Did the Universe Begin to Exist?

by Luke Muehlhauser on June 16, 2009 in Kalam Argument

Part 4 of my Mapping the Kalam series.

bigbangLast time, I outlined the premises of the Kalam Cosmological Argument (KCA). Now I’m going to summarize Craig & Sinclair’s defense of premise 2:

The universe began to exist.

Their first argument in favor of premise 2 is given as a syllogism in sub-premises:

2.11. An actual infinite cannot exist.

2.12. An infinite temporal regress of events is an actual infinite.

2.13. Therefore, an infinite temporal regress of events cannot exist.

Basically, they’re saying that the universe can’t be infinitely old, so therefore it must have begun to exist a finite period of time ago.

Later, Craig & Sinclair present the scientific evidence that the universe began to exist 13.7 billion years ago in an explosion known as the Big Bang. But first, they present their philosophical argument against the possibility of an infinitely old universe.

This is going to get heady, but their main point is intuitive: If the universe was infinitely old, how could we have ever reached the present moment?

Actual vs. potential infinite

Craig & Sinclair argue that an actual infinite can’t exist:

The only legitimate sense in which one can speak of the infinite is in terms of potentiality: something may be infinitely divisible or susceptible to infinite addition, but this type of infinity is potential only and can never be fully actualized.

For example, the number of positive integers is potentially infinite, but you could never actually achieve infinity because you can always add one more.

Of course, the actual infinites “exist” in mathematical theory. They are given symbols like \infty and א 0. But Craig & Sinclair aren’t arguing that the actual infinite has no “mathematical existence.” They are arguing that the actual infinite is not “instantiated in the mind-independent world.” That is, the actual infinite doesn’t exist as anything more than a concept. Many mathematicians, like David Hilbert, have thought that the actual infinite has mathematical existence (mathematical legitimacy), but is not instantiated anywhere in the world. Hilbert wrote:

The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought…  The role that remains for the infi  nite to play is solely that of an idea.1

The point is that the actual infinite does not exist in the same sense as “Fish exist in the sea.”

So even if “transfinite” mathematics is logically consistent, that doesn’t mean the actual infinite exists anywhere in the world. So Craig & Sinclair do not argue that the actual infinite is logically impossible, but rather that it is metaphysically impossible: the actual infinite can’t exist in the real world. But this means the authors must use modal logic, not simple Aristotelean logic, to show that the actual infinite is metaphysically impossible. Craig & Sinclair explain the problem this raises:

Arguments for metaphysical possibility or impossibility typically rely upon intuitions and conceivability arguments, which are obviously much less certain guides than strict logical consistency or inconsistency. The poorly defined nature of metaphysical modality cuts both ways dialectically: on the one hand, arguments for the metaphysical impossibility of some state of affairs will be much more subjective than arguments concerning strict logical impossibility; on the other hand, such arguments cannot be refuted by facile observations to the effect that such states of affairs have not been demonstrated to be strictly logically inconsistent.

Premise 2.11

So, can an actual infinite exist in the real world?

Some say that the work of Georg Cantor proved that the actual infinite could exist, but many disagree with Cantor. Not only do some hold that the actual infinite lacks even mathematical existence, but of course many think that mathematical objects do not “exist” in the way that fish exist in the sea. There are many ways that mathematicians and philosophers think about the existence of abstract objects like numbers:

(page 107)

(page 107)

The point is that a Platonic Realist might say that there is an actually infinite number of mathematical objects, and because mathematical objects really exist, this disproves premise 2.11. But to do this, the Realist is going to have to rebut the arguments for Anti-Realism coming from Conventionalists, Deductivists, Fictionalists, Structuralists, Constructibilists, and Figuralists.

Craig writes elsewhere2 of one philosopher (Sobel) who embraces Platonic Realism in order to defeat the KCA:

It is ironic that Sobel should be so painstaking and and cautious when evaluating theism, yet so cavalier and uncritical when it comes to embracing the sweeping metaphysical commitments of Platonism.

(This is one of those moments where I pumped my first in the air for Craig. I might add: “It is ironic that atheist philosophers should be so painstaking and cautious when evaluating theism, yet so cavalier and uncritical when it comes to embracing the sweeping metaphysical commitments of certain theories of moral realism.”)

Craig & Sinclair leave the Realist with this rather difficult task of rebutting metaphysical anti-realists, and move on to support premise 2.11 “by way of thought experiments that illustrate the various absurdities that would result if an actual infinite were to be instantiated in the real world.”

In the next post, we will consider the first such thought experiment: Hilbert’s Hotel.

  1. On the infinite, 1964. []
  2. J Howard Sobel on the Kalam Cosmological Argument []

Previous post:

Next post:

{ 66 comments… read them below or add one }

Ben June 16, 2009 at 10:07 pm

Luke,
Do you know of any other example where we know of something that is mathematically consistent and yet impossible metaphysically?  In other words, is there some confirmed example of this?
Ben
 

  (Quote)

Taranu June 16, 2009 at 10:18 pm

This is fantastic stuff. Of all the arguments you talked about thus far the KCA is definitely my favorite. Please don’t stop.
 

