The Kalam Cosmological Argument: punkforchrist vs. Dante Alighieri

[KnightWhoSaysNi]

This thread has been set up for a formal debate between punkforchrist and Dante Alighieri who will debate the following resolution:

"Resolved: the Kalam Cosmological Argument provides rationally compelling support for the belief in a personal Creator."

punkforchrist will affirm and Dante Alighieri will oppose. The debate will have four rounds and punkforchrist will go first, per the parameters (http://www.iidb.org/vbb/showpost.php?p=4850191&postcount=8).

A Peanut Gallery (http://www.iidb.org/vbb/showthread.php?p=4865382#post4865382) is set up in the Existence of God(s) forum for the rest of us to comment on the debate.

Enjoy the debate!

- KWSN, FD Moderator


Addendum (Oct. 21): punkforchrist and Dante Alighieri have agreed to increase the word limits for their debate. See the parameters thread for details. Consequently, I have agreed to copy and paste in a slightly different version of punkforchrist's opening statement which had been his original statement (it had been previously declined). Very little has changed other than a few hundred more words.

[punkforchrist]

First of all, I’m delighted to be able to participate in this important debate. I confess I feel a lot like David going up against Goliath. I just hope that history repeats itself! :) My thanks and appreciation go to Dante Alighieri for joining me, as well as KnightWhoSaysNi for moderating, and finally to everyone following this exchange on the IIDB.

Does God exist? Some prefer to put aside questions regarding rational bases to answer this question. Isn’t it all just a matter of faith? Well, I certainly think it is a matter of faith, but alongside other philosophical theists, I contend that faith can be rational. Among the most compelling arguments for the existence of God, in my opinion, is the kalam cosmological argument. We can formalize the argument the following way.

1. Whatever beings to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

As is the case in any debate, it is of the utmost importance to define our terms. What do we mean by “begins to exist” and “cause”? To begin with the former, by “begins to exist” all that is meant is the transference of potentiality to actuality. We all know what a chicken egg looks like. However, imagine that I hold the egg in the air and proclaim, “chicken!” Well, besides getting some puzzled expressions, I will surely be corrected and told that the egg is not in actuality a chicken, but is only a chicken in potentiality. The egg must go through a number of complex processes in order to be actualized as a chicken. In actuality, it is an egg; in potentiality, a chicken. In order for something potential to be actualized, it must have a cause.

What, then, do we mean by “cause”? As alluded to above, something is said to be a cause if it is the responsible factor for a given effect. There are a number of causes for the egg’s becoming a chicken. In sum, what we are referring to is an efficient cause: that which is responsible for something else.

But what is meant by “universe”? Some object to the kalam argument on the basis that since the universe is everything, nothing could exist outside of the universe to cause it. Well, I will concede this point so long as that is the working definition. However, by “universe” what is normally entailed is all space, time, mass, and energy. If one wishes to define the universe is such a way that nothing at all can exist outside of it, then that is fine, since all that I intend to argue is that the universe has a cause insofar as all space and matter (etc.) has a cause. The cause of these things would simply be part of the universe. (But I will simply be using the standard definition of “universe” as all space, matter, etc.) Now that we have defined our terms, let us finally turn to the argument.

Whatever begins to exist has a cause.

The first premise of the kalam argument is rooted in the metaphysical principle that out of nothing comes nothing. This truth is often taken as self-evident, but there are two reasons I will explicate in support of it. The first is metaphysical; the second, scientific.

Is it reasonable on metaphysical grounds to suppose that something could come from nothing? I do not believe it is. For how could being arise from non-being? By definition, all that non-being produces is nothing! I see no reason to continue elaborating on this, since it seems almost indubitably true. If something could arise from nothing, then that nothing is in reality something.

Secondly, this principle is constantly confirmed by observation. Rain falls from clouds, plants grow from seeds, and Democrats raise taxes. (Okay, the last one was a joke). In any case, the opponent of the first premise almost invariably thinks inconsistently with his other observational tendencies. Imagine that Dante and I are walking toward a coffee shop. However, to our surprise, we discover an elephant standing in the middle of the road. Dante asks me, “where did that elephant come from?” and I answer, “nowhere, it just popped into being out of nothing”. What would Dante’s response be? Well, he would rightfully shake his head and dismiss my comment as a ruse. Surely, he reasons, something has to be responsible for the elephant’s standing there in front of us. The truth is, I wholeheartedly agree with what his judgment would be. While everyone is reading this, no one is worried that a bear might pop into being out of nothing and proceed to go through his refrigerator! Such a thought would be irrational. The question, then, becomes: if this principle applies to things as great as elephants and bears, why would it not apply equally to the universe if it had begun to exist?

This leads us to our second premise.

The universe began to exist.

In support of this claim, I wish to offer two philosophical arguments, and then briefly mention the scientific confirmation that has surfaced in recent years. The first of these is the impossibility of an actually infinite set of things. The second is the impossibility of collecting an actual infinite by successive addition. The first argument goes like this.

1a. An actually infinite set cannot exist.
2a. A beginning-less universe is an actually infinite set.
3a. Therefore, a beginning-less universe cannot exist.

Once again, it is of great importance that we define our terms. What do we mean here by “actual infinite”? Well, the focus of the argument is not concerned with the legitimacy of infinite quantities being used in a purely mathematical realm. Instead, what the argument intends to demonstrate is the impossibility of such an infinite existing in the real world. As Stephan Korner points out, legitimate mathematical systems, like Euclidean geometry do not necessarily reflect the way things are in reality. In the case of Euclidean geometry, the axioms are actually irreconcilable with Einstein’s special theory of relativity. [1] But what about the concept of infinity? I maintain not that infinity cannot be used for purely mathematical purposes, but instead that infinites cannot be translated into the real world. So any mention of an “actual infinite” will apply only to the latter, unless otherwise mentioned.

The denial of an actual infinite is not something that is very astonishing among philosophers and mathematicians. Even mathematicians who accept the notion of an actual infinite in the mathematical realm do not assert that this means there are any actual infinites in reality. David Hilbert writes, “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 infinite is solely that of an idea”. [2] This is interesting, since Hilbert himself praises Cantor for his work on transfinite arithmetic in the same tract. He comments, “No one shall drive us out of the paradise which Cantor has created for us.” [3] The reason for this contrast is that while infinite sets may be fine in a mathematical realm, it does not imply that they have any real world possibility. Abraham Robinson echoes, “Cantor’s infinites are abstract and divorced from the physical world.” [4]

So why do we claim that there are no actual infinites in reality? I believe this is because actual infinites would result in highly counterintuitive absurdities. Imagine a farm with an infinite number of carrots. Once the time for harvesting arrives, the farmer uproots all of the carrots. Infinity - infinity = 0. Now, suppose the farmer instead digs up all the odd-numbered carrots; all of the even-numbered carrots remain in the ground. Infinity - infinity = infinity. Again, imagine the farmer digs up all the carrots numbered ten and higher. Infinity - infinity = 9. In the three equations above, we subtract identical quantities and end up with contradictory answers! As a result, subtraction and division are prohibited in transfinite arithmetic. However, in the real world, nothing would prevent the farmer from digging up any of the carrots. This suggests that infinite sets exist only in the mind as an idea, not as something that may exist in the physical world.

Given the above considerations, I believe we can come to a strong conclusion in favor of (1a). As for (2a), I think this is obviously true. If the universe is beginning-less, then that would mean that an infinite amount of time has passed. Since an infinite amount of time is an actual infinite, then an infinite amount of time, and hence an beginning-less universe, cannot exist. We now move on to the second philosophical argument.

What if, in spite of the resulting absurdities, an actual infinite could exist in reality? The second argument in favor of premise (2) accommodates such a position. For even if there could be an actual infinite, it could not be collected by successive addition. This is also known as the impossibility of traversing the infinite. The argument goes like this:

1b. An actually infinite set cannot be formed by successive addition.
2b. A beginning-less universe is an actually infinite set formed by successive addition.
3b. Therefore, a beginning-less universe cannot exist.

As before, (2b) seems undoubtedly true, so the key premise is (1b). Why can an actual infinite not be formed by successive addition? The answer really has to do with the very nature of infinity. As we add one element, it is always and indefinitely possible to add another. This means that no matter how large a number we collect, it will always be a finite number. For if we could ever arrive at infinity, then that would mean that we could no longer add anything to it in order to make the whole set any greater. However, this contradicts what was said before--namely, that we can add one more element indefinitely. If infinity has no end, then it is impossible to complete it.

Another analogy may be helpful. Let us suppose I ask Dante if I can borrow a book from him, say Karl Popper’s Objective Knowledge. He says I may, but first he has to borrow the book from a friend, and that friends has to borrow it from another friend, and so on out to infinity. The question is, who actually has the book? It would further seem that I would never get the book, since before I did there would always have to be another person that receives it from a previous person. [5] In essence, if the universe did not have a beginning, then it would be as if one were to count down from infinity and end in zero! But this is impossible, which means that an infinitely old universe cannot exist; otherwise, the present would have never arrived.

However, imagine that the present somehow could arrive in spite of an actually infinite past. This raises all sorts of paradoxes (perhaps more accurately considered as contradictions). Why, for instance, did the present not happen yesterday, or the day before that, or at any point in the finite past? At whichever point in the finite past we look at, an actually infinite amount of time would have already occurred. Again, this suggests that the universe really is not beginning-less, but had a definite starting point.

Therefore, the universe has a cause.

This concludes the two philosophical arguments in favor of premise (2). If both premises are true, and I believe a highly plausible case for their verisimilitude can be made, then the conclusion, “Therefore, the universe has a cause”, necessarily follows.

In the twentieth century, some extraordinary discoveries in scientific research have been made that confirm that the universe’s past is finite. In 1929, Edwin Hubble discovered that the recession of galaxies from our own Milky Way galaxy is proportional in velocity to their distances. This recession in the observed source has come to be known as a redshift. [6] This observation has had incredibly significant consequences for our understanding of the universe. What this means is that when we “rewind” the motion of the universe, so to speak, there comes a point in which all the space, time, matter, and energy of the universe is infinitesimally condensed into a single point called a “singularity”. In other words, if we go back far enough, there comes a point in which the universe had a beginning. The resulting explosion of all matter and energy from this singularity is known by scientists as the Big Bang. This is remarkable in light of the kalam cosmological argument, since if there is a Big Bang, there must be a Big Banger!

Now, a number of alternative hypotheses have been put forward in an attempt to undermine the standard Big Bang model, like the steady state and oscillating models, but no other theory has so accurately made predictions and been confirmed by subsequent observations as the Big Bang. Stephen Hawking comments, “Almost everyone now believes that the universe, and time itself, had a beginning at the Big Bang.” [7]

We have gone over the philosophical and the empirical arguments in favor of the kalam cosmological argument. However, what are some of the qualities that the cause of the universe has? Well, as the cause of time, this being must be timeless; as the cause of space and matter, it must be immaterial, changeless, infinite, and enormously powerful. Let us go through some of these characteristics.

The First Cause as pure actuality [8]

As the maker of all things in potentiality, things that change (i.e. of the universe), the cause of the universe must exist in such a way that it is fully actualized potentiality. This is to say that this cause is absolute and immutable. As the source of all potentiality, this being must be pure actuality.

The First Cause as one

Sometimes it is alleged that there may be more than one First Cause of the universe. However, if the First Cause is pure actuality, then there cannot be more than one. Consider it this way. If there were more than one First Cause, then there would be distinctions between them. However, distinctions among things entail limitations, and limitations entail potentiality. But there is no potentiality in the First Cause, so therefore, the First Cause must be one.

The First Cause as immutable

This observation is demonstrated similarly. Change implies potentiality, but in the First Cause there is no potentiality. Hence, the First Cause must be changeless, or immutable.

The First Cause as eternal

This conclusion likewise follows in light of the above considerations. For if time entails change and potentiality, then the First Cause must be eternal and timeless.

