The Kalam Argument, Zeno's Paradoxes, and Omniscience

In my previous post on this topic I argued (a) that Craig's argument against the possibility of actually infinite collections of real things doesn't work given presentism, and (b) Craig's argument against the possibility of traversing an actually infinite series in finite, step-wise fashion doesn't work given a B-theory of time.

My post generated quite a discussion among three of my commentators (Tom, HammsBear, and Don Jr). In this follow-up post I'd like to address a couple of the issues they raise.

1. The first issue concerns (a). Both HammsBear and Tom suggest that, given my proposal that presentism works best when combined with a version of theism in which God's memories provide truthmakers for truths about the past, Craig's first argument would work against a presentist who held that time had no beginning for that would mean that God has an actually infinite number of memories of past events.

Frankly, I don't see this as a big issue. It seems to fare no better or worse than another challenge to Craig's argument, namely, that an omniscience God would have to know an actually infinite number of propositions (e.g., 1+1=2, 1+2=3, etc.). Hence, either Craig's argument works, in which case it implies that God cannot be omniscient, or we have to conclude that the argument doesn't work. But this seemingly nasty dilemma has, I think, a straightforward reply: God's knowledge is a single unified gestalt - in one cognitive act he grasps all there is to know about all there is to know. Thus, we shouldn't think of God's knowledge as built-up piecemeal from atomic propositions but rather as a continuous field that contains all true propositions virtually, from which particular truths may be distinguished by abstraction. In much the same way, a continuous geometrical plane is not built-up out of discrete points but is a field within which endless numbers of points may be picked out by abstraction. This is not a new proposal, by the way, but the classical way of thinking about God's omniscience.

2. The second issue concerns (b) by way of Zeno's paradoxes of motion. Do these paradoxes imply that there is, say, an actually infinite number of spatial points between any two locations, or an actually infinite number of events between any two times? If so, then any sort of change or motion would require traversing an actually infinite collection in stepwise fashion.

One response (proposed by HammsBear) is finitism - space and time come in finite indivisible quanta. This view (defended by A.N. Whitehead) deals nicely with Zeno's paradoxes - if correct, then between any two places there can only be a finite number of places and between any two times there can only be a finite number of events. On the other hand, finitism is very counter-intuitive. First, even if Planck time shows that there is a physically minimal quantum of time, it is metaphysically possible that that quantum be smaller, indefinitely. So in some other possible world the quantum is smaller, and so forth for any non-infinitesimal quantum. What, then, makes the quantum the size it is? Second, imagine two quantum-sized particles travelling in a parallel line in the same direction, with the first going exactly twice as fast as the second. Suppose they both start at (t0,x0). Clearly, when the first particle is at (t4,x4), the second one will be at (t2,x2), but where is the second particle when the first is at (t3,x3)? It seems that it would have to be between (t1,x1) and (t2,x2). By hypothesis, however, no such location exists. That's weird.

A second response to Zeno's paradoxes, and the one I favor, is the one proposed by Aristotle. Basically, Aristotle introduced a distinction between actual and potential infinites (the same distinction Craig uses in the kalam argument). The number of points between any two places, said Aristotle, is potentially infinite in that it is endlessly divisible, but not actually infinite. In other words, continuity is metaphysically prior to discontinuity - discontinuities can only exist in a more fundamental continuity. Here's a mathematical analogy: What is more basic, the line or the points on the line? Aristotle would say the line. Points have zero dimension, so you can string them together end to end and never build up a line of any length whatsoever. You could, of course, pick a point and drag it, thereby defining a line segment, but to drag it in the first place there has to be some kind of continuous field in which to drag it.

Of course, this doesn't remove all the perplexity behind Zeno's paradoxes, but either approach, Aristotle's or the finitist's, would give us a way to avoid countenancing an actual infinity of spatial places or temporal events.

How Many Darwinists Does It Take to Screw in a Lightbulb?

As satire goes, this is pretty funny. Here's my favorite:

Richard Dawkins: To say that it took a Darwinist to do the screwing in of the lightbulb is to explain precisely nothing. The obvious question becomes: Who did the screwing to create the Darwinist screwer? And who did the screwing to create that screwer? There would have to be an infinite regress of screwers. And if you invoke some invisible, mystical Unscrewed Screwer (for which we have no credible evidence) to start the whole thing off, why not just say that the lightbulb screwed itself in and be done with it?

