Can you defend this argument for the kalam argument's premise "the universe had a beginning" (finite past)?

[ethereality]

philosophyofreligion.info summarizes the defense of this premise that the past is finite.

It appears to me these are all the same argument, simply phrased in three different ways, which I’ve recently encountered again:

Anonymous:

the fact that there is a today proves there was a beginning. The idea of an infinite finite is absurd. Imagine a lady opening a flower shop. If she had infinite flowers to count, she could never open her flower shop. Just the fact that we are experiencing a “now” that is in motion toward a “tomorrow” and from a “yesterday,” proves there was a beginning.

Trent Horn has likewise repeated the third argument about traversing an infinite past (“we could never arrive at the present”) on the air. I am so frustrated by seeing this error that I am here begging for resolution, either a clear answer on why the rebuttal I will give is wrong, or vindication that I am correct.

I think all these formulations of what is essentially the same argument fail due to forgetting one’s definitions: One is introducing the contradiction into the scenario by trying to start at the beginning of an infinite past and then counting one’s way forward. The argument semantically, logically, doesn’t work to refute an actual past infinity because it neglects what a past actual infinity means. It says, “Let us start at the first element of this set which, by definition, has no first element.”[1] That is where the error is introduced into the argument.[2]

So this argument does not prove the kalam argument’s second premise. Yes, you arrive at a contradiction if you try to select the first element of a set which has no first element, because you’ve introduced the contradiction by assuming it to the object in question. However, it is perfectly consistent to look back at the past from the present and understand that each moment had one before it, just as you can look at a long railroad track, stretch of road, or ocean, and recognize that it continues beyond the furthest point that you can see, and that if you continued, you would find more of it. I don’t have to walk the length of Route 66 to know it’s there – nor do I have to do so to appreciate its length: People living geographically along it can each build a portion near where they live and we can obtain its full length piecemeal through the limited contributions of those along it.

It is frightening to suppose that an actual infinity exists – and this same realization of something wholly other from our finiteness is one reason for the biblical “Fear of the Lord” – but it is not self-contradicting nor clearly false. It is unimaginable, but not inconceivable.

Switching gears, as I alluded to above, the proper consideration is not whether a single element can span (or traverse) an infinity, but whether an infinite number of elements can. Regarding single beings, only one existing in eternity (outside of time) can span an infinite past (traveling through all of time all at once), but an infinite number of finite elements can also do so (each finite element traversing a finite length), just as x meter-wide planks can fill in a fence of length x meters).[3]

Additional Thoughts
[1] As another demonstration of this argument’s logical error, we believe our souls to be eternal, that we have an “infinite future” as Jimmy Akin said recently, perhaps on the last day of Catholic Answers’ pledge drive. You can deny this infinite future using precisely the same argument: Start at the last moment of the infinite future and then count your way back to the present. “It can’t be done! Therefore we cannot have an infinite future.” No, the problem is that you are contradicting what ‘infinite’ means: For an infinite future, there is no “last point” from which you count back to the present. Likewise for an infinite past, there is no “first point” from which you begin counting to the present.

Of course I understand the qualitative difference between past and future being actual rather than potential (from the perspective of going forward), that one seeks to prove that one cannot have an actual infinity whereas a potential infinity is fine (because it is not actual), but my point here is simply to show the logical problem with the argument.

[2] All the arguments are about counting in this way, just counting with different methods: numerically in abstraction, or equivalently via grains of sand or steps taken. So the three formulations on that site are the same argument committing the same error.

[3] Or, if you like, N planks of width M meters filling in fence of length L, where M = L/N. Thinking about infinity is getting my physics gears going…

 

[utunumsint]

Interesting.

