• Hole in the Bottom of Maths (Video)
    I don't mean to be too intrusive but I do want to pick your brain regarding some interesting aspects of Godel's theorems but in a much broader context.

    As I mentioned earlier, Godel uses the liar paradox to wit, the sentence L = This sentence is false. Such sentences are referred to as self-referential but that's an incomplete description. There are two characteristics that L has,

    1. Self-reference. This sentence is false (not true).
    2. Negation that causes, how shall I put it?, tension between what's being negated and what's part and parcel of the self that's being referred to. This sentence is false (not true)

    A few things that come to mind:

    a) Descartes' cogito argument. A variation of it would be: I do not exist. When one uses the "I", it appears that existence is baked into it. Then comes the negation "do not exist" which denies what the "I" incorporates viz. existence.

    b) An interesting but probably nonsubstantive quality of L is that it refers to itself, yes, but, if my English is correct, in the third person ("this") and not "I" (first person). It kinda creeps me out - there's another possibly but not necessarily dangerous agency - the true but hidden liar - who our poorly evolved "spider sense" has detected and that's why we feel more comfortable using "this" and not "I". Warning! I'm prone to flights of fancy but then there's the Cartesian deus deceptor problem we haven't yet solved.

    c) What about the Buddhist notion of anatta (non-self)?

  • Deus Deceptor Maximus Et Veritas, Veritas E Mendaciis
    Wrong. Only propositions have truth-values.180 Proof

    I defer to your better judgement.
  • Deus Deceptor Maximus Et Veritas, Veritas E Mendaciis
    p = p is a tautology.
    ~p = ~p is a tautology.
    p = ~p is a contradiction.

    "p v ~p" is a bivalence expression, and therefore neither a tautology nor a contradiction.
    180 Proof

    p v ~p is always true. That makes it a tautology.

    I learned to read Latin solely from books, and in a long and desultory manner.Todd Martin

    And look at how you've turned out! Master, show me the way! :grin:
  • Hole in the Bottom of Maths (Video)
    Aw shucks.... :yikes:Wayfarer

    Seriously, luck's on your side and/or you know exactly which words to type into the search box if every search you do takes you to high quality material.

    I must confess that I didn't. I've not studied symbolic logic, and my mathematics is rudimentary, but I'm interested in why Godel's Theorems 'are unquestionably among the most philosophically important logico-mathematical discoveries ever made' (says this article.) I feel as though I intuitively understand why that is, but when I read up on it, I find it very hard to follow. Which is why I found that video was helpful although as we see, opinions are divided.Wayfarer

    Get your hands on an introductory course on logic. It'll take about a month to get a good understanding of basic logic. Some call it, derogatorily I suspect, baby logic but, if you ask me, that's a misnomer. I guarantee that you won't regret it.

    Returning to the main point in re Godel's argument, the version in the video, it proceeds as follows:

    a) K = the sentence with the Godel number g is unprovable
    b). The sentence with the Godel number g is K itself.

    Suppose there's a proof for K. It would prove K is unprovable. That's a contradiction: the unprovable is provable.

    1. If K is provable then K is unprovable (Godel's key premise)
    2. K is provable (assume for reductio ad absurdum)
    3. K is unprovable (from 1, 2)
    4. K is provable and K is unprovable (2, 3 taken together)
    Ergo,
    5. K is unprovable (1 to 4 reductio ad absurdum)

    The problem is premise 1. If K is provable then K is unprovable is logically equivalent to the statement, K is unprovable. See vide infra,

    If K is provable then K is unprovable = K is unprovable or K is unprovable = K is unprovable

    In other words, I can substitute "K is unprovable" for "K is provable then K is unprovable" and then Godel's argument becomes,

    1. K is unprovable [because, if K is provable then K is unprovable = K is unprovable]
    2. K is provable
    4. K is provable and K is unprovable (2, 3 taken together)
    Ergo,
    5. K is unprovable (1 to 4 reductio ad absurdum)

    Notice statement 1 (Godel's key premise) = statement 5 (the conclusion). This is, as you already know, a circulus in probando (circular argument).
  • Hole in the Bottom of Maths (Video)


    First off, thank you for the video. It's uncanny, you know, how you seem to be able to find good quality videos on the www and by quality I'm not referring to the video resolution. You've made what is essentially chance into an art. It must take both intelligence and loads of luck to boot to turn what is essentially a roll of a die into a skill. Kudos! Thanks again.