  (Quote)

Derek June 16, 2009 at 11:34 pm

“The point is that a Platonic Realist might say that there is an actually infinite number of mathematical objects, and because mathematical objects really exist, this disproves premise 2.11. But to do this, the Realist is going to have to rebut the arguments for Anti-Realism coming from Conventionalists, Deductivists, Fictionalists, Structuralists, Constructibilists, and Figuralists.”
Even if one is a “Platonist” about abstracta such as sets with infinite cardinalities, you can consistently hold hat nothing extended (either temporally or spatially) can be (actually) infinitely expanded or divided.  The non-ad hoc reason for this is that actual infinite paradoxes (e.g. Hilbert’s and Zeno’s) only get off the ground when applied to extended things (hotels and racetracks).  On this view, actual infinites do exist, qua non-extended abstracta, but any extended  non-abstracta, such as the material universe, are only “potentially” infinite. 
Cf. J.P. Moreland’s ”A Response to a Platonistic and Set-theoretic Objection to the Kalam Cosmological Argument,” Religious Studies 39 (2004): 373-390.

  (Quote)

Steven Carr June 16, 2009 at 11:56 pm

How could there have been ‘years’ before there was a sun for the earth to orbit in 1 year?
 
Congratulations on getting the entire universe and its history in one picture. I know JPEGs use very efficient compression techniques but I had no idea technology had advanced so far.
 
Does this alleged god know the answer to such sums as 4571291928192819281928192819289 + 1? And does he know the answer to similar arithmetic sums for numbers which don’t actually exist in our universe, (as our universe contains only a finite number of numbers)?
 
CRAIG
‘….such arguments cannot be refuted by facile observations to the effect that such states of affairs have not been demonstrated to be strictly logically inconsistent.’
 
Has Craig told Plantinga that his defenses to the Logical Problem of Evil are ‘facile observations to the effect that such states of affairs have not been demonstrated to be strictly logically inconsistent’?
 
There is also nothing inconsistent about Hilbert’s Hotel, especially in Craig’s use of it.
 

  (Quote)

Reginald Selkirk June 17, 2009 at 5:54 am

1.1 An actual infinite cannot exist.
1.2 Onmiscience is an actual infinite.
1.3 Therefore, omniscience cannot exist.
 
2.1 An actual infinite cannot exist.
2.2 Omnipotence is an actual infinite.
2.3 Therefore omnipotence cannot exist.
 
3.1 An actual infinite cannot exist.
3.2 Omnibenevolence is an actual infinite.
3.3 Therefore omnibenevolence cannot exist.
QEFD
 

  (Quote)

Reginald Selkirk June 17, 2009 at 5:56 am

This is going to get heady, but their main point is intuitive: If the universe was infinitely old, how could we have ever reached the present moment?

If the past were infinite in time, we couldn’t have reached the present moment, because that would take, like, forever!

  (Quote)

Dave June 17, 2009 at 5:59 am

Not that I’m taking Sobel’s side on this, because I also reject Platonic Realism, but I think that the guy who wrote the first chapter of “Reasonable Faith” has no right to call ANY epistemological process “cavalier and uncritical,” unless he’s doing stand-up.

On an unrelated topic, I finished an initial reading on the Blackwell chapter on religious experience. I thought it was pretty solid, considering it was pretty solid, considering that Kwan was only aiming for the weak conclusion of subjective prima facie justification, and while I’ve spotted a couple of flaws I would not consider them fatal ones. Why do you feel it was the weakest chapter in the volume?

  (Quote)

Reginald Selkirk June 17, 2009 at 6:01 am

Later, Craig & Sinclair present the scientific evidence that the universe began to exist 13.7 years ago in an explosion known as the Big Bang.

Scientific evidence says that the Big Bang happened ~ 13.7 billion years ago, and it is commonly regarded as the beginning of space-time – as we know it. And yet is very easy to find speculative theories from respectable cosmologists on what might have preceded the Big Bang.
Glimpse Before Big Bang Possible

“It’s no longer completely crazy to ask what happened before the Big Bang,” Kamionkowski said. “All of that stuff is hidden by a veil, observationally. If our model holds up, we may have a chance to see beyond this veil.”

  (Quote)

lukeprog June 17, 2009 at 6:30 am

Ben,

That’s a tough question. I’m not very well-studied in metaphysics. Perhaps cartesian knows?

  (Quote)

lukeprog June 17, 2009 at 6:31 am

Derek,

Cool. I will eventually get to Moreland’s article and add it to the argument map.

  (Quote)

lukeprog June 17, 2009 at 6:36 am

Dave,

I think it’s the weakest argument because it essentially argues for nothing at all, and does not even respond to the most obvious objection: mutually contradictory religious experiences.

  (Quote)

lukeprog June 17, 2009 at 6:40 am

Reginald,

Notice that this Kalam argument does not conclude that God is omniscient, omnipotent, or omnibenevolent. But great point, because I think Craig affirms these elsewhere, and I’m not sure how he would refute step 2 in each of your arguments.

  (Quote)

Ben June 17, 2009 at 7:01 am

Luke,
My tentative conclusion is that if something is mathematically possible, then there’s no reason to suppose it is not physically possible.  Infinity would be the only exception if it was one.
Have you considered that apologists like WLC who believe in immortality and God’s omniscience have to believe in actual infinities?  Even if God’s omniscience is non-physical (whatever that means), it has to be a witness to every moment of a <i>physical</i> everlasting life.  If immortality is portrayed as just a “potential infinite” then there are future moments that God would not know about.  WLC is totally stuck.  He can’t even say the resurrection is nonphysical because that contradicts the doctrine of Christ’s physical resurrection.  Just as God knows creation from beginning to end, he would know immortality from beginning to no end and that makes the latter an inescapable <i>actual infinite</i> in their view.  They would have to compromise at least one of three fundamental items to their view (immortality, God’s omniscience, or a physical resurrection) or give up on a disproof of an actual infinite in terms of naturalistic alternatives.  Of course this doesn’t prove that an actual infinite is possible, but it does show they can’t maintain their position against naturalism.
Ben

  (Quote)

Taranu June 17, 2009 at 7:28 am

Isn’t god Himself  supposed to be an actual infinite?
I mean can’t you say:
1 An actual infinite cannot exist.
2 God is an actual infinite.
3 Therefore, God cannot exist.