This is Spitzer’s summary of Hilbert’s prohibition:

A C-Infinity, like a B-infinity, is both a mathematical infinity and an application of infinity to a finite or aggregative structure.
The important difference, however, between the B and C-infinities is that the C-infinity implies the existence (actuality) of a mathematical infinity within a finite or aggregative structure.
As noted above, examples of C-infinities would be

• an actual Cantorian set with an actual infinite number of members
• or an infinite number line with an actual infinite number of positions
• or an actually existing infinite spatial magnitude,
• an actual occurrence of an infinite number of events in the past.

If C-infinities could really exist, there could be

• infinite space,
• infinity degrees Fahrenhiet,
• infinite mass density,
• infinite physical force,
• infinite past time.

These notions seem irresolvably pradoxical prima facie, because the mathematical infinity applied to them destroys their intelligibility as finite or aggregative structures.
The proof for this goes beyond prima facie intuition. It extends to the requirements for mathematical intelligibility itself. Thus, as Hilbert shows, a mathematical infinity existing within a finite or aggregative structure undermines the very possibility of finite mathematics, and therefore the very possibility of quantifying those finite or aggregative structures. Therefore, a C-infinity must, in all cases, be illusory.

I think in Aristotelian and Hilbert’s parlance, a C-infinity is an actual infinity which is actually present in the now, within a finite space of time. So by definition, it cannot extend back into the past, because what is in the past is no longer actual and what is in the future is only potential. Thus, with time, we have an instance of a potential infinity only, stretching back in the past and towards the future.

So yes, it does seem strange that Spitzer applies this concept to time. I have to look at Hilbert’s original paper to see if he includes time in his prohibition.

God bless,
Ut

 

[utunumsint]

Here are some other interesting arguments from Book I Chapter 13 of the Summa Contra Gentile

[1] We have now shown that the effort to demonstrate the existence of God is not a vain one. We shall therefore proceed to set forth the arguments by which both philosophers and Catholic teachers have proved that God exists.

[2] We shall first set forth the arguments by which Aristotle proceeds to prove that God exists. The aim of Aristotle is to do this in two ways, beginning with motion.

[3] Of these ways the first is as follows. Everything that is moved is moved by another. That some things are in motion—for example, the sun—is evident from sense. Therefore, it is moved by something else that moves it. This mover is itself either moved or not moved. If it is not, we have reached our conclusion—namely, that we must posit some unmoved mover. This we call God. If it is moved, it is moved by another mover. We must, consequently, either proceed to infinity, or we must arrive at some unmoved mover. Now, it is not possible to proceed to infinity. Hence, we must posit some prime unmoved mover.

[4] In this proof, there are two propositions that need to be proved, namely, that everything that is moved is moved by another, and that in movers and things moved one cannot proceed to infinity.

[11] The second proposition, namely, that there is no procession to infinity among movers and things moved, Aristotle proves in three ways.

[12] The first is as follows [VII, 1]. If among movers and things moved we proceed to infinity, all these infinite beings must be bodies. For whatever is moved is divisible and a body, as is proved in the Physics [VI, 4]. But every body that moves some thing moved is itself moved while moving it. Therefore, all these infinites are moved together while one of them is moved. But one of them, being finite, is moved in a finite time. Therefore, all those infinites are moved in a finite time. This, however, is impossible. It is, therefore, impossible that among movers and things moved one can proceed to infinity.

[13] Furthermore, that it is impossible for the abovementioned infinites to be moved in a finite time Aristotle proves as follows. The mover and the thing moved must exist simultaneously. This Aristotle proves by induction in the various species of motion. But bodies cannot be simultaneous except through continuity or contiguity. Now, since, as has been proved, all the aforementioned movers and. things moved are bodies, they must constitute by continuity or contiguity a sort of single mobile. In this way, one infinite is moved in a finite time. This is impossible, as is proved in the Physics [VII, 1].