    Last I checked, Godel's incompleteness employs a variation of the liar sentence which, as you know, is "this sentence is false." According to the video, Godel's version of it is, K (for Kürt) = "the sentence with Godel number g is unprovable", the sentence with Godel number g being K itself. Thus, if K's provable, then it's unprovable [inconsistent because of the contradiction] and if K's unprovable then some mathematical truths are unprovable [incomplete].

    As you might've already guessed, at the heart of Godel's therems lies the liar paradox. Before I go any further I need to draw your attention to the rather odd fact that Godel and anyone else who uses different versions of the liar sentence for whatever purposes is, all said and done, resorting to a L-I-A-R. Would you or anyone put to service a liar to prove something, anything? Perhaps I'm being too dramatic and perhaps I'm barking up the wrong tree; after all, the word "liar" may have been used just to grab our attention - only for effect, nothing else.

    That out of the way, let's revisit K = the sentence with Godel number g is unprovable and the argument presented in the video which hopefully is a variation, salva veritate, of Godel's own.

    Argument A [Adele, Godel's wife]

    1. K is provable [assume for reductio ad absurdum]
    2. If K is provable then K is unprovable [K = the sentence with Godel number g (K itself) is unprovable]
    3. K is unprovable [1, 2 Modus Ponens]
    4. K is provable and K is unprovable [contradiction] [..Math is inconsistent]
    Ergo,
    5. K is unprovable [1 - 4 reductio ad absurdum][..Math is incomplete]

    A few points that seem worth mentioning.

    a) Look at N (Nimbursky, middle name of Godel's wife) = premise 2. If K is provable then K is unprovable [K = the sentence with Godel number g (K itself) is unprovable]. The assumption that has to be made for argument A to do its job of breaking math as it were is that N makes sense, in logical terms, makes sense implies that a truth value can be assigned to it.

    The first clue that something's off is that N is a derivative of the liar sentence and we know that the liar sentence doesn't make sense. One could say that the liar sentence is a poisoned well so to speak and every bucket of water, N being one, drawn from it will be lethal or, in this case, highly dubious. Common sense! No?

    b) Consider now the fact that argument A is a reductio ad absurdum which, as you know, derives a conclusion and uses that to reject/negate one or more of the assumptions made in the preceding lines of an argument. If you're not familiar, a reductio argument looks like this:

    1. p
    2. q & ~q [inferred from p]
    Ergo,
    3. ~p

    Now in the argument A, the following assumptions/premises occur
    1. K is provable
    2. If K is provable then K is unprovable [K = the sentence with Godel number g (K itself) is unprovable]

    The two assumptions lead to the contradiction below,

    4. K is provable and K is unprovable

    We are now justified in rejecting "one" of the premises but it doesn't necessarily have to be the one Godel has rejected which is 1. K is provable. After all, a reductio absurdum doesn't actually identify which premise is false. A reductio ad absurdum is like a detective in faer earlier stages of a murder investigation - fae knows only that someone is the murderer but doesn't know who the murderer is. Thus, I could reject N = 2. If K is provable then K is unprovable [K = the sentence with Godel number g (K itself) is unprovable and if I do that Godel's argument falls apart.

    Given premise 2. If K is provable then K is unprovable [K = the sentence with Godel number g (K itself) is unprovable] has highly ignoble origins (the liar sentence), shouldn't we reject it rather than reject 1. K is provable, a perfectly reasonable proposition?

    c) There's another issue with statements like N = 2. If K is provable then K is unprovable [K = the sentence with Godel number g (K itself) is unprovable].

    Given a proposition P,

    1. If ~P then P
    2. ~~P or P [from 1 implication]
    3. P or P [2 double negation]
    4. P [3 tautology]

    The statement, If ~P then P can be thought of as P itself, it can be reduced to P. In other words, the conditional if ~P then P is an illusion of sorts because it actually means P

    Let's look at the version of the liar sentence that Godel uses which is, if K is provable then K is unprovable.