  (Quote)

Lorkas June 17, 2009 at 7:51 am

Ben: In other words, is there some confirmed example of this?

I would propose imaginary numbers as a good candidate.

Reginald Selkirk: QEFD

LMFAO

  (Quote)

mitch June 17, 2009 at 8:05 am

keep it up luke. i check your site daily and am in awe of your dedication and pursuit of knowledge and understanding – neither of which is ever easily. thankyou so much :) really.

  (Quote)

Rups900 June 17, 2009 at 8:08 am

Perhaps not a major issue, but as Craig and Sinclair are aiming to refute a beginningless past, is not,

“2.12. An infinite temporal regress of events is an actual infinite”,

technically irrelevant, as a beginningless past would have ordinal:
{…,-3,-2,-1,0},
whereas an infinite temporal regress has ordinal:
{0,-1,-2,-3,…}

Thus 2.12 should be “A beginningless series of temporal events is an actual infinite.”

  (Quote)

Jeff H June 17, 2009 at 8:12 am

Later, Craig & Sinclair present the scientific evidence that the universe began to exist 13.7 years ago in an explosion known as the Big Bang.

Wow! 13.7 years ago, eh? That means that I existed before the universe did. That means I’m God! Sweet. I’m gonna go make a list of people I’m going to send to hell….
Haha seriously, though, good job summarizing the argument. It’s a fairly complex one for sure. I’ve been told that set theory fairly easily deals with this problem of infinites, although I’m no mathematician. (I vaguely understand the idea behind it, but have no way to say it’s better or worse than any other theory.) Perhaps this is something you’ll need to cover when examining the criticisms/counter-arguments of the KCA.

  (Quote)

Reginald Selkirk June 17, 2009 at 8:15 am

Would this argument also be applied to a circular time cycle?
 

  (Quote)

Chuck June 17, 2009 at 10:02 am

Jeff H: Wow! 13.7 years ago, eh? That means that I existed before the universe did.

Ha!

  (Quote)

Derrida June 17, 2009 at 10:07 am

Is temporally finite synonymous with beginning to exist? As the argument for premise two has been laid out, it seems that Craig and Sinclair are assuming the premise:
2.14 A finite temporal regress of events has a beginning.
Doesn’t this need to be positively argued for?

  (Quote)

William June 17, 2009 at 10:22 am

Steven Carr wrote, “Does this alleged god know the answer to such sums as 4571291928192819281928192819289 + 1? And does he know the answer to similar arithmetic sums for numbers which don’t actually exist in our universe, (as our universe contains only a finite number of numbers)?”

Hmmmm…carry the one…aha!4571291928192819281928192819290.

(@ Steve: I hope that I was helping you to balance your checkbook.)

Now the question becomes does this number really exist in our universe? Or do our thoughts not really exist? I will leave that question to those smarter than myself to ponder. I going to back up a couple of days and re-read Luke’s post about wasted efforts. There may have been something there that I missed.

Peace!

Oh! And just for the record, I am pretty sure that I can provide you with the answer to other “similar arithmetic sums.” But I am not making any claims to deity.

  (Quote)

CharlesP June 17, 2009 at 11:06 am

lukeprog, again thanks are due for your well written piece… when I’m not quibbling over biological possibilities (well actually even, or especially, then) I’m enjoying your site greatly.
and Reginald Selkirk needs thanking for his comedic stylings (“that would take, like, forever”) and good points regarding the Omni’s.
Thank you to you both.

  (Quote)

Reginald Selkirk June 17, 2009 at 11:47 am

CharlesP: and Reginald Selkirk needs thanking for his comedic stylings (”that would take, like, forever”)

While that was phrased as a joke, it is my most serious objection. Craig has not proven an infinite sequence of events to be impossible, he has merely invoked a circular cognitive bias against it.
 

  (Quote)

CharlesP June 17, 2009 at 12:00 pm

Oh yes, certainly not discounting the possible/probable truth contained a joke well made, but was simply making note of the well made joke aspect.

  (Quote)

Steven Carr June 17, 2009 at 12:20 pm

WILLIAM
Now the question becomes does this number really exist in our universe?
 
CARR
If that number does not exist, then what makes sums involving that number true?
And if there are numbers which do not exist, what effect would it have on space-time causality if I accidentally typed in the number 12123923819123108310381030139103991828528497374921041310 …. and typed a number which did not exist?
 
Spooky….
 
WILLIAM
And just for the record, I am pretty sure that I can provide you with the answer to other “similar arithmetic sums.” But I am not making any claims to deity.
CARR
But if I ask you enough of these arithemetic sums, you might end up knowing more facts about arithmetic than an ‘all-knowing God’ who either knows only a finite number of facts about arithmetic.
 
