## Thursday, August 30, 2007

### What Logic Requires Us To Believe About The Existence of God--Part 3

As we continue with the series What Logic Requires Us To Believe About The Existence of God, it is probably helpful to provide a link to our previous points. You can read Part 1 here and Part 2 here.

As was mentioned previously, philosophers make a distinction between “being” and “becoming” as characterized by the distinction in the statements “What is, is” and “What is, is changing.” Furthermore, we already spoke of how the idea of “becoming” could be viewed atemporally as the concept of “being” frozen in specific points of time, but we can also define A in the identity “A is A” as having a temporal aspect as well. In both cases, we are presented with a question of time.

Time has fascinated me greatly for years, and it is quite possible for me to go on a lengthy bunny trail on this subject. However, I will resist that and instead limit our discussion for the moment to only those specific aspects of time that we can logically link to the concept of existence (as described in the last post). First of all, we must ask: what is meant by time?

This is a difficult question to answer, much as defining “existence” is difficult. We could take Einstein’s view that “Time is that which clocks measure.” Or we can take the other physicist’s common idea: “Time is what keeps everything from happening all at once.” Neither of these is very satisfactory.

We are not helped much by the advent of Special and General Relativity. Instead of simplifying the problems for us, conceptually it increased the difficulty. There is no such thing as a universal time anymore. The rate of time depends upon the rate of movement through space, such that the faster you move through space the slower you move through time. In fact, one way of illustrating this is by imagining that you have an engine that can move through four dimensions (three space and one time), but that the combined rate of movement must equal exactly the speed of light. As such, since light moves through space at the speed of light, it moves through time at a speed of 0. On the other hand, we move through space at a much slower rate, and the leftover bits get transferred to how fast we move through time. Thus, the faster we move through space, the slower we move through time.

While this brings up immediate bunny trails (for instance, how would one determine my “age” when, for instance, no time has elapsed for a proton that escaped the sun at the exact moment I was born—although this is weakened by the fact that according to relativity, there is no such thing as simultaneous events anyway), again we need only speak of a few points here.

The first is this: no matter how we look at time, we are always reduced to a question of existence. If time is that which clocks measure, then clocks must exist before there can be knowledge of time. Note that this does not mean your bedroom alarm clock must exist before time exists! A clock is simply a device that has repetition built in. The Earth rotating once on its axis is a clock—1 rotation = 1 day. The Earth rotating around the Sun is also a clock—1 rotation = 1 year. Furthermore, most of our watches today are built by counting the frequency of quartz crystals that vibrate at a specific rate when electricity passes through them—32.768 kHz = 1 second.

Naturally, while clocks measure time clocks are not time themselves. Indeed, we can imagine that if all physical processes stopped, time could still move on. However, time’s “moving on” is only meaningful if things later change back to movement. Then, the period between the stop and the start of physical process would be a unit of time. Time is meaningless if all physical processes ceased and never picked up again.

This leads us to a related point: the perception of time. We are primarily convinced of the existence of time because we are able to perceive change. We know things today that we didn’t know yesterday, and we can remember learning these things. We can put a piece of bread on the counter and watch as it first becomes stale and then eventually grows moldy. We perceive these changes.

Again, this does not mean our perceptions are valid. Just as we cannot prove other objects exist via our perception of those objects, we cannot prove that those objects change via our perceptions. But we can prove we have the perception of change, for we have memories of the change.

In this case, however, our perception is not able to do for time what it could do for existence. That is, while our perception means we know existence exists by direct knowledge, our perception of the passage of time could be an illusion. Our memories could be false memories. We could possibly exist as beings outside of time with false memories of the passage of time, including thoughts of our remembering certain things occurred “more recently” than other things. But while this might be possible, it is hardly probable. Indeed, it is difficult to see how it would be possible for a timeless existence to have beings that exist with the memories of time, especially as elaborate as these memories are.

So let us assume the existence of time. It is not only most likely to be right, but if it is a false assumption it doesn’t matter. After all, if this is a false assumption then I can never change my mind on the issue as I will be forever frozen with this idea that time is real. No one can “convince” me otherwise, as that would require change and change can only be expressed through time. Thus, there remains absolutely no reason to doubt the existence of time.

Let us now couple this notion of time with our previous post’s ideas of existence. Since I know for a fact that something most certainly exists due to my direct knowledge of my own perceptions (and due to the fact that even if my perceptions are imaginary, I must exist in order to be deceived by them) and since there is no reason to doubt the validity of time, what does this mean for us?

First (and most paradoxically) it means that there must be some form of existence that is outside the realm of time! In other words, existence within time presupposes existence outside of time too. How does this work? To answer that question, we must first ask another: where did my own existence come from, or did it come from anything?