    1. If K is provable then K is unprovable
    2. ~K is provable or K is unprovable [from 1 implication]
    3. K is unprovable or K is unprovable [from 2, ~K is provable = K is unprovable]
    4. K is unprovable [3 tautology]

    In essence, 1. K is provable then K is unprovable is logically equivalent to (I've used only equivalence rules of natural deduction), is nothing but, the statement 4. K is unprovable wearing heavy disguise.

    What this means is that Godel's argument as presented in the video becomes,

    1. K is provable [assume for reductio ad absurdum]
    2. K is unprovable [If K is provable then K is unprovable = K is unprovable]
    3. K is provable and K is unprovable [1, 2 Conjunction]
    Ergo,
    4. K is unprovable [1 - 3 reductio ad absurdum]

    Did you notice what went wrong? The conclusion, 4. K is unprovable is also a premise 2. K is unprovable. A petitio principii.
  • Deus Deceptor Maximus Et Veritas, Veritas E Mendaciis
    You have honored me and my knowledge, sir.Todd Martin

    You deserve the honor then. :smile:
  • Deus Deceptor Maximus Et Veritas, Veritas E Mendaciis
    Proposition 8 is a false dichotomy. Both p & not-p can be false. Both can be true iff p is epistemological and not-p is ontological.180 Proof

    I don't see how that's possible. p v ~p is a tautology and if, as you claim, both can be false as in ~p &~~p, we get the contradiction ~p & p. Again, if you say both can be true, p & ~p, another contradiction.
  • Deus Deceptor Maximus Et Veritas, Veritas E Mendaciis
    Google Translate :sweat:

    You seem to know Latin, enough at least to find error when others commit them. :up:

    veritas e mendaciis”, “the truth out of lies”.Todd Martin

    Will make the required corrections in my post.
  • Can the universe be infinite towards the past?
    I would like to return to the opgod must be atheist

    Why? Are you expecting a gift?
  • Can the universe be infinite towards the past?
    I will disagreeMww

    But you don't have to, right?
  • Can the universe be infinite towards the past?
    Should we just make stuff up?jorndoe

    As long as we're making shit up, go hog-wild, you know — Bill Hicks
  • Can the universe be infinite towards the past?
    There is no such thing as "infinite" other than to describe a feature of infinity.god must be atheist

    adjective, noun? :chin:
  • What is your understanding of 'reality'?
    some philosophies do seem to strip everythingJack Cummins

  • God Debris
    omnipotent God annihilated himselfCountVictorClimacusIII

    Atlantis syndrome?

    God would now exist as a combination of the smallest units of energyCountVictorClimacusIII

    That desperate huh?

    feel alone and abandoned?Kenosha Kid

    Ok! I am.

    we should act as bridgesCountVictorClimacusIII

    What about floods, hurricanes, earthquakes?
  • Vaccine acceptence or refusal?
    I stand correctedJames Riley

    You can sit down. It's much easier to correct if you do.
  • Vaccine acceptence or refusal?
    No, you are rightJames Riley

    On behalf of Janus, thanks!
  • Vaccine acceptence or refusal?
    You know I just happened to learn yesterday that China will now allow married couples to have three childrenfishfry

    Interesting. Do couples want more than 3 children?
  • Illusion of intelligence
    You know how sometimes you look at someone and you just know they are super smart.TiredThinker

    No!

    without words.TiredThinker

    Go on!

    I doubt itTom Storm

    Are you sure?

    it depends on the situationPossibility

    You're on to something there.
  • What is your understanding of 'reality'?
    There is no "problem"180 Proof

    You mean to say I don't have to look for a solution! Yaay!

    That’s not it, either.Wayfarer

    :up: You make me look like a moron but I've never felt so proud of being one!

    If you strip away the symbols, all you would see is entangled densities of energy with emergent function.Pop

    Let's strip that away too and if there's still something left, let's strip that away too, strip, strip, strip until we get to nothing and we strip that away too.
  • Can the philosophical mysteries be solved at all?
    ExactlyAthena

    Really? Exactly?

    can they wanderAthena

    Why not? I don't recall there being a moratorium on wandering.

    fortunately, we all tend to be good peopleAthena

    Are you sure?

