25. 25
    daveS says:

    Latemarch,

    It was obvious that P’ was false. Any two particular cells are a finite distance apart.

    I agree with you that P’ is false!

    KF on the other hand has argued quite vigorously that P’ is true if the tape is indeed infinite.

  26. 26
    LocalMinimum says:

    daveS:

    I suppose it would hinge on your definition of “preassigned”.

    I would assume in the most common fashion, any Natural number is assigned a value based on its order, which pretty much reduces it to your “basic” divergent countable infinity; but, again, that assumes the definition of “preassigned”.

    Now, assuming a standard divergent countable infinity, if we play with sequences of Natural numbers, we can take away a finite number of elements and still have an infinite sequence. The problem is, in my experience, you have to take away from the beginning, with a finite sequence; or in intervals throughout, with infinite subsequences that similarly diverge. Therefore, referencing a position at or past any sort of infinity seems impossible from my limited point of view.

    However, insisting on access to an absolute “origin” rather than a local one, i.e. a “starting point”, from the midst of infinity is a similar pickle. If you can reference a starting point finitely, I would expect you aren’t in the midst of infinity…Well, not a countable infinity, at least, as you can slap around infinities within infinities nice and discretely within the Reals. It’s all in the sauce.

  27. 27
    daveS says:

    LocalMinimum,

    I don’t think I quite understand your post, specifically the part about the word “preassigned”. Maybe if I just state what I believe the import of the word to be in this context it will help.

    The Turing machine tape is infinite because if you give me any positive integer n first, as a sort of “challenge”, I can find two cells in the tape which are separated by more than n steps.

    n is “preassigned” because you chose it first, and then I have a chance to search through the tape for cells at least n + 1 steps apart.

    This is opposed to the situation where I have to choose two cells first, and then you can choose some finite value second.

    If in your last paragraph you’re referring to a “beginning point” of an infinite past, then I affirm that such a thing does not exist in the picture I have in mind. People have written about some very bizarre topologies for time, so I’m not saying such a thing is impossible, but I am thinking about an infinite past modeled along the lines of the negative real numbers, or some subset thereof.

  28. 28
    kairosfocus says:

    DS, for the sake of argument I represented the counting numbers as a thought exercise involving pink and blue tapes endless to the right. That has no implication such can be actualised physically, not least they would require infinite material resources. My further point has been significantly different from what you just represented. Namely, the implication of a claimed actual traversal of the transfinite span requires completing the stepwise traversal of such an imaginary tape or the equivalent as a sequence. What I have vigorously argued is that such a stepwise successive traversal is not actualisable in a temporally linked stage by stage causal world; I even spoke of the fallacy of using an imagined stepwise process to traverse and so end the endless. I then highlighted that the claim of an infinite actual temporal, causally connected step by step cumulative past clearly requires such a traversal, most recently representable as

    . . . I, I+1, I+2, –> . . . P,

    where the ellipses involves traversing the transfinite in finite stage steps; I focus on the second ellipsis. I conclude such is not possible and conclude that we are only warranted to speak of a finite past, an infinite one implying an impossible traversal. And yet, were there such an infinite past, it MUST require that there is some I that was once the present which then causally led to I+1 as the successor present, then +2 etc across a transfinite span to the big bang and on and on to the current present P. This is contrary to the logic of structure and quantity and so is to be regarded as falsified. There was no I, the picture of an infinite past is one of those things we can say in words and perhaps imagine vaguely but once we analyse on relevant logic of structure and quantity, vanishes as a mirage. To find the necessary being root of current physical reality, we must look beyond a space-time causally successive order. Eternity stares us in the face. KF

  29. 29
    daveS says:

    KF,

    DS, for the sake of argument I represented the counting numbers as a thought exercise involving pink and blue tapes endless to the right. That has no implication such can be actualised physically, not least they would require infinite material resources.

    Yes, I think we all understand we are discussing a thought experiment, not an actual physical tape of infinite length.

    And yet, were there such an infinite past, it MUST require that there is some I that was once the present which then causally led to I+1 as the successor present, then +2 etc across a transfinite span to the big bang and on and on to the current present P.

    Hm. How remote in the past is this I? Infinitely (“endlessly”) remote, correct?

    That is, in an infinite past, there must have existed some point I in time such that I is separated from the present by an infinite number of seconds.

    Are we agreed that your position includes this assertion? One can check simply by scrolling upward a few posts.

    If we are in agreement on that point, how would you rephrase this assertion about time in terms of the tapes thought experiment? Specifically, how would your rephrasing differ significantly from my P’ from above?

  30. 30
    kairosfocus says:

    DS, I am not counting seconds but stages of causally connected development. I am not sure that we can reasonably equate time as we measure it to whatever preceded the big bang, but there is usually some sort of quasi-physical causally successive temporal ordering that would be on the table with things like before and after in a grand sense — simultaneity is a big issue with relativity on the table, but the BB type model gives us some sort of framework. I am saying that at some point I, before that finitely remote point, if there were a truly infinite past, I would once have been present and would now be infinitely past as further causally successive states have followed as the present then receded into the past. The current present, we inhabit. In effect, counting stages, we could start the pink tape at I and continue thereafter forever, counting or marking stages that were successively once the present. Beyond I we can count up to some large but finite point, I +k. Then, in succession I + (k+1), I + (k+2) etc. lay alongside the imagined blue tape at k, so that we see k as a new reference point. The second tape can count alongside, displaced by k. Given the endlessness from I, neither would be able to exhaust the endlessness in steps to get to P. In short there is no finite value Q such that Q+1 = P, the endlessness beyond I cannot be traversed. this can be seen by putting say a purple tape at k + j (j very large but finite) and starting afresh, with endlessness still beyond. The same can then be done with the purple tape as with pink and blue, etc to any degree we please. An endless succession cannot be exhausted in successive causally linked, finite stage steps. KF

  31. 31
    daveS says:

    KF,

    DS, I am not counting seconds but stages of causally connected development. I am not sure that we can reasonably equate time as we measure it to whatever preceded the big bang, but there is usually some sort of quasi-physical causally successive temporal ordering that would be on the table with things like before and after in a grand sense — simultaneity is a big issue with relativity on the table, but the BB type model gives us some sort of framework. I am saying that at some point I, before that finitely remote point, if there were a truly infinite past, I would once have been present and would now be infinitely past as further causally successive states have followed as the present then receded into the past.

    Am I interpreting this correctly: Assuming an infinite past, you do not now claim that there must have been some moment in the past (by some clock’s reckoning) which elapsed an infinite number of seconds before the present?