God bless,
Ut

 

[utunumsint]

Ah, here is Hilbert’s paper.

math.dartmouth.edu/~matc/Readers/HowManyAngels/Philosophy/Philosophy.html

God bless,
Ut

 

[utunumsint]

So just to focus on your objection:

I think all these formulations of what is essentially the same argument fail due to forgetting one’s definitions: One is introducing the contradiction into the scenario by trying to start at the beginning of an infinite past and then counting one’s way forward. The argument semantically, logically, doesn’t work to refute an actual past infinity because it neglects what a past actual infinity means. It says, “Let us start at the first element of this set which, by definition, has no first element.”[1] That is where the error is introduced into the argument.[2]

Just comparing this statement to the first proof in the link you provided at the start. The one on the paradoxes that occur if you accept inifinite time.

A similar paradox arises if the past is infinite. If there exists an infinite past, then if we were to assign a number to each past moment then every real number (i.e. every postive integer) would be assigned to some moment. **There would therefore be no unassigned number to be assigned to the present moment as it passes into the past. **However, by reassigning the numbers such that moment number one becomes moment number two, and moment number two becomes moment number three, and so on, we could free up moment number one to be assigned to the present. If the past is infinite, therefore, then there both is and is not a free number to be assigned to the present as it passes into the past.

I think just this one at least is an argument that does not commit the fallacy that you mention. The argument is that you never get to the present if there is an infinite number of past moments. So it is clearly not assuming that there has to be a first moment. Only that there can be no present moment if there are an infinite number of past moments.

[1] As another demonstration of this argument’s logical error, we believe our souls to be eternal, that we have an “infinite future” as Jimmy Akin said recently, perhaps on the last day of Catholic Answers’ pledge drive. You can deny this infinite future using precisely the same argument: Start at the last moment of the infinite future and then count your way back to the present. “It can’t be done! Therefore we cannot have an infinite future.” No, the problem is that you are contradicting what ‘infinite’ means: For an infinite future, there is no “last point” from which you count back to the present. Likewise for an infinite past, there is no “first point” from which you begin counting to the present.

Good point.

Of course I understand the qualitative difference between past and future being actual rather than potential (from the perspective of going forward), that one seeks to prove that one cannot have an actual infinity whereas a potential infinity is fine (because it is not actual), but my point here is simply to show the logical problem with the argument.

Right. A soul is only potentially infinite. I believe the only actual infinite is God, according to traditional definitions. Unless, we somehow gain an actual infinity by our participation in God. But perhaps this is another discussion.

Still, I remember Jimmy’s discussion of this topic, and it is a little unfair to expect him to get into fine grained philosophical details of this sort on a Q&A open forum. No?

God bless,
Ut

 

[utunumsint]

I suppose, if we allow that an actual infinite past leads to the paradox mentioned in the link about never reaching the present, that leaves you with only potential infinite past being possible, which means there must be a first point, otherwise it would be an actual infinity afterall, and you would have the same problem with paradoxes again.

I suppose my problem with this argument is that it assumes that the only way to resolve the problems created by an actual infinity is that there has to be a beginning. Perhaps this is not the only resolution.

God bless,
Ut

 

[Bahman]

Actually the beginning of time in finite past is problematic too if we define time as a measure of changes since the beginning of time is a substantial change hence we need another time to allow this change which is paradoxical.

 

[inocente]

philosophyofreligion.info summarizes the defense of this premise that the past is finite.

That website seems to be someone’s blog. If you go to whois.net/ and type in the url, you’ll see you can buy similar names, such as philosophyofreligion.net, for $11.59 a year.

His arguments are flawed. He thinks Hilbert’s Hotel isn’t possible, but the hotel is perfectly valid logically. It isn’t intuitive, but it’s how infinite sets work. His second and third arguments are based on the strange notion that “the past has been created by successive addition”. Nope, that’s just weird. Math may not be his strong point. Still, he could always buy mathofreligion.info or mathexpert.info, both available for $12.39 a year.

 

[JapaneseKappa]

philosophyofreligion.info summarizes the defense of this premise that the past is finite.