There only seem to be a grand total of three possible options here:

1. I am self-created.
2. I am self-existent.
3. I am created by something else that is self-existent.

(Another option that philosophers have used is “4. My existence is an illusion” but we have already disproven this notion.)

So what would it mean if I were self-created? Basically put, it would mean that at one point there was nothing, and out of that nothing I created myself. But this explanation already seems absurd (and it is), for if there is “nothing” then not even I existed then. But if I didn’t exist then, then I would not be able to create myself. Self-creation, therefore, results in a logical contradiction: I exist and yet I non-exist at the same time and in the same relationship, if I am self-created.

So self-creation is illogical. Logic dictates instead that there must be some form of self-existence. What is self-existence then?

Self-existence means simply that the self-existent object has the “power” of existence with itself. If I am self-existent, then I contain as one of my attributes the attribute of existence. This, in turn, would make me a necessary being—for if I hold the power to existence within myself then it is impossible for me to cease to exist without ceasing to be me.

But my perceptions are not that I am myself a self-existent being. Instead, I perceive that I have parents. Let us suppose this perception is right (and I have no reason to deny it). The question moves back one step. Where did my parents come from? Either they are self-existent, or they too were created by something else.

My parents claim to have parents. The chain moves back up another link and we repeat the question again. Soon, we have travelled quite some distance. In fact, some might be tempted to ask “Why isn’t it possible that there are an infinite number of links in this chain? If the chain is infinitely long, then we never need to stipulate that there was some being that was self-existent.”

The problem with the infinite chain idea is the infinite time involved. See, if my existence comes from something else, and that something else’s existence comes from another something else, and this continues forever, then we have continual change. Change, as we talked about earlier in this post, is the essence of time. An infinite chain of change would take an infinite amount of time to form. But if it took an infinite amount of time to form, then we could not presently be in our current time—we would still be an infinite time in the past from this point!

In other words, an infinite chain involves us with what is called an infinite redux. The same position must be taken back one step an infinite number of times, and therefore nothing is ever gained. The only way to stop this is if, at some point, we break out of the chain and stipulate there must be something to start the chain, and that chain-starter must be self-existent.

For the same reasons as the infinite redux, this self-existent being must be able to transcend time itself. In other words, the self-existent being must be eternal (by eternal we do not mean infinite, as that would bring us back to the infinite chain problem; we mean only that an eternal existence is not bound by time). It exists apart from time (which, being linked to space as demonstrated in our example of the engine, means that the self-existent chain-starter must have non-physical existence too).

Thus we have established that logic demands that there be some form of self-existence. Since all I have direct knowledge of is my own existence, I might be that self-existent being. But if my perceptions are right, I am most certainly not that self-existent being. How can we tell if I am this self-existent being or if I am instead created by this self-existent being after a long series of other creations? What other things does logic require us to believe at this point?

We shall find out in our next post.

1. Peter,

Nice job. It’s a nice representation of the old argument from contingency. I do have some worries. First, let me refine what you said. You said, “If I am self-existent, then I contain as one of my attributes the attribute of existence.” Well, yes, that’s true, but non-self-existent beings also contains the attribute of existence; that is, because they exist. I think what you mean is that “If I am self-existent, then I necessarily contain the attribute of existence.” Now, you did say that in the next sentence, but you can also refine it this way, “If I am self-existent, then I essentially contain the attribute of existence.” Now, when you speak of containing the attribute of existence, it seems that you are speaking of existence as a property. So, this means that a self-existent being has existence as its essential property. Of course this will go to the problem of whether existence is a property or not. But that’s just a minor point, I think.

Now you said there are three possibilities:

1. I am self-created.
2. I am self-existent.
3. I am created by something else that is self-existent.

Here are some criticisms a skeptic might give. First, in asking “where did my existence come from?” one may say that you are already assuming the principle of Causation (PC). One might say that you have not provided an argument for that. Maybe the reason for the existence of myself is not a causal explanation. So I think one might object by saying that you have not provided a case why we should apply PC rather than, say, the principle of sufficient reason (PSR). Both are not the same thing (I think Anscombe also pointed this out in her critique of Lewis). I think it would be much better off if you used PSR rather than PC in this case. Second, those three are not just the three possibilities if by possibilities you mean logical possibility. Take:
(4) I am created by a contingent being