    And in fact you are not claiming that it would be inconsistent for the past to be infinite, yet all time intervals measured between points in the past to be finite?

    How about all this applied to space? Could the universe be infinite in space, yet all distances measured between spatial locations be finite?

  32. 32
    kairosfocus says:

    DS, try to define what a second means in a pre-BB world in which perhaps Cesium atoms do not exist [as in so many cycles of a line in the spectrum of], as just one consideration as to why I do not speak in terms of our standard time units. I am therefore looking at a broader index of temporality, causally connected succession of stages of finite duration, each of which is the present in turn. Then, we can apply a count to that succession. Onward, we can look at the more central issues. KF

  33. 33
    daveS says:

    KF,

    Well, if you don’t want to discuss time intervals, there still is the issue of demonstrating that an infinite past entails the existence of these causal chains where some particular stage occurred infinitely many links prior to some later stage. We have the same dispute, only with “seconds” replaced with “stages”.

    The tapes argument doesn’t prove these causal chains must exist in an infinite past.

    Clearly one tape can be put into one-to-one correspondence with any “tail” of the other tape, starting at any position k, but how you infer that means there exists some cell infinitely far from the end is a mystery.

    Have you ever read such an argument in a philosophy, mathematics, or logic book? Have you ever encountered an axiom or principle anywhere which justifies this step?

  34. 34
    kairosfocus says:

    DS, the issue on defining second is real, and counting stages gets around it. The second issue is in the end one of coherent meaning. An infinite actual past entails that there was some I, once present but now past through causally linked succession to I+1, I+2 etc, until it reaches the present, P. Where, for the past stage I to be infinitely remote, the I in question has to be transfinitely many stages antecedent to P. This is an issue of the meaning of claiming an infinite actual temporal past. My concern then is, time by inherent nature proceeds in causally successive stages, so for this to be the case an actual traversal of the transfinite in steps would have to happen. But that cannot be done in finite stage steps and so we are not warranted to hold that any actually transfinitely remote point I ever existed. Even more strongly, were an I to have existed and succeeded in succession to P, that I necessarily will not have been transfinitely remote: finite traversal is possible, as opposed to transfinite. The stepwise, finite stage traversal of the transfinite fails. KF

  35. 35
    daveS says:

    KF,

    An infinite actual past entails that there was some I, once present but now past through causally linked succession to I+1, I+2 etc, until it reaches the present, P. Where, for the past stage I to be infinitely remote, the I in question has to be transfinitely many stages antecedent to P. This is an issue of the meaning of claiming an infinite actual temporal past.

    That’s contrary to the definition you posted in the other thread:

    extending beyond, lying beyond, or being greater than any preassigned finite value however large

    A causal chain is infinite iff for any positive integer n, there exists a stage more than n steps before the present.

    Now we are back to my post #23, only we’re talking about stages rather than seconds/years, etc:

    P: Given any positive integer n, there exist two stages in the causal chain separated by more than n steps.

    P’: There exists a particular stage in the causal chain that is infinitely many steps from the present.

    I believe you maintain (at least) that if a causal chain is infinite, then it satisfies property P’

    If you still trust that dictionary definition, then that would mean if a causal chain satisfies P, it satisfies P’.

    Is this correct?

  36. 36
    kairosfocus says:

    DS, nope, I am being fully consistent with my earlier argument. The issue remains that an infinite actual past requires that there were actual past times that are now infinitely remote. Given the nature of temporal-causal succession by FINITE stages, this then poses the challenge of traversing a transfinite span with endlessness in it, by finite stage steps. Note, my emphasis on finite stage, causal-temporal succession. This traversal of the transfinite in finite stage steps is an impossibility, as described and explained in brief above. So, any past stage I* — let us distinguish for clarity — that can actually reach the present P through such stepwise stages is finitely remote. This is what I am arguing, and it pivots on the issue of temporal-causal, finite stage succession. Until I see how your proposed propositions above address that explicitly, I decline to engage them as being dangerously ambiguous. Your P fails to address it at all, and someone else has pointed out that once you pin down two specific points you imply a finite interval given temporal succession, which is consistent with my point. Again, I highlight that the pivot is the meaning of what an infinite actual past means. I contend, it means that there would have been past stages I as I have described, which then leads to an impossibility. So, there were no real quasi-physical world stages I that are now actually infinitely removed in finite stage successive steps as described. KF

    PS: We are now very much on a tangent, and I see no-one has been willing to address the implications of trying to pull a cosmos out of a true utter nothing.

  37. 37
    daveS says:

    KF,

    DS, nope, I am being fully consistent with my earlier argument. The issue remains that an infinite actual past requires that there were actual past times that are now infinitely remote.

    Yes, I’m definitely not saying you are being inconsistent with what you have said before.

    As far as I can tell, it’s almost the exact same argument, based around the claim (which I consider to be dubious), that there must be particular past times/stages that are infinitely remote. In other words, that the revised version of P’ is true.

    On the other hand, if the past is infinite, but all time intervals between particular points in time are finite (in terms of seconds), then the only way causal chains with property P’ could occur is if we have infinitely many stages occurring in some particular finite (in seconds) time interval, i.e., something like Zeno’s paradox.

    But this would have to have happened in some finite subset of the past, hence this would actually be a problem for finite-past proponents as well.

    PS: We are now very much on a tangent, and I see no-one has been willing to address the implications of trying to pull a cosmos out of a true utter nothing.

    Well I don’t see how it would be possible for a cosmos to emerge out of “nothingness”. Even attempting to reason about such a thing ties one up in knots.

  38. 38
    Fair Witness says:

    If you could point to a spot where there was absolutely nothing, what would it be surrounded by ?

  39. 39
    kairosfocus says:

    FW, a spot is not nothing, it is not non-being. KF

  40. 40
    kairosfocus says:

    DS, I put it to you that a claimed infinite past that does not have in it stages that were once the present but now are transfinitely many stages in the past is meaningless. KF

  41. 41
    daveS says:

    KF,

    DS, I put it to you that a claimed infinite past that does not have in it stages that were once the present but now are transfinitely many stages in the past is meaningless. KF

    Well, it would satisfy the definition of infinite you posted:

    extending beyond, lying beyond, or being greater than any preassigned finite value however large

    Furthermore, virtually everyone who has published on the subject finds the notion meaningful.

    Can you at least understand why some of us think the way we do? Notice that Latemarch immediately understood that in your tape example, all cells have finite distance from one another. It’s “obvious”. All cells must be reachable (in a finite number of steps) from the end. If not, the unreachable cells could not be connected to the reachable portion, since no unreachable cell can be adjacent to a reachable cell. So your tape would consist of two parts that cannot touch. That’s not how tapes (even infinite thought-experiment tapes) behave.

