142 replies to this topic

[MysticKnight]

What about time zero? What is the moment prior to it?

[Dante Alighieri]

(1) through (5) are quite clearly problematic in your argument against an infinite past and betray the nature of the confusion of most arguments against an infinite past. You explicitly define your idea of "temporal passage" as moving from some prior time to a later time and talk about "temporal passage" with respect to some segment of time. As you make quite clear, you have in mind starting at some point and then moving onto some later point. But, this is precisely what is denied by the definition of an infinite past: for every interval of time, there is an earlier interval of time. The idea is not that you somehow started at some point infinitely distant at which time somehow "became" infinite, but, that in effect, the past was always infinite. It is clear that your notion of "completing" an infinite past explicitly invokes the idea of there being a beginning point to the traversal, from which you can trivially and circularly obtain that such a past is impossible. I can appreciate that there may be some good scientific arguments that yield the plausibility of the entirety of spacetime having either a first moment or first interval of time, but I am unaware of any good philosophical arguments to that end.

Edited by Dante Alighieri, 11 July 2012 - 05:11 PM.

[MysticKnight]

What I meant by time zero, is the first "moment" of time.

[Dante Alighieri]

Obviously, there is no prior interval to an infinite past, so I fail to see the relevance of your reply. My problem is not with your idea of temporal passage - I have no problem saying that (in tensed terms anyway), passage consists of moving from prior to later intervals. My problem is in your collected ideas apparent in (1) through (5) is your idea of "completion" explicitly invokes and requires the notion of some beginning point of an infinite past. This is obvious in your definition of "completion" where you take some interval of time to be "completed" if you can subtract intervals from it to obtain 0. To give the analog, consider the real interval [0,10]. We might say that such an interval is "completed" by subtracting perhaps unit intervals from the beginning at 0 until we reach the end point of 10. But, this has nothing to do with an infinite past. To say that a past is infinite is to say that for an interval of time t, there exists some interval of time t' prior to t. Simply because every arbitrary finite interval you pick out has been "completed" per se does not mean that you have somehow "completed" the infinite past in the same sense because there is no beginning from which you can talk about "completing" said infinite past. This is to betray confusion as to what an infinite past actually means.

We could run an analog of your same argument against the existence of the integers or any field isomorphic to it in the same absurd fashion:

(1*) Unique integers are ordered by less-than and greater-than relata.
(2*) An interval consisting of the integers is comprised of n successive integers.
(3*) Each succession within an integer interval subtracts one integer from n integers until that interval is completed.
(4*) The set of negative integers is an interval.
(5*) The set of integers has been completed until 0 is left.
(6) ∞ - 1 = ∞

Conclusion: The integers cannot be defined as an infinite set.

Hence, by your same reasoning, the integers cannot actually be defined at all.

Edited by Dante Alighieri, 11 July 2012 - 05:36 PM.

[Dante Alighieri]

Jebreil, on 11 July 2012 - 05:44 PM, said:

"Completed" just means that the time-segment had n moments until "time passed" and the moments are "gone forever". In other words, all the moments have been successively negated, i.e. subtracted, from the whole until a new moment and a new time segment (Present and Future) begins.

If infinite past cannot be compatible with this evident fact about time, then the idea is incoherent