    Immediately Einstien comes to mindAthena

    Have you ever thought why?
  • Is life a "gift?"
    133
    Can life really be a gift?
    TiredThinker

    And if it is...

    benefitsNils Loc

    More benefits! I say, more and more benefits.

    When one takes a shit, who does one take it from?James Riley

    :rofl: Gift shit!?

    I'm not sure if I understand.TiredThinker

  • Israel killing civilians in Gaza and the West Bank
    Israel's defenders on this thread (and in the media) have one major play, equivocating between "Israel has the right to defend itself" and "Israel has the right to defend itself [by any means]".Baden

    :up: :clap:

    The 1967 war was complexBenkei

    And so...

    I agree as well and I don't deny Israeli crimes, although I think we may disagree on the scope of these crimes.BitconnectCarlos

    Indeed, let's not discuss death but how many deaths and how the deaths were brought about. Something tells me we're in a whole lot of trouble. Nevertheless, a fine point.

    Israel in the past has definitely been a victim that has faced annihilation on several occasionsBitconnectCarlos

    What follows as of necessity?

    Israeli citizens are frequently killed which is considered by Jews everywhere as Israel being attacked.BitconnectCarlos

    In Israel the homicide rate produced by criminal activities is relatively low: in 2015, there were 2.4 people killed per 100,000 inhabitants (in Switzerland the number is 0.71, in Russia it is 14.9, in South Africa it is 34, in Venezuela it is 49). In 2009, 135 people were murdered in Israel. The percentage of women killed by their partners who were Arab decreased from 9 out of 11 in 2009 to 10 out of 15 in 2010 and 11 out of 24 in 2011.

    According to Israel's police, the number of murders is continually decreasing. In 2018, 103 people were the victims of homicide, compared with 136 people in 2017. The murder rate in 2018 was 1.14 people per 100,000 inhabitants.
    — Wikipedia

    "In Israel the homicide rate produced by criminal activities is relatively low"...but not ZERO, at least not yet. Sorry to hear that!

    And I 100% agree that Israel has committed atrocities in the pastBitconnectCarlos

    That sure, huh? Heisenberg would've been mortified.

    He that is without sin among you, let him first cast a stone at her. — Jesus Christ
  • What evidence of an afterlife would satisfy most skeptics?
    To even ponder a question like that we need to agree on the definition of words that we use. Like soul, existence and mind.Don Kotlos

    Bravo! :up:

    :smirk: (Play nice.)180 Proof

    I thought it was Play fair!

    But what type of evidence would be reasonable to convince skeptics that an afterlife probably is a real possibility?TiredThinker

    Beats me!

    A can of worms, with immortal worms in it.Wayfarer

    Immortal being the key word! Worms irrelevant unless one is being parasitized by eternal helminths. :vomit:

    *Wayfarer

    That asterisk (*) sums up the thread to a T. Nice work!
  • Can the universe be infinite towards the past?
    So you are saying that an infinite amount of time “passed” in that infinite past universe, but not since any particular moment in time. What do you mean by “passed” then?Amalac

    Great question and I don't have a good answer but for what it's worth, I offer my own point of view below.

    It can be said that both time and space are more or less the same concept [Minkowski space-time in which time is the 4th dimension].

    That out of the way, does it make sense to ask about the passage of space. Nothing weird happens to our brains when we talk of space being infinite. I'm here in Dublin, Ireland and the space in front of me could be infinite and so too the space behind me and the same goes for up, down, the left, and the right of me and no one has any trouble accepting that. In fact, it seems so believable to imagine space like that (infinite in all directions) that it's become second nature to one and all.

    Time, on the other hand, is viewed as something that passes and thus the difficulty some face in accepting an infinite past - time has to begin for the passage of time to make sense. After all, time passage is, all said and done, an interval which, by definition, requires at least two points (in time), a beginning and an end.

    You might've already guessed what the nub of the issue is by now. It seems to be the difference in perception of space in time - space is static [we don't say space flows/passes and time is dynamic [we say time flows/passes]

    Do we have valid reasons to justify such differential treatment of space and time? Why is time (thought to be) in "motion" and space (thought to be) is "motionless"?