Unless this supposed god knows an infinite number of facts about numbers , which means this alleged deity knows arithmetic facts about non-existent numbers….
 
 
 
 

  (Quote)

Steven Carr June 17, 2009 at 12:30 pm

If immortality is portrayed as just a “potential infinite” then there are future moments that God would not know about


Luke,
My tentative conclusion is that if something is mathematically possible, then there’s no reason to suppose it is not physically possible.Infinity would be the only exception if it was one.
Have you considered that apologists like WLC who believe in immortality and God’s omniscience have to believe in actual infinities?Even if God’s omniscience is non-physical (whatever that means), it has to be a witness to every moment of a <i>physical</i> everlasting life.If immortality is portrayed as just a “potential infinite” then there are future moments that God would not know about.WLC is totally stuck.He can’t even say the resurrection is nonphysical because that contradicts the doctrine of Christ’s physical resurrection.Just as God knows creation from beginning to end, he would know immortality from beginning to no end and that makes the latter an inescapable <i>actual infinite</i> in their view.They would have to compromise at least one of three fundamental items to their view (immortality, God’s omniscience, or a physical resurrection) or give up on a disproof of an actual infinite in terms of naturalistic alternatives.Of course this doesn’t prove that an actual infinite is possible, but it does show they can’t maintain their position against naturalism.
Ben

  (Quote)

Steven Carr June 17, 2009 at 12:35 pm

BEN
If immortality is portrayed as just a “potential infinite” then there are future moments that God would not know about
 
CARR
God knows every detail of every event of this infinite future.
As an actual infinity is not possible, what is the longest film God could make depicting future events?

  (Quote)

Kevin June 17, 2009 at 12:39 pm

“This is going to get heady, but their main point is intuitive: If the universe was infinitely old, how could we have ever reached the present moment?”
Perhaps you’ll get to this later, but I’ve always found this question misguided.  It seems to assume that the present moment (if such a thing exists) is somehow privileged.  It seems to me, though, that even if the universe is infinitely old, it’s always now somewhen.  It’s almost as if an infinite length of time makes any present moments of time impossible.
I don’t think this defeats the overall argument of course, but might this way of phrasing the objection be misguided?

  (Quote)

Kevin June 17, 2009 at 12:44 pm

Luke and Reginald,
Craig has addressed Reginald’s various second premises (e.g., omnipotence is an actual infinite).  Craig’s claim is not that God’s power (knowledge, etc.) are infinite in the sense that it is incremental, as if God has n+1 power, and humans have some finite amount. Instead, infinite here is used to indicate that there is nothing that can be done that God can’t do.  Or better, God can do anything it is possible to do.  I suppose the range of things it is possible to do might be finite (though immense), and likewise with knowledge if omniscience means “knows all true propositions.”
Bottom line: Omni- doesn’t equal infinite.

  (Quote)

Steven Carr June 17, 2009 at 12:45 pm

‘For example, the number of positive integers is potentially infinite, but you could never actually achieve infinity because you can always add one more.’
 
Presumably the decimal expansion of pi stops at some point. It is not actually infinite, only potentially infinite.

  (Quote)

Dace June 17, 2009 at 2:40 pm

Whenever the present is, there you are. What’s to ‘reach’?
 
Arguments for metaphysical possibility or impossibility typically rely upon intuitions and conceivability arguments, which are obviously much less certain guides than strict logical consistency or inconsistency. The poorly defined nature of metaphysical modality cuts both ways dialectically: on the one hand, arguments for the metaphysical impossibility of some state of affairs will be much more subjective than arguments concerning strict logical impossibility; on the other hand, such arguments cannot be refuted by facile observations to the effect that such states of affairs have not been demonstrated to be strictly logically inconsistent.
This sounds like a good reason to shy away from arguments that rely on metaphysical impossibility altogether. But I wonder why Craig and Sinclair didn’t just opt to say that an actual infinite was physically impossible – wouldn’t that do the trick?

  (Quote)

Mitch June 17, 2009 at 3:20 pm

Just to clarify a few things:
1. An actual infinite is PHYSICALLY impossible, not metaphysically. Metaphysical time is unknown to finite minds.
2. Within Mathematics, there is no ACTUAL infinite. You can continue to divide a number in half, but you will never ACTUALLY cease from such activity; you never ACTUALLY reach the infinite, which by definition is unreachable. This is why an ‘actual infinite’ is intuitively impossible.
3. Omniscience includes God knowing all truth in any moment of his metaphysical existence.
4. Hilbert’s hotel is demonstrated to be actually impossible. In other words, the Hilbert hotel can not actually exist in a physical, finite world (like ours).
5. The KCA allows one to see beyond the veil of the Big Bang, since we know many attributes about the Effect. One point about the Big Bang, by definition, is that there must already exist some combustionable elements in order for the Bang to bang. The Big Bang is not about the origin of the universe, but the earliest identifiable physical event.
6. By definition, a number is finite in our actual world. Remember, there does NOT exist an actual infinite number of anything in the physical world. (Note that the terms infinite and number can not modify each other, by definition.) Hence, one could not type or write down a number that did not exist. This is why the actual infinite concept is ludicrous.
7. There is no actual number of facts, no actual infinite number of anything actually exists. Many responders here are repeating the same assumption.
I’ll pose an observation for others to reflect upon. The Trinity (God the Father, God the Son, and God the Holy Spirit; these are not three persons and yet one God, but these are three persons who exist in one Godhead; they are three separate beings) would have had conversations among each other antecedent to creation (even before angelic creation). Would the cumulative number of verbal exchanges be finite or infinite? Hint: we are dealing with metaphysical time.
Mitch
 

  (Quote)

lukeprog June 17, 2009 at 3:32 pm

Ben,

If something is mathematically possible, this is FAR from showing it is physically possible according to the hundreds of rules that govern our universe! I don’t know anyone who holds your position.