  42. 42
    Fair Witness says:

    KF: I will rephrase….

    What would absolutely nothing be surrounded by?

    If it were surrounded by “more” nothing, (if that even makes sense) then what would THAT be surrounded by?

  43. 43
    kairosfocus says:

    Non-being, by definition, has no spatial location.

  44. 44
    kairosfocus says:

    DS, you overlook the peculiar nature of time: a present, ever receding into the past, while being succeeded by the next, causally connected present. So, the proposition that there was an infinitely remote past implies a once present that is now transfinitely removed in finite-step stages from us. Time is not a mere abstract set that one can set up and play the clever game of members endlessly beyond any that we care to identify. No real stage of our world that is now past can be so unless it was once the actual present. That is pivotal. KF

  45. 45
    daveS says:

    KF,

    DS, you overlook the peculiar nature of time: a present, ever receding into the past, while being succeeded by the next, causally connected present. So, the proposition that there was an infinitely remote past implies a once present that is now transfinitely removed in finite-step stages from us.

    Is it conceivable to you that you are wrong on this point?

  46. 46
    daveS says:

    OT: A digital clock in Conway’s game of life.

    What the clock looks like while running.

  47. 47
    kairosfocus says:

    DS, kindly explain to me what time is, in such a way that the actual world’s timeline is not at all as I described. KF

  48. 48
    daveS says:

    KF,

    Do you have any response to my questions in #41 and #45?

  49. 49
    kairosfocus says:

    DS, it seems to me rather that it is you who needs to explain how a real world past stage is such that it was not once the present but has been succeeded by causally linked subsequent stages to the current present. I think this is what is generally understood to be the actual past. It is this which then poses the issue of transfinitely many intervening stages to our present. I suggest that your non-answer on this point is pivotal. KF

  50. 50
    daveS says:

    KF,

    DS, it seems to me rather that it is you who needs to explain how a real world past stage is such that it was not once the present but has been succeeded by causally linked subsequent stages to the current present.

    Eh? I’m pretty sure that’s not my position. Is there a typo in there somewhere?

    I just don’t see any justification or “proof” that there must have existed infinitely remote stages in an infinite past.

    The correspondence between pink and blue tapes argument seems to me to be a non-sequitur. If anyone following along can explain it to me step-by-step, I’m happy to be corrected.

  51. 51
    kairosfocus says:

    DS, pink and blue tapes only show that a transfinite span cannot be traversed in finite stage steps, as at any high but finite k on the first you can in effect start over again, as though k were 0 and will still face endlessness; in effect subtracting a finite segment from 0 to k from an endless sequence of successive steps does not change the onward endlessness. As for the discussion of what the past is, I summarised what we could call a common-sense observation. I think this is the general sense of actual past that is commonly used, and it brings out key issues on the nature of temporal succession. I have yet to see how any claimed infinite past does not therefore imply that there are points such as I that were once the present but have now been succeeded to the point that they are transfinitely remote. The problem I posed then follows, trying to effect a stepwise finite stage traversal of the transfinite. Which is manifestly futile. That is why I conclude such a claimed past cannot be the real temporal past of our world. KF

  52. 52
    daveS says:

    KF,

    DS, pink and blue tapes only show that a transfinite span cannot be traversed in finite stage steps, as at any high but finite k on the first you can in effect start over again, as though k were 0 and will still face endlessness; in effect subtracting a finite segment from 0 to k from an endless sequence of successive steps does not change the onward endlessness.

    Well, you’re counting “upward”, starting at the first cell of the tape. This is the equivalent of counting backward in time, which is the wrong direction.

    If we use the tape as a model of the past, you must always be moving toward the end of the tape, not away from it. Any discussion of traversing the tape in the opposite direction is irrelevant, as far as I can see.

    I have yet to see how any claimed infinite past does not therefore imply that there are points such as I that were once the present but have now been succeeded to the point that they are transfinitely remote.

    Can you explain in simple, clear language how this implication works? If the pink and blue tapes illustration doesn’t prove the existence of these transfinitely remote points, what does?

  53. 53
    kairosfocus says:

    DS,

    no.

    Did you not see the leading ellipsis in the series

    . . . I, I+1, I+2, . . . P –>

    That indicates prior states, and does not commit to any first. What is being counted is from state I in the sequence forward, I being taken as already described.

    That is I is on the hyp of a transfinite past, ONE stage that now happens to be supposedly transfinitely remote, there being no requirement that it be the first.

    The counts are onward from I as a relevant but not unique start-point. And in effect pink is aligned from I and blue from I+k, k a large but finite-steps-removed from I stage. The point being, starting over from k has the same problem of traversing endlessness to P.

    I think the matter is long since clear enough. Temporal succession has each moment ever being replaced by a causally linked successor, like a song being played note by note. (A happy birthday song on ZJB just now.) The present moment is marching on like a play head so to speak, though the notion of a fixed determined future is dubious, choice and chance are credibly real. More relevantly, once a given moment occurs it is already fading into the past, even as is happening as I type this string. BBC News is coming up now, birthday songs are past.

    Already.

    And that now past reality fades ever further into the past as successive stages play out one by one in succession.

    The issue then is that the genuine past can only contain stages that were once the present but which have been succeeded by a chain of onward, causally connected stages.

    All of this should be readily apparent on a moment’s reflection.

    (I take it, you see why I am reluctant to try to project beyond, say, the big bang by using seconds or a similar unit as means of evaluating span of time.)

    In this context to claim an infinitely remote past requires that there were stages that were once the present but are now transfinitely remote behind a chain of onward, causally connected finite step stages.

    The challenge then is that this requires spanning that transfinite gulf in finite stage steps and by aligning pink with I, counting forward k steps and aligning blue, we see a conundrum. No finite sequence of steps, no matter how large, can even begin to exhaust or traverse or span the onward endlessness.

    The only I’s that can credibly succeed to P in steps are finitely removed ones, I* for reference.

    The real past was finite.

    KF

  54. 54
    kairosfocus says:

    PS: I come back over half hour later, and the past is receding, but it is there as the once present.

  55. 55
    daveS says:

    KF,

    DS,

    no.

    Did you not see the leading ellipsis in the series

    . . . I, I+1, I+2, . . . P –>

    That indicates prior states, and does not commit to any first. What is being counted is from state I in the sequence forward, I being taken as already described.

    That is I is on the hyp of a transfinite past, ONE stage that now happens to be supposedly transfinitely remote, there being no requirement that it be the first.