Of course you go into this with regards to infinity and such which I will come back on later. However, (4) is definitely a possibility. Suppose you created a robot. Now, that robot created object X (put in here whatever you want). Now, X was not created by me. It was created by the robot. One might ask, Why am I not like X? Why do I have to be either self-created, self-existent, or created by a necessary being? Why can’t I just have been created by a contingent being, like X being created by the robot? Before you go with the infinite explanation, you will have to speak of (4). (4) is definitely a logical possibility. Contingent beings create things all the time. Also, take the example of the number 2. Does one ask “where does the number 2 come from?” Do they need to be created? (I know Plantinga actually made an argument for God’s existence on numbers and properties, etc). Again, a heavy question that needs a lot of other explanations. So, one might say, does the number 3 either have to be created, self-exist, or self-created? If not, then why do I have to be? In other words, why am I not like abstract objects? So I think you have to say something along the lines of, concrete individuals that are not uncaused need an explanation for its existence. Of course, the question then becomes: why does there have to be be a sufficient reason for my existence? Suppose I am a being with no sufficient reason to exist. Is that illogical? No. Metaphysically counterintuitive? Maybe. Nonetheless, it does seem to defeat your position which is a *logical* argument. Again, I think it would be better if you are making an argument from metaphysical possibility and necessity rather than logical possibility and necessity. Metaphysical possibility is a bit “weaker” and that would be an advantage, I think. In fact, I think when you speak of logical, you seem to speak of metaphysics.

Now with infinity. I am created by my parents. We ask, are my parents self-existent? And so on to infinity. You then ask, why can’t we have an infinite series? Well, here are a couple of problems. First, maybe a *linear* infinite series cannot fulfill PSR but a non-linear infinite chain can fulfill PSR, say, like a web, like the way the Coherentists argue about epistemic justification. So why think that causation or SR has to be linear? If Coherentism is right, then a “web” infinite series may fulfill PSR. Just a though. Second, I actually lean towards the Aristotelian distinction between potential and actual infinity, but it is hard to define the difference once you look at it closely. Maybe you have an argument on this. Third, you said,

“But if it took an infinite amount of time to form, then we could not presently be in our current time—we would still be an infinite time in the past from this point!”

Someone will respond: that’s not true. Take a line. A line is made up of points. Points are zero-sized. So, Zeno asks, “If 0+0+0+0…infinity..= 0, then how can there be a line?” Or, take a 2 feet line. From 1ft to 2ft, there are an infinite number of points. But we do not say, “if there is an infinite number of points, there would be no 2ft!” However, there is 2ft. So, it seems that it is in some way possible. Also, in mathematics, .1+.1+.1, infinity does equal to 1. That is what mathematicians tell me. I may be wrong, but that seems to be what mathematicians say. So one can counter your argument by saying that time is like a line. Or take the numbers between 1 and 2. Are they infinite? Yes. Are they actual? Well, yeah, because numbers are actual; not concrete, but actual. Why can’t concrete events or causes by like numbers? If you have an argument for this, I would like to hear it because I have been struggling with this for years. For more on this, see Frank Arntzenius’s stuff. I would also recommend Alex Pruss’s book on the principle of sufficient reason.

But I don’t want to leave in a simple criticism because I want your argument to succeed. In fact, I have made my own version of it when I debated an atheist. However, I have began to doubt my own argument. Here is something that might be worth looking at as it has been used by contemporary philosophers (Plantinga, Pruss, Gale, etc.) Take this argument:

< > [ ] P --> [ ] P

[ ] P--> [ ] P

< > [ ] P

[ ] P

P

Take argument is valid. The first premise is true. It is axiom S5. Now, Let P= there exists a supreme, intelligent, all-powerful, all-good, etc creator. Here you have a proof for God’s existence. Or, let P= God.

Is it sound? That’s the big question. There may be an equivocation on “possibility”, though, one of the premise being metaphysically possible but the other premises being logically possible. If that’s the case, then it’s no good. For more on this, see Alex Pruss/Gale’s cosmological argument. See also Robert Koons’s own cosmological argument. I think it would be better off if you use this type of argument, using axiom S5. Also, of course, the key premise would be:

< > [ ] P

Here, you will have to use, I think, PSR. Now, for arguments against PSR, cf. Conee/Sider Riddles of Existence.

2. Oh, and also, I think with regards to causation, you can argue:

there is either always something at every t or nothing at some t.

Is this a good premise? Well, I don't know if the disjunction holds, it seems that it does. But, the question is, what exactly is "nothing"? Well, someone might say, a set with no existential value. Or, "an empty set." But that seems to be hard to grasp. Can we really speak of an empty *set*? So, maybe there must be something at every t. Of course the argument with this is that God exists outside of time (I don't know what your view on this is as other Christians like Craig, Woltersoff, etc have different views on God and time). However, I think one can adjust the premise above. I don't know. It does seem there is something there.