    If, just for the heck of it and nothing else, we stop treating time as something that flows and consider it as just another kind of space, the problem that we're discussing will be resolved - the concept of pass, passing, passage can't be applied to time, it would be a category error of sorts. If so, your question about between which two points did the infinite past pass becomes meaningless.
  • Can the universe be infinite towards the past?
    Oh dear, just answer the question: Assuming the universe was infinite towards the past, and that an infinite amount of time passed all the way to the present, since which moment down to the present did it pass? Since when to when did it pass?Amalac

    This question has an underlying inconsistency. When you assume "...the universe was infinite towards the past...", you shouldn't be asking "...since which moment down to the present did it pass? Since when to when did it pass?" because that question, whatever else it is, presupposes a beginning, a starting point, to time - the "which moment", the"when" in "when to when".

    It's difficult to wrap your head around such matters. Before you know it, you're going around in circles.
  • Can the universe be infinite towards the past?
    That does follow if 1 and 2 are true.Amalac
    Infinite Regress.

    there is nothing logically inconsistent about a universe with an infinite past,Amalac

    :up:

    I'm rejecting is Kant's argument which states that the universe couldn't have been infinite towards the past because that would imply that an infinite amount of time would have elapsed up to to the present moment.

    That one would be the one that begs the question, by assuming tacitly that the universe must have had a beginning in time
    Amalac

    Bravo! :up:

    I don't have a problem with the idea of time passing, but with the idea that “if the universe has an infinite past then an infinite amount of time must have passed”.Amalac

    The proof that an infinite amount of time has passed rests, in my humble opinion, on the proposition that the past is infinite. You claim to have no problems with an infinite past but then you say you can't accept that "if the universe has an infinite past then an infinite amount of time must have passed". It doesn't add up. :chin:
  • Are there legitimate Metaphysical Questions
    I mean if you can incorporate this topic to Susan's Haack's "Innocent Realism", then the thread can stay of topic as it concerns the nature of reality and how it sometimes appears in parts.Manuel

    Precisely. The underlying assumption that leads to us thinking that stories of days past are myths i.e. are hyperbole/meiosis is that how it's now is how it was in in re factors relevant to actions/events that we suspect are exaggerations/understatements. On the face of it, this assumption might seem rather benign with respect to truth in that it doesn't distort veritas but then one only needs to compare the present (2021) with the past (say 3000 BC) to realize how wrong it is to think/assume that nothing relevant to the argument that stories/tales from long ago are simply myths can change.

    Take the mutli-purpose, now ubiquitous cell phone complete with all the support infrastructure it needs, go back in time to 3000 BC [Pharoanic Egypt]. Wouldn't you, who did that, become a legendary sorceror, a hero even if you play your cards right? Your story, if it survives the test of time, would be treated as a myth in 2021 but you of all know it's the truth, the whole truth and nothing but the truth. In short, to dismiss tales/stories from the ancient era as nothing but myths [veridically suspect] amounts to ignoring some possibilities, like the cell phone scenario above, that might very well have been true. I guess at some point those who study/read stories/tales of yore simply can't deal with the multitude of extremely complex possible scenarios that could be true and take the easy way out - just treat these narratives as myths, problem solved! Thus, in my humble opinion, we would be doing ourselves a great favor by reminding ourselves that the word "myth" is a synonym for "it was just too complex".

    It must be mentioned that the above cell phone scenario is meant to just give you an idea of how what reality means can undergo radical modification depending on technology demonstration across different ages/time periods with the aid of time travel machines

    There's another, far more interesting way with which myths can be...er...explained. Change in metaphysics itself i.e. change in fundamental substances, and the laws of nature (have I left anything out?) could greatly alter the landscape of the possible, impossible, probable, and improbable.

    I mentioned that if gravity were weaker, superhuman feats would be child's play and if one factors in differences in muscle mass between individuals, a Hercules ("myth") is plausible.

    How do myths, viewed with an open mind as I did above, matter to metaphysics?

    There's no good reason at all to think the metaphysics of the past is identical to the metaphysics of the present or that the metaphysics of the present will remain constant as we enter a future age. After all, what we think are myths could have been, under my interpretation, facts; it's just that our present metaphysics doesn't support the storie/tales of our distant ancestors but the metaphysics back then might have.