Sure... which is what I already pointed out is irrelevant to an infinite past. This notion of completion, as I've pointed out multiple times, can only be defined, as you make clear, only with starting at some point and then subtracting intervals of time to reach some particular point. But, obviously, an infinite past has no starting point so I fail to see how your argument impugns against an infinite past. There is no point "infinitely distant" in an infinite past from which you can start subtracting. In fact, the very notion of an infinite past, corresponding to a half-open, half-closed real interval like (-∞, 0], derides that notion. -∞ is not some member of this interval from which you can start subtracting. There is no question of having to "subtract" from infinity as you do when you consider ∞ - 1 = ∞. In fact, for any moment whatsoever in this interval that you choose, you can subtract moments to reach the present moment. As you yourself note, all that this would mean is that the difference between particular endpoints of an interval tend to infinity as you choose further and further endpoints (i.e. the measure of [-5,0] is larger than [-2,0]), but that doesn't mean there is some infinitely distant point at -∞ from which you can start subtracting. All that an infinite past states is that prior to any particular interval you choose, there is another interval. The only way your argument would apply is that, given an infinitely distant beginning, the measure of the temporal intervals that pass would be infinite. But, this is obviously not the case with an infinite past, which eliminates a beginning, even an infinitely distant one, entirely. The only pre-theoretic intuitions of time that we tend to hold as essential are (i) dyadic ordering relata between moments or intervals of time (earlier than, simultaneous with, later than) and (ii) tensed predicates about moments or intervals (past, present, future). Your particular conception of "completion" is only relevant to finite intervals of time. But, obviously, an infinite past is hardly a finite interval.

Quote

You are confusing temporal succession with logical succession, which can coexist. The set of integers does not move from infinity (past) towards 0 (present) and actually reach 0 (present). Your analogy misses the crux of temporal succession

.
In what relevant sense does the logical or temporal succession matter here? In fact, the entire notion of "temporal succession" is explicitly described with respect to "logical succession" in some appropriate field. Otherwise, you couldn't even invoke the idea of an interval, infinity, or the slew of mathematical concepts needed to make your argument. This notion of "logical succession" is the precise analog of your notion of temporal succession. Consider the structure of your argument: "Using the notion of temporal succession, an infinite past cannot be completed. Hence, the past is finite." Likewise, "Using the notion of 'logical' succession, an infinite interval of integers cannot be completed. Hence, the integers cannot be defined as an infinite set." The fact every finite integer interval can be "completed" does not imply that the whole of the integers is "completed" or imply their necessary finitude. Likewise with temporal succession.

Edited by Dante Alighieri, 11 July 2012 - 06:12 PM.

[Dante Alighieri]

Jebreil, on 11 July 2012 - 06:14 PM, said:

The entire set of integers are held in an instant. However, time is a movement. The set of integers is not defined by movement (here represented by the act of subtraction). Time is.

Actually, the integers are defined precisely by that. The integers are defined by the set of equivalence classes (x, y) in N x N , where (x₁, y₁)R(x₂,y₂) for x₁ - y₁ = x₂ - y₂ where R is an equivalence relation (reflexive, symmetric, and transitive) . So, the integers are precisely defined by subtracting the natural numbers. The natural numbers themselves are defined by taking a successor function of 0. Another equivalent definition to make this even clearer is to consider the integers as the set-union of the natural numbers, zero, and the additive inverses of the natural numbers. But, while the natural numbers are defined by a successor function of 0, the additive inverses of the natural numbers are defined by a predecessor function of 0. So, there is quite literally no relevant difference here that I can see. By the same reasoning in your argument, neither the natural numbers nor the integers at all can be defined. And hence, likewise, we are unable to define the rational numbers or the real numbers. This goes more so with any appeal to intervals defined on the integers.

Quote

Time is a successive movement from moment to moment. Where the prior moment is negated the posterior moment is posited. The posterior movement is not posited until all prior moments have been negated.

If an infinite past notion is assumed, it assumes a successive negation of infinite moments, which once complete permits us to posit the present moment. Infinite moments cannot be successively negated. Therefore, the present moment cannot be posited.

(1) temporality is a successive movement of negation and position of moments;

(2) the past must be successively negated for the present to be posited.

Do you doubt any of these?

If not, then

(3) if the past contains infinite moments, then infinite moments must be successively negated for the present to be posited.

(4) the present is posited

(5) infinite moments have been successively negated (impossible per ∞ - 1 = ∞)

I'm glad you wrote this because this makes clear as day the problem with your argument. There is no moment prior to the infinite past from which to negate. There is not some moment -∞ from which you can start negating to reach the present moment. There is literally no question of "counting down from infinity" as you invoke. All that an infinite past states is that prior to any arbitrary interval of time, there is another interval. You can indeed pick any arbitrary past point, construct the relevant interval, and successively negate it to reach the present. In fact, you can do this with both a finite and infinite past. The problem your argument draws is from this notion of "starting at -∞" from which to negate. But, -∞ is not in the set of past intervals so your argument is irrelevant. See also my earlier replies that explain this problem.