The First Cause as infinite

It is important that we not equivocate our use of the term “infinite” as it applies to the First Cause with what we mean by the impossibility of the universe’s being infinite. In the latter case, we are strictly dealing with the impossibility of an actually infinite set formed by definite and distinct finite members. [9] However, the First Cause’s infinite quality is simply an inference drawn from the fact that it possesses no spatial constraints (i.e. because it is the cause of space). So the very meaning of the word, “infinite”, means one thing with respect to the universe and another thing with respect to the First Cause.

With all of the above considerations, we may conclude that the First Cause of the universe is pure actuality, one, immutable, eternal, and infinite. However, I believe the kalam argument is not only a good case for a kind of Aristotelian impersonal cause of the universe, but that it also brings us to the universe’s personal creator.

Remember, we concluded that the First Cause must be pure actuality. Now, in potentiality there are personal and knowledgeable beings, like ourselves. What is remarkable, though, is that if a being with pure actuality is lacking nothing that is in potentiality, then that means that the First Cause of such potential beings must itself be personal and knowledgeable, because pure actuality is fully actualized potentiality. Many are you are probably familiar with the claim that intelligence cannot arise from non-intelligence. Well, I think with the above considerations being drawn, this is highly plausible. So the universe not only has a cause of its being, but it has a personal creator, which as Thomas Aquinas notes, is what we call God.

To end, I would just like to respond to some common criticisms of the kalam argument. There are two, in particular (besides the ones I have already mentioned), that are often raised.

Quantum physics

Some object to the first premise and claim that quantum fluctuations are an example of things that happen causelessly. I will make just two points about this. First, this conclusion can only be drawn based on the Copenhagen interpretation of quantum fluctuations. But there are about a dozen alternatives to this view. Secondly, even on the Copenhagen interpretation, it is not asserted that something can come from nothing. On this model, quantum fluctuations may be causeless in the sense that they are random, but they do not arise from nothing. [10] In any case, something is always responsible for what begins to exist (qua actuality). John Barrow and Frank Tipler comment, “the modern picture of the quantum vacuum differs radically from the classical and everyday meaning of a vacuum-- nothing. . . . The quantum vacuum . . . defined simply as local, or global, energy minima”. [11]

Fallacy of Composition

Atoms are small, and atoms are the fundamental building blocks of mountains. Therefore, mountains are small. Of course, this is not true. Could the universe as a whole be unlike its parts? Well, sometimes the whole is like its parts. A mountain is indeed caused by the formation of its atoms, and likewise, the universe is caused by the formation of its parts.

[I]References

[1] Korner, Stephan. The Philosophy of Mathematics: An Introductory Essay. Page 29. Dover Publications, Inc. 1968.

[2] Hilbert, David. “On the Infinite” in Philosophy of Mathematics. Edited with Introduction by Paul Benacerraf and Hilary Putnam. Page 151. Prentice-Hall. 1964.*

[3] Ibid., page 141.*

[4] Robinson, Abraham. “The Metaphysics of the Calculus” in The Philosophy of Mathematics. Edited by Jaakko Hintikka. Page 163. Oxford University Press. 1969.*

[5] Kreeft, Peter. “Arguments for God‘s Existence”. Texas A&M Veritas Forum. 1995. http://www.peterkreeft.com/audio/08_arguments-for-god.htm

[6] Craig, William Lane. The Kalam Cosmological Argument. Page 112. Wipf and Stock Publishers. 1979.

[7] Hawking, Stephen and Penrose, Roger. The Nature of Space and Time. Page 20. Princeton University Press. 1996.**

[8] Inspired by Kidd, James. “A Proof of the Existence of God” in This Rock. May-June 2006. http://www.catholic.com/thisrock/2006/0605uan.asp

[9] Craig, page 70.

[10] Craig, William Lane. “Cosmological Argument (Pt. 2)”. Reasonable Faith. 2007. http://www.reasonablefaith.org/site/PageServer?pagename=podcasting_main

[11] Barrow, John and Tipler, Frank. The Cosmological Anthropic Principle. Oxford: Clarendon Press.***

* Drawn from Craig, William Lane. The Kalam Cosmological Argument . . . 1979.

**Drawn from Craig. “The Question of Origins: God and the Beginning of the Universe”. http://www.leaderu.com/offices/billcraig/docs/ultimatequestion.html. 2002.

***Drawn from Craig. “The Caused Beginning of the Universe: A Response to Quentin Smith”. British Journal for the Philosophy of Science 44. Page 623-639. http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=5171

[KnightWhoSaysNi]

Dante, please note that your statement is overdue. However, you're granted a 3-day grace period to submit it.

KWSN, FD Moderator

[Dante Alighieri]

Introduction

Hello everyone! I’d like to thank the IIDB moderators and staff for making this debate possible. I’d like to thank punkforchrist for engaging in this discussion with me. I wish him the best of fortune. I shall discuss causation, infinities, and the nature of the first cause with respect to the Kalam Cosmological Argument. I shall leave various other topics (such as cosmology) for my succeeding posts.

Causation

The causal premise is whatever begins to exist is caused. What does this mean? Perhaps1

(1) x begins to exist at t iff for times prior to t, x doesn't exist.

Craig holds the universe to begin at time's beginning; there weren't prior times when the universe didn't exist: the universe didn't begin to exist. Craig replies2 [It] seems very strange that x's beginning to exist at t entails the existence of temporal instants prior to t... The fact that x begins to exist ought to leave the question of existents prior to x altogether open.
Craig posits

(2) x begins to exist at t iff there aren't times prior to t at which x exists.

(2) entails the universe's beginning. Craig believes that God created the universe and put Himself in time: God begins to exist.3 Craig replies4 [Our] intuitive understanding of "begins to exist" is violated if we must say that a being which never fails to exist begins to exist.
He offers

(3) x begins to exist at t iff there aren't times prior to t at which x exists and no actual states of affairs involving x's timeless existence.

The universe begins to exist, but God doesn't.

Craig equivocates. Something beginning to exist doesn't merely entail an earliest time of existence but its coming into existence: times when it didn't exist. There was an earliest time in the universe's existece, but it didn't come into existence: there weren't times prior to its existence.

(2) becomes more problematic given an analysis of time. Time is the sequence of SOAs ordered by the relations prior to, simultaneous with, and after. Time isn't independent of events; for what would time be? Realist views of time empty the term "time" of content; hence, I'll assume relational views of time. The universe is uncaused, otherwise its first moment (time’s beginning) would be caused; but, nothing's prior to the first moment.

Craig offers timeless causation:5 For the Creator sans the universe, there simply is no time because there are no events; time begins with the first event, not only for the universe, but also for God, in virtue of His real relation to the universe. The act of creation is thus simultaneous, or coincident, with the origination of the universe.
Craig believes that simultaneous causation supports timeless causation. Both are incoherent. Simultaneity's a temporal relation; it can't relate the timeless and temporal.

That x causes y entails that x is prior to y in an asymmetric relation; in the ordering of causes, where x exists, y doesn't: if it did, what would x be causing since if y exists where x exists, then y's already actual, and hence, x cannot cause y. That's what "prior" means. Presuming simultaneous causation, x and y occupy the same temporal position; but wherein x exists, y does not exist; but, y exists since it occupies that temporal position and was caused by x, therefore, y both exists and doesn't. Causation requires change since y exists at some point and no longer exists at some other point; if change occurs in a single temporal position, the above incoherency applies, hence, causation is necessarily temporal, for no atemporal SOAs can change.

Presume that God timelessly causes the universe: (A) God saying Be! and (B) the universe exists. There's the ordering {A,B}. These SOAs are incompatible (the total SOAs changed ; prior to the universe, A & ~B and when the universe exists, ~A & B); A is prior to B: this ordered sequence of incompatible SOAs is what is meant by a temporal sequence, therefore, timeless causation is impossible.

Incompatible SOAs cannot be timeless, for both'd be actual i.e. there's a contradiction. One cannot be temporal and the other timeless: the temporal SOA corresponds to the proposition at t, p. The timeless SOA corresponds to the proposition at any t, ~p. This entails at t, ~p, contradicting the above.

God can't place Himself in time for He'd become temporal; but, if God was atemporal, becoming temporal would be a change and atemporal beings are changeless: God puts Himself at time at the very first moment and He was atemporal; God changed at that time, so He was also temporal: God was both atemporal and temporal.

Craig holds that the principle derives from the axiom ex nihilo nihil fit6 [The causal premise] is based on the metaphysical intuition that something cannot come out of nothing
The axiom doesn't support the causal premise7 because Craig says8 With regard to the universe, if originally there were absolutely nothing-no God, no space, no time-, then how could the universe possibly come to exist? [Bolding mine]
Craig holds that the universe's beginning marks time's beginning, so there weren't times prior to the universe for nothing to exist. Atemporally construed,

(4) If nothing existed, then nothing could exist.

"Could" signifies a modal operator and may have either a wide or narrow scope. On the wide scope:

(5) Necessarily, if nothing existed, then nothing would exist.

(5) is a trivial tautology that would be true even if the universe was uncaused. On the narrow scope:

(6) If nothing existed, then necessarily, nothing would exist.

(6) speaks of nothing as if nothing were a condition of something. But, nothing isn' a condition of anything; it isn't a strange sort of something, but a lack of anything at all. (6) is modally fallacious; p's truth doesn't entail p's necessity.

The axiom can only be construed temporally, for it involves the sequence of nothing then something as impossible. Therefore,

(7) If nothing existed at t, then nothing would exist at all times after t.

This construal doesn't support the causal premise's applicability to the universe: there weren't times prior to the beginning of the universe for nothing to exist. Therefore, ex nihilo nihil fit is irrelevant. The axiom doesn't apply for temporally embedded SOAs; such SOAs are by definition preceded by other SOAs which constitute something and not nothing (nothing isn't an event): causeless SOAs aren't preceded by nothing and hence don't come from nothing. Ex nihilo nihil fit provides no support for the causal premise.

In sum: (1) is correct, for (2) entails timeless causation. Then, the universe is beginningless. Relational views of time show (1) to be correct; the First event being caused would have the cause prior to the First event; but nothing's prior to the First event. Craig's arguments against infinite regresses become irrelevant. Timeless causation is the only option available to the KCA. Time either had a beginning or didn't: if the former, the KCA holds time to be caused, and hence, the cause was timeless. The KCA holds the latter as impossible. But, timeless causation is incoherent. Therefore, the KCA fails.

Infinities

Against infinite regresses, Craig offers four theses involving infinite libraries.9

1. In an infinite library with red and black books, respectively enumerated by even and odd natural numbers, the number of red books is equal to the number of red and black books. This is impossible.

Response: Craig accepts Cantorian set theory. Each book corresponds to a natural number. The set of even numbers has the same size as the set of natural numbers. The mathematics maps directly onto the physical facts; there isn’t room to accept one and deny the other. It seems intuitive that such sets are of equal size, namely, infinite.

2. One can’t add to the library: each book corresponds to a natural number; there aren’t natural numbers left to add – since any addition wouldn’t be numbered, the infinite cannot be added to. The set of books is as complete as the natural numbers; just as one cannot add a new natural number, one cannot add a new book. But, people can add books as they please. Hence, actual infinites are impossible.

Response: The natural numbers consists of a set of labels corresponding to the books; it’s possible to add a book without any number i.e. the set of books can be mapped onto the set of their titles. An inability to number the book doesn’t entail an inability to add it. The set of natural numbers is complete in that it is the set of all natural numbers: however, the infinite library isn’t to be confused with the set of all possible books. Also, the addition can be numbered. One can use the ordinal ω + 1; or renumber the books by mapping the extant books onto {2,3…} and the addition onto {1}; or use the unused negative integer {-1}. Craig objects to the first as ω + 1 has the same cardinality as ω and a new cardinal number is required; however, the addition hasn't increased the cardinality of the set of books – a new ordinal suffices. Craig objects to the latter suggestions since it’d change the initial conditions. However, the conditions are no longer initial since one has added a book. It’s crucial to note that the books could be numbered; their actual numbering is irrelevant.