    Ok, I see. The primary problem in that case is that you haven’t shown such any such I, infinitely remote from the present, exists. It appears you also are starting a count at I, but let’s set that aside for the moment.

    The issue then is that the genuine past can only contain stages that were once the present but which have been succeeded by a chain of onward, causally connected stages.

    All of this should be readily apparent on a moment’s reflection.

    This much is obvious. At least we both agree on it.

    PS: I come back over half hour later, and the past is receding, but it is there as the once present.

    Of course.

    In this context to claim an infinitely remote past requires that there were stages that were once the present but are now transfinitely remote behind a chain of onward, causally connected finite step stages.

    Where is the argument/proof that shows these stages must exist?

    This is literally the only question I’m asking at this point.

  56. 56
    kairosfocus says:

    DS, Perhaps it has escaped your notice that it is you and others who have championed or argued to support the notion of an infinite past. I have simply pointed out what that would require, given the patent nature of temporal succession. For that succession to amount to an infinite actual past, that would require that some once present stage I is now transfinitely removed in successive steps, or there would not be an infinite actual past. In short, the issue is what an infinite past means, given the well-known nature of temporal succession as I illustrated earlier today, which left traces in the thread but is now receding ever further into the past already. As in, the once now receding into the past as further stages succeed is a commonplace fact; if your view of the past leads you to doubt something like this, then that does not speak well of the theory. The problem is, a transfinite succession cannot be traversed in finite stage successive cumulative steps, and this implies there was no infinite temporal past in our world. KF

  57. 57
    daveS says:

    KF,

    I have simply pointed out what that would require, given the patent nature of temporal succession. For that succession to amount to an infinite actual past, that would require that some once present stage I is now transfinitely removed in successive steps, or there would not be an infinite actual past. In short, the issue is what an infinite past means, given the well-known nature of temporal succession as I illustrated earlier today, which left traces in the thread but is now receding ever further into the past already.

    If you’re saying that these infinitely removed stages must exist by definition, no, that’s not the case. The definition you posted makes no mention of them.

    If you can find a definition which does mention them, I’d like to see it.

    As in, the once now receding into the past as further stages succeed is a commonplace fact; if your view of the past leads you to doubt something like this, then that does not speak well of the theory.

    No, I do not doubt this.

  58. 58
    kairosfocus says:

    DS, not by definition, that’s a neat loaded projection. Time as past comprises formerly present stages, now succeeded. That is crucial. The span of the past to any stage S can be evaluated by count of intervening ones to P the current “now,” if we are lucky in even stages such as years or nanoseconds. That means that we can conceive of an infinitely remote past and this will require that some I will have had transfinitely many intervening stages to P. If not, we will only be able to identify finite past spans, i.e. a finite past. This is where the step by step succession comes in, and shows us such a transfinite traverse cannot be done in finite stage steps, as at every stage we meet, we have only ever completed a finite number. We can contemplate a potential infinite where such may continue endlessly but we cannot actually complete it. Now is a terminus and a transfinite past to now will require that some past stage would have had to traverse such a span in steps to reach now. Notice, W is defined on the endlessness of the counting numbers in succession, not the completion of the traverse. No prizes for guessing why. KF

  59. 59
    daveS says:

    KF,

    DS, not by definition, that’s a neat loaded projection.

    Projection? It was just an honest question. To be clear, I was speaking in the context of an assuming infinite past.

    That means that we can conceive of an infinitely remote past and this will require that some I will have had transfinitely many intervening stages to P. If not, we will only be able to identify finite past spans, i.e. a finite past.

    Ok, let me try again. You are definitely saying here that by definition, an infinite past must include infinitely remote stages, correct?

  60. 60
    daveS says:

    KF,

    Do you consider the past in Hoyle’s Steady State theory of cosmology to be finite?

    Also, s/assuming/assumed in my #59

  61. 61
    kairosfocus says:

    Hoyle tried to resurrect the old eternal material cosmos view. That one can conceive of a world in which by dint of continuous spontaneous creation there is an ongoing counter to entropic decay and suggest it is eternal. This of course first failed the empirical evidence test as at the 1960’s. The fact that it was on the table suggests the recognition that a world that now is requires something that always was, and put up a materialistic candidate. This does not escape the issue I am speaking to as the issue is one of the logic of structure and quantity. Just because seady state, oscillating, budding and the like cosmologies have been put forward does not answer to the need to span the transfinite to get here. KF

    PS: I am not saying anything by definition, I am pointing to the peculiar nature of temporal succession and what the past is as a result, then I am putting on the table what happens when we try to stretch the temporal quasi-physical world beyond the big bang and onward to the suggested transfinite past. In short, if we can only ever come up with finitely remote past points I*, then NONE of them can be transfinitely remote from the present stage, P. Thus, we cannot get to a transfinite duration. If we then insist on imposing some past stage I that is transfinitely remote, we see the challenge of stepwise, finite stage succession facing a transfinite span. The claim of an infinite material past of our world runs into a nest of incoherences. This is because a temporal ordering in succession of stages is not like an abstract set, times take their reality from being actualised, which then leads to the causally connected next stage. Then, the next, and soon the number of onward stages starts to rack up. But such a process inherently cannot span the transfinite. And indeed we impose W as order type of the endless count of the natural counting numbers without ever completing the count. That is why we see that the ellipsis in the usual presentations does a LOT of heavy-lifting.

  62. 62
    daveS says:

    KF,

    I’m asking about Hoyle’s (and other theories which posit a beginningless universe) because while they are described as involving an infinite past or infinitely old universe, most if not all do not include any infinitely remote times in the past. That would indicate that these cosmologists would disagree with your contention.

    Edit: Does the “eternal material cosmos view” involve an infinite past?

    In short, if we can only ever come up with finitely remote past points I*, then NONE of them can be transfinitely remote from the present stage, P. Thus, we cannot get to a transfinite duration.

    This is actually saying something about definition, because:

    extending beyond, lying beyond, or being greater than any preassigned finite value however large

    says nothing about a transfinite duration requiring transfinitely remote points. Rather, it only requires that there be arbitrarily remote, finitely remote points.

  63. 63
    daveS says:

    KF,

    I’m asking about Hoyle’s (and other theories which posit a beginningless universe) because while they are described as involving an infinite past or infinitely old universe, most if not all do not include any infinitely remote times in the past.

