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Debating A Theist: The Infinite Ladder - by John Prytz

My ever ongoing debating theist (MG) insists that ifthere is a past temporal infinity then it is impossible to reach the presentsince you have to participate in an infinite number of events before you canarrive at any current event. He introduced the analogy of "the infiniteladder" and how if you climb such a ladder you will never reach the top.However, he muddled his own analogy big time as the following series ofexchanges made over many moons, and which I've cobbled together, demonstrate.


My key distinction here is that if you have a finitelifespan and you started an infinite amount of time ago, then clearly you can'treach the present. However, if you happened to be blessed with an infinitelifespan, like say an up-quark (which can neither be created nor destroyed) thenthere's no problem. A finite lifespan can only travel through a finite timeperiod; an infinite lifespan is under no such restrictions. 


[Note: previous to-and-fro discussions resulted in thefollowing exchanges.]


MG – “As such, you have a series where each event iscloser to a line than the previous ones, and eventually the series arrives atthat line. Infinite series cannot do that. It's like having an infinite numberof rungs on a ladder, but claiming to have arrived at that top just now. It is incoherent.”


JP – If you were climbing a ladder with infinite rungs,why would you ever claim that you had reached the top? We’ve already agreedthat infinity has no endpoints – no top in other words.


MG - "If you agree that you can't climb to the top ofan infinite ladder, and you see someone at the top, the right conclusion isthat the ladder wasn't infinite after all!!"


JP - Whoa! It's 1) incorrect to use the word"you" since "you" is a finite event, and 2) you destroyedany and all logic by saying that "you see someone at the top". SinceI have said that infinity has no endpoints, it's illogical for me to state thatI see someone (again a fallacy since someone is also a finite event) at theendpoint.


MG - "The ladder is the past series of events (not"moments"; "events", like the Civil War, my breakfast thismorning, etc.) and it ends at the present event (me typing this sentence)because that's what "past" MEANS. I made it past all of the rungs ofthe PAST series of events, and am at the top (the present event). But, as yousaid, you cannot reach the top of an infinite ladder. Therefore the past is notinfinite."


JP 1 - It is more than possible to get from an infinitepast to the here-and-how if you yourself have an infinite lifespan. This is nota difficult concept.


JP 2 - Of course "you" can't since humans havea finite lifespan, but that doesn't mean it can't be done, especially if youdon't actually have a finite lifespan. Now if you take an infinite time andinfinite events, the two infinites cancel and you have just time and events.You can cross any number of events if you have enough time. You can cross aninfinite number of events if you have an infinite amount of time. I'm justgoing to substitute something that doesn't have a finite lifetime (i.e. -"you") with something that does, say an up-quark. Actually never mindabout the timing of your First Cause argument for the moment. Just tell me howold an up-quark actually is.


MG - "It was a current event, just like every rungon the ladder below me was once the current rung. I still can't complete aclimb of infinite steps. It's logically incoherent. It defies even yourdefinition of "infinite", and you know it."


JP - Of course YOU can't climb an infinite ladder sinceyou are a temporally finite event. But if something (i.e. - an up-quark) is atemporally infinite 'event' then I fail to see the problem.


MG - "So, your argument is "well, I agree thatyou can't make it to the top of a ladder with infinite rungs, but... I guessthat infinite particle MUST have done it, since it's here and it'sinfinite"??????"


JP - The proof of the pudding is in the eating. Atemporally infinite particle [like an up-quark] just happens to find itself inthe here-and-now. For all I know it tunneled through a wormhole, but here itis. Now you can negate this by 'creating' the particle out of existence, thusrefuting or negating the idea that a particle is invincible!


MG– “[A]nd you can't get out of that by saying "the proof is in thepudding".


JP – But the proofIS in the pudding. The Cosmos is infinite and yet there are particleshere-and-now. Deal with it! Noweven if there is an infinite past and an infinite future, your concept of"The Present Moment" where we find those particles has to fallsomewhere on that timeline. Let’s call that High Noon in New York City (NYC).There was a High Noon in NYC the day before. There will be a High Noon in NYCthe day after. It's no big deal to time-travel that finite interval betweenHigh Noon the day before "The Present Moment" to High Noon the dayafter "The Present Moment" - a 48-hour period. The existence of aninfinite past / future is irrelevant. Now keep pushing that concept back andforwards as far back and as far forward as your imagination can imagine.