Re: omniscience and infinities, see Reginald’s quote on this post.

  (Quote)

lukeprog June 17, 2009 at 3:34 pm

Rups900,

Two ways of saying the same thing, far as I can tell.

  (Quote)

lukeprog June 17, 2009 at 3:35 pm

Reginald:

Regarding a circular time cycle, no. The argument only works if we assume an A theory of time.

  (Quote)

lukeprog June 17, 2009 at 3:38 pm

Derrida,

I don’t see why that needs to be argued for. “Had a beginning” is logically entailed by a finite temporal regress of events.

  (Quote)

lukeprog June 17, 2009 at 3:44 pm

Kevin,

I do not trust my intuitions about the infinite, so I can’t answer. Hopefully, your objection has been raised in the literature (by someone who understands these issues better than either of us), in which case this objection will surely be added to the argument map in due time. If it is not in the literature, I may still add it.

  (Quote)

Lorkas June 17, 2009 at 5:39 pm

Mitch: The Trinity (God the Father, God the Son, and God the Holy Spirit; these are not three persons and yet one God, but these are three persons who exist in one Godhead; they are three separate beings)

Whoa, Mitch! Most Christians don’t even buy that this is how the Trinity works, so what makes you think that any of the atheists here would buy it?
 
The model of the Trinity that I was always taught is Three Persons, One Essence (or Three Persons, One Being). This is totally different from your assertion that they are actually three different beings. In other words, standard Christian theology asserts that the Father, Son, and Holy Spirit are “three persons and yet one God”, contrary to what you suggest. Otherwise, you aren’t really a monotheist anymore–you would be a tritheist.
 
What sect do you belong to, which espouses tritheistic theology?

  (Quote)

Derek June 17, 2009 at 6:41 pm

Reginald Selkirk: 1.1 An actual infinite cannot exist. 1.2 Onmiscience is an actual infinite. 1.3 Therefore, omniscience cannot exist.   2.1 An actual infinite cannot exist. 2.2 Omnipotence is an actual infinite. 2.3 Therefore omnipotence cannot exist.   3.1 An actual infinite cannot exist. 3.2 Omnibenevolence is an actual infinite. 3.3 Therefore omnibenevolence cannot exist. QEFD  

lukeprog: Reginald,Notice that this Kalam argument does not conclude that God is omniscient, omnipotent, or omnibenevolent. But great point, because I think Craig affirms these elsewhere, and I’m not sure how he would refute step 2 in each of your arguments.

Taranu: Isn’t god Himself  supposed to be an actual infinite? I mean can’t you say: 1 An actual infinite cannot exist.2 God is an actual infinite.3 Therefore, God cannot exist.

I’m pretty sure that, in his God and Time, Craig argues (or maintains) that God’s attributes are “maximal” as opposed to “infinite”.  So if God is maximally omniscient, this means that God knows everything there is to know, and there’s no reason to think there’s an infinite amount of things to know. And the same goes for His omnipotence, omnibenevelonce, etc.  I think Craig notes that people  tend to prefer the adjective “infinite” as opposed “maximal” because the former sounds more impressive.  But, Craig insists, if there’s no reason to think there are actual infinites, then there’s no reason to qualify His attributes as “infinite”.  ”Unlimited”, I think, would be a more neutral way to quantify His attributes, because “unlimited” could be understood as maximal or infinite, but it communicates what most people think is communicated by saying “infinite” without the philosophical baggage. 
 
Just a side note, too.  Most of the Scholastics were adamant that God is infinite.  But for the most part, especially for Aquinas, when he calls God “infinite” he doesn’t have anything quantitative in mind, like an infinite set of whatever.  Rather, for those in the neo-platonic/aristotelian tradition, things are known by their “limit”.  For example, “man” is intelligible because we can distinguish it from “the earth”, that is, they have definite limits to their being, and these limits make them knowable to our discursive minds.  But God, since he is Ipsum Esse (existence itself) has no limit, He cannot be defined. So only in this sense did the Scholastics mean that God is infinite- he has no qualitatively limited essence- indeed no nature but existence per se. Hence the need to use analogical language in predicating qualities to God. 

  (Quote)

Derek June 17, 2009 at 6:53 pm

Another way putting my last comment:  when something is knowable, we say it has “de-finite” conditions for its being: it is knowable because it has qualitative limits.  But the negation of “definite” (de-finite) is “in-finite”: that which has no qualitative restrictions on what it is– viz. that which has no limit (in a qualitative sense). 

  (Quote)

Dace June 17, 2009 at 9:08 pm

Definitely, God does not exist. Enlightening stuff, Derek. :)

  (Quote)

Sledge June 17, 2009 at 10:14 pm

If time turns out to be a type of space as Einstein seemed to hold, and is actually circular, then everyone is going to feel real silly.  In this way, our universe can be finite but unbounded temporally just as it is spatially, ever cycling through creation and destruction and never having a proper “beginning” that could ever be discerned.
I agree heartily with the metaphysical proof against infinity, though.  Good Stuff.