3. argh, correction: the second premise should look like:

[ ] P--> P

4. Apolonio said:
---
I think what you mean is that “If I am self-existent, then I necessarily contain the attribute of existence.” Now, you did say that in the next sentence....
---

Which makes this "objection" (not sure I'd actually call it that, but I can't think of a better word at the moment) is really a stylistic difference. I should note that my posts are not designed to address every single philosophical issue here. Rather, they stem from the fact that I've used a much simpler form of the entire discussion and had e-mails from non-philosophers who asked if I could expand it. I could have responded with philosophical jargon, but that would not have helped them; this is why my style is more "populus" based at the moment, although I'm trying not to go too simple either (given the subject matter, I don't think that's really possible anyway...) ;-)

Apolonio said:
---
First, in asking “where did my existence come from?” one may say that you are already assuming the principle of Causation (PC). One might say that you have not provided an argument for that. Maybe the reason for the existence of myself is not a causal explanation.
---

In which case I would say this is equivalent to stating that I am self-existent, which is one of the three categories I gave. In other words, if I am not a self-existent being (and since self-creation is illogical) then the causation must follow.

Both the self-existent and self-created categories do not rely on causation. Non-causal arguments would apply into one of them (although feel free to demonstrate how existence can be non-self-existent and yet also non-caused).

Apolonio said:
---
Take:
(4) I am created by a contingent being

Of course you go into this with regards to infinity and such which I will come back on later. However, (4) is definitely a possibility.
---

Actually, the point about this with regards to infinity is why I didn't mention it explicitly as one of the three options. At some point, you are still left with the origin on the chain being self-existent. While this does not mean that my own existence would be directly from a self-existent being with no intermediate steps, my existence is, at some point, bound to that self-existent being. The logic of the argument doesn't change if we add in any chain of length n (where n is >= 0 and < infinity) and reword it to:

(3) My existence is contingent upon a self-existent being after n number of intermediate steps of non-self-existent beings.

Stating it in this manner would have required more explanation at this point in my post than I felt warranted by my target audience, which is why I did not include it explicitly but instead only gave the example of why an infinite chain would not be logically possible.

Apolonio said:
---
Also, take the example of the number 2. Does one ask “where does the number 2 come from?” Do they need to be created?
---

I don't believe that the number 2 has existence or being as has been defined so far. Remember, I am speaking in this post with a severely limited context. Existence has thus far only been established as that which is known by direct knowledge via perception (and as such, thus far I have only been able to prove that I exist, and that if anything exists then something must exist self-existently--I haven't even established yet whether I am that self-existent being or not, for the existence of other objects has not yet been "proven" by my argument). This is why I provided the links to the previous posts and why this post is "Part 3" instead of "Part 1" :-)

Apolonio said:
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Suppose I am a being with no sufficient reason to exist. Is that illogical?
---

Depends on how you define logic here. (Again, I refer you to my first post so you can see how I am using this term here.)

Oh, and to answer the question, I would say it is "unreasonable" that a being without sufficient reason to exist would exist, in keeping with the framework of the sentence (i.e. It addresses reason rather than logic proper, so to jump from reason to logic in the answer is a category error).

Apolonio said:
---
Someone will respond: that’s not true. Take a line. A line is made up of points. Points are zero-sized.
---

But time is not zero-sized; it is quantized at Planck time. Remember, we are dealing with time as defined by "that which clocks measure" (i.e. physical processes) and since the Heisenburg principal shows we cannot measure smaller than Planck length, we cannot measure smaller than Planck time either (the length of time it takes light to go the Planck length).

By the way, quantization neutralizes all of Zeno's paradoxes :-) See, for instance, having Fun With Infinity.

In any case, I appreciated your response (although your level of philosophical training was not the level I was originally writing to, which was for beginning philosophers). After I'm done with these series, if I have time I'll go over it more indepth to address the deeper philosophical questions.

5. Apolonio,

Don't listen to Peter. The answer is "eight".

6. Shows what Mathetes knows.

7. Peter,

Cool. Sorry if I read too much into it. Let me give a little reply.

You said that if I am not a self-existent being, then causation must follow. One may reply this way. First, that's not intuitive. Second, there is certainly a way where I can be a non self-existent being and still have no causation following. Suppose I am a property of X. X would *entail* my existence. But we would not say that X causes my existence. Rather, what we would say is that X is a sufficient reason why I exist. There is a difference between ground-consequent and causation. So, one can say that I do not need a cause but I do have a ground for my existence. Of course one can say that I am not a property of X, but the point is that there need not be causation.

Also, you spoke of an infinite chain being logically impossible. But I think what you are speaking of is metaphysical possibility/impossibility.