(Note: This is not a quote from Dawkins himself, but it creatively parodies his favorite knock-down 'refutation' of the design argument, namely, that the Designer would need a designer, and so forth.)

Need an Anagram?

One of the reasons I named this blog 'Alanyzer' is because that's an anagram of "analyzer", which is what I like to do. I just discovered a cool website that generates anagrams from a target input phrase into one of several different languages. To my chagrin, anagrams of my full name 'Alan Robert Rhoda' include:

ADORABLE RAT HORN
HERBAL DNA ORATOR
ALTAR REHAB DONOR

Here's an interesting anagram of 'philosophy':

HOLY HIPPOS

The Kalam Cosmological Argument and the Nature of Time

William Lane Craig has done much in recent years to develop and defend what's now known as the kalam cosmological argument for the existence of God. The core of the argument runs as follows:

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

As it stands this argument won't get one all the way to full-blown monotheism, but if it is sound, then naturalism is in serious trouble, for the natural universe would have been shown to be contingent and to owe its existence to an apparently transcendent cause.

The crucial premise is the second one, for it's not obvious why the universe must have had a beginning. Here Craig offers four arguments - two philosophical, and two scientific. The latter two involve appeals to the Big Bang theory and to the Second Law of Thermodynamics. I'm not going to get into those right now. What I'm interested in are the two philosophical arguments.

The first argument contends that actually infinite collections of actually existing things are impossible. (An actually infinite collection is one which can be put into one-to-one correspondence with one of its proper subsets, e.g., the set of natural numbers can be put into 1-1 correspondence with the set of even numbers.) Why? Without going into the details, Craig basically argues that actually infinite collections of actually existing things would generate all sorts of logical paradoxes and for that reason have to be barred from any coherent ontology. The relevance of this to the beginning of the universe is as follows:

1. If the universe has no beginning, then an actually infinite number of events has elapsed.
2. If an actually infinite number of events has elapsed, then there is an actually infinite collection of existing things (i.e., past events).
   
3. But actually infinite collections of existing things are impossible.
4. Therefore, it is false that an actually infinite number of events has elapsed.
5. Therefore, the universe has a beginning.

One worry about this argument premise 2, for if one holds to the version of the A-theory of time known as presentism, then past events simply don't exist anymore, so it's not clear why the elapsing of time would entail that there is an actually infinite collection of existing things. On the other hand, if the B-theory of time or any of the versions of the A-theory that retain past facts (e.g., the 'growing block' theory or the 'moving spotlight' theory), and if the universe has no beginning, then it follows straightaway that there is an actually infinite collection of existing things. It seems, then, that this philosophical argument for the second premise of the kalam argument must presuppose the falsity of presentism, ironic since Craig is a staunch defender of presentism.

The second philosophical argument for premise two of the kalam argument contends that an actually infinite collection cannot be sequentially run through or traversed by a series of finite steps. Here's a straightforward formulation of the argument.

1. If the universe had no beginning, then an actually infinite collection would have been sequentially tranversed by a series of finite steps.
2. But it is impossible to sequentially traverse an actually infinite collection by a series of finite steps.
3. Therefore, the universe had a beginning.

Premise 2 can be defended as follows. If the universe had no beginning, then an actually infinite number of events has elapsed prior to now. The collections of negative numbers ending in zero {..., -3, -2, -1, 0} is an actually infinite collection. Since actually infinite collections can be put into 1-1 correspondence, let's pair up the series of past events with the series of negative numbers ending in zero. To suppose, then, that the actually infinite collection of past events has been traversed in step-wise fashion is to suppose that it's possible to get from -∞ to 0 one number at a time. But that's impossible, since -∞+1 = -∞. Hence, one could never arrive at 0 or the present moment.

Now, I think this is a pretty good argument, but here again, one's view on the nature of time makes a big difference. Why? Well, if one is a B-theorist, then there is no such thing as the 'flow' or passage of time. All the events that ever have or will exist exist (tenselessly). So if the past is infinite, then there timelessly exists a completed actually infinite collection of past events. The collection isn't formed successively in finite steps because it's not formed at all - it's just there. On the other hand, if one is an A-theorist (of any sort), then this argument seems pretty compelling because then one would have to somehow run through or form an actually infinite collection by successive finite addition. It seems, then, that this philosophical argument for the second premise of the kalam argument must presuppose the falsity of the B-theory of time.