  (Quote)

Derek June 17, 2009 at 10:38 pm

Dace: Definitely, God does not exist. Enlightening stuff, Derek.

Right. Nice equivocation. 

  (Quote)

Derrida June 18, 2009 at 1:04 am

Luke,
I agree that, if a temporal series of events is finite, then has a beginning in the sense that it has a first event, but does having a beginning imply “begins to exist”?
My worry was that, if something like the “B theory” of time is correct, then the universe is temporally finite, but doesn’t begin to exist. However, looking at your reply to Reginald above, you acknowledge that the argument assumes an A theory.

  (Quote)

William June 18, 2009 at 5:17 am

Steven Carr said:”But if I ask you enough of these arithemetic sums, you might end up knowing more facts about arithmetic than an ‘all-knowing God’ who either knows only a finite number of facts about arithmetic.”

Did you finish this statement? ‘Cause it seems to be just hanging there.

  (Quote)

Reginald Selkirk June 18, 2009 at 6:26 am

Derek: So if God is maximally omniscient, this means that God knows everything there is to know, and there’s no reason to think there’s an infinite amount of things to know. And the same goes for His omnipotence, omnibenevelonce, etc

God would know all the positive integers, which is an infinity. God knows all the real numbers, which is another infinity, etc.
 

  (Quote)

Reginald Selkirk June 18, 2009 at 6:28 am

Sledge: If time turns out to be a type of space as Einstein seemed to hold, and is actually circular, then everyone is going to feel real silly.

Except perhaps the Hindus.
 

  (Quote)

Lorkas June 18, 2009 at 7:11 am

Derek: I’m pretty sure that, in his God and Time, Craig argues (or maintains) that God’s attributes are “maximal” as opposed to “infinite”.

Convenient that you choose these examples, but don’t forget that God is also asserted as existing into the infinite past and the infinite future. Is eternity an actual infinite? If so, then God can’t possess this attribute.
 
Is it possible to give up his eternal nature? If you do say that God didn’t exist into the infinite past, then God must have begun to exist. See how this argument shoots the Kalam in the foot? If God began to exist, then he must have had a cause, according to Craig’s argument.
 
Besides, I’m not so sure that there is an obvious maximum to power. You could test his power by saying “Can God lift a 50kg rock?” (this has obvious problems, but let’s assume constant, Earth-strength gravity for this thought experiment). If yes, then “Can God lift a 50+1kg rock?” “…50+1+1…?” There is not even a theoretical maximum for weights that God could lift (unless he’s limited to lifting weights in this universe, that is).
 
For another example, you could “Can God create a 50kg rock?” and go on increasing the number as in the first. We could do both experiments at once, and try to give an objective answer to the question, “Can God create a rock so heavy he can’t lift it?”

  (Quote)

Pete June 18, 2009 at 12:46 pm

Hey Luke,
 
some quick points:
“For example, the number of positive integers is potentially infinite, but you could never actually achieve infinity because you can always add one more.”
This seems false to me.
It is an arithmetical truth that there are infinitely many positive integers.  If mathematical realism is true, this commits us to the existence of an actual infinity of numbers; if anti-realism holds, it does not commit us to anything (or might not even be true, strictly speaking).  But we can’t speak of a potential infinity here.
“a Platonic Realist might say that there is an actually infinite number of mathematical objects, and because mathematical objects really exist, this disproves premise 2.11. But to do this, the Realist is going to have to rebut the arguments for Anti-Realism coming from Conventionalists, Deductivists, Fictionalists, Structuralists, Constructibilists, and Figuralists.”
I’m no Platonist myself, but I don’t quite see why the burden of proof should be on the Platonist here. You might as well say: “KLC can only succeed when there are no numbers. So Craig has to show that some version of anti-realism is correct (and for this reason, he has to refute all the arguments leveled by realists against anti-realism); otherwise, his argument is not successful.”
By the way: It seems to me that Craig is in a particularly bad position to argue against Platonism, because the strongest reasons for rejecting Platonism are (a) broadly naturalistic reasons (which Craig plainly cannot cite) and (b) reasons having to do with the Platonist’s problem to explain our epistemic access to the mathematical realm (which Craig could easily ‘solve’ by saying “God made our immaterial soul in such a way that it is able to connect with the realm of mathematical facts”).
One final quibble:
““Had a beginning” is logically entailed by a finite temporal regress of events.”
Not quite. If we suppose that a time interval has infinitely many moments (what seems plausible to me, but what Craig will never grant, of course), we could have the following time interval: (0, 1], i.e. the interval from 0 to 1 without the 0. this so-called “open interval” would be finite, yet it would have no beginning.

  (Quote)

Dace June 18, 2009 at 2:25 pm

Derek: Right. Nice equivocation.

No sense of humour? Oh well.
 
There’s something else in these arguments to think about: whilst we might not be comfortable with an infinite past, most people are happy with the idea of an infinite future, and tacitly assume it. Why does this not worry Craig and Co.? Well, because it is assumed that the past is real and the future is not (yet) real. But can this temporal chauvinism be justified?