Your link is surprisingly weak. For example, Hilbert’s Grand Hotel is not an actual paradox, despite the claims to the contrary. It is instead a demonstration of how counter-intuitive infinite quantities are.

en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel#Analysis

 

[rossum]

Can you defend this argument for the kalam argument’s premise “the universe had a beginning” (finite past)?

Your question depends on how you define “universe”. If you define “universe” as “all that exists”, then if God exists the universe, so defined, does not have a beginning.

rossum

 

[lmelahn]

I am afraid that the Kalam Argument has a fatal flaw. Here is now the argument is usually presented (for the benefit of readers):

1. 
   *]Everything that begins to exist has a cause;
   *]The universe began to exist;
   *]The universe has a cause.
   
   That is sufficient, because the flaw is in this syllogism. Actually, there are several flaws, but the most serious one is the minor (second) premise.
   
   The major premise is correct, but it has the disadvantage of not being perfectly obvious. There is also no way of telling, just by examining something, that it has ever “begun to exist.” Another issue is that “the universe” is not a unified thing, and saying that “the universe” (as if it were a single thing) has a cause is a rather problematic statement.
   
   Those are, however, relatively minor issues that could be fixed. The fatal flaw is the minor premise. There is, in fact, no philosophical way to prove that the universe had a beginning in time, at least in the way that we commonly understand that.
   
   And the problem is that those who propose the Kalam argument, I think, imagine themselves starting with the present moment, and counting backwards until they reach the temporal “beginning” of the universe. Clearly, when this method is employed in a universe that extends indefinitely into the past (an “eternally old” universe), it is impossible to count the number of years elapsed. And this, they claim, makes an “eternally old” universe impossible—a contradiction, in fact.
   
   However, such a scenario is not impossible: in the absolute sense; that is, not logically contradictory.
   
   St. Thomas Aquinas explains that a succession in time may be infinite provided, that the events do not strictly depend on each other for their existence. In fact, causal dependence for Aquinas must be perfectly simultaneous. Once the cause is remove, its effect is also removed at the same moment.
   
   What that means is that previous events are not, strictly speaking, the causes of posterior events, but—if you like—the occasion for posterior events.
   
   God, however, is infinitely powerful. He can create, if He wishes, an infinitude (not technically an “infinite” number, because infinitudes are uncountable) of creatures, and so there is nothing preventing Him from sustaining in existence an universe that extends indefinitely into the past: that is “infinitely old.”
   
   Therefore, arguing whether the universe is infinitely old or not is a rather fruitless endeavor, in my opinion, at least as regards the existence of God.

 

[seagal]

Another issue is that “the universe” is not a unified thing, and saying that “the universe” (as if it were a single thing) has a cause is a rather problematic statement.

If you take “the universe” as “everything that exists” then you can call it a unified entity. In the same way you could call each cell in my body part of a unity. “I” began to exist the moment the first cell of my body came into being. No matter that the first cell multiplied and became 2 and those cells multiplied until the billions of cells that are “me” were created. If that first cell hadn’t existed, neither would the rest of me. The universe also came from an initial singularity that, if it hadn’t happened, the universe as a whole wouldn’t have happened.

 

[lmelahn]

If you take “the universe” as “everything that exists” then you can call it a unified entity. In the same way you could call each cell in my body part of a unity. “I” began to exist the moment the first cell of my body came into being. No matter that the first cell multiplied and became 2 and those cells multiplied until the billions of cells that are “me” were created. If that first cell hadn’t existed, neither would the rest of me. The universe also came from an initial singularity that, if it hadn’t happened, the universe as a whole wouldn’t have happened.

Full disclosure: I am very much a theist. I just don’t think the Kalam argument works, because it makes use of a mistaken concept of causality. I think a proof for God’s existence is possible, but that Kalam isn’t one of them.