Finally, since only non-presentists are likely to find the first argument compelling, and since only A-theorists are likely to find the second argument compelling, only non-presentist, A-theorists are likely to find both arguments compelling. To my knowledge, no discussions of the kalam argument to date have noticed these connections.

Former UNLV Philosophy Prof. Denied Tenure for Being Too Conservative

I recently learned that Dr. Francis Beckwith, one of my favorite philosophy professors here at UNLV when I was an undergraduate and an affable and prolific scholar, has been denied tenure at Baylor University. From the published accounts so far, it looks like Beckwith's open support of a pro-life, pro-intelligent design position is what did him in, despite the fact that he has a stellar publication and teaching record. The tenure committee was apparently stacked against him by some influential Baylor professors and alumni who were hostile to Beckwith's views. In my opinion, this is a serious error on Baylor's part and, as might be expected, is drawing considerable negative press (see, for example, here, here, here, here, and here). The case is currently under appeal. Hopefully, Baylor will reverse the judgment and give Beckwith the tenure he cleary deserves.

Sertillanges on the Intellectual Life

I've just starting reading a neat book that a friend clued me in to. It's called The Intellectual Life: Its Spirit, Conditions, Methods, by A. G. Sertillanges, O.P. First published in 1920 and revised in 1934, the book is written by an accomplished Thomistic scholar as a guide for anyone who is interested in pursuing a life of learning. I'm finding that it's chock full of good, pithy advice on how to make the most of your time and become the best scholar you can be. Here are some choice quotes from the Preface and first chapter:

Do you want to do intellectual work? Begin by creating within you a zone of silence, a habit of recollection, a will to renunciation and detachment that puts you entirely at the disposal of the work; acquire that state of soul unburdened by desire and self-will which is the state of grace of the intellectual worker. Without that you will do nothing, at least nothing worth while. (p. xviii)

Weak work or pretentious work is always bad work. A life with too ambitious an aim or one content with too low a level is a misdirected life. (pp. xxii-xxiii)

The most mediocre mind may hit on an idea, like a rough diamond or a pearl. What is difficult is the cutting of the idea, and, above all, its setting into a jewel of truth which will be the real creation. (p. xxvi)

A vocation is not fulfilled by vague reading and a few scattered writings. It requires penetration and continuity and methodical effort, so as to attain a fulness of development which will correspond to the call. (p. 3)

The life of study is austere and imposese grave obligations. It pays, it pays richly; but it exacts an intial outlay that few are capable of. The athletes of the mind, like those of the playing field, must be prepared for privations, long training, a sometimes superhuman tenacity. We must give ourselves from the heart, if truth is to give itself to us. Truth serves only its slaves. (p. 4)

Love truth and its fruits of life for yourself and for others; devote to study and to the profitable use of study the best part of your time and your heart. (p. 5)

To get something without paying for it is the universal desire; but it is the desire of cowardly hearts and weak brains. The universe does not respond to the first murmured request, and the light of God does not shine under your study lamp unless your soul asks for it with persistent effort. (p. 6)

The future is always the heir of the past; the penalty for neglecting, at the right time, to prepare it, is to live on the surface of things. Let each one think of that, while thinking may be of some avail. (p. 7)

Truthmakers vs Truth Conditions

I'm involved in a vigorous discussion with Ocham and Tom on a couple earlier posts (Link1, Link2) concerning presentism and causation and we've gotten onto the issue of the relation between truthmakers and truth conditions. Are they the same thing? If not, what's the difference?

For what it's worth, here's my take.

Most philosophers, myself included, hold to some version of the correspondence theory of truth, which basically says that some sort of 'truth-bearer' is "true" if and only if it represents reality in a manner that corresponds to how reality actually is. As Aristotle famously put it, "To say what is that it is, and of what is not that it is not, is true" (Metaphysics 1011b25).

As for truth-bearers, pretty much everyone agrees that these can be things like beliefs, statements, and propositions. I take propositions to be the primary truthmakers, however. Beliefs are true in virtue of having as their content a true propositions. Statements (by which I mean declarative sentences) are true in virtue of expressing a true proposition. But true propositions are not true in virtue of the truth of anything else. Rather, they are true in virtue of corresponding with reality.