  (Quote)

Mitch June 18, 2009 at 6:58 pm

Lorkas:
I had hoped to generate more substantial discussion than this question about the Trinity. There really does need to be a scholarly atheistic blog and discussion for atheists and theists to discuss issues in a scholarly level.
Too many of the statements made by lukeprog and others do not represent even the weak forms of theism. You really need to have an evangelical theist who represents the theist position rather than an atheist. Lukeprog alone has made many false inferences after quoting from a theist. See my post above for the odd statements made by some atheists just in this post alone.
Anyway, regarding the Trinity. The Son was separated from the Father — for three hours — while on the Cross. In Trinitarian Theology this is not at all interesting. It was to be expected. The Father and the Son are NOT the same being; there are 3 persons/beings within the one Godhead. To say there are three Gods because there are three Members within the Godhead is childish thinking.
Remember in the OT Israel’s Shema verse (Deut 6.4)… Hear O Israel, The Lord our God, the Lord is one.
This is the critical verse on G_d to the Jews. It is a sacred passage.
The word ‘one’ is ‘echad’ in Hebrew. It is the same word used of Adam and Eve when we are informed that Adam and Eve shall become ‘one’ flesh. Adam and Eve did not become one person/being numerically; they were two people/beings, two separate beings. This is exactly the same for the Godhead. The Father and the Son are echad.
Jesus says the same in John 10; I and the Father are one. So, in Greek, this makes perfect sense, I (masc) and the Father (masc) are one (neut). This change of gender sticks out like a sore thumb in the Greek. Hence, Jesus says that He and the Father were one (not being), but some kind of unity (like Adam and Eve), but not one person (that would require the masc word for ‘one’).
Many of the older Trinitarian Theologians were very ambiguous on this subject. You are exactly right. But, the younger, newer Trinitarians are well trained on this “one” concept being a unit, a unity, or one thing, but not one person. This would be blasphemy.
Finally, I think you overlooked something I said. A ‘tri-theist’ sees the members of a Godhead existing at different levels with regard to their natures, like the gods that make up the pantheon (where Zeus is stronger in some areas, but not as strong in other areas; same with Apollo and the others). But within the Trinity, the Father loves you with an infinite, perfect love; the same is true of the Son. Their love for you is exactly identical. All the attributes of the three Members of the Trinity are exactly identical. Their knowledge is said to be omniscience. Hence, their knowledge is identical; each Member knows you with the same level of intimacy; the Son knows you to the same extent and degree that the Holy Spirit knows you. In all their attributes the three Members of the Godhead are equal in every respect, unlike Zeus and Apollo.
Just remember that nowhere in the Bible is God identified as “one” in the numerical or mathematical sense. One God means One Godhead. All Members have the same love, righteousness, omnipotence, etc. as the other Members. This is why ‘one’ God is not “numerically one.” So, in this sense, you would indeed be correct. The Father and the Son and the HS have the same nature, but they are separate beings.
Here’s one that will throw you for a loop. In the famous GJohn 1.1-3, many heretical groups translate it such that it reads “and the Word was a god.” This is obvious a foreign concept to the NT writers, but I actually translate this passage thus: “and the Word was a God.” The Father is a God, the Son is a God, and the HS is a God. If each Member of the Godhead had differing divine attributes, then you would call this tri-theism. But if the Members of the Godhead had exactly the same attributes in exactly the same proportion and degree, then you have Monotheism. And remember, Monotheism is not Unitarianism, which is partly what you were inadvertantly saying. Islam is Unitarianism; they believe in only one (numerical) God, Allah. Many other cults that deny the deity of Christ are actually Unitarians, not Monotheists. Just keep in mind that “unit”arian believes in one numerical God, whereas Monotheists believe in “one Godhead, and the number of Members in Trinitarian Theology is Three.” You could still have Monotheism and have 5o Gods, by definition.
Best of luck to you. I’m off to find a different level of discussion on these issues.
Mitch Larramore

  (Quote)

lukeprog June 18, 2009 at 7:12 pm

Pete, great comments.

  (Quote)

Lorkas June 18, 2009 at 8:06 pm

Mitch: Best of luck to you. I’m off to find a different level of discussion on these issues.

Heh. Good luck then.

  (Quote)

Lorkas June 18, 2009 at 9:07 pm

Mitch: the Father loves you with an infinite, perfect love

By the way, this falls directly into the trap that we’ve been discussing on this very thread.

  (Quote)

Taranu June 18, 2009 at 10:23 pm

Mitch: Just keep in mind that “unit”arian believes in one numerical God, whereas Monotheists believe in “one Godhead, and the number of Members in Trinitarian Theology is Three.” You could still have Monotheism and have 5o Gods, by definition.

According to who’s definition?

  (Quote)

William June 19, 2009 at 4:06 am

Dace,
“Most people” don’t think about these things. And I don’t think that Craig & Co. are making the argument that the universe has an infinite future. If they are then I believe that they are being inconsistent, because they stand upon current Theories of Relativity to argue that the past is finite. These theories also tell us that the future is finite because the universe will end in a cold “heat death.” If you could really call that an ending.

Lorkas,
Did you really ask the question, “Can God create a rock so heavy he can’t lift it?” You are just playing around. Right?

  (Quote)

Lorkas June 19, 2009 at 8:10 am

William: Lorkas, Did you really ask the question, “Can God create a rock so heavy he can’t lift it?” You are just playing around. Right?

I was joking when I said that part, but I’m serious about there not being an easy maximum to something like power. If you don’t think that’s the case, then what is the maximum weight for a rock God can lift?
 
If creation is a measure of power, then can God create 2 universes at once? 3? 4? What’s the limit?