    I’m going to withdraw the above, based on the following quote from WLC in his essay on the Kalam Argument:

    In stating that the initial conditions “have to be set in an acausal way (in the infinite past),” Ellis puts his finger on a nettlesome philosophical issue in cosmological models featuring an infinite past, namely, they often seem to treat the infinite past as though it featured an infinitely distant beginning point. Several of these models are discussed in this essay. But, as we have already seen in our discussion of philosophical kalam arguments, such a supposition is illicit, since such an infinitely distant point is merely an ideal limit characteristic of the potential infinite, not a moment that actually once was present. If we are allowed to speak of the condition of the universe at past infinity, then Zenonian paradoxes (see p. 119) are unavoidable.

    and this:

    It is always possible to find a conformal transformation which will convert an infinite universe to a finite one and vise-versa. One can always find a time coordinate in which a universe that exists for a finite proper time . . . exists for an infinite time in the new time coordinate, and a time coordinate in which a universe that exists for an infinite proper time . . . exists for only a finite time. The most appropriate physical time may or may not be the proper time coordinate. (Barrow & Tipler 1986, p. 636)

    I don’t know what this means in terms of “stages” in a causal chain, however. Edit: Perhaps nothing?

  64. 64
    kairosfocus says:

    DS, Hoyle did not originate the steady state view. The core idea is an undetectably low spontaneous creation of fresh matter, leading to a “very long term” steady state; as I was taught back in the 70’s. Hence, the name. It failed the prediction test by the 1960’s and was gradually abandoned in the face of the cosmic microwave background, where oscillatory models also failed. The issue of a cosmos with no beginning is that, again, it faces an infinite descent from the past, stage by causally connected stage — and I am not talking about any beginning point without earlier stages, just that there has to be a descent “forever” from earlier and earlier stages. Real time only holds in a context of each stage having once been the present, leading dynamically to the next then the next etc to now. This wets up the problem of a stage at transfinite remove, if the past was actually of infinite prior duration. And this is not about mathematical transforms. KF

    PS: durations are between particular, present or once present stages of the world, Unless you can get beyond finitely remote ones, you are not going beyond the potentially infinite but only actually finite. Infinite is not a synonym for too long ago for us to count up, it has to address the beginning-less and endlessly remote beyond any conceivable specific finite value. That is where descending a transfinite chain of succeeding stages comes into the picture, and not by dismiss-able definition.

  65. 65
    daveS says:

    KF,

    DS, Hoyle did not originate the steady state view. The core idea is an undetectably low spontaneous creation of fresh matter, leading to a “very long term” steady state; as I was taught back in the 70’s. Hence, the name. It failed the prediction test by the 1960’s and was gradually abandoned in the face of the cosmic microwave background, where oscillatory models also failed.

    I’m aware of that, just wondering if you consider “beginningless” steady state theories to include an infinite past or not.

    The issue of a cosmos with no beginning is that, again, it faces an infinite descent from the past, stage by causally connected stage — and I am not talking about any beginning point without earlier stages, just that there has to be a descent “forever” from earlier and earlier stages.

    Yes, it’s clear that you are not referring to any beginning point. The point I in particular is not assumed to be a beginning of the cosmos.

    This wets up the problem of a stage at transfinite remove, if the past was actually of infinite prior duration.

    My goal in these last questions was to determine why you believe an infinite past entails the existence of these infinitely remote points.

    I can think of only two possible reasons, given our discussion:

    1) It’s true by definition, in which case one needs only to read the definition of “infinite” to determine this.

    2) It’s true because it follows logically from the definition, but it’s not explicitly stated in the definition. In this case, some argument would be required.

    Is it #1, #2, or something else?

    PS: durations are between particular, present or once present stages of the world, Unless you can get beyond finitely remote ones, you are not going beyond the potentially infinite but only actually finite.

    How can a collection of already existing things (past moments/stages) be a potential infinite? WLC states in his discussion of the Kalam Cosmological Argument, referring to one of the premises (emphasis added)

    The second premise states that an infinite temporal regress of events is an actual infinite. The point seems obvious enough, for if there has been a sequence composed of an infinite number of events stretching back into the past, then the set of all events in the series would be an actually infinite set.

    He then goes on to describe how this view has not always been dominant, but that now most hold it.

    Some more discussion from WLC:

    … So in a beginningless series of past events of equal duration, the number of past events must be infinite, for it is larger than any natural number. But then the number of past events must be ℵ0, for ∞ is not a number but an ideal limit. Aquinas’ own example of a blacksmith working from eternity who uses one hammer after another as each one breaks furnishes a good example of an actual infinite, for the collection of all the hammers employed by the smith is an actual infinite. The fact that the broken hammers still exist is incidental to the story; even if they had all been destroyed after being broken, the number of hammers broken by the smith is the same. Similarly, if we consider all the events in an infinite temporal regress of events, they constitute an actual infinite.

  66. 66
    kairosfocus says:

    DS,

    the logic of being shows that something is a necessary and beginningless being.

    The steady state cosmos theory received a lot of widespread support in that context. The big bang perspective, which arose from the shocking discovery of the red shift phenomenon, spent forty years as under-dog. So, clearly the point of the steady state cosmology is, it has no beginning and has an infinite past. Likewise with other models that have been put up, oscillating [turns out this does not work] budding-off sub cosmi etc.

    Beyond this, I am astonished to see you belabouring and trying to push a burden of proof on me regarding my understanding that an actually infinite past of the physical world will require stages that are transfinitely remote, endlessly remote beyond any conceivable particular stage. Thus, that an infinite past requires that there has been some I that is transfinitely many stages from now.

    As for WLC, he is not there addressing whether an actual infinite is physically feasible, he is speaking in the context of those whose thought implies that. Aquinas has a smith hammering away till a hammer breaks, then getting a new one and so forth. If that series could be completed it would have an infinite collection of broken hammers. We can think about it but cannot actually physically do it, even were he to recycle the actual hammers endlessly.

    The problem I highlight is, he cannot complete the chain from an infinite past. No successive collection of hammers like this can attain to aleph-null cardinality, or as a counting order, achieve the order type of the naturals, W.

    I repeat, if every stage in the cosmos’ history was only finitely remote by count of stages, none of them will be at infinite remove and the chain as a whole will be finite, though perhaps indefinitely large. For duration is from one point to the next.

    Further to this, in going stage to stage, a transfinite span cannot be completed step by step. We can only go to an indefinitely large but finite value and point beyond.

    But the history of the cosmos requires actual stage by stage temporal succession to reach here and we can be confident if it has it has not traversed a transfinite span.

    If you doubt this, or imagine I impose arbitrary definitions, simply explain to us how this endless descent of actual stages can amount to traversing the transfinite to reach us today. (As in, spell out the dynamics, please.)

    Over to you: ______________ .