I feel compelled to point out though, long story short, I actually agree with you that the universe probably had a beginning. I just think your philosophical argument to that conclusion is unsound. But, insofar as our positions go, that is ultimately a moot point.

Edited by Dante Alighieri, 11 July 2012 - 06:38 PM.

[wundermonk]

Jebreil, on 11 July 2012 - 04:48 PM, said:

(Premises)

(2)
A "time-segment" is a collection of n successive moments.

(4)
The past is a time segment.

Together these imply - "The past is a collection of n successive moments."

If the past is infinite, there is no upper bound on n. Hence, the statement "The past is a collection of n successive moments." for every value of n is question-begging in the context of what this argument is intended to establish.

Jebreil, on 11 July 2012 - 04:48 PM, said:

(Premises)
(2)
A "time-segment" is a collection of n successive moments.

Further, unless it is proven that one moment of time has a successive moment, this premise can not be allowed. For example, the real number 0.5 has no "next" or "successive" real number in R (the set of real numbers).

In other words, could you come up with the list of n (for any value of n) successive moments from yesterday (11th July, 2012) till today (12th July, 2012)?

If you can not, it would mean that the purported list would contain uncountably infinitely many moments - in which case, an uncountaly infintely many moments of time can be traversed in finite time (between 11th July 2012 and 12th July 2012).

If you CAN, I would like to see the list.

[wundermonk]

Jebriel:

What I am suggesting is that a "time segment" assumes a starting point and an ending point. When the universe is considered to be eternal, it means precisely that there is no starting point. Therefore, you cannot claim that the past is a time segment. It is more like a ray that has an end point but no start point. See for instance, http://www.learningw...ons/lines1.html - specifically the difference between a line segment and a ray. It is question begging to argue using the notion of a "time" segment here.

Re the other issue...it relates to the nature of time. Is there a least count for time? i.e. is there a smallest unit of time? i.e. millisecond, microsecond, nanosecond, etc.? If there is, then talk of a collection of successive moments makes sense. If not, the very idea of a successive moment of time does not make sense. Perhaps you may want to rephrase your argument using time intervals rather than moments.

[No body]

wundermonk, on 12 July 2012 - 01:20 PM, said:

Re the other issue...it relates to the nature of time. Is there a least count for time? i.e. is there a smallest unit of time? i.e. millisecond, microsecond, nanosecond, etc.?

Planck time

[Lanatin]

Time has infinite potential, but it's still a transitory phase the universe goes through at the end of the day. The underlying substrate of the universe is eternal though, and that substrate is God.

Edited by La'nat Ma Man, 12 July 2012 - 01:48 PM.

[wundermonk]

No body, on 12 July 2012 - 01:45 PM, said:

Planck time

Well, the OP presents a philosophical argument. So, I would rather wait for the OP'er to prove philosophically that a smallest unit of time (whether is is the Planck time or not) exists. Until then, the argument would be incomplete and the conclusion unproven.

Regarding Planck time, not all scientists themselves are in agreement that that is indeed the smallest unit of time. So, the scientific jury is still out there. But I am not a scientist. So, I'd rather focus on the philosophical aspects of the OP.

Thx.

[Dante Alighieri]

Jebreil, on 11 July 2012 - 06:54 PM, said:

Why do you assume we must subtract from a starting point at an infinite distance in the past? We can subtract from yesterday. We can subtract from the middle. We can subtract from anywhere we like. As long as we subtract it all. We can subtract one by one or we can subtract in one giant, divine sweep - as if in God's mind - and still the Past will not be exhausted and not all its moments will be negated and there will be no Present.

Consider the way you understood "completion."

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Each "temporal motion" within a "time-segment" subtracts 1 moment from the n moments until that segment is completed (i.e. there are no moments left within that segment. 0 moments remain.