3. One can’t remove from the library: cardinal subtraction is typically undefined (aleph-null – aleph-null) since subtracting transfinite sets of equal cardinality doesn’t lead to uniform results i.e. {1,2,3…} – {1,3…} = {2,4…} which has a cardinality of aleph-null but {1,2,3…} – {4,5,6…} = {1,2,3} which has a cardinality of 3. Hence, one can’t remove from the infinite. But, people can remove books as they please. Hence, actual infinites are impossible.

Response: Craig confuses the formal subtraction operation with removing an element. That transfinite cardinal subtraction is undefined doesn’t mean that one cannot remove elements from a set, but that the removal doesn’t derive a formal subtraction definition that specifies a determinate solution. As seen above, that two transfinite sets are subtracted doesn’t determine a specific cardinal number. Hence, transfinite cardinal subtraction is undefined. However, the removal of elements is clearly consistent with set theory and well-defined. Just as people can check out books, mathematicians can remove elements in infinite sets. The mathematical facts map directly onto the physical facts. There’s no room to accept one and deny the other.

4. The real problem lies in the inconsistent triad

(8) Two sets have the same cardinality iff there’s a one-to-one correspondence between their elements.

(9) A whole is “greater” than its part: any set has a greater cardinality than its proper subsets.

(10) There are actual infinites.

Per (8), infinite sets can have the same cardinality as some of their proper subsets. Craig suggests that (8) is matched by Euclid’s Maxim: the whole is greater than a part. Both are intuitively obvious and but create the “absurdities” for actual infinites. Cantorian set theory maintains consistency by rejecting (9); but, in reality, (8) and (9) hold. Therefore, (10) is false.

Response: Craig equivocates. Sets are obviously greater than their proper subsets as they’re supersets of such subsets: they contain their proper subsets. And this is prior to whether or not the sets have the same size. EM derives from (8); naturally, one maps the common elements between two sets, and the superset has elements “left over.” The natural method fails to find a one-to-one correspondence and hence (8) drives EM, but fails to motive it for infinite sets as the failure of one method of one-to-one correspondence to show equal cardinalities doesn’t entail the failure of all methods. So, EM perfectly applies to infinite sets; instead, Craig must modify EM to (9). Craig appeals to the prior “absurdities” to support (9) – however, one finds such “absurdities” as such because one is already committed to (9); these illustrate violations of (9), but they don’t establish (9). (9) applies to any finite set; but, why suppose it to be so with infinite sets? There doesn’t seem to be any support for (9) other than the notion that only finite sets can exist. But, that would beg the question at hand. If we reject (9) in the “mathematical realm”, it’d seem that one would reject it in the “physical realm”; the mathematics at hand directly maps onto the physical facts. And there’s reason to favor (8) over (9): while correspondence relations don’t vary with ordering, part-whole relations do. Hence, (8) appears to be correct and (9) false.

Against infinite regresses, Craig offers three theses from successive addition.10

1. No actually infinite set can be formed by successive addition. A beginningless past would have to be formed by successive addition; hence, beginningless pasts are impossible.

Response: The argument holds true for any past that has a beginning and it’s true that no infinite set can be formed; but, why suppose that beginningless pasts are formed? That the beginningless past was “formed” indicates that the past was made beginningless; there was some point in which an infinite set of times was produced; but, that’d mean that prior to when this was produced, the set of prior times was finite. These theses aren’t entailed by a beginningless past since infinite sets aren’t formed; they’re always there. At any time t, there are times prior to t – this entails that at any time t, the set of times prior to t is infinite. There is no point where such a set is ever formed at all. Perhaps one is inclined to reason that since each event begins to exist, the infinite series begins to exist. There’d have to be some infinitely distant beginning which’d have to be traversed – an impossibility. But, this commits the fallacy of composition. An infinite number of events being “formed” doesn’t entail that the whole is “formed.” An example would be the negative integers mapped onto the set of events: each event is “formed” but the whole isn’t.

Craig offers two replies.

2. “If one cannot count to infinity, how can one count down from infinity?”

Response: Craig equivocates. Craig recognizes that counting down from infinity corresponds to counting the ordinal ω* {…-3,-2,-1}; not starting from aleph-null and counting down, since aleph-null isn’t an element in the set of integers nor does it have an immediate predecessor. A count from aleph-null to {-1} is impossible. The same applies for counting from {1} to aleph-null. There are two distinct notions here. It’s possible to count the ordinal ω* {…-3,-2,-1} and the ordinal ω {1,2,3…}; in the former, one never starts, in the latter, one never ends. But, the set of one’s counting comprises an actual infinite that directly maps onto the set of counted numbers. What’s impossible is counting the set {aleph-null…-3,-2,-1} and {1,2,3…aleph-null}. But, the latter is irrelevant to an infinite past, as discussed above. What motivates this confusion is that ω* terminates with a last member. With respect to the past, the past has been “traversed.” However, if one attempts to “retrace” one’s steps, one is effectively counting ω, which doesn’t terminate with a last member. Only by confusing these entirely different counts does Craig derive this argument.

3. Suppose someone counted the ordinal ω* {…-3,-2,-1} today and an element a day. Why didn’t finish yesterday or the day after? An infinite time elapsed, so he’ll be finished then. At no point will the man count, for he would have finished at any point.

Response: Craig confuses counting infinitely many negative integers with counting all negative integers. Yesterday, the man counted up to {…-3,-2} and today {…-3,-2,-1}; both sets have the same size (aleph-null) but the former is a proper subset of the latter. Counting aleph-null integers doesn’t mean that the man counted all the integers. Craig responds by stating the objector reasons that since prior to today, aleph-null days have elapsed, by the Principle of Correspondence, all numbers should have been counted. Craig points out that this reasoning backfires on the objector; it opens up the objector to the original argument. However, the opponent’s response Craig offers commits the same mistake as Craig and isn’t the correct reply to Craig. The proper response is point out that “Sure, the count could have finished yesterday. But, it could have also finished today.” Is any answer beyond “This is how we imagined the scenario” necessary? Perhaps Craig is appealing to the principle of sufficient reason; that there must be some reason for this situation. That’s an entirely different argument to address and beyond the scope of this post: the argument from contingency.11

Personality

Craig argues that the timeless first cause is personal:12 given an eternal first cause, how could a temporal effect arise? Causes are sufficient for their effects, hence, eternal sufficient causes entail eternal effects. But, the universe isn’t timeless. The only way out is an appeal to a free agent i.e. a man sitting from eternity may freely will to stand up, creating a temporal effect.

Response: The argument appeals to an indeterministic process, which isn’t exclusive to libertarian free agents i.e. quantum-mechanical processes are possibly indeterministic or even metaphysical indeterministic processes. Moreover, the appeal is confused. Craig moves back and forth between timeless and everlasting conceptions of eternity. A free agent’s willing an action is sufficient for the action, for to will something is to actualize it, and actualize something is sufficient for the thing being actual. If an entity timelessly wills something, then qua Craig, since their will is sufficient for the effect, the effect ought to exist timelessly. Craig’s picture of a non-eternal effect arising out of an eternal cause only makes sense if we conceive of an everlasting conception of eternity; however, the KCA requires the cause be timeless. Moreover, there’s no temporal gap in an entity timelessly causing something. Furthermore, the argument confuses what’s the cause of the effect. One doesn’t explain an action by citing the existence of the agent, but pointing out that the agent did something i.e. one appeals to a causal state of the agent. And plainly, the causal state is sufficient for the effect. Besides the above, God has both the intention and the power to create the universe. An intention is such that if x had the power to actualize A, x would actualize A. Obviously, God has the power to actualize the universe. Given the conjunction of his intention and power, this is sufficient for God’s actualizing the universe, which is sufficient for the universe being actual. Contrary to Craig, the causal act is entailed by the conjunction of intention and ability.

Finally, it’s worth pointing out that libertarian free will is incoherent. Qua LFW, given identical circumstances, there’s some possible world where you act otherwise. Hence, LFW choices are uncaused (this contradicts the KCA’s causal premise); if my choices are uncaused, how are they my choices? I exercise no causal influence over them – they just happen. Perhaps I cause them. But, what about my causing them? Is that caused or not? And so, we continue down an infinite regress. But, nothing’s prior to an infinite regress; it just happens to be and I exercise no influence over it. Hence, LFW is incoherent. Plainly, people are caused by their desires, beliefs, etc. But, we know we have free will. Hence, compatibilist freedom is true. Qua compatibilism, I cannot do otherwise (as libertarians interpret it): given identical circumstances, I do the same action. However, why would I do otherwise at all? Given who I am, I will the act the same necessarily. Hence, our nature (who we are) is causally connected to our actions, in other words, we will our actions; that’s what it means to be free in the first place. The only external causal thing is really our creation i.e. the host of genetic, environmental, etc factors that instantiate our nature. All Consequence Arguments miss that fact. Nothing self-instantiates; hence, our natures are instantiated by causal factors, and from there, we act freely. However, compatibilism entails that our causal states are sufficient for effects, hence, Craig’s argument fails.13

Nonphysicality

Craig believes that if the universe were caused, the cause is nonphysical. That line of reasoning seems to hold if the observable universe (as we know it) comprises the whole of physical reality. But, why suppose that it is? What rules out ekpyrotic scenarios or multiverse theories? Craig must first establish that the observable universe comprises the whole of physical reality.

Conclusion

In summary, the KCA fails. As presented, the KCA relies on timeless causation, which I argued was incoherent. I also analyzed the a priori attack against actual infinities, which I argued was both irrelevant and a failure. I also discussed two aspects of the first cause, namely, that if there is one, there is no reason to suppose it to be either personal or nonphysical. The only coherent scenario for a theistic creation scheme would consist of God being temporally prior to the universe and causing the universe to exist. To show this, Craig must establish (a) the universe has a finite past (b) the universe was preceded by prior events i.e. the universe first moment isn’t time’s beginning (c) the universe comprises the whole of physical reality i.e. there couldn’t have been prior physical causes (d) the cause was personal. Craig’s philosophical arguments for (a) have failed. With respect to (b), he has not shown this and moreover, he assumes the falsity of (b) in constructing an argument for (d)! He hasn’t established (c) at all, but merely assumed it throughout his argument. And his argument for (d) depends upon the falsity of (b), much less that it also fails. The KCA has much work cut out for it. Right now, it appears to be a forceless argument.

Notes

[1] Craig, William. "The Origin and Creation of the Universe. (http://www.leaderu.com/offices/billcraig/docs/origin.html)"

[2] Ibid. (http://www.leaderu.com/offices/billcraig/docs/origin.html)

[3] Morriston, Wes. "Must the Beginning of the Universe Have a Personal Cause? (http://www.colorado.edu/philosophy/wes/wes2craig1.pdf)" 154-155.

[4] Craig. "MBUPC?: A Rejoinder. (http://www.leaderu.com/offices/billcraig/docs/morriston.html)"

[5] Craig. "Prof. Grunbaum on Creation. (http://www.leaderu.com/offices/billcraig/docs/grunbau.html)"

[6] Craig. "The Existence of God and the Beginning of the Universe. (http://www.leaderu.com/truth/3truth11.html)"

[7] Morriston. "MBUPC. (http://www.colorado.edu/philosophy/wes/wes2craig1.pdf)" 152-154.

[8] Craig. "EGBU. (http://www.leaderu.com/truth/3truth11.html)"

[9] Dever, Josh. "Worlds Apart. (https://webspace.utexas.edu/deverj/personal/papers/worlds.pdf)" 1-12.; Morriston. "Craig on the actual infinite. (http://stripe.colorado.edu/%7Emorristo/craig-on-the-actual-infinite.pdf)" 147-155.