    KF

  67. 67
    daveS says:

    KF,

    The steady state cosmos theory received a lot of widespread support in that context. The big bang perspective, which arose from the shocking discovery of the red shift phenomenon, spent forty years as under-dog. So, clearly the point of the steady state cosmology is, it has no beginning and has an infinite past.

    Thank you.

    Beyond this, I am astonished to see you belabouring and trying to push a burden of proof on me regarding my understanding that an actually infinite past of the physical world will require stages that are transfinitely remote, endlessly remote beyond any conceivable particular stage. Thus, that an infinite past requires that there has been some I that is transfinitely many stages from now.

    Well, it’s your claim, so the burden is yours, no?

    As for WLC, he is not there addressing whether an actual infinite is physically feasible, he is speaking in the context of those whose thought implies that.

    Well, obviously not, since another one of his premises is that an actual infinity cannot exist in the world.

    He does say, however, that an infinite past would have to comprise an actual infinite rather than a potential infinite.

    If you doubt this, or imagine I impose arbitrary definitions, simply explain to us how this endless descent of actual stages can amount to traversing the transfinite to reach us today. (As in, spell out the dynamics, please.)

    Over to you: ______________ .

    I didn’t say I could explain anything. I simply said I don’t believe you can show that an infinite past is impossible using these mathematical/logical arguments. I also don’t believe you can prove the existence of the hypothesized infinitely remote points you refer to. That’s all. I can’t do these things either.

  68. 68
    kairosfocus says:

    DS, On fair comment I have repeatedly shown why I concluded as above. You obviously disagree but instead of explaining why and showing what an infinite actual past means other than that there was at least one [and in fact indefinitely many] once present moments that are now after successive stages transfinitely remote, you have tried to suggest that I have failed to show why I have concluded as above. What part of durations in time are between specific stages is hard to understand? What part of, if stages X and Y have only finitely many stages between them, the duration is necessarily finite, is hard to acknowledge? What part of, if EVERY past time we can identify or even symbolise as having occurred will be finitely remote, then there are no such identifiable transfinite durations, is so hard to see? What part of, just proceeding with ever more finitely remote cases and suggesting ever more FINITELY remote cases can be added does not get us to an infinite duration, is so hard to then recognise? Going on, what part of, if even so there were an actually transfinitely remote stage I, then its step by step successors I+1, I+2 etc will face the impossibility of traversing an endless transfinite span in finite-stage steps, is so hard to acknowledge? KF

  69. 69
    daveS says:

    KF,

    DS, On fair comment I have repeatedly shown why I concluded as above. You obviously disagree but instead of explaining why and showing what an infinite actual past means other than that there was at least one [and in fact indefinitely many] once present moments that are now after successive stages transfinitely remote, you have tried to suggest that I have failed to show why I have concluded as above.

    The only explanation I’ve seen is a series of observations about the nature of time (present moments recede into the past, stages in causal chains succeed one another, etc). After reading through these observations many times, I still do not see how we can conclude, “hence, infinitely remote stages must exist”.

    What part of durations in time are between specific stages is hard to understand?

    That’s very easy to understand.

    What part of, if stages X and Y have only finitely many stages between them, the duration is necessarily finite, is hard to acknowledge?

    Also very easy.

    What part of, if EVERY past time we can identify or even symbolise as having occurred will be finitely remote, then there are no such identifiable transfinite durations, is so hard to see?

    Obviously true. Edit—One qualification: I interpret this to mean there are no intervals of infinite length between particular stages.

    What part of, just proceeding with ever more finitely remote cases and suggesting ever more FINITELY remote cases can be added does not get us to an infinite duration, is so hard to then recognise?

    This is where some issues arise.

    I would not use the word “added” here. No finitely remote stages are being “added” to the supposed infinite past. They already exist in the past. Nevermind this if you didn’t mean to imply otherwise.

    In any case, here’s how I would describe the situation: Given any preassigned finite value (that is, any natural number n), there exist stages which occurred more than n steps before the present stage.

    If that’s synonymous with what you intended above, then that’s fine.

    But my formulation makes it clear how an infinite duration arises.

    I have no problem with your very last “what part of … is hard to recognize”.

  70. 70
    kairosfocus says:

    DS, if you can only ever find finite durations and imposing a claimed transfinite one leads to the impossibility of traversing the infinite in finite stage steps, enough has been shown. KF

    PS: It is patent that now at any point is succeeded by a following stage, then this repeats etc so that the first referenced recedes into the past stage by stage. I refer to finite steps for the obvious reason. Such a process of recession can indicate a potential infinity but it never actually does so between any one past stage and now. Now, extend to all such stages in the past that came about that way. Are there any stages of the actual past arrived at other than in this way? I put it to you, not; so all durations to the actual past’s stages will be finite, as they all got to the past through an inherently finite though potentially infinite process. (That is, there is no limit imposed on further succeeding stages; although at any particular now, we have only finitely many stages so far.)

  71. 71
    daveS says:

    KF,

    DS, if you can only ever find finite durations and imposing a claimed transfinite one leads to the impossibility of traversing the infinite in finite stage steps, enough has been shown. KF

    That’s not quite right. The duration of the past (in total) can be infinite without causing any problems. The duration of the past is infinite if, given any finite value n, there exists an interval between two particular stages whose duration exceeds n. (Guess where I got that :P). And that’s exactly what I am positing (see below after the ***). There is then no problem of the type presented by particular infinitely remote stages.

    PS: It is patent that now at any point is succeeded by a following stage, then this repeats etc so that the first referenced recedes into the past stage by stage.

    Yes, a particular once-present moment recedes more and more deeply into the past when viewed from the perspective of a sequence of “present” points advancing into the future.

    I refer to finite steps for the obvious reason. Such a process of recession can indicate a potential infinity but it never actually does so between any one past stage and now.

    Question: Exactly what is this potential infinity? In other words, how would you fill in the blank: “This is a potentially infinite collection of ______”.

    To specify more clearly what sort of answer I am asking for, I will borrow this definition of potential infinity from wikipedia. If you have a better citation, please post it:

    This is contrasted with potential infinity, in which a non-terminating process (such as “add 1 to the previous number”) produces an unending “infinite” sequence of results, but each individual result is finite and is achieved in a finite number of steps.

    Referring to my bolded question above, what precisely is the “infinite” sequence of results that your process generates?

    *** Begin Parenthetical Statement

    To be very explicit, here is what I posit as an infinite past, from the perspective of a particular stage (the “present”).

    Fix stage_0 to be that which occurred at t_0 = 12:00:00 UTC March 17, 2017, say.