MG - "From that one particle's frame of reference,something is happening right now, regardless of how other frames of referenceconsider "now". And, if its lifespan is infinite, then it has gonethrough and completed an actually infinite number of events prior to thecurrent one it's going through now. Correct?"


JP - Yes.


MG - "But it can't actually complete an infinitenumber of steps prior to a point; that would be like climbing an infiniteladder and actually arriving at the top rung. It's impossible. You've alreadyagreed to that. Basically, just like R [another poster], you keep agreeing withboth the premises, but refusing to accept the conclusion."


JP - If you have a finite lifespan you can complete afinite journey. By that same reasoning, if you have an infinite lifespan youcan complete an infinite journey (i.e. - an infinity that's up to that pointyou are nominating), even though there is still an infinite journey still aheadof you. Infinity (from past to "point") plus infinity (from"point" to future" still equals infinity.


MG - "Icompletely understand that you're saying an infinitely long-lived particlecould be in the midst of an infinity of events, but what I'm saying is that itcannot actually have COMPLETED an infinite number of events prior toits current event, because that would be conceptually equivalent toclimbing to the TOP of a ladder with infinite rungs. Do we agree on this much(leaving aside what the alternatives would have to be, like matter/energy beingcreated or whatever else)?"


JP - No. Wouldn'tyou agree that couldn't your infinite God have completed an infinite number ofevents prior to creating life, the Universe and everything as per Genesis 1 andGenesis 2? If your God could do that, then an infinitely-long-lived particlecould have done likewise. If your God couldn't have completed an infinitenumber of events prior to His "In the beginning", then He's not allthat all-powerful now, is He?


MG - "No, even God cannot have completed an actuallyinfinite number of events prior to a point. ... Completing an actually infinitesequence prior to a point is logically incoherent. It violates the very conceptof "infinite".


JP - Wow! Now here I thought that your invisible magicman in the sky had some control over time. I stand corrected. Bummer! I guessthat means that a particle with an infinite lifespan is more powerful than yourinvisible magic man in the sky.


MG– “But you've admitted that an infinite set of steps cannot be completed, andthat an infinitely long-lived particle would have gone through an infinitenumber of events prior to its current one. That's the same as saying that aladder with infinite rungs cannot be climbed all the way to the top, and yetthis particle has done that. It's a self-contradiction…”


JP– Speaking of contradictions, "infinite rungs" and "top" isa logical contradiction quite unworthy of you. Anyway, the answer is"No". Even if the particle has only made it halfway to the top ofyour ladder it still has made it through an infinite number of steps. 


MG – “So, theproblem with reaching the top rung of an infinite ladder isn't that it'slogically impossible to complete an infinity; it's just that the climber hasn'tlived long enough?? This is nonsense. You've already agreed an infinite numberof steps cannot be completed prior to a point because the very concept ofinfinity is that it is never completed. But then you blithely throw that asidewhen it would mean that the particle must have done something logicallyimpossible or else your worldview needs to be adjusted and the past had abeginning.”


JP - While all answers are replies, not all replies areanswers! Now here this – there is a vast difference between that which has aninfinite lifespan (like a particle) and that which has a finite lifespan (likeyou). You can’t climb an infinite ladder and live to tell the tale; anelementary particle can keep on keeping on. Even a particle will never reachthe end since there is no end to infinity so your claim that there is a “toprung of an infinite ladder” is in and of itself a total nonsensical claim. Youwere the one I recall who introduced the ridiculous idea or concept of"the top rung on an infinite ladder".


MG - "In any case, you have failed to understand theladder analogy."


JP - I understand that contrary to your statements, mystatement is that you can't have a top rung on an infinite ladder. Caseclosed. 




Is there not an infinite number of lines (rungs on aladder analogy) that you could draw between the starting line and finishingline of say a race? And yet you can both start and finish the race!


Now the question for readers is, who is right? MG or JP?

Science librarian; retired.

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