[10] Morriston. "Must the Past Have a Beginning? (http://stripe.colorado.edu/%7Emorristo/infpast.html)"; Morriston. "Must Metaphysical Time Have a Beginning? (http://www.colorado.edu/philosophy/wes/metaphysical-time.pdf)" 289-295.

[11] Under the handle “rayndeon,” I’ve tackled the argument at the Debunking Christianity blog. (http://debunkingchristianity.blogspot.com/2007/10/leibnizian-cosmological-argument-part-i.html)

[12] Craig. "EGBU. (http://www.leaderu.com/truth/3truth11.html)"; Morriston. "MBUPC. (http://www.colorado.edu/philosophy/wes/wes2craig1.pdf)" 163-168.; Craig. "MBUPC?: A Rejoinder. (http://www.leaderu.com/offices/billcraig/docs/morriston.html)"

[13] I elaborate a little more here (http://www.iidb.org/vbb/showthread.php?t=218808), towards the bottom.

[punkforchrist]

You will remember during my opening statement I gave several arguments in favor of just two premises, which if true, lead us to the necessary conclusion that the universe has a cause.

1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

Further, I argued that this cause of the universe must be a personal creator. Let us look, then, at each premise.

Whatever begins to exist has a cause

Now, Dante believes that the causal principle is exclusively temporal. In other words, even if the First Cause acts simultaneously with its effect to bring it about, this First Cause cannot itself be timeless. In his own words, Dante claims:

That x causes y entails that x is prior to y in an asymmetric relation; in the ordering of causes, where x exists, y doesn't: if it did, what would x be causing since if y exists where x exists, then y's already actual, and hence, x cannot cause y.

He believes that in order for x to be the cause of y, then x must exist temporally prior to y. However, what reason does he give for this conclusion? Well, he says that if x and y occupy the same temporal position, then y would both exist and not exist with respect to x’s being temporally prior to y.

This conclusion, however, is unsound, since Dante equivocates the notion of priority. He conflates x’s ontological priority to y with x’s temporal priority to y. God (x) acts at y to cause y, which makes x’s causal (or ontological) priority to y temporally simultaneous with the effect of bringing about y. Imagine a ball resting on a cushion from all eternity. The cause is simultaneous with its effect, since neither the ball nor the cushion is temporally prior to the other.

Dante makes the further claim that if God is timeless, then the universe cannot be temporal. Essentially, he asks, how can a timeless cause produce a temporal effect without there being a change in the timeless agent itself (hence, contradicting its immutability)? The problem with this is that it presupposes temporal priority with respect to a timeless cause. Why assume from the outset that God had to somehow change in order to bring about a temporal effect? What if He willed from all eternity to bring about a universe that exists in potentiality? In fact, that is exactly what the kalam cosmological argument (and the argument from motion) contends. In other words, Dante’s equivocation causes (pardon the pun) him to assume that since temporal priority requires change that so does all ontological priority. But why should one accept the view that what applies to temporal relations will apply to relations between timeless and temporal agents? It seems that this is an unwarranted assumption.

Now, even granting the notion of temporal priority, I do not believe a case can be made against the kalam argument. Although Dante suggests that arguments against an infinite regress are irrelevant, let us suppose that there is a first moment in time (I will address this specifically below). Assuming this, there is still a First Cause, since without this first moment there could be no successive moments. One might respond by asking, why does this have to God and not something in the physical universe? The reason for this is because no being in potentiality is sufficient in and of itself to bring about all other potentialities. In order for there to be an egg, there must be a chicken; likewise, in order for there to be potentiality, there must be pure actuality. But if there is pure actuality, then all the other divine attributes necessarily follow, and hence, God exists. Time is merely the measurement of an interval of change. God, existing at say time-x, is immutable, since the transition from x to y does not necessitate there being a change in what exists in x, but only in y. At x, God exists as pure actuality, and the universe in potentiality. The transition from x to y only brings about the universe’s existence from potentiality to a state of actuality.

Let us now look at the second premise.

The universe began to exist

I offered two philosophical arguments in favor of this premise. The first one goes like this:

1a. An actually infinite set cannot exist.
2a. A beginning-less universe is an actually infinite set.
3a. Therefore, a beginning-less universe cannot exist.

Dante does not seem to dispute premise (2a), so the real disagreement is over (1a). With respect to the claim that the whole is greater than its parts, he says that since Cantorian set theory allows the set of even numbers to be equal to the set of natural numbers that the whole and its parts may well be equal. The problem with this is that there are many examples of mathematical axioms that do not turn out to reflect the real world. In my opening, I gave the example of Euclidean geometry. Therefore, Dante’s claim that the mathematics maps directly onto the physical facts is clearly not always the case. The difficulty with Cantorian set theory is not that it is an illegitimate mathematical theory, but that when we try to translate it into the real world, we are left with a number of absurdities (i.e. that the whole may not be greater than its parts).

In each of his objections, Dante presumes that if something works in the mathematical realm, then it must correspond directly to the physical world, but I see this as a non sequitur. The very reason that actual infinites cannot be translated over into reality is because of the many absurdities that are brought to surface. As a result, mathematicians who work with Cantorian set theory prohibit the use of subtraction and division. But is this how the real world works? Can we really not remove things from a given set?

Dante anticipates this response and says that subtraction is not the same thing as the removal of an element. I would simply recommend to anyone following to look up the term in any dictionary or mathematics textbook. The Encarta Dictionary defines subtraction like this: “a withdrawal or deduction of something from a larger whole”. [1] The removal of one element is such a deduction. If infinite quantities exist in reality, then a sufficient reason for the exception must be made; otherwise, it is an instance of special pleading.

Next, my worthy counterpart claims that Euclid’s Maxim (“the whole is greater than its parts”) does not necessarily apply to infinite sets. However, he has not provided any reason for this, but instead says that it begs the question to assume that because certain rules apply to finite sets that they must apply to infinite sets. Now, I do not deny that it is legitimate to prohibit certain rules when it comes to abstract mathematical concepts, but it is not enough to say that if something works in the mathematical realm it must correspond to reality. That is both begging the question and a non sequitur. When we add elements to an already infinite set, is the set really not any bigger? Well, according to Cantorian set theory the answer is yes, but as pointed out several times before, that is not sufficient to presume that Cantorian set theory is descriptive of reality. In the real world, the year 2007 adds an additional year to the time already elapsed. Is this set really no greater than everything from 1980 and prior to it? If they are the same size, how can 1980 and 2007 be distinct years?

The second philosophical argument in favor of premise (2) I presented is the following.

1b. An actually infinite set cannot be formed by successive addition.
2b. A beginning-less universe is an actually infinite set formed by successive addition.
3b. Therefore, a beginning-less universe cannot exist.

With this argument, Dante accepts premise (1b), but rejects (2b). He says that if there is no beginning to the infinite set, then it is reasonable to postulate that the universe has not been formed by successive addition. This, in my opinion, is not a sound objection, either. Consider it this way. At any point in the finite past (let us call this c), an infinite amount of time has already been traversed. Before c could arrive, b would have to precede it, and before b another time would have to proceed that time, and so on to infinity. If one cannot form an actual infinite by adding events to the future, then neither can one form an actual infinite by adding events to the past. In the example I gave in my opening, before I could ever get the book from Dante, he would first have to receive it from an infinite number of friends. This is exactly what forming an actual infinite by successive addition is. Since nobody actually has the book, how can I ever receive it? Saying that the collection never begins does not solve the problem, and is in fact, begging the question. In essence, Dante is saying that if yesterday his immediate friend had the book, then I would finally be able to get it. However, why would his friend have gotten the book yesterday instead of the day before, or the day before that, etc.? Merely defining yesterday as {-1...} arbitrarily sets up a smoke screen with respect to the problem of how yesterday actually was able to arrive in the first place.

Consider it another way. According to Dante, yesterday an infinite series of events must have elapsed, and then the present day arrived after it. Infinity + 1 = infinity. But what happens when we subtract from both sides? We end up with: infinity = infinity - 1! However, anything less than infinity must be finite, and so we would end up saying that infinity is equal to a finite quantity, which is absurd. No matter how we approach this, we are forming an actual forming by successive addition, and since this is impossible, then the past series of events must be finite.

Dante next argues that there is a difference between an infinite set of negative integers with all possible negative integers. However, this is merely a way of obscuring the difficulty. Is there anything an infinite set lacks? If it is truly infinite, how can it possess only some of the negative integers. If there are some negative integers not included, then there are limitations to the infinite set, which is a contradiction in terms. By definition, infinity knows no limits.

Turning to Big Bang cosmology, Dante has not yet attempted an answer. To be fair, though, word limits often prevent us from addressing each point in the kind of detail preferred. I suspect Dante will address the issue of the empirical evidence in his rebuttal, as he has suggested.

As for the personality of the First Cause, Dante has addressed only William Lane Craig’s argument. You recall from my opening that I appealed to a Thomistic argument in which a being that is pure actuality will necessarily possess the maximal characteristics found in potentiality, including knowledge which presupposes personality. Since the First Cause is pure actuality, it follows logically that the First Cause is personal.

Finally, Dante asks why an immaterial entity must exist in order for our finite universe to have been created? What about a multi-verse theory, for instance? I will make two observations about this. First, Ockham’s Razor suggests that we should not compound additional causes where it is unnecessary to do so. Ask yourself whether an infinite number of multi-verses is simpler than a single creator of the universe we live in. Second, multi-verse theories only bring us back one step, since the absurdities that the two philosophical arguments against an actual infinite demonstrate the same kind of absurdities of an infinite number of multi-verses.

Therefore, the universe has a cause

With the two premises having survived critique, the conclusion that the universe has a cause necessarily and logically follows. But not only have we arrived at the cause of the universe, but to its personal creator.

Works Cited

[1] http://encarta.msn.com/dictionary_/subtraction.html

[KnightWhoSaysNi]

Dante, please note that your next statement is overdue. However, you have a grace period of 48 hours from the time of this post.

KWSN, FD Moderator

[KnightWhoSaysNi]

Due to extenuating circumstances, Dante has requested a 24 hour extension to his grace period. I have agreed to grant his request. He will have 24 hours from the time of this post to submit his next statement.

KWSN, FD Moderator

[Dante Alighieri]

I would like to thank punkforchrist for his defense of the KCA and I would now like to examine his last two posts.

The Cause

1. In his opening, Punkforchrist has argued for the personality and oneness of time's cause from Aristotelian metaphysics.

Response: An egg is potentially a chicken, or a rotting carcass, or any particular state in the development of the egg. To say that x is potentially y does not determine some unique y, since there are many changes in that thing, leading a number of different states, hence, each state has as much claim to potentiality as any other. Hence, potentiality is change i.e. temporality. If the universe's cause is was also the cause of all change (which we have no reason to believe), then the cause is changeless changeless. But, it isn't "fully actualized potentiality" since changes are incompatible i.e. there is in potentiality, beings knowledgeable and not, so, the cause cannot be both. In other words, that the cause lacks nothing in potentiality is impossible. Indeed, there's nothing about immutability that entails that it lacks no properties as found in what it causes.

2. Punkforchrist argues that multiverse theories aren't parsimonious.

Response: Ockham's Razor shows that types of entities shouldn't be unnecessarily multipled. For instance, it may be more parsimonious to assume that, in a murder case, there is more than one killer. The same sort of situation applies here. There's nothing to show that the universe constitutes all of physical reality. If indeed the universe were caused, it's more parsimonious to hypothesize a physical cause since we know of physical causes and to a lesser degree, multiverses (see inflationary theory). There isn't knowledge of disembodied nonphysical minds. Hence, given the data, if the universe has a cause, it is more parsimonious to assume a physical one.