Charitably interpreting this, consider some closed interval of measure n. For example, the interval [0,10]. We can then subtract uniform intervals from this interval such as [0,1), [1,2), and so on until we have "reached" 10 per se. Or perhaps you prefer the example using [-10,0], but it's all the same. This way of viewing the matter is somewhat awkward, so let's use an equivalent but simpler representation: to pass from -10 to 0 we can represent it as successively adding uniform intervals until 0 is arrived at. What about adding intervals from -20? What about -1000? And so on. But now, we can see the mistake that drives your argument. Per your argument, we would argue that since you cannot form an infinite past via successive addition of intervals, it follows that an infinite past is impossible. But, as pointed out, this is irrelevant to an infinite past. To say that the past is infinite is not to say that somehow became infinite, but that is has always been infinite. What an infinite past says is quite basic: for any interval of time, there is an interval of time prior to it. This particular notion of "successive addition to form an infinite" assumes some beginning point to a formation, which is precisely what an infinite past denies. In fact, consider what your original notion commits you to: you seem to have this idea of subtracting intervals from some prior time. Extend that time further and further... and then you make the argument to the effect that consider the time infinitely distant in the past - we cannot subtract intervals to reach the present. But, this is precisely what an infinite past denies - there is no beginning point at all. But since your argument cannot be made except in lieu of assuming a beginning point, we must regard it a failure at showing an infinite past to be impossible. Perhaps you wish to make the argument since that every finite past interval you can conceive of has been formed, the entire past has been similarly "formed." But this quite trivially commits a fallacy of composition. In fact, there is nothing preventing you from adding events to an infinite past to reach the present. For instance, you could pick from -10 or -1000 or -10¹⁰⁰ even. Even considering the integers, the distance from any of those points to 0 is finite, even though the set as a whole is infinite. Moreover, the distance from any arbitrary point to the present is finite, completely preserving intuitions regarding temporal passage. All that an infinite past states however is that prior to any of these moments, there is another interval of time. The only way your argument runs is if you absurdly assume that there was some time infinitely distant into the past. The thesis of the infinite past doesn't state that there is some closed interval of past times that includes such a point.

Quote

I am under the impression that numbers are defined by static relationships, not dynamic ones. Time is dynamic. The relations you speak of are still static and instantly held. Better expressed, I can denote an infinity from a formula -- {2n : n member of N} for the even natural numbers -- but I cannot dynamically cover an infinity by going through all its members. Time requires the latter. Arithmetic does not

.

Right, you cannot start writing down the even numbers successively and then complete your transcription. But, as discussed earlier, this is completely irrelevant to the notion of an infinite past. The 'static' relations I mentioned earlier are precisely the relations used to model an infinite past to begin with. You seem to be belaboring over this idea of an "actual" infinite vs a merely "mathematical" infinite. There is no relevant difference between the two - the former is just a concrete event or series that can be represented by the latter. That is in fact what all mathematical objects are - for instance, consider the mundane example of 2 + 2 = 4. Suppose you take two apples and place them next to two apples to get four apples. Have you "done" 2 + 2 = 4? If I destroy the apples, have I somehow "destroyed" 2 + 2 = 4. Of course not - none of the mathematics is being "done" in the concrete world so to speak, but all of it is done abstractly in a way to represent the situation at hand. Bringing two apples with two more applies helps to facilitate the abstract representation of bringing two two-member sets to form the canonical 4-member set {0,1,2,3} or equivalently in the Peano Arithmetic, S(S(0)) + S(S(0)) = S(S(S(S(0)))). You cannot argue against some abstract property of some concrete objects being possible without similarly arguing against the properties themselves. Your argument doesn't really depend on the notion of dynamic time (as in presentism) to do its work. All of it derives from this notion of having to "form" an infinite, which speaks just as much against abstract infinities as it does against "actual" infinities, if the argument is successful at all.