    The past, P0, from the perspective of stage_0, is the collection of all stages which were once but no longer are present.

    Assumption: Given any finite value n, there exists a stage_0 in P0 which occurred more than n stages before stage_0.

    Note that P0 would clearly be infinite, by definition.

    Also note that there is no process for producing elements in P0 involved here. The collection of past stages in P0 are assumed to already exist. Therefore the collection of past stages in P0 comprise an actual infinity. This is not a finite collection that can be extended to any finite size, one element at a time.

    So, P0 is an actually infinite collection of past stages.

    Now contrast P0 with whatever the results of your “recession” process are. Your potentially infinite collection is a collection of what?

    *** End Parenthetical Statement

    Back to your post:

    Are there any stages of the actual past arrived at other than in this way? I put it to you, not; so all durations to the actual past’s stages will be finite, as they all got to the past through an inherently finite though potentially infinite process.

    Well, the stages were “arrived at” by time flowing in the forward direction. Any particular stage followed the stage immediately preceding it. So yes, all the stages were “arrived at” in a different way than how you described.

    I will acknowledge that every past stage (from the perspective of stage_0, say) is finitely remote from stage_0, of course.

  72. 72
    kairosfocus says:

    DS, your problem is not what an infinite duration looks like but getting to it dynamically by what is essentially a push down, one stage at a time stacking process. The process continues at least potentially indefinitely future-wise (causation being the was the next stage emerges from the present) but that push-down effect is inherently stepwise, finite stage by finite stage. Consequently the two cannot be separated. Also, at no point will we have an actual transition to the counted out transfinite. Notice, we get to W of cardinality aleph null without ever actually completing a stepwise count beyond the naturals, we revert to the ellipsis, and the pink/blue tapes thought exercise readily shows why. So, inherently the process that creates a past through causally linked succession of stages is finite but potentially infinite. This ends up where I have pointed over and over again. So, what we are actually seeing is the addition of the unjustified claim of a past infinite, joined to failure to resolve how the past-generating process proceeds to do just that, leading to inherent inability to traverse a transfinite span. KF

  73. 73
    daveS says:

    KF,

    DS, your problem is not what an infinite duration looks like but getting to it dynamically by what is essentially a push down, one stage at a time stacking process. The process continues at least potentially indefinitely future-wise (causation being the was the next stage emerges from the present) but that push-down effect is inherently stepwise, finite stage by finite stage. Consequently the two cannot be separated.

    Two? What are the two things that cannot be separated again?

    Also, at no point will we have an actual transition to the counted out transfinite.

    If you’re saying that there is no stage at which the past (relative that stage) will transition from finite to infinite, that’s correct. I think we discussed that long ago. In fact the past will always have been infinite at any stage.

    I can’t parse the next portion, but in reply to:

    So, inherently the process that creates a past through causally linked succession of stages is finite but potentially infinite.

    Consider the past P0 I described above, the past from the perspective of noon on St Patrick’s day.

    If that is potentially infinite, that means it’s a finite collection together with some process by which any finite number of additional stages can be added to it.

    Does this make any sense to you? How can you possibly add more stages to it now?

  74. 74
    daveS says:

    KF,

    I see I misread the last part of your post, so strike my last question above for the moment. My question is then, would an infinite past be a potential or an actual infinite?

  75. 75
    kairosfocus says:

    DS, it would seem that as the past is inseparably generated by the same causal chain that generates the next stage of the future [which thus becomes the next present] it is of like character, in principle potentially infinite so long as stepwise causation of a next stage continues. KF

  76. 76
    daveS says:

    KF,

    There is a very clear difference between the character of the collection of stages occurring before noon on March 17 (denoted P0) and those occurring after noon March 17 (let’s call it F0)

    As of noon, March 17, no stages can be added to P0, but stages can be added to F0 in perpetuity.

  77. 77
    kairosfocus says:

    DS, picking an arbitrary time and saying that there is a fixed past to that point does not change the nature of the process that generates the past, causally driven emergence of the next present, which at the same time pushes each past step back one in the stack. KF

  78. 78
    daveS says:

    KF,

    DS, picking an arbitrary time and saying that there is a fixed past to that point does not change the nature of the process that generates the past, causally driven emergence of the next present, which at the same time pushes each past step back one in the stack. KF

    I’m speaking strictly to the question of whether the fixed past to a particular point, assuming it is in fact infinite, is potentially or actually infinite. If you don’t want to discuss that issue, then I can’t stop you. 😛

  79. 79
    kairosfocus says:

    DS, the particular point from the stream of actualised nows is not like some fixed point along a road, an address that is always there more or less, like I can in principle go back to every house I have lived in. The present moment is an ephemeral reality that arises from a chain of cause-effect stages, each giving rise to its successor as it fades into the past. that strep by step chaining inherently implies a stepwise, finite stage process, and no such process can traverse a transfinite span. So, the number of past stages (by whatever yardstick is appropriate) will be finite. And once the particular case is more or less frozen like a certain moment on Sunday July 20, 1969 when Armstrong first stepped unto the Moon’s surface, the number prior to that will be finite. Potential infinite-ness comes from the onward march of “now” that keeps on stretching forward. The actual infinite on such a process would require a completion of a transfinite span in steps of finite stage and that will not happen, inherently. Every step in the chain will be finite and bounded by the next. KF

  80. 80
    daveS says:

    KF,

    Just to clarify, do you adhere to the A-theory or B-theory of time? (Or perhaps something different, if that is possible).

    I would agree that if you consider the collection of all “stages” that have ever occurred, if the past is indeed finite, then this collection of all stages could be called a potential infinite. But that’s not what I’m talking about. I am discussing the past relative some fixed stage, and whether or not that could be infinite, and whether it would then be a potential or actual infinite.

    The present moment is an ephemeral reality that arises from a chain of cause-effect stages, each giving rise to its successor as it fades into the past. that strep by step chaining inherently implies a stepwise, finite stage process, and no such process can traverse a transfinite span. So, the number of past stages (by whatever yardstick is appropriate) will be finite.

    No, this does not follow from any argument you have presented. The closest you have come is in post #68. Let me try to rephrase that here, dispensing with the “what part of…” motif:

    1. Between any two stages, there is a duration.

    2. If X and Y are two stages and there are only finitely many stages between them, then the duration of the interval from X to Y is finite.

    3. If every past stage is only finitely remote, then there are no infinite durations between specific stages.

    4. If there are no infinite durations between specific stages, then the duration of the past cannot be infinite.

    I think #2 is unnecessary, but there’s no harm in leaving it. Premises #1–#3 are “obviously true” in my opinion.