But what is it in reality in virtue of corresponding with it that "makes" a true proposition true? This is where 'truthmakers' come in. Truthmaking is a relation between some parcel of reality and a proposition. In general, a truthmaker T for a proposition P is any parcel of reality the existence of which is sufficient to necessitate and thereby ground the truth of P.

For example, the proposition expressed by "Canines exist" is made true by the existence my in-laws' dog Barkley. Even if no other dogs existed, that proposition would still be true just because of Barkley. But we don't need Barkley to do the job - any canine with do. Since there are in fact many dogs, each of which is sufficient to necessitate the truth of that proposition, there are many distinct truthmakers for that proposition (as many as the number of subsets of dogs). Here's the main point though, truthmakers are parcels of reality - in this case, ones that can bark, bite, and bury bones.

Not so with truth conditions. Truth conditions are semantic explications of the meaning of statements. They tell us in very precise terms what has to be true for a particular statement to be true. For example, a B-theorist like Nathan Oaklander will say that the truth conditions of the sentence "The 2006 Winter Olympics are over" is given by the sentence "The 2006 Winter Olympics end earlier than the date of this utterance". Thus truth conditions are meaning entities like statements that are used to spell out or analyze the meaning of other statements.

Here's a way to keep the distinction between truthmakers and truth conditions clear. Remember the saying, "Sticks and stones may break my bones but words will never hurt me"? Well, sticks and stones can function as truthmakers (e.g., "This stone has a mass of 5 kg" is made true by the stone itself) but not as truth conditions. By contrast, truth conditions are just words; they can't hurt you (physically), but they can help you articulate yourself.

What Should We Do with the Ebola Virus?

Biologist Eric Pianka advocates using the ebola virus to kill 90% of world’s population and gets a standing ovation from the Texas Academy of Science (Link). The scary thing is that he seems to be serious. (HT: Victor Reppert)

Update (4.12.06): There's been a lot of discussion in the blogosphere over this incident and over whether Dr. Pianka actually meant to advocate using ebola to this the world's population (as Forrest Mims, the author of the article linked to above concludes) or whether he just meant to say that it would be a good thing if ebola wiped out 90% of the human race. That may be a somewhat fine distinction, though. Here's one source that defends Mims' interpretation. Here's another that disputes it. Here's a partial transcript of the controversial speech. You be the judge.

More on Presentism and Causality

My friend, commentator, and sometime collaborator, Tom Belt, makes some good suggestions regarding the problem of reconciling presentism with diachronic causal relations (my emphasis in bold):

What about distinguishing between two kinds of causality? You could posit a proper/direct sort of causality as 'the effect of t1 upon its immediate successor t2'. The temporal transition from t1 and t2 is the point of genuine 'becoming'. But t2 then has its own directly causal relationship on t3, and t3 on t4, and so forth. ... Causal relations between temporal locations not directly ‘touching’ would be a second sort of causality, an indirect causality. ... Consider the passing of the baton in a relay race. The causality involved in the passing of the baton between runners 1 and 2 is of a different kind than that involved in the passing of the baton between runners 1 and 4. We say runner 1 passed the baton to runner 4, and we grant the truth of this propositionally as well. But getting into the metaphysics of it reveals at least two distinct kinds of causal relation and distinguishes truth-grounds at t3 as 'caused by' only t2 realities. And where t2 and t3 meet IS the present.

I think this is right and I'd like to try and develop it further by stipulating a distinction between events and actual states of affairs (or "facts").

An actual state of affairs is an aspect of reality. For example, my cat Tiffany is now lying on the bed. Hence, there now obtains the state of affairs Tiffany's being on the bed. Similarly, whenever it rains here in Las Vegas (which isn't often), the state of affairs It's raining in Las Vegas obtains or is actual.

An event, by contrast, is a diachronic transition between two actual states of affairs. Thus, when Tiffany gets off the bed to get some food, an event occurs in that a state of affairs that was actual (Tiffany's being on the bed) gives way to another state of affairs (Tiffany's not being on the bed). So conceived, an event is like the passing of a baton from one state of affairs to another. Here the baton is existence or actuality and the passing of the baton is the bringing about of another state of affairs.

What I have in mind is this sort of picture:

... S1 | S2 | S3 | S4 ...
...    E1   E2   E3   ...
...    t1   t2   t3   ...

where S1, S2, etc. denote successively actual states of affairs, and E1, E2, etc. denote successive events, and these events in turn define succesive moments of time (t1, t2, etc.). Note, that given my definitions, states of affairs can become constituents in events. For example, E1S2E2 is a diachronic transition between S1 and S3. Hence it is a compound event, one that includes at state of affairs S2 and two non-compound or simple events as constituents. (For example, we can think of WWII as a compound event.)