In any case, a human body exhibits a unity that is much more profound than the set of objects in the universe (which are mostly inanimate). You don’t think that all of us form a sort of “super-organism” together with the universe, do you? If not (and I hope not ), then the physical universe consists in an aggregate of objects that do not have an obvious order among them (unlike the cells in my body).

It is true that the first cell was a cause of your existence—a material cause—back when you were conceived. But that cell exists no longer, so it cannot be a cause of your existence now. (Right now there are a whole bunch of other cells that are causing your existence, but not that zygote.)

 

[seagal]

Full disclosure: I am very much a theist. I just don’t think the Kalam argument works, because it makes use of a mistaken concept of causality. I think a proof for God’s existence is possible, but that Kalam isn’t one of them.

In any case, a human body exhibits a unity that is much more profound than the set of objects in the universe (which are mostly inanimate). You don’t think that all of us form a sort of “super-organism” together with the universe, do you? If not (and I hope not ), then the physical universe consists in an aggregate of objects that do not have an obvious order among them (unlike the cells in my body).

No, I don’t think we’re “one with the universe” I was just using the body as an analogy. If you look closely enough (as I’m sure you’re aware) you’ll see that we’re made up of more space than matter. All those molecules and atoms can be thought of as an aggregate of objects that make up the whole. I admit it’s not a perfect analogy, just an illustration of my point that everything in the universe came from a singular starting point.

It is true that the first cell was a cause of your existence—a material cause—back when you were conceived. But that cell exists no longer, so it cannot be a cause of your existence now. (Right now there are a whole bunch of other cells that are causing your existence, but not that zygote.)

That’s true, the originating cell of my body no longer exists. But the singularity that caused the universe no longer exists either and is not now the cause of the universe. Only when it happened at a fixed point in the past. (Call it the Big Bang if you like, although I understand the concept of a “bang” is not considered entirely accurate.)

 

[lmelahn]

No, I don’t think we’re “one with the universe” I was just using the body as an analogy. If you look closely enough (as I’m sure you’re aware) you’ll see that we’re made up of more space than matter. All those molecules and atoms can be thought of as an aggregate of objects that make up the whole. I admit it’s not a perfect analogy, just an illustration of my point that everything in the universe came from a singular starting point.

That’s true, the originating cell of my body no longer exists. But the singularity that caused the universe no longer exists either and is not now the cause of the universe. Only when it happened at a fixed point in the past. (Call it the Big Bang if you like, although I understand the concept of a “bang” is not considered entirely accurate.)

Well, scientists might have trouble with the statement that the universe began at a “fixed” moment in time. (If it is truly a singularity, then presumably there was no time “at” the singularity itself.) But that is a secondary issue.

The important thing is this: on the philosophical level, the Big Bang is not the cause of the universe any longer. We cannot, therefore, appeal to it as strictly necessary for the universe’s present existence.

Hence, it cannot be a vehicle for proving the existence of God. Instead, we need to look at those causes that are strictly necessary for our existence, here and now.

 

[hasantas]

I am afraid that the Kalam Argument has a fatal flaw. Here is now the argument is usually presented (for the benefit of readers):

1. 
   *]Everything that begins to exist has a cause;
   *]The universe began to exist;
   *]The universe has a cause.
   
   That is sufficient, because the flaw is in this syllogism. Actually, there are several flaws, but the most serious one is the minor (second) premise.
   
   …
   
   Therefore, arguing whether the universe is infinitely old or not is a rather fruitless endeavor, in my opinion, at least as regards the existence of God.

1. 
   Every evidence give opinion to grasp existence of God. There is not a proof which could force and impose all people to believe in God. Many people saw miracles from prophets but they did not believe. So anybody may think different on argument of Kalam.
   
   For instance you regard existence of God and you say God could do in that way! That is a probability which based on non evidence. And other may think countless and infinite Big Bangs or such thing like which is possible as conception but those are not based on any evidence. But that is a fact that everything need a cause to begin. And the age of universe is finite. So a cause must start universe. And that cause must be infinite otherwise an other cause would be need.
   