  (Quote)

William June 19, 2009 at 8:53 am

Lorkas,

I think that you are right; there is no fast and easy “maximum” to something like power unless you can clearly define the system under consideration.

And I don’t know how “creation” can be a measure of power. I guess I am not smart enough to see the connection there.

  (Quote)

Lorkas June 19, 2009 at 10:36 am

William Lane Craig argues that we know that the being must be powerful, because he created the whole universe. Maybe it’s not a measure of power–I’m just trying to speak Theist here (which is, admittedly, Greek to me at times).

  (Quote)

William June 19, 2009 at 11:53 am

Lorkas,
Oh! If the Greek is tripping you up, you could try switching to ancient Hebrew or maybe a little Aramaic.

I am not really familiar with the details of Craig’s argument here, but if it is what you say it is, then the only claim that he could make is that the power of the creator exceeds that of the universe. This would be consistent with the notion that no effect is greater than its cause. But I am still not sure how defining a maximum for power relates to the discussion of the existence of God.

  (Quote)

Lorkas June 19, 2009 at 12:07 pm

William: But I am still not sure how defining a maximum for power relates to the discussion of the existence of God.

You’ll have to refer to the discussion that preceded my comment. One premise of Craig’s argument is “An actual infinite can’t exist”, and we were discussing whether or not omniscience, omnipotence, eternal-ness (er… someone can help me form a noun out of “eternal”, I’m sure), and omnibenevolence are “actual infinites”. If so, then that premise shoots Craig’s argument in the foot, since he’s trying to argue for the existence of an actual infinite to avoid an infinite regress of causes.
 
So, Craig would either have to throw out that premise, or give up the “infinite” aspects of God for his argument to be consistent. It was argued that the aspects of God are “maximal”, rather than “infinite”–that things like power, knowledge, and goodness have a natural maximum. I was arguing that this is a poor way to resolve the contradiction, because there isn’t, in fact, a natural maximum to power in the comment that of mine that you first replied to. That brings us up to now.
 
So defining a maximum for God’s power doesn’t address the question of whether or not God exists, it addresses the question of whether or not the Kalam is a good argument for God’s existence. Those are two different questions.

  (Quote)

Dace June 19, 2009 at 8:13 pm

William,
I realize that Craig and Co. are not claiming anything about the future. What I meant to put across is that though the idea of a finite past is intuitively correct, and so this lends credibility to the impossibility of an actual infinite, the idea of a infinite future is just as intuitvely plausible (at least, it seems as though things could go on forever).  The reason why Craig and Co. wouldn’t see this as a problem is that they, like most people, see the past as real and the future as not yet real.
My claim is that no such asymmetrical treatment of the past and future can be justified – either we should say that the past and future and both real, or we should say that neither are real. If neither are real, then no actual infinite exists even if there have been an infinity of moments before this one. If both are real, then Craig and Co. are committed to arguing that the future is finite. You mention the ‘heat death’ as a solution to this, but although this is mentioned as ‘the end of time’, it is unclear whether this phrase refers to an end state which lasts for perpetuity, or whether it is to be taken literally.  I’m going to try to find this out, but in the meanwhile, I found at least one page which unequivocally states that:

The heat death of the universe will only occur if the universe will last for an infinite amount of time (i.e there will be no big crunch).

  (Quote)

jim June 26, 2009 at 8:32 pm

I’ve sort of tried to approach the argument backwards, placing the burden of proof on those who claim that there can’t be an actually infinite timeline. Imagine yourself walking into the past, with each step representing a ‘moment’ in time. My question is this- describe to me the qualities of the ‘deviant’ moment, that spot on the timeline where a step becomes not-a-step. In other words, how does one describe a moment unlike any other moment, where the rules suddenly change, or cease to be? When does it happen? When CAN it happen? The way I see it, ‘moments’ are necessarily generic, and the same argument used to end time x amount of years in the past must necessarily apply to ANY moment, even the one that passed 1 second ago.
I wrote a little more about the idea <a href=”http://reasonvsapologetics.blogspot.com/2009/01/will-finite-kalam-crack-under-infinite.html”>here.</a> I know Craig leans heavily on the ‘anti-intuitiveness’ of infinities, but personally I find the opposite POV a lot harder to swallow.
 
 

  (Quote)

James June 30, 2009 at 4:00 pm

With regard to this comment and question:

“Later, Craig & Sinclair present the scientific evidence that the universe began to exist 13.7 billion years ago in an explosion known as the Big Bang.”

“Would this argument also be applied to a circular time cycle?”

The Blackwell article does not attempt to prove that the standard hot Big Bang theory is true. Rather, it surveys the current state of the field (including pre-Big Bang models) and attempts to categorize, in general, what the field seems to be saying about universe origins. I think a lot of people make the mistake of thinking that WLC is trapped in a 1979 defense of General Relativity and the Big Bang.

With regard to “time machine” theories, the Blackwell piece does discuss and critique one of the more prominent candidates: the Gott-Li universe. Luke is correct that this type of model is not compatible with the theory of time that underlies Kalam.

  (Quote)

Daniel July 14, 2009 at 11:36 pm

Isn’t the assertion “if the universe was infinitely old, how could we have ever reached the present moment?” the same as  the assertion used by creationists to prove that evolution can never have happened because living organisms are too complex to have evolved by chance?
We’re here because we’re here and if we weren’t we couldn’t talk about being here.

  (Quote)

Leave a Comment