More on the Impossibility of an Infinite Regress

I typically defend two arguments against an infinite regress of sustaining causes. The first is deductive. The regress of sustaining causes at any finite period of time is either itself finite or infinite. However, it would take infinite time for an infinite regress of sustaining causes to cause anything at all. Therefore, at any finite period of time, the regress of sustaining causes is finite.

The second argument is inductive, or probabilistic. If all of the known attributes of X are finite, and Y is an attribute of X, it stands to reason that Y is most likely finite. Since the regress of sustaining causes for any finite object is an attribute of that finite object, it follows that the regress of sustaining causes for any finite object is itself most likely finite.

Perhaps the objection to these arguments I hear most often is that between 0 and 1, there are infinitely-many points. Therefore, concludes the objector, an infinite regress can and does obtain within a finite object and/or finite period of time. The immediate response to this objection is that once all of the points between 0 and 1 are added up, the sum is a finite number, which is disanalogous to what the objector is purporting to demonstrate. Moreover, the points between 0 and 1 are arguably abstract, and not concrete, so one is not permitted to beg the question is favor of their concrete reality without additional argumentation.

Today, as I was listening to a 70's mix I had made a couple weeks ago, it occurred to me as I would turning up the volume that I could also turn the volume down to the point where the music would eventually be muted entirely (0 dB). Let's say, then, that at a relatively loud rock concert - roughly, 100 decibels - the volume is turned down progressively. Between 0 dB and 100 dB, there are infinitely-many points that correspond to a certain decibel level. Yet from this, it simply doesn't follow that there is an infinite regress. After all, the decibel level is bounded at 0 dB, which is a decibel level that is possibly obtained. In order for there to be an infinite regress, at least in any relevant sense, there should be no smallest decibel level; but since this is manifestly false, it follows that the regress is finite.

Random Thought on the Theist/Deist Distinction

Roughly, theists and deists agree that there exists a God (a being that is a necessary First Cause, Creator and Designer of the universe). At the core, the difference lies in the acceptance of miracles. A miracle is generally agreed to be a highly unusual event with salvific implications. The theist believes in miracles, whereas the deist rejects them.

Consider now the hypothesis that God exists, and it is within God's power to bring about a miracle, but God chooses not to do so. Would this fall under the realm of theism or deism?

God and the Environment

The Judeo-Christian view of environmentalism is typically one of stewardship. We ought to care for the environment because it is a gift that God has bestowed on us (Gen. 1:28-31 - the term, "subdue" should not be interpreted as "exploit").

I also came across this passage in the Koran that we can likely agree with insofar as it accords with Biblical teaching: "So remember (all) the bounties of Allah and do not evil, making mischief in the earth" (Surah 7:74).

Under a divinely-instituted caretaker understanding of environmental ethics, we can make sense out of our obligation to care for the earth, and for the environment, generally-speaking. The environment has an intrinsic value to it because a personal agent (God) has created and designed it, and only persons have value or can give value to something.

For the naturalist, though, environmentalism seems out of place. I suppose the naturalist could argue that our care for the environment is pragmatic, e.g. we need to care for the environment in order for human beings to flourish. But of course, why should human beings be so highly valued? Are we not deceiving ourselves, under naturalism, by acting as if we are worth more than the impersonal environmental forces we are so oddly concerned about?

Of course, I am convinced that rationality, intelligence, intentionality, and value are all attributes of human beings best explained by an ultimate cause that possesses those same attributes, albeit in an analogical way.

The Aesthetic Argument

The aesthetic argument for God's existence is an intriguing subset of the teleological (design) argument. Think of the following:

1. Music displays simplicity in diversity. (Premise)

2. Simplicity in diversity is beautiful. (Premise)

3. Therefore, music is beautiful. (From 1 and 2)

What makes a song so aesthetically pleasing? If it were all the same (simplicity), it would be boring. If it were all different (diversity), it would be chaotic. It is the combination of these two elements that makes music beautiful to the listener.

Consider now the laws of nature. They are simple (e.g. Newton's law of universal gravitation) throughout a great diversity of objects. This makes the laws of nature beautiful.

4. The laws of nature display simplicity in diversity. (Premise)

6. Therefore, the laws of nature are beautiful. (From 2 and 4)

7. Beauty is the product of design. (Premise)

8. Therefore, the laws of nature are the product of design. (From 6 and 7)

Music isn't beautiful by chance alone, much less by some physical necessity (law). Rather, music is the expression of a personal agent, such as Mozart or Bach. What this suggests is a parallel of design between music and the laws of nature. Given that both exemplify beauty, we may infer that the laws of nature are the way they are because of the design of a personal* agent.

*Or in the view of Christians, tri-personal.

Just one reason I love reading the early Church Fathers...

"We must begin by purifying ourselves before purifying others; we must be instructed to be able to instruct, become light to illuminate, draw close to God to bring him close to others, be sanctified to sanctify, lead by the hand and counsel prudently. I know whose ministers we are, where we find ourselves and to where we strive. I know God's greatness and man's weakness, but also his potential." -St. Gregory of Nazianzus

I would only add, and I'm sure Gregory would agree, that our potential can only be actualized by the grace of God, "for it is God who works in you to will and to act according to his good purpose." (Phil. 2:13).