Causation

1. Punkforchrist charges that I conflated ontological and temporal priority.

Response: I don't see where he shows the conflation. I said that if we take the causal ordering (i.e. the ontological ordering), a cause x is prior to the effect y, such that at the position the cause occupies, x exists, y doesn't: at the cause's position, we have the state of affairs (x & ~y); at the effect's position, (y) - cause and effect are ordered as per the ordered pair {(x & ~y), (y)}. So, we have incompatible states of affairs here. The reason this is so is because the cause is prior to the effect; if both occupy the same ontological position, then the effect is already actual at the cause, so the cause isn't causing anything. Now, if both occupy the same temporal position t, then at t, [(x & ~y) & (y)]. This entails (y & ~y). This was already detailed.

Punkforchrist's example of a ball resting on a cushion doesn't answer the above concerns. I think it is also confused. A ball's resting on a cushion isn't simultaneous with the impression it forms. Notice that no causal state is simultaneous: both ball and cushion are composed of moving particles in temporal sequence, the interactions forming an impression. We have continously vibrating atoms which interact to form an impression, but this interaction is hardly simultaneous.

2. Punkforchrist argues that I mistakenly presuppose temporal priority for timeless causes.

Response: I don't see how. I gave arguments for the impossibility of timeless causation. Causation involves the ordered pair {(x & ~y), (y)} -since one has (x & ~y) and then (y), this is obviously a change, since incompatible SOAs follow in sequence - I pointed out that such sequences are by definition temporal. I explained than an atemporal God cannot become temporal, for that would that would means that God became temporal and hence changed; changeless beings cannot change. That is precisely what is required if God causes the singularity in the same moment of its existence. I gave an argument showing timeless causation as impossible and that timeless SOAs can't cause temporal SOAs. Since cause and effect are incompatible,

Incompatible SOAs cannot be timeless, for both'd be actual i.e. there's a contradiction. One cannot be temporal and the other timeless: the temporal SOA corresponds to the proposition at t, p. The timeless SOA corresponds to the proposition at any t, ~p. This entails at t, ~p, contradicting the above.
3. "[No] being in potentiality is sufficient in and of itself to bring about all other potentialities." Hence, there cannot be a temporal First Cause that isn't pure actuality.

Response: I already indicated the incoherence of pure actuality. But, why believe Punkforchrist's statement? It amounts to sheer assertion, but, why cannot a being that changed be the First Cause i.e. a singularity? There's nothing incoherent about that I can see.

With respect to Punkforchrist's defense of temporal immutability, changes in persons are changes in causal structure i.e. the causal structure that humans inhabit is a material body. God inhabits a nonmaterial concrete object. This causal structure changes, per the above, in terms of actions, thoughts, etc. For instance, in my actions, I go from a state of not acting, to acting, to no longer acting. These actions are accomplished via my causal structure. Hence, God's acting itself constitutes a change in causal structure. He must initiate an action, which He then completes and hence is no longer acting that action.

Infinities

1. Punkforchrist says that I assume that "if something works in the mathematical realm, then it must correspond directly to the physical world."

Response: I don't hold to that proposition. What I was trying to get at was: Craig's anti-infinitist arguments are in the form of a reductio. He presumes the existence of an actual infinite and then argues that there are "absurdities" to disprove their possibility. There aren't absurdities to be had, since if there is an actual infinite, then the mathematics map directly onto the physical facts. Craig accepts Cantorian set theory. There's no room to accept one and deny the other, therefore, no "absurdities" follow. Just as infinite sets may have the same cardinality as some of its proper subsets, so does the infinite library. This is the same position of Josh Dever, as I cited earlier.

2. Punkforchrist attributes to me the claim that subtraction isn't the same as removing an element; he proceeds to assert that it is - therefore, since Cantorian set theory prohibits subtraction, one cannot subtract from an infinite set.

Response: I said that the subtraction of transfinite cardinals is standardly undefined, not the subtraction of infinite sets. I drew out the difference earlier. The subtraction of two infinite sets such as {1,2,3...} - {4,5,6...} is defined under Cantorian set theory. What is undefined is the subtraction of the transfinite cardinal numbers i.e. aleph-null - aleph-null. As said earlier, the subtraction of infinite sets doesn't derive a formal subtraction definition for the transfinite cardinals that specifies a determinate solution. That two sets of transfinite cardinality are subtracted doesn't entail a specific cardinal number. The specific solution depends on the sets subtracted and that maps directly onto the physical facts. So, Punkforchrist confuses that the subtraction of transfinite cardinals are undefined as entailing that the subtraction of infinite sets is undefined. This is, as I detailed, mistaken. This is the same position of Josh Dever and Wesley Morriston, as I cited earlier.

3. Punkforchrist claims that I reject that Euclid's Maxim applicability to infinite sets and that its inapplicability leads to absurdities.

Response: I argued that Euclid's Maxim consistently applies to infinite sets, not that it doesn't:

Sets are obviously greater than their proper subsets as they’re supersets of such subsets: they contain their proper subsets... So, EM perfectly applies to infinite sets; instead, Craig must modify EM to (9).
As said earlier, (9) is problematic. (9)'s inapplicability doesn't lead to "absurdities." Such absurdities illustrate violations of (9), but don't establish it, since one finds such "absurdities" to be as such because one's already committed to (9). Since the mathematics map onto the physical facts here, if there is an actual infinite, then (9) fails to apply. So, Craig's reductio cannot work.Finally, "there’s reason to favor (8) over (9): while correspondence relations don’t vary with ordering, part-whole relations do. Hence, (8) appears to be correct and (9) false." Indeed, I explained how Euclid's Maxim is derived from (8); there is a natural method by which we determine that something is greater than something else, by counting all common members, and the superset has members left over. This drives Euclid's Maxim that the whole cannot be greater than the part, but it fails to motivate it properly since the failure of one method of correspondence doesn't entail the failure of all methods.

Punkforchrist asks

In the real world, the year 2007 adds an additional year to the time already elapsed. Is this set really no greater than everything from 1980 and prior to it? If they are the same size, how can 1980 and 2007 be distinct years?
Adding elements doesn't increase the cardinality of the prior set, but the new set is a superset of the prior set: it contains the subset. Imagine some infinitely long ruler, marked ...-3,-2,-1,0. Add at 0 some piece of wood. The ruler's length is as infinite as ever. However, we have added to the ruler, and this is reflected mathematically by virtue of the fact the corresponding new set is a superset of the prior set even though they have the same cardinality. There are new elements. So, these years are distinct by virtue of the fact that the set of years extending up to 2007 is a superset of the set of years extending onto 1980. They are different elements; sets have identical cardinalities and yet be different sets by virtue of the fact that they contain different elements.

4. Punkforchrist argues if there is infinite regress, then each moment would have to be traversed. "If one cannot form an actual infinite by adding events to the future, then neither can one form an actual infinite by adding events to the past."

Response: Indeed, each past moment has passed. But, that doesn't mean that the infinite regress "passed" if we define "passes" as "something beginning and then ending", which isn't the case for infinite regresses.

Punkforchrist's statement is a variation of "If one cannot count to infinity, how can one count down from infinity?" As said earlier, the argument confuses the reversal of the sequence {...-3,-2,1}. The reversal of that sequence is {1,2,3...}. Neither the infinite future or past are formed, but are always there. The confusion is motivated by that the former terminates with a last member. But, the reversal doesn't involve terminate with a last member, but a first member. It's not as if the reversal of the {-3,-2,-1} is {1,2,3...aleph-null}, since aleph-null isn't a member of the set of integers. Such a set is to form an actual infinite. But, it's irrelevant to the former two sets. Neither the infinite future nor infinite past terminate in some infinitely distant point in the future/past.

Punkforchrist's book example shows this confusion, since it corresponds to the set {1,2,3...aleph-null}, in which he asks a friend for a book (i.e. the set has a beginning) and after an infinity of inquiries, he receives the book (the sequence terminates). This example is irrelevant, as explained. A relevant example would be if there were an infinity of lenders, each lending the book to each other until it reached me. This corresponds to {...-3,-2,-1}. No problems arise with this example. There's no original owner of the book, but the sequence is just as successive, just like the negative integers.

Punkforchrist continues

Infinity + 1 = infinity. But what happens when we subtract from both sides? We end up with: infinity = infinity - 1! However, anything less than infinity must be finite, and so we would end up saying that infinity is equal to a finite quantity, which is absurd.
This was already tackled with respect to elements and cardinality. Anything less than aleph-null is indeed finite; that is, any set with a cardinality lower than aleph-null is finite. But aleph-null - 1 is not finite, any more than {1,2,3..} - {1} = {2,3,...}.

5. Punkforchrist argues that infinity knows no limits, hence, there's no distinction between an infinite set of negative integers and all negative integers.

Response: There's no such mathematical definition. Affix the definition "lacking nothing" onto the term "punkfinite." Fine, there isn't anything "punkfinite"; the natural numbers lack the nonpostive integers, TVs, etc. Indeed, there can't be anything punkfinite, as Russell's paradox and Cantor's power sets show. But, punkfinity is irrelevant. What's relevant is infinity. There is a distincton between an infinite set of negative integers, such as {...-3,-2} and all negative integers, as any mathematical analysis bears out.

Cosmology

Much can be said about the cosmology invoked in the KCA. I shall restrict myself to only a few comments. First of all, it is unclear whether there even was an initial singularity to begin with. One of the current great conflicts in cosmology is relativistic cosmology in contrast with quantum cosmology, the latter tending to eliminate singularities. Morever, it is widely known that general relativity breaks down and becomes inexplicable in the initial moments of the universe per Big Bang cosmology, namely, prior to 10-43 seconds after the Big Bang. So, it is unclear whether current physics tends to support the existence of singularities.

Furthermore, Big Bang cosmology address the origin of the observable universe, namely, this portion of spacetime. It says nothing with respect to the possibility of other regions of spacetime, which, for instance, is a typical prediction of inflationary theory. In other words, there's no reason to assume that the observable universe constitutes all of physical reality.

Finally, it's worth pointing out that relativistic interpretations of Big Bang cosmology conflict with the KCA. The singularity at the first moment had infinite density and temperature under most relativistic interpretations, hence constituting an actual infinite. Therefore, the defender of the KCA cannot reasonably hold on the denial of the possibility of actual infinites and relativistic interpretations of Big Bang cosmology.

Intuitions

An astute reader will notice that most of the arguments against actual infinites or uncaused events are appeals to intuition. Such holds for the argument for the general impossibility of actual infinites and causation. I wish to examine that line of thought.1

With respect to causation, it appears that many of the intuitions we have with respect to it cannot apply in the cosmological case. The initial singularity marks not only the beginning of the universe, per Craig's intepretation of Big Bang cosmology, but, moreover, it marks the beginning of the entire natural order. Now, Craig has continually appealed to a variety of appeals to intuitions. As he says, for instance, no one could really believe, for instance, that a raging tiger could simply come into existence uncaused. He then invites the same intuition with respect to the universe.

Let us examine this intuition. It's clear that we have such an intuition, but why do we have such an intuition? The answer is obvious: we know that tigers do not simply come into existence uncaused. There is a familiar context in which we operate with respect, supplied by the sum of our collective experience. Contrast such a case against the first moment. Unlike the raging tiger, the First Moment does not come into existence since it is not as if there were preceding moments. It's clear that none of our intuitions apply in such a case. We don't have experience with singularities or the origin of all of natural order.

And, in fact, Craig takes it to be more obvious the singularity could not exist uncaused, as he argues that the singularity would have to literally come from nothing. But, this move, as I explained earlier, is utterly confused, as I argued as the axiom ex nihilo nihil fit. Moreover, one is puzzled by the claim that there is continual empirical verification of universal causation. We observe beginnings in the context of time and within time, but we do not observe the beginning of time itself. Hence, our intution does not apply here. And it's interesting to note that there is no attempt to apply our intuitions onto timeless, disembodied minds, which we have no experience with either.

Now, consider infinities. The actual infinite is said to be absurd. But, in what sense? The general complaint is that an infinite set may have the same cardinality as some of its proper subsets. For instance, the integers and the natural numbers have the same cardinality. But, why should this strike one as absurd? It seems intuitive that both sets would have the same size, namely, infinite. Indeed, what was truly revolutionary of Cantor was showing that infinite sets can have different sizes i.e. there are sets with cardinalities strictly larger than aleph-null, such as the real numbers. Moreover, a number of helpful analogies arise. Consider some infinitely long ruler, extending from 0 onwards. It's length is clearly infinite. Moreover, it's clear that adding a piece of wood on the end doesn't alter its length. But, one has certainly added to ruler, as I explained earlier.

Furthermore, it's clear that our intuitions conflict. For instance, while we may have the intuition that nothing is uncaused, many seem to have the intuition of libertarian free will, which conflicts with causation. Or, consider infinities. For instance, time is either continous or discrete. If it is continous, then there are an actually infinite number of moments, although the metric of time may be finite. But, suppose time were discrete. Then, there would be atoms of time, such that, between some two moments, there are no other moments. Time, hence, doesn't "flow continously" but "jumps from moment to moment." But, that plainly does seem counterintuitive. And yet, to accept time's continuity is to accept actual infinities. Or, consider non-Euclidean geometry. Some of them require parallel lines to always meet (Riemannian geometry) or get further and further apart from the other (hyperbolic geometry). And yet, despite the intuitive nature of Euclidean geometry, it as well requires actual infinity. Moreover, it seems that God must be infinite in various respects. He must know infinitely many propositions, have knowledge of an infinite future, and his power scopes over an infinity of possible actions.

In other words, intuition is not an accurate guide to much of reality beyond us. That something is counterintuitive doesn't entails its impossibility and we must remember that our intuitions are formed in relation to some context. Reality is more complex and counterintuitive than we merit it, as we can see with quantum mechanics, general relativity, and non-Euclidean geometry.

Conclusion

So, in conclusion, we have examined various concerns relevant to the KCA. Both the first and second premises of the KCA remain unsupported, and at this point, the KCA strikes one as a totally forceless argument. There have been a number of fatal errors committed by the KCA, as I detailed here and in my first post. Hence, we are left to conclude that the KCA neither provides rationally compelling nor rationally acceptable support for a personal Creator.

[1] The following regarding causation is from Morriston, Wesley. "Causes and Beginnings in the Kalam Argument: Reply to Craig." (http://www.colorado.edu/philosophy/wes/wes2craig2.pdf) Faith and Philosophy 19 (2002): 234-241.

[punkforchrist]

In his thoughtful rebuttal, Dante has objected to both my claims regarding Aristotelian/Thomistic inferences about the First Cause, as well as my arguments against an infinitely old universe. Let’s take a look at each of his claims.

Pure actuality

First, Dante disagrees that if there is a cause of all potentialities, it must be changeless (I will address this in detail below). He further disputes my contention that we can infer on the basis of this that the First Cause must be personal. He reasons that since there are things in potentiality that are knowledgeable, and others that are not, then a being that is pure actuality could not be both. I agree with this. My original claim was simply that a being with pure actuality must possess maximal potentiality. Consider it this way: the intelligence of a human being is more potent than that of a koala bear. What would we therefore expect of a fully actualized being? God does not need to be both intelligent and non-intelligent in order to be maximally potent.

Next, Dante objects against my use of Ockham’s Razor, stating that a plurality of physical causes is simpler than an immaterial one. However, this really begs the question with respect to his own position. Two points can be made here. First, as I will detail below, if the universe cannot be infinitely old on the basis of the two philosophical arguments against an actual infinite, then it is impossible for there to be an infinite chain of physical universes. Second, Dante takes the bold position of having to defend a purely ontologically monistic theory of reality. Why assume from the outset that immaterial causes add complexity to the issue? Even the skeptical Karl Popper would not agree with this assessment. Further, if there are only physical causes, then the operations of our cognitive faculties are solely the result of physical determinism. In this case, Dante’s conclusion that the kalam argument is unsound is no more rational than his having a headache!

Causation

Now on to the question of causation, Dante defends his claim that timeless causation is contradictory. He tells us that the ontological ordering of God’s timeless causation would require to posit both (x & ~y) as well as (y) within the same position. Although Dante denies it, this does conflate ontological priority with temporal priority. The reason is because x and y do not need to occupy the same ontological position. How could they unless they were identical? As for the ball and cushion example, the point is simply that if they were in a timeless state, where no change occurred at all, then the cause would be simultaneous with its effect. Saying that a ball and cushion are composed of moving particles is only applicable if we are talking about temporal causes. To rule out timeless causation on this basis is to beg the question.

Dante next defends his claim that there must be a change in God in order for Him to create the universe. He states that he does not presuppose temporal causation for timeless causes. However, he does do this, since he claims that there is a change between (x & ~y) and (y), but I see no reason to assume there was ever a temporal position of (x & ~y) to begin with. Hence, his appeal to temporal causation by definition, is circular. The fact that God is changeless does not imply that He cannot create, since God may have willed creation from all eternity without having changed at all in His essence. Just because temporal agents change as they act should not suggest to us that this applies to timeless agents. However, even if God is temporally prior to the universe, it is largely irrelevant, since I have already pointed out that in order to go from (x & ~y) to (x & y) there does not need to be any change in x.

Finally, Dante wants to know why the cause of potential beings must be purely actual. I have already touched on this, but I will attempt to make it more explicit. First, a being that is in potentiality can both be and not-be. But if God is eternal (re: timeless), He cannot not-be. Hence, there is no potentiality in God; therefore, God is pure actuality. Second, beings that are raised from potentiality to actuality are raised to actuality by something already in actuality. For example, a piece of wood is made hot by an already hot fire. This means that any being that goes from potentiality to actuality must have something that precedes it in actuality. But since this cannot go on forever (as I will argue below), what is ontologically first must be purely actual.

Infinites

With respect to the problems facing an actual infinite, Dante states that if there are no absurdities, then the mathematics maps directly onto the facts. However, this is untrue, since there are many coherent systems that have no basis in reality. Further, his point that there are no absurdities is the crux of the debate, anyway. I accept Cantorian set theory because there are no internal inconsistencies within it, but that is not the same as saying that it can be translated into reality. I see no reason to assume that actual infinites can be mapped directly onto the facts, since the very point of Hilbert’s Hotel was to demonstrate the absurdities that would result from doing so.

My opponent’s next point is in drawing a distinction between subtracting transfinite cardinals versus infinite sets. He says that there is a difference between the subtraction of each, one being undefined, and the other not. While we may grant this point, it does little to counter the fact that when we subtract two infinite sets, we arrive at contradictory answers. What does this suggest? Well, it simply means that two unlimited sets may possess different cardinalities. But does it not beg the question to assume that reality is like this? If a set is truly going to be unlimited (re: infinite), how can it possess only part of the whole of all real numbers?

With respect to Euclid’s Maxim, Dante believes that because supersets contain their proper subsets, then it is indeed the case that Euclid’s Maxim applies to infinite sets. This, of course, grants the point that when we subtract infinity from infinity, then we arrive at contradictory answers. Infinity - infinity = infinity, infinity - infinity = 0, and infinity - infinity = 9 are all acceptable equations. I am aware of no philosophers of mathematics that argue that Euclid’s Maxim can be consistent with the principle of correspondence found in set theory. In fact, most philosophers who object to the kalam argument based on set theory are willing to do away with Euclid’s Maxim on the grounds that set theory is inconsistent with it. See J.L. Mackie on this point.

Forming an actual infinite by successive addition

Dante states that an actually infinite past may exist if we grant that it was not formed by successive addition. In his own words, neither an actually infinite future nor past is formed, but is always there. I will make two points about this. For one, he assumes a view of time at conflict with the prevailing position that time is dynamic. Unless there is a misunderstanding here, it seems that Dante believes that there is only apparent change and that future contingencies are really not what they appear to be. However, if he is going to take this position, then a reason ought to be presented that compels us to abandon a view so intuitive. Second, Dante’s assertion that{1, 2, 3...aleph-null} is not the reverse of {…-3, -2, -1} I think is confused. Indeed, if there is no point in the past that is aleph-null, then why postulate that the universe had no beginning anyway? Because the past has been actualized and is not waiting to be so (i.e. the past is not potential), it makes little sense to suggest that there is no point in the past that is aleph-null, and yet maintain that the universe is infinitely old.

As a follow up, my counterpart objects to the analogy of a borrowed book I gave in my opening. I stated that if I were to ask Dante for a book, and yet before he could lend it to me an infinite number of friends would have to receive it first, then I would never actually get the book. In answering this, he denies that if there is no original owner, then an actual infinite is not formed by successive addition. While this of course is the heart of the debate concerning this issue, consider it another way. If the present has been preceded by an infinite number of owners, then at aleph-null an infinite number of owners would have to be traversed. In this case, there is still an actual infinite being formed by successive addition, which is impossible. The problem is only alleviated if the past is finite; otherwise, there would have to be a passable infinite set, but this is a priori absurd. Remember, my receiving the book is not the beginning of a set formed by successive addition; it is the end of it. The set terminates at the moment I receive it.

Now, Dante correctly points out that there is no mathematical definition of infinity that implies “lacking nothing”. This actually highlights a distinction that I have been making all along--namely, that there is a fundamental difference between things that exist in the mathematical realm versus things that have a metaphysical basis in reality. In the real world, there is nothing that prevents us from subtracting members of a given set, so why make an exception for infinites unless one is trying to avoid the conclusion that the universe began to exist?

Empirical Confirmation

Dante makes two general points about the scientific evidence surrounding the origin of the universe. He says that there is some conflict within the scientific community about whether or not the universe began to exist. Further, he argues that if there is a singularity, then it constitutes an example of an actual infinite, and hence, contradicts the arguments above.

First, it is not at all clear how much conflict there really is among scientists. Not only is the Big Bang theory almost universally acknowledged as the most tenable position, but it is the only theory to be so precise and so highly evidenced in observation that rival theories have come simply come and gone. It is certainly possible that another theory could come along, but a core tenant of science is that we ought to look for the best available explanation, and not rely on what we can only imagine.

Onto the second point, even Dante admits that the General Theory of Relativity breaks down at some point. When he says that the singularity possesses an actually infinite density, then, we are warranted in being skeptical. Scientists withhold from commenting about the nature of the singularity itself for the most part, but the evidence does suggest that there was one. If this is the case, it is highly improbable on philosophical grounds that it banged all on its own.

Intuitions and the kalam cosmological argument

Dante lastly appeals to the fact that sometimes our intuitions are flawed. There are indeed examples where our initial ideas do not reflect reality. It appears that the cosmos revolves around the earth, but in reality the earth is gravitationally bound and revolves around the sun.

While this approach has some benefits, consider how many intuitions are actually confirmed by evidence. I do not doubt on any practical or realistic grounds that I am currently having an exchange with another mind (specifically, another human being) rather than a computer that sends automatic responses. None of us wakes up and worries whether we are just brains in a vat controlled by a mad scientist. In other words, our intuitions are indeed often trustworthy. In fact, it is likely that the vast majority of our intuitions are based in part on reality.

Dante says that our current experience of causation is one of temporal priority. That is fine. As I explained above, the fact that there is a change from (x & ~y) to (y) does not entail that there is any change in x itself, so long as x willed from eternity to bring y from potentiality to actuality. But further, Dante presupposes that there are only temporal causes, even in our own experience. However, we can think of examples where this is not the case, just as in the ball and cushion example.

A point about God’s infinitude should also be addressed. As I stated in my opening, there is a major difference between the universe’s being infinite and God being infinite. In order for the universe to be infinite, it would have to be composed of a collection of distinct and finite members. God’s infinitude, on the other hand, is not, since God’s is essentially simple rather than composed. As for God’s knowing infinite propositions, this too is fine under a conceptualistic paradigm. This only becomes a problem if one is a Platonist, but no arguments for mathematical Platonism are forthcoming.

Conclusion

Dante’s thoughts are well-presented, and I commend him for his intellectual giftedness. With that said, however, the objections to the kalam argument are unconvincing. Unless one wishes to postulate a universe that comes from nothing or entertain the idea that an infinite set has been traversed in order to arrive at the present, we have ample reason to conclude that the universe has a personal creator.

[diana]

Dante, please note that your next statement is overdue. However, you have a grace period of 24 hours from the time of this post.

d

[Dante Alighieri]

Again, I thank punkforchrist for his reply and I would again like to examine the previous post.

Causes

First, Dante disagrees that if there is a cause of all potentialities, it must be changeless.

I didn't say this.

Me: "If the universe's cause is was also the cause of all change[,] then the cause is changeless[.]"

We have no reason to believe (a) the universe constitutes all change nor (b) the cause is "fully actualized potentiality."

My original claim was simply that a being with pure actuality must possess maximal potentiality.

Me: "An egg is potentially a chicken, or a rotting carcass, or any particular state in the development of the egg. To say that x is potentially y does not determine some unique y, since there are many changes in that thing, leading a number of different states, hence, each state has as much claim to potentiality as any other."

A koala bear is more ignorant, smellier, etc. There's no objectivity here. Punkforchrist must handpick qualities to be "potential" and others as not. If a purely actual being lacks nothing potential, how can it lack ignorance and knowledge, cleanliness and dirtiness, etc?

Why assume from the outset that immaterial causes add complexity to the issue?

All causes found by modern physics concerning the framework of the universe have been physical. There are also multiple physical universe creation scenarios i.e. cyclic theory and inflationary theory. In fact, the latter has actually been recently confirmed in 2006. Since nothing in good evidence supports the role of nonphysical causation for the origin of the universe, immaterial causes decrease parsimony.

Further, if there are only physical causes, then the operations of our cognitive faculties are solely the result of physical determinism.
The noological argument is the beyond this debate's scope. Moreover, this problem doesn't involve physicalism but determinism. I explained in my first post how determinism is required for rationality and freedom. Finally, even admitting immaterial causes, we have only therefore found reason to posit them for minds. But, the universe is not a mind and all causes found or proposed pertaining to its origin and framework have been physical.

Causation

...this does conflate ontological priority with temporal priority [for] x and y do not need to occupy the same ontological position.
That is what the state of affairs (x & ~y) means. At the causal position, the cause does not exist with the effect. This is what cause being ontologically prior to effect means. If cause and effect are temporally simultaneous, then the causal and effectual positions coincide, which is a contradiction.

As for the ball and cushion example, the point is simply that if they were in a timeless state, where no change occurred at all, then the cause would be simultaneous with its effect.
I misunderstood your example earlier. Here, there is no cause and effect, because nothing is happening or occurring: there is nothing causing or being caused. All we have are a static ball, cushion, and impression. There are no moving particles or anything.

...he claims that there is a change between (x & ~y) and (y), but I see no reason to assume there was ever a temporal position of (x & ~y) to begin with.
As I said earlier, the cause is prior to its effect, ontologically. So, that means at the causal position (x & ~y) and at the effectual position (y). This is what the cause being prior to the effect means. This cannot be denied.

Obviously, there is a change from (x & ~y) to (y), therefore, all causation involves change, therefore causation is neither timeless nor simultaneous.

The fact that God is changeless does not imply that He cannot create, since God may have willed creation from all eternity without having changed at all in His essence...in order to go from (x & ~y) to (x & y) there does not need to be any change in x.
Me: "changes in persons are changes in causal structure i.e. the causal structure that humans inhabit is a material body. God inhabits a nonmaterial concrete object. This causal structure changes...in terms of actions, thoughts, etc...in my actions, I go from a state of not acting, to acting, to no longer acting. These actions are accomplished via my causal structure. Hence, God's acting itself constitutes a change in causal structure. He must initiate an action, which He then completes and hence is no longer acting that action."

Of course a person doesn't change in their essence otherwise they would cease being that person. But, they certainly change in their causal structure.

a being that is in potentiality can both be and not-be. But if God is eternal (re: timeless), He cannot not-be. Hence, there is no potentiality in God; therefore, God is pure actuality.
What this means is that potentiality is a synonym of "temporality" and pure actuality is a synonym of "eternality." I already agreed to that, but I pointed out that "pure actuality lacking nothing potential" doesn't follow from this.

InfinitiesDante states that if there are no absurdities, then the mathematics maps directly onto the facts.
I never said this. I said that if there are physical phenomena such that they correspond to the mathematical facts, there's no room to accept one and deny the other. Hence, no reductio ad absurdum arguments can follow as such.

While we may grant this point, it does little to counter the fact that when we subtract two infinite sets, we arrive at contradictory answers.
Punkforchrist says he grants my point, but then he then goes against it. By saying that when we subtract two infinite sets, we get contradictions, what he is saying is that the subtraction of their cardinalities results in different answers, because only the subtraction of their cardinalities gives different answers. But, he just accepted that the subtraction of their cardinalities was undefined. Punkforchrist is contradicting himself. Indeed, he goes on to say that "Infinity - infinity = infinity, infinity - infinity = 0, and infinity - infinity = 9 are all acceptable equations." This is explicitly a subtraction of their cardinalities, which he just accepted as being undefined.

If a set is truly going to be unlimited (re: infinite), how can it possess only part of the whole of all real numbers?
A set that is unlimited is infinite, but not all infinite sets are unlimited. For that matter, the idea of an "unlimited" set was long ago disproved by Russell's paradox and Cantor's power sets. The natural number is infinite, yet they lack all the real numbers.

In fact, most philosophers who object to the kalam argument based on set theory are willing to do away with Euclid’s Maxim on the grounds that set theory is inconsistent with it.
Not true. In fact most philosophers today believe it to be totally compatible with modern set theory. I cited a couple of them: Wes Morriston and Josh Dever.

Unless there is a misunderstanding here, it seems that Dante believes that there is only apparent change and that future contingencies are really not what they appear to be.
There is a misunderstanding. Nowhere did I defend eternalism. A presentist could also consistently say "Right now there are an infinitude of events that were present and events that will be present."

Indeed, if there is no point in the past that is aleph-null, then why postulate that the universe had no beginning anyway? Because the past has been actualized and is not waiting to be so (i.e. the past is not potential), it makes little sense to suggest that there is no point in the past that is aleph-null, and yet maintain that the universe is infinitely old.
How? Firstly, the same argument could be made of the infinite future. Secondly, if there were a point infinitely distant, then the universe would have a beginning, an infinitely distant one. Punkforchrist is positing that a beginningless universe actually begins.

There's nothing about an infinite past that implies that there is an infinitely distant beginning. All the infinite past means is that "for every interval t, there is an interval t' which is prior to t." This doesn't imply an infinitely distant point, indeed, that would be like saying that the negative integers contain aleph-null as a member, which they don't.

In answering this, he denies that if there is no original owner, then an actual infinite is not formed by successive addition.
Actually, I accepted that: "A relevant example would be if there were an infinity of lenders, each lending the book to each other until it reached me. This corresponds to {...-3,-2,-1}. No problems arise with this example. There's no original owner of the book, but the sequence is just as successive, just like the negative integers."

If the present has been preceded by an infinite number of owners, then at aleph-null an infinite number of owners would have to be traversed. In this case, there is still an actual infinite being formed by successive addition, which is impossible.
How? This is only the case if you define "traversed" the same as you defined "formed," which I pointed out that neither is possible. An infinity is not "traversed" as such, but is in effect always there. To say that it was "traversed" as it being "formed" is a mistake, especially if you construe traversal as starting from the beginning of an interval and then continuing to its end.

Remember, my receiving the book is not the beginning of a set formed by successive addition; it is the end of it. The set terminates at the moment I receive it.
Yes. But your asking for the book is the beginning of the set, which as I said earlier, "Punkforchrist's book example shows this confusion, since it corresponds to the set {1,2,3...aleph-null}, in which he asks a friend for a book (i.e. the set has a beginning) and after an infinity of inquiries, he receives the book (the sequence terminates). This example is irrelevant, as explained."

This actually highlights a distinction that I have been making all along--namely, that there is a fundamental difference between things that exist in the mathematical realm versus things that have a metaphysical basis in reality.
Not at all. There are also no unlimited mathematical objects either. Russell's paradox and Cantor's power sets demonstrate this. All unlimited things (there can't be any) are infinite, but not all infinite things are unlimited.

In the real world, there is nothing that prevents us from subtracting members of a given set, so why make an exception for infinites unless one is trying to avoid the conclusion that the universe began to exist?
Nothing prevents subtracting from an infinite set. This too was long ago answered.

Confirmation and Intuitions

First, it is not at all clear how much conflict there really is among scientists. Not only is the Big Bang theory almost universally acknowledged as the most tenable position, but it is the only theory to be so precise and so highly evidenced in observation that rival theories have come simply come and gone.
I never challenged Big Bang cosmology. I challenged what you construed to be talking about. I pointed out that Big Bang theory doesn't support the idea of the universe having a beginning, nor does it show physical reality having a beginning, since there is no reason to believe that the observable universe is all of spacetime. Inflationary theory attests to this.

Onto the second point, even Dante admits that the General Theory of Relativity breaks down at some point. When he says that the singularity possesses an actually infinite density, then, we are warranted in being skeptical.
Indeed. We are then warranted in withholding judgment on whether there was a singularity at all. Unfortunately, this is entailed by relativistic interpretations of Big Bang cosmology (as even W.L. Craig points out, due to the Penrose-Hawking singularity theorems) and contradicts punkforchrist's anti-infintist arguments. One must go. However, without a relativistic interpretation of BBC, there's not even support for supposing that this region of spacetime had a beginning, let alone all of it.

Scientists withhold from commenting about the nature of the singularity itself for the most part,
Not true. Singularities are universally agreed upon to be infinitely dense, where its measurement becomes infinite. This is the definition of a singularity in the first place.

but the evidence does suggest that there was one.
Not at all. As I said earlier, the restrictions placed upon by the Planck epoch and the failure of general relativity here simply indicates that there is a problem. Most cosmologists take singularities to signify a problem in the theory itself, not an indication of reality.

If this is the case, it is highly improbable on philosophical grounds that it banged all on its own.
Why? This is actually entailed by the dynamics of naked singularities.

None of us wakes up and worries whether we are just brains in a vat controlled by a mad scientist. In other words, our intuitions are indeed often trustworthy. In fact, it is likely that the vast majority of our intuitions are based in part on reality.
There is a vast dissimilarity between punkforchrist's examples and mine. His examples concern what we cannot rationally doubt as being rational agents. Doubting induction, all of our memories, our very material existence, or other minds are things that we cannot doubt. These are pragmatic concerns, but they are pragmatic concerns set by the very foundations of rationality itself.

My examples were a great deal more mundane and things that could be denied. For instance, quantum mechanics, non-Euclidean geometry, etc. All are counter-intuitive and yet they all obtain. So, our intuitions are not good guides to most of reality at all.

Dante says that our current experience of causation is one of temporal priority. That is fine.
But, then that undermines whatever support there is for the causal premise, which requires timeless causation. Punkforchrist's other comments were previously addressed.

He has also not dealt with my comments on continuous time, Euclidean geometry, or other such things. It would seem counter-intuitive that time is non-continuous or that space is non-Euclidean. But, both continuous time and Euclidean geometry entail infinites. For that matter, we know that there are infinites i.e. inflationary theory shows that space is infinite in size and general relativity shows that time is continuous, and cosmology shows that there is an infinite future. Since Craig's argument for the causal premise and the first argument against infinity is purely one of intuition, therefore, the fact that intuitions are not good guides to reality undercuts those points.

God’s infinitude, on the other hand, is not, since God’s is essentially simple rather than composed.
This is not true. For instance, God's power scopes over an infinitude of actions. His knowledge scopes over infinite propositions and for that matter, an infinite future.

As for God’s knowing infinite propositions, this too is fine under a conceptualistic paradigm.
How?

This only becomes a problem if one is a Platonist, but no arguments for mathematical Platonism are forthcoming.
How does conceptualism suddenly do away with the problem? Platonism and conceptualism are not relevant here. That said however there are multiple arguments for Platonism such as the Quinean indispensability argument or the Fregean singular argument.

[Alcyonian]

punckforchrist has asked to make some changes to his previous (and final) post to correct some errors. Dante Alighieri has agreed to this.

Alcyonian (FD&D Moderator)

[punkforchrist]

I’d like to begin my closing statement by again thanking the moderators, the IIDB forum, and finally Dante Alighieri. He has been a most gracious and knowledgeable opponent.

The Kalam Cosmological Argument has just two premises, and if they are true, then the conclusion that the universe has a cause necessarily follows. Each of the two premises I have outlined are supported by several arguments. Let us take a look at them again and see if we can come to a verdict.

Whatever begins to exist has a cause

Dante never denied that out of nothing comes nothing. Instead, he has offered arguments against things like timeless causation and the impropriety of immaterial causes. Of the former, he says

At the causal position, the cause does not exist with the effect. This is what cause being ontologically prior to effect means. If cause and effect are temporally simultaneous, then the causal and effectual positions coincide, which is a contradiction.

He has denied any conflation between ontological and temporal priority, but I think it is clear that he commits this fallacy in the above statement. The fact that God is ontologically prior to the universe does not in any way suggest that He is temporally prior it. The fact that (x) and (y) are simultaneous does not indicate that there is any ontological position of (x & ~y), unless he only means that x is not identical to y. The fact is that x does not need to be temporally prior to y in order to be the cause of it.

The example of the ball and cushion is a perfect illustration of this. Dante claims that there is no example of causation here, since there is never a moment where the impression comes into being (that is, it never came into existence after not existing). Once again, this merely presupposes temporal causation. Without the ball, there would be no impression. It is only with the ball being on the cushion that an impression exists. Hence, the ball acts as a cause of the impression. I think this is fairly obvious, with all due respect to Dante.

Concerning immaterial causes, Dante believes that only physical causes qualify for the use of Ockham’s Razor. He says that all causes discovered by modern physics have been physical in nature. Now, of course this is true if we grant that there is no dualism, but then Dante is making a bold claim in support of ontological monism with respect to the mind/body problem. I see no reason to make this assertion unless one is trying to avoid the conclusion that the universe has a transcendent cause. Since nothing comes from nothing, then the universe must have had such a cause if it had a beginning.

Dante also says that my objection about determinism does not concern physicalism. I must disagree with this, as well. If physicalism is true, then what room is there for anything other than determinism? Dante’s compatibalism does not leave room for indeterminist events. My point is not to argue in favor of libertarianism, but rather to point out that Dante’s position forces him to defend a number of other views.

On a final thought, my counterpart says

Of course a person doesn't change in their essence otherwise they would cease being that person. But, they certainly change in their causal structure.

“Causal structure” can mean a number of things. Since I deny any change in the essence of God as a result of His bringing about the universe’s existence, I consequently disagree with the implication that Dante is making. However, I do agree that there is a change in the relationship between God and creation. At any moment Z, Y will be related to X in a different way than Y was at M. But so long as X wills to bring about Y eternally, then there is no contradiction in saying that X precedes Y temporally. X may have willed for Y to begin at a moment later than X’s eternality.

The universe began to exist

With respect to the second premise, I am glad that Dante has clarified what he meant regarding actual infinites and their mapping onto the facts. He says

I said that if there are physical phenomena such that they correspond to the mathematical facts, there's no room to accept one and deny the other.

Of course, this is true, but whether or not there are such physical phenomena is the very question at hand. Hence, it begs the question to assert that actual infinites exist in the physical world when there is no basis for it other than their existence in the abstract realm. Dante believes that the subtraction of infinite cardinalities is undefined. I agree with him here. Where I disagree with him is over whether or not this constitutes an impossibility of actual infinites existing in the physical world. I urge everyone to think of the problem this way: when we subtract books from a library, or dig up carrots from a farm, is it possible for the remainder of objects to be undefined? Do we not have a definitive solution? I think we do. If we cannot talk about these kinds of objects as undefined, why should we accept the notion of a beginning-less universe when it requires the exact same thing? To assert that we can without providing a sufficient reason is a case of special pleading.

To make the case a little clearer, in set theory we can create a one-to-one correspondence between the set of all positive integers with the set of all positive odd integers: {1, 2, 3, 4. . . } with {1, 3, 5, 7 . . . }. Both sets contain the same number of elements. But when we remove all the odd integers in both sets, we are left with {2, 4, 6, 8 . . .} and 0 (0 not being part of the original set of odd integers). In a second example, we have {1, 2, 3, 4 . . .} and {10, 11, 12, 13}. Suppose we subtract all integers numbered ten and higher. We now have {1, 2, 3, . . . 9} and 0. In both examples, we subtract identical quantities and arrive at contradictory answers. Saying these solutions are undefined makes no difference, since nothing in real life would ever prevent the subtraction of such elements.

Onto the second philosophical argument for a beginning to the universe, I claimed that if there is no point in the infinite past, then the universe must be finite. He says that the same could be said of the infinite future. However, I am not sure what his point is. If we are going to accept a tensed version of time, then all past events have been actualized, whereas all future events are merely potential. There is nothing inherent in the concept of future events that requires us to believe that there is an actual point in the infinite future, since all such points are merely potential and will only approach infinity as a limit. The past is different, since all past events have historically occurred.

Now, Dante denies having adopted a static view of time, such as eternalism. However, if all past events co-exist in this sense, then how is this not a denial of a dynamic view of time? Dante postulates that all members of the set aleph-null are eternally present, but if he is going to take this position, then he must deny that change actually takes place on a dynamic position.

Next, my opponent comments on my book analogy. I said that if I wanted to borrow a book from Dante, and he had to borrow it from another, and so on to infinity, that I would never receive the book. He responds by saying that my asking for the book is the beginning of the set. However, this misconstrues the analogy. The act in question is not my asking for the book, but the transition from one person to another in lending the desired object. Since no person actually has the book, then how can I ever get it? Further, if I receive the book today, why did I not receive it yesterday?--since by that time, the same amount of time had already elapsed. These paradoxes are not problematic if we accept that the universe had a beginning. We only involve ourselves in mental gymnastics in order to accommodate this with an infinitely old universe.

Empirical Confirmation

Throughout the debate, Dante and I have disagreed as to whether the standard Big Bang theory points to a beginning of the universe. He insists that a multi-verse theory can solve the problem, but how? I do not see any reason to accept a multi-verse theory unless one is trying to avoid the conclusion that the universe began to exist. There is no evidence in support of multi-verses, and we have seen that the very notion of them only adds complexity to modern cosmogony. Dante has also appealed several times to inflationary theory and indicates that this undermines the empirical support for the universe’s beginning. This, of course, was theorized by Andrei Linde, since an absolute beginning of the universe troubled him. As Arvind Borde and Alexander Vilenkin point out, though, “A model in which the inflationary phase has no end . . . naturally leads to this question: Can this model also be extended to the infinite past, avoiding in this way the problem of the initial singularity? . . . this is in fact not possible in future-eternal inflationary spacetimes as long as they obey some reasonable physical conditions: such models must necessarily possess initial singularities.” [1]

Next, Dante again contends that the notion of a singularity implies infinity, which contradicts the two philosophical arguments (although it really only contradicts the first; the second only says that an actual infinite cannot be formed by successive addition, which is different than saying the universe’s singularity was infinitely dense). I think this also misapprehends what scientists claim about the singularity. As physicist Brian Greene states, the Big Bang theory “delineates cosmic evolution from a split second after whatever happened to bring the universe into existence, but it says nothing at all about time zero itself.” [2] Thus, there is no reason to assume that the singularity is in fact infinitely dense, since nothing is known about the nature of the absolute beginning of the universe.

Back to infinity

Dante also believes that continuous time undermines the idea that actual infinite are impossible to traverse. This, of course, only helps his case if time is, in fact, continuous as opposed to discreet. As G.J. Whitrow points out, “The modern theory of infinity . . . is essentially a static theory of infinite sets. Similarly, the modern theory of the variable . . . is again a static theory, for the variable is no longer regarded by pure mathematicians as representing a progressive passage through all the values of an interval but the disjunctive assumption of any one of the values in the interval. Thus the acceptance of the modern theory of the continuum cannot be invoked as a valid argument automatically disposing of Kant's antinomies . . . , since this theory has been developed by specifically omitting all previous intuitive reference to the concept of time.” (emphasis mine). [3]

Finally, Dante asserts that if there are no actual infinites, then God’s thoughts cannot be infinite. At first glace this appears to be a reasonable objection to the kalam argument. However, we have a couple of options. First, we could simply deny that God’s thoughts are actually infinite, and say that they are potentially infinite. Of course, that is not an appropriate position in light of what I have been defending. I think the best way to answer this is to point out that the conceptualism I have been suggesting does not entail that infinity cannot exist in the mind. Indeed, I have never argued against that. The fact that God knows an infinity of propositions does not in any way suggest that infinity can exist in the physical world. Dante denies that Platonism is relevant here, but I encourage everyone to look into this themselves.

The KCA Undefeated

With the above considerations, I believe a strong and compelling case can and has been made for the belief in a personal creator of the universe. There is only one caveat. So what? Who cares if there is some creator “out there”. What does this being have to do with any of us? Well, as a Christian, I believe that this creator God has revealed Himself to mankind. Some of you who are following along may not agree with me, but I think all of us are in pursuit of truth. Whether or not you agree with me that God has made Himself known to us through Christ, the Kalam Cosmological Argument ought to provide an incentive for further inquiry into the issue. I hope this exchange has been as intellectually stirring for you as it has been for me.

[1] Borde and Vilenkin, "Eternal Inflation and the Initial Singularity," Physical Review Letters 72 (1994), pp. 3305, 3307.

[2] Greene, Brian. The Fabric of the Cosmos. (New York: Vintage Books, 2004), p. 272.

[3] Whitrow, G.J. British Journal for the Philosophy of Science 5, p. 217.

[Dante Alighieri]

Introduction

I'd like to thank punkforchrist for being an excellent opponent and the moderators for their hard work. Punkforchrist has truly been a most engaging opponent.

Causation

Punkforchrist states that I've confused ontic and temporal priority. I disagree. In a cause-effect relation, cause is prior to effect. The effect comes into existence: ontically, at the causal position, it does not exist. Hence, if causal and effectual positions are temporally simultaneous, then the states of affairs at the CP (x & ~y) are simultaneous with the states of affairs at the EP (y). Another way of putting this is that ontically, the effect comes into existence: at the CP, the effect does not exist and at the EP, it exists. Hence, if CP and EP are temporally simultaneous, a contradiction is entailed. Punkforchrist has not yet elaborated what conflation is present here. Moreover, I have also pointed out that simultaneous causation is not actually timeless causation.

In his ball-and-cushion example, he says that I presume temporal causation. But, universal to the notion of "cause" is that the cause makes the effect actual; there is an ontic priority here, as I elaborated above. If nothing is coming into existence, then nothing is happening, and nothing is being caused. The fact that the impression does not come into existence is enough to show that the impression was not caused.

He continues to argue against my objections with respect to the parsimony of physical causes. First of all, at best, dualism if true (note that punkforchrist has not argued for this), only shows that PoPC does not apply for the cause of personal causes. But, punkforchrist has not convincingly argued that the cause of the universe (if it had one) was personal. Moreover, I was merely pointing out that all physical phenomena in cosmology have been explained by physical causes. Hence, attempting to explain the cause of the universe as being nonphysical goes against our data set, acquiring a low parsimony. One need not point out that the hypothesis of a personal creator is but one of many for the purported cause of the universe, of which there are multiple physically possible causes.

Punkforchrist also thinks