In terms of this categorization, I want to suggest that causal relations do not take events (compound or simple) as relata but states of affairs. We should talk not of event-event causation, but of state-state causation. Direct causation is a simple event by which one state of affairs gives rise to a new state of affairs. Indirect causation is a compound event by which one state of affairs gives rise to a new state of affairs.

But in calling causation a relation between states of affairs, we should not think of there being two actual states of affairs that are then connected by a third thing, a causal relation. Such a view would clearly rule out presentism since it would require the existence of two successive states of affairs that, qua successive, could not be simultaneously present. No, causation is an dynamic relation in the sense of S1 giving rise to S2. It is a power or set of powers operative in S1 that transforms it into S2.

Furthermore, since time is continuous, between any two states of affairs there are a potentially infinite number of other states of affairs and a potentially infinite number of simple events. Thus, the state that is NOW is in continuous transition. It is simultaneously both receiving the baton from its predecessor and already passing it on to its successor.

Presentism and Causation

I'm rather attracted to presentism, the view that the present is coextensive with the real. The past is no more; the future is not yet; whatever exists simpliciter exists now.

Presentism is one of several views that affirms an A-theory of time (roughly, the A-theory says that temporal becoming is real, and not merely apparent). One of presentism's advantages over other A-theory variants is that it nicely avoids McTaggart's Paradox. Presentism's main advantage over B-theories of time (roughly, the B-theory says that temporal becoming is merely apparent, not real) is that it squares much more closely with common sense.

But presentism is not without its problems. One apparent difficulty is called the truthmaker objection. Since presentism denies that past facts exist, the presentist needs to find something else to ground truths about the past, and it's by no mean obvious what that could be. I think this difficultly can be answered and have proposed a solution here. The solution trades on the idea that the past leaves causal traces in the present. Given that these traces satisfy certain contraints that I spell out, they can serve as truthmakers for truths about the past.

But this brings us to another difficulty, one that I am just beginning to think about and am not yet sure how to answer. It is expressed rather well by Robin Le Poidevin (a B-theorist) in his book Travels in Four Dimensions:

Consider the statement 'The past leaves causal traces on the present.' What, according to the presentist, makes this statement true? Well, present fact, presumably, since that is the only kind of fact available. But what purely present fact could make true a statement about the causal relations between different times? We can make sense of a past event leaving its causal traces on the present (last night's wild party has left a number of traces around my sitting-room, for instance: the smashed wineglass, the shoe-marks on the piano, the underwear draped over the sofa), but can we make sense of the causal relation between that event and the present traces itself leaving its traces on the present? The idea is a distinctly odd one. Any statement about the relation between different times (or between the events that occurred at those times) requires us to stand, in thought at least, outside those times and view them as of equal status. There cannot be a relation if one of the things the relation is supposed to relate is just not part of reality. It looks, then, as if the presentist is not entitled to assume the only mechanism that can explain, in terms of present fact, how statements about the past can be true. (p. 139)

Here's the problem in a nutshell: To meet the truthmaker problem, the presentist needs to appeal to causal traces left by the past on the present. But this looks to be positing a real causal relation between past events and the present. A real relation, however, obtains only if all of its relata obtain. Hence, past events can be causally related to present events only if past events really exist. But presentism denies that past events exist (only the present is real), so it seems like the presentist cannot answer the truthmaker objection after all.

Is this a decisive objection against presentism? Well, I'm not convinced, for reasons explained below. Anyway, off the top of my head I can think of a few possible lines of response.

1. Deny that causation is a relation, despite appearances to the contrary.
   
2. Deny that all real relations are existence entailing. Ordinary relations imply the existence of their relata but some relations, among them (some) causal relations, don't.
3. Deny that causal relations are relations between events, but rather relations between some other category of thing - perhaps "states of affairs" or "substances".
4. Deny that causal relations are relations between event tokens, but rather relations between event types. Hence, causal relations hold between abstract objects.

These may not be the only options, but none of these looks particularly attractive. 1, 2, and 4 are extremely counter-intuitive. 3 is more plausible, but it runs counter to long-entrenched views in philosophy that