    So, for instance, consider the matter of human souls. Souls might've been real and there might've been plenty of evidence for them thousands of years ago. Over millennia, the metaphysics might've altered in such a way that souls became nonviable entities and disappeared [species have gone extinct when the environment transformed and became hostile to them (fossils)]. Thus, what was true in the past is false in the present.

    As you will have realized by now, my objective is to raise doubts about the well-hidden assumption that the metaphysics of the world doesn't change. If the laws of nature, the fundamental substances, the fabric of reality can alter, and there seems to be no good reason why not, we have to radically change our approach to metaphysics, this change in perspective can be summed up as anything's possible! or if you prefer the negative formulation, nothing's impossible!.
  • Are there legitimate Metaphysical Questions
    It's so much easier to critique stuff you haven't understood.Banno



    A fresh, unprejudiced perspective is supposed to be healthy, right? :grin:
  • Can the universe be infinite towards the past?
    world” and “universe"Amalac

    It appears this "world" or "universe" isn't a simulation after all. Infinite computing power is required for an infinite past. I don't know if I should laugh or cry.
  • Can it be that some physicists believe in the actual infinite?
    1. For any moment in time, we can always ask what the time was before that.

    2. If for any moment in time, we can always ask what the time was before that then, the past is infinite

    Ergo,

    3. The past is infinite [1, 2 MP]

    4. If the past is infinite and we're in the present then, the infinite past is an actual infinity

    5. We're in the present

    6. The past is infinite and we're in the present [3, 5 Conj]

    7. The infinite past is an actual infinity [4, 6 MP]

    8. If the infinite past is an actual infinity then, there are actual infinities

    9. There are actual infinities [7, 8 MP]
  • Can the universe be infinite towards the past?
    But when someone says an infinite amount of time “passes”, if they don't mean that it passes from some moment in time to some other moment in time (which clearly cannot be the case), then I do not understand what is meant by “passing”. In the case of a universe with an infinite past, the idea that time must “pass” from a beginning moment all the way to the present seems false, since by definition such a universe has no beginning momentAmalac

    Review my arguments below.

    Argument A

    1. It makes sense to ask about a time before any given moment in time

    2. If it makes sense to ask about a time before any given moment in time then, the past is infinite

    Ergo,

    3. The past is infinite [1, 2 MP]

    Argument B

    4. We are in the present, the now

    5. If we're in the present, the now and the past is infinite then, the infinite past (has passed) is an actual/completed infinity

    6. We're in the present, the now and the past is infinite [3, 4 Conj]

    Ergo,

    7. The infinite past (has passed) is an actual/completed infinity

    You're bothered by how if the past is infinite, time has no beginning and ergo, you contend that time couldn't possibly pass. This, if you really think about it, is just another way of expressing the idea that the past is finite. In other words, there has to be a beginning for time = the past is finite. Simply put, a petitio principii - you can't claim the past is finite because the past is finite.

    As for the passage of time, we're here, in the now, right? Considering the past is infinite (see proof above) and we're here, in the now, time has passed.
  • Are there legitimate Metaphysical Questions
    There's also the curious aspects of many myths. I assume such stories are told more or less accurately, but as hundreds if not thousands of years go on, aspects of the story become exaggerated to the point were there maybe very little if anything is such myths, which is a true description of events. I have in mind national myths and ancient folklore and the like.Manuel

    Chinese Whispers [No offense intended, Chinese people]

    This is probably off-topic and there's a risk that your thread might be derailed but, since you seem to be interested, I'll offer a hypothesis regarding so-called myths and the impression that people have about them being hyperbole.

    To the extent that I'm aware, the theory of evolution, vis-à-vis genetics, claims that genotypic and thus phenotypic variation in a species is greater in ancestral populations than in their descendants. In other words, considering myths seem to be about exaggerated abilities (giants, deformities, superstrength, superintelligence, etc. superpowers), there's a small but non-zero probability that such mythological beings were real people, flesh and blood although possessed of exceptional abilities. Over time, populations tend to become homogeneous and I suspect some of the superpowers got diluted and/or lost.

    Also, there's an assumption that we make which is that homo sapiens thousands of years ago were more or less like us. This could be wrong. What if people back then were smaller, shorter, weaker, etc. than we are now? If this were true, any one of us, even weaklings [say Steve Rogers before he takes the serum] would be comparatively superhuman.