Jebreil, on 12 July 2012 - 04:36 AM, said:

Assuming, just for the sake of argument, that time was based on the Real Numbers
Each moment has to come and go.If yesterday was 0 and today was 1, we would never reach today. We would tend to 1, but never reach it. We would go on and on and on and on through the moments and never attain 1. What's worse, it would be unthinkable to reach 2, meaning tomorrow. Perhaps more alarming is the fact that we would not even start our temporal journey. Time is successive, in that a prior moment (here represented by a smaller number) must be posited first before we can posit a posterior moment (here represented by a larger number). Thus, to move from 0 to 1, we need to move from 0 to the next larger number. There is no such number. And yet, Time does move from prior to posterior (represented by the move from smaller number to the next larger number). Therefore, Time is incompatible with the Real Numbers.

I think this betrays a large number of mathematical confusions right here. The set of real numbers is not some discrete field with a successor function. In fact, quite obviously, there is no successor to another number. There is no question of time successively progressing on the field of reals, but that time continuously progresses on such a field. To move from a prior to later time simply means to move in an interval, not to somehow go to the "next" moment. By this same reasoning, you could argue that the real numbers are indefinable since no successor function can be defined on it, which would be absurd to say the least. The failure of one function to define a particular field does not entail the failure of all functions.

[wundermonk]

Jebreil, on 12 July 2012 - 09:14 PM, said:

(5)
The Past is a totally-ordered set of n elements where n is the member of the negative integers Z^-.

(8)
A negatively-infinite (-∞) number of totally-ordered elements cannot be constantly added by the magnitude of 1 to give 0.
-∞ + 1 = -∞
(this can be phrased as that which tends to negative-infinity + 1 = that which tends to negative-infinity)

The Past contains infinite totally-ordered elements (i.e. n = -∞).

There are problems with the above.

Let us define Z (the set of all integers as follows).

(1)0 belongs to Z
(2)For every x that belongs to Z, there exists u (which belongs to Z) and v (which belongs Z) such that x - 1 = u and x + 1 = v, where u, v and x are pair-wise different.  

This is my definition of Z.

Do you agree/disagree?

If you do agree, then,  n = -∞ does NOT belong to Z as long as you maintain -∞ + 1 = -∞.

The problem is, you are defining  -∞ as that which tends to negative-infinity. Z has a very precise definition (see above). It allows no room for having elements which are described as that which tends to negative-infinity. You would need to frame this part of the argument more clearly.

[No body]

well if it is just about numbers then Cantor's work point towards infinite infinities.
i am sorry i don't mean to disrupt, this is a beautiful thread......

Edited by No body, 13 July 2012 - 08:40 AM.

[wundermonk]

Jebreil, on 13 July 2012 - 07:48 AM, said:

n is the number of elements (called "sections" and defined in prem. (1) ) in the Past set.

Ok.

Quote

You, as an infinitarian, believe that the Past set contains an infinite number of such elements.

I do not know what an infinitarian means or what such a person believes. What I believe is that there is no upper bound on the number of elements in the past set. You are trying to convert this into math using the integer number system, Z, and building up an argument but as I pointed out in post #22, the argument is faulty.

Quote

Hence, for you, n (the number of elements in the set) is ∞.

Again, in premise (5) you said n belongs to Z. But ALL elements of Z are such that there is a different 'prior' element and a different 'posterior' element. From this, and from your premise (8) it would follow that n=∞ or n=-∞ do NOT belong to Z.

Putting this another way, for every n that belongs to Z, it is NOT true that n + 1 = n. Why are you then claiming in Premise 8 that n+1 = n is true of n = -∞?

Quote

If n is not ∞ but another integer as you define it, then it would be finite, and we would be in agreement about Temporal Creation.

This is based on a faulty understanding of ∞.

Quote

This is beside the point, but I am also under the impression that the Set of Integers (positive, negative or all) is a set of infinite elements.

Yes. What this means is that for EVERY integer, there is another smaller integer and another higher integer. So, there is no largest or smallest integer.

Edited by wundermonk, 13 July 2012 - 09:48 AM.