A C-Inductive Argument for the Assumption of Mary

Richard Swinburne has defined a correct C-inductive argument as, "an argument in which the premisses add to the probability of the conclusion (that is, make the conclusion more likely or more probable than it would otherwise be) . . ." [1]

For example, if there were a bank theft, and John's fingerprints are found on the safe, that increases the likelihood that John committed the crime. In other words, this fact makes it more likely that John committed the crime than it would have been had his fingerprints not been found on the safe. The fingerprints are not sufficient evidence to conclude that John committed the crime, but they increase the probability.

Correct C-inductive arguments stand in contrast to correct P-inductive arguments, the latter of which "make the conclusion [itself] probable." [1]

With this in mind, a number of C-inductive arguments for the Assumption of Mary can be given. Suppose you find yourself convinced that the remains of the bodies of most Biblical saints (both OT and NT) are claimed by at least one city. Now suppose that the remains of Mary's body are not claimed by any city. Under the hypothesis that Mary's body was assumed into heaven either right before her death or immediately after her death (which is a teaching of the Roman Catholic Church and, presumably, of some traditions of the Eastern Orthodox Church), Mary's body would not remain on earth. The fact that no city claims her remains would be expected if she were assumed into heaven. In stark contrast, this would be relatively unexpected had she not been assumed into heaven (unless an equally plausible explanation can be given).

This fact, therefore, arguably constitutes a correct C-inductive argument for Mary's assumption into heaven. More colloquially, this is known as "circumstantial evidence." This is not sufficient evidence, but it makes her assumption more likely than it would have been had her remains been claimed.

[1] Richard Swinburne, The Existence of God, Second Edition, Oxford University Press, 2004, p. 6.

Belief in God as Properly Basic

Take the crude evidentialist's axiom:

E: One should not believe that some proposition P is true without sufficient evidence.

Let's now assume that all of the arguments of natural theology are unsound. Let us further stipulate that there cannot be any sound argument of natural theology. Under such assumptions, there is no evidence for God's existence and there cannot be any such evidence. (Of course, I think these assumptions are mistaken.)

Taking these contentions at face-value, it follows that one should not believe that the proposition, "God exists," is true. However, a major difficulty arises when we begin examining some of our relatively uncontroversial beliefs. I'm thinking in particular of the following beliefs:

1. There exists an external world.

2. Minds other than my own exist.

3. The past has existed for more than five minutes.

The list can be extended much further, but it should be clear by now that none of these beliefs can be supported by way of evidence. How, for example, would one go about providing evidence that the past is more than five minutes, and that one's memories of an older past is not just illusory?

The problem is compounded further when we ask: what evidence is there in support of the E? If there is none, then E should be rejected on its own terms.

It seems, then, that the acceptance of these additional beliefs, if rationally believed, can be used as a part of a reductio ad absurdum against E. These rationally-held beliefs that happen to be non-evidence-based are called "properly basic beliefs." One is justified in believing that an external world exists, etc., even though he/she cannot prove via evidence or otherwise that the external world is not just illusory.

Plantinga and other philosophers have postulated that belief in God is also properly basic, and that belief in God can be rationally held with or without corresponding evidence. One obvious objection to this is that belief in God is not indispensable. A person may function just fine in society without believing in God. However, I think this objection falls short of being persuasive. I say this because other properly basic beliefs do not appear to be indispensable, either. If I were to adopt solipsism and believe that I am the only mind that exists, probably very little would change in my behavior. There are certain advantages in being kind, etc., even if altruism is illusory and it is for my own benefit alone. I would prefer to have pleasant illusions rather than unpleasant ones, after all.

Therefore, it seems quite unmistakable that indispensability is not the sole criterion for what constitutes a properly basic belief. As for belief in God being properly basic, there is likely something to that claim. Anthropology has shown an almost universal acceptance of God-belief among different cultures. This may suggest that theism is a naturally-held belief (a belief independent of specific culture), and if naturally-held beliefs are properly basic (are they?), it would follow that belief in God is properly basic.

A Theory of Everything and Cosmic Fine-tuning

It has become overwhelmingly apparent that the universe is fine-tuned for life. It is astronomically more likely for a universe to exist which prohibits life, but here we are nonetheless. I will write more about this at a later time, but for now I just want to comment on attempts to develop a theory of everything (T.O.E.).

String theory is arguably one of the more promising T.O.E.'s circulating among physicists and cosmologists. What this theory, if successful, would show is that the four main forces of nature (gravity, electromagnetism, and the strong and weak atomic forces) are all expressions of a single force and type of particle: tiny vibrating strings. String theory proposes eleven dimensions of space and time.

What strikes me as odd is how some allude to string theory as an explanation for the universe's fine-tuning. While the theory would hypothetically explain the forces of nature, it simply pushes the question of the origin of fine-tuning back a step. Why, for example, does there have to be eleven dimensions of space and time? As Craig aptly notes, this just shifts the problem to one of "geometrical" fine-tuning.

The multiverse hypothesis is multiply flawed, as well. I will only mention here, because I am short on time, that even if there is a multiverse, the mechanism that produces the multiverse still needs to be explained. If the mechanism itself is fine-tuned, then the fine-tuning is still quite plausibly explained by intelligent design.