    Another possibility is things might've been more than a little bit different back in the days of Hercules. What if gravity were weaker? A person would be able to leap great heights [Neil Armstrong on the moon], lift immense objects, do things now quite impossible. Of course, this would apply to everybody but just a slight difference in muscle mass could mean the difference between lifting a gigantic boulder and a humble rock.

    Continuing along the same trajectory, heroes of the past could've been aliens from a more massive planet. Their bodies adapted to greater gravity would be capable of feats of strength no human could match [Neil Armstrong on the moon].

    It's relative and it also depends on variations in the laws of nature.

    Just sayin'
  • Can the universe be infinite towards the past?
    What about the series of negative integers? It has no first term of course, but it ends in -1, so that it is “completed” in that sense. Why can't the timeline of the universe be like that (with -1 being the present, so to speak)?

    If being “completed” means that one must be able to write down all of the elements of the series, then why should we accept that criterion as the one which determines whether a series of elements can “exist” or not?
    Amalac

    I'm afraid you misunderstood me or did I not get what you're saying?

    The past is infinite and an actual infinity at that; after all, we're at some point in time (this now) that can be only if infinite time did pass [another way of saying completed/actual infinity].

    I like what you said :point: "...if being "completed" means that one must be able to write down all the elements of the series..." I think you're on the right track.
  • Can the universe be infinite towards the past?
    For what it's worth, to think there's a problem with an infinite past in the sense such can't be for the simple reason that infinite anything can't be completed is to assume Aristotle's position that there are only potential infinities and no actual infinities.

    It's quite clear why Aristotle thought that way; after all, the definition of infinity is such that the very notion of completion/an end is incompatible with it.

    The only supposedly actual infinity I'm aware of is the set of natural numbers {1, 2, 3,...} but then it's an axiom [something arbitrarily assumed as true].

    Suppose we do accept that there are actual infinites like in set theory vide infra. If so, an infinite past maybe one of the possibly many actual infinities out there.


    Argument A

    1. For any given point in time, one can always ask what preceded it temporally? [premise]

    2. If for any given point in time, one can always ask what preceded it temporally? then, the past is infinite [premise]

    3. The past is infinite [1, 2 MP]

    Argument B

    4. There is no actual infinity [premise??]

    5. If there is no actual infinity then, false that the past is infinite [premise]

    6. False that the past is infinite [4, 5 MP]

    As you can see, line 6. False that the past is infinite, requires premise 4. There is no actual infinity [in bold]. The problem is the subargument 1 through 3 with the conclusion 3. The past is infinite, seems perfectly sound. If so, one option we have is to abandon the belief, albeit itself reasonable as per the definition of infinity, that 4. There is no actual infinity.

    Put simply, an infinite past is an actual infinity [completed].
  • Polosophy
    Sometimes this site is like a battlegroundJack Cummins

    I'll fight by your side anytime. Show me the enemy Jack! :rofl:
  • What is your understanding of 'reality'?
    I don't want to end up in hospital or in a grave yetJack Cummins

    You won't! :up:
  • What is your understanding of 'reality'?
    It's actually a pretty good argument... hard to ignore facts like that.Tom Storm

    It's hard to not think that way. Therein lies the rub.
  • What is your understanding of 'reality'?
    Not me. I've never believed it, and never said it.Wayfarer

    You are not like the rest of us. :smile:
  • What is your understanding of 'reality'?
    we are even trapped in the physical world, because we have to use physical means to do things. Even as I communicate on this site, I am reliant on my phone and my fingers. I remember the time when I had a broken wrist, and it was the right one, I spent 6 weeks struggling to do most things because we rely on physical reality, and our bodies.Jack Cummins

    If I were a nonphysicalist, I would say, "this is exactly what I'm talking about. The so-called physical world can't be ignored unless you want to end up in a hospital or worse, a grave. However, this doesn't constitute an argument. At best it's a scare tactic (argumentum ad baculum) or at worst parallels God level indoctrination that would leave communists, known for their so-called re-education camps, shamefully red-faced." A pinch of sodium chloride, anyone?