   If you think an infinite universe is possible in any way that help materialism because they recognise matter and universe as infinite in anyway.

 

[seagal]

Well, scientists might have trouble with the statement that the universe began at a “fixed” moment in time. (If it is truly a singularity, then presumably there was no time “at” the singularity itself.) But that is a secondary issue.

I didn’t say “in time”. But there was a fixed point at which everything, matter and time, began.

The important thing is this: on the philosophical level, the Big Bang is not the cause of the universe any longer. We cannot, therefore, appeal to it as strictly necessary for the universe’s present existence.

Hence, it cannot be a vehicle for proving the existence of God. Instead, we need to look at those causes that are strictly necessary for our existence, here and now.

I don’t think the Kalam is trying to prove anything more than the beginning cause of the universe. The first premise states “everything that begins to exist must have a cause”. It doesn’t include the phrase “and continues to exist”. But, to borrow a phrase from W. L. Craig, “it would be a strange God indeed” that could bring the universe into being but was incapable of keeping it going.

 

[hasantas]

I don’t think the Kalam is trying to prove anything more than the beginning cause of the universe. The first premise states “everything that begins to exist must have a cause”. It doesn’t include the phrase “and continues to exist”. But, to borrow a phrase from W. L. Craig, “it would be a strange God indeed” that could bring the universe into being but was incapable of keeping it going.

Yes you are right. That argument of Kalam is to prove existence of God at point of beginning. But that argument can be improved.

 

[lmelahn]

Every evidence give opinion to grasp existence of God. There is not a proof which could force and impose all people to believe in God. Many people saw miracles from prophets but they did not believe. So anybody may think different on argument of Kalam.

For instance you regard existence of God and you say God could do in that way! That is a probability which based on non evidence. And other may think countless and infinite Big Bangs or such thing like which is possible as conception but those are not based on any evidence. But that is a fact that everything need a cause to begin. And the age of universe is finite. So a cause must start universe. And that cause must be infinite otherwise an other cause would be need.

If you think an infinite universe is possible in any way that help materialism because they recognise matter and universe as infinite in anyway.

The reason that we cannot force someone to believe in God is that it is not perfectly obvious to us that God exists—not in the same way that it is perfectly obvious to me that the pine tree outside my window exists.

Instead, knowing that God exists requires a very difficult and rigorous demonstration (if we wish to use reason alone) or else the help of faith.

Such a demonstration is possible, but the Kalam argument, which is one of the more popular theodicies nowadays, has a fatal flaw. (And in fact, if you check the Internet, atheists have a field day with that flaw.)

In order to fix that flaw, we need to consider, not the remote temporal origins of the physical universe (which are neither here nor there), but the causes that permit the universe (or better said, the things in the universe, including ourselves) to exist now.

(For what it is worth, an “infinitely old” universe would be no help to materialism, because God would actually be showing His omnipotence by creating an infinitude of creatures. Remember that to God, all His creatures are present, because He is outside of time.)

 

[lmelahn]

I didn’t say “in time”. But there was a fixed point at which everything, matter and time, began.

I don’t think the Kalam is trying to prove anything more than the beginning cause of the universe. The first premise states “everything that begins to exist must have a cause”. It doesn’t include the phrase “and continues to exist”. But, to borrow a phrase from W. L. Craig, “it would be a strange God indeed” that could bring the universe into being but was incapable of keeping it going.

The problem is that they seem to think that the temporal beginning of the universe is necessary for their proof of the existence of the Creator. That is probably because they have accepted the idea (which comes from René Descartes and especially David Hume) that “cause” means “succession in time.”

In reality, a temporal beginning is not necessary. Instead, and much more reliably, we can look at the causes that are in operation here and now and discover that there must be a unique First and Uncaused Cause.