    I have pointed out that #4 is problematic, in view of the dictionary definition, which says nothing about a requirement for infinite durations between specific stages (in this context).

    If you think I have misstated or missed anything in your list of premises, please post an edited version, keeping each one to one sentence if possible, and please number them.

  81. 81
    kairosfocus says:

    DS, I am pointing to observable dynamics of causally linked temporal succession in our world; A/B theories of time are secondary to such and must answer to it. If there are no transfinite durations between stages, all durations are finite, thus there is no warrant for claiming an infinite duration on the set of stages. Then, the step by step sequencing involved shows itself inherently finite though it may progress ever onward. Stepwise finite stage processes do not span transfinite traverses, as has been repeatedly discussed. KF

  82. 82
    daveS says:

    KF,

    If there are no transfinite durations between stages, all durations are finite … .

    This is exactly the issue in question. I have tried several times to encourage you to tell us in detail why we should accept this premise (see my post #80). If I continue to see no substantial response, I will be forced to infer (provisionally of course 🙂 ) that you do not have any reasons why we should accept this premise.

  83. 83
    kairosfocus says:

    DS, all means all (as in, no exceptions), that’s all. There is nothing left over to get a transfinite duration snuck in under the back door. KF

  84. 84
    daveS says:

    KF,

    Thanks, I know what the word “all” means.

    Once again, I’m asking for an explicit argument supporting the quoted statement in #82.

    To prove the contrapositive of #82, you would need to show that if the duration of the past is infinite, there is some transfinite duration between stages, i.e., that:

    For every natural number n, there exists a stage I such that I occurred more than n steps before the present.

    implies:

    There exists a stage I such that, given any natural number n, I occurred more than n stages before the present.

  85. 85
    kairosfocus says:

    DS, all means all, the rest plays out as above. KF

  86. 86
    daveS says:

    Well, that’s certainly persuasive. >_<

  87. 87
    kairosfocus says:

    DS, I am not trying to be persuasive at all, I am pointing to the implication of all inter-temporal stage durations being finite. All means all in that connexion. The process of generating successive stages as a given present triggers its successor and automatically adds yet another stage to the past so that all previous stages are one further back [having been repeatedly pushed down in the stack stepwise from when they were once the present], is stepwise as discussed above, and cannot traverse the transfinite. KF

    PS: Notice much the same happening with this thread!

  88. 88
    daveS says:

    KF,

    The challenge to you is to prove (yes, persuasively!) the conditional statement in #84.

  89. 89
    kairosfocus says:

    DS, the warrant is there, long since, based on the process by which temporal succession obtains. No stepwise, finite stage process can span a transfinite traverse. Readily shown, long since repeatedly shown, and just plain common sense. The most we can say of the past is it is potentially infinite but finite at any given moment, as the next step comes along and exceeds then also bounds the last. As a direct result, all durations between steps are finite and there are thus no transfinite durations to actual past stages that were once the present but have been succeeded step by step since. At this stage, I have no belief you are going to accept that reasoning, but I again state it to show that there is a reason that I have consistently maintained that is accessible to the inquirer and which would help him/her see why it is that I have challenged the notion of an infinite actual past. the burden of proof you need to meet is to provide a credible means by which we can get a transfinite actual past. That you have not done so and instead try the tactic of oh you have not proved this to my satisfaction (while seeming to essentially assert this as a default assumption . . . as, required for an evolutionary materialistic world picture to obtain any credibility? [sounds a lot like that . . . ]), speaks volumes. KF

  90. 90
    daveS says:

    KF,

    If you think you can prove the following statement, which is logically equivalent to your premise quoted in #82:

    For every natural number n, there exists a stage I such that I occurred more than n steps before the present.

    implies:

    There exists a stage I such that, given any natural number n, I occurred more than n stages before the present.

    then I’d like to read it, and will definitely respond. You haven’t done this so far, IMHO because it’s impossible in the context of the assumptions we are making regarding the nature of time.

    It’s less likely that I’ll respond to red herrings concerning my motives, “evolutionary materialism”, etc.

  91. 91
    kairosfocus says:

    DS, we are not dealing with the abstraction, natural numbers. We are dealing with the dynamics of temporal succession of stages. To assert that before any stage I there are endlessly more stages evades and begs the point. Every actual past stage s had to have once been the present then succeeded by s+1 a causally connected successor, then so on to now. That process is inherently stepwise with finite scale steps in this context. (We are not dealing with infinitesimals.) That stepwise process for reasons repeatedly gone through, inherently generates a finite number of successors to any stage I*. Looking back grom now, no stage I* — a general symbol — can be greater than a finite number of steps of succession “down” in the push-down stack. That is the problem, to get to an I that is infinitely remote we would have to have traversed the transfinite in stepwise stages. We can imagine an infinite past but lack a generation process to get there. What we can get to is a potentially infinite past but which will always only be actually finite but with successors keeping on coming up. KF

  92. 92
    daveS says:

    KF,

    DS, we are not dealing with the abstraction, natural numbers. We are dealing with the dynamics of temporal succession of stages.

    Sure. I’ve never claimed that the stages are actually abstract entities themselves, to be clear.

    To assert that before any stage I there are endlessly more stages evades and begs the point.

    The question is, assuming an infinite past, in which case there must have been infinitely many stages before any given stage, whether there must exist an infintely remote stage. No questions are being begged.

    Every actual past stage s had to have once been the present then succeeded by s+1 a causally connected successor, then so on to now. That process is inherently stepwise with finite scale steps in this context. (We are not dealing with infinitesimals.)

    Yes.

    That stepwise process for reasons repeatedly gone through, inherently generates a finite number of successors to any stage I*. Looking back [f]rom now, no stage I* — a general symbol — can be greater than a finite number of steps of succession “down” in the push-down stack.

    Yes, and I have repeatedly agreed with this. Every past stage has finitely many successor stages. Always.

    That is the problem, to get to an I that is infinitely remote we would have to have traversed the transfinite in stepwise stages.

    Now you’re invoking the conditional statement I gave in my #84.

    And once again, you do not provide any argument which shows this statement is true.

    Do you understand that I’m asking specifically for such an argument? And that that’s all I’m asking for at this point?

  93. 93
    kairosfocus says:

    DS, you cannot assume an infinite past, you have to dynamically get there. KF

  94. 94
    daveS says:

    KF,

    DS, you cannot assume an infinite past, you have to dynamically get there. KF

    By phrases such as “assuming an infinite past, must there exist an infinitely remote stage?”, I simply mean “if the past is infinite, must there exist an infinitely remote stage?”.

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