As for the other infinity and the existence of numbers, I'll let that go for now because I don't want my head to start spinning and I don't want to open another can of worms...It *is* Friday.. :-)

If you're interested in zeno's paradox and infinities, see:

http://fas-philosophy.rutgers.edu/arntzeni/

Go down to the draft of book chapters. He presented it to the seminar I was in. It's very good and changed the way I thought. Again, it seems that I still lean towards Aristotle on infinity but there are some problems I still have to face.

8. Oh, and also...you spoke of me being irrational if I don't have a sufficient reason. Well, that needs arguing for. Of course that would go through a lot of things that might go beyond the scope of your posts. But it may not be irrational, maybe it's just...non-rational. There is a difference. But what do you think about this:

in every event or object, there must be a *necessary* reason for its existence. so instead of sufficient reason, we look for a necessary reason. for more, see hawthorne's principle of necessary reason.

9. Bah! 42 is so cliche!

10. Apolonio said:
---
Cool. Sorry if I read too much into it.
---

No need to apologize :-) Actually, I enjoy philosophical discussion. It just turns out that most other people don't. And I will acknowledge I am still sorting through certain portions of my entire argument, and if you can convince me that I erred at some point I would be more than happy to change.

In any case, you said:
---
You said that if I am not a self-existent being, then causation must follow. One may reply this way. First, that's not intuitive.
---

I disagree--I think it's the most intuitive answer. Think of it this way: if we assume that all we perceive is real and has actual existence and is not just some kind of imaginary thought or illusion, what we see everywhere we look is ex nihilo nihil fit--out of nothing, nothing comes. This has lead some people to posit that everything must have a cause (although this is logically invalid, as it puts us into an infinite redux problem too--if you want details I can provide, but I think you already know this).

Despite that, the overwhelming perception is that nothing gets you nothing and that everything comes from something else. Intuition would lead us to think that this must always be the case; but logic tells us we enter into infinite redux problems unless something is outside the loop, so to speak.

So I would disagree as to which view is more intuiative--but then, intuition isn't "proof" so this doesn't do anything for the argument.

Apolonio said:
---
Second, there is certainly a way where I can be a non self-existent being and still have no causation following. Suppose I am a property of X. X would *entail* my existence. But we would not say that X causes my existence. Rather, what we would say is that X is a sufficient reason why I exist. There is a difference between ground-consequent and causation. So, one can say that I do not need a cause but I do have a ground for my existence. Of course one can say that I am not a property of X, but the point is that there need not be causation.
---

If we propose that I am a property of X, then the question must immediately become "Where did X come from?" This seems to be, therefore, another sub-set of the "self-existent" category. For instance, we could say: "(4) I am a property of a some other being that is self-existent" but we are still left with something being self-existent. (And this should also be read with the unexpressed idea of the chain of length n between X and the self-existent being as previously defined too.) Again, while this could have been stated in the original post, I think it would have caused confusion rather than understanding for most of our readers. After all, philosophy is hard enough for the average person to care about without piling it all on on top of them!

Apolonio said:
---
Also, you spoke of an infinite chain being logically impossible. But I think what you are speaking of is metaphysical possibility/impossibility.
---

Allow me to clarify: It's logically impossible for our concepts of space/time to be compatible with an infinite chain, as the two premises are contradictory. Naturally, one could argue either that our notion of space/time is flawed or that an infinite chain is impossible. I have chosen the latter, since I believe the former has already been established. However, to the extent that the validity of our concepts of space/time requires a metaphysical view, then you are correct that this is a metaphysical argument. The logical impossibility would be between the metaphysical idea of space/time and the idea of an infinite chain.

Apolonio said:
---
If you're interested in zeno's paradox and infinities...
---

Thanks, I'll check the link out. And on a similar note, have you read The Motion Paradox by Mauzer (I forget his first name)? It is useful at showing the quantized nature of time as it applies to Zeno's paradoxes too.

Apolonio said:
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Oh, and also...you spoke of me being irrational if I don't have a sufficient reason.
---

Actually, I said you would be "unreasonable" not "irrational." My response was attempting to keep the correlation between the term you used ("sufficient reason") and the response I gave ("unreasonable"). I agree that if I said you were illogical or irrational that would require arguing for, as I would have to illustrate why it is illogical and irrational to be illogical (which I think can be done--but why bother when the word "unreasonable" works perfectly well?) :-)

Apolonio proposed:
---
in every event or object, there must be a *necessary* reason for its existence. so instead of sufficient reason, we look for a necessary reason.
---

At first glance, this does seem valid. I'll think on it some more and let you know if I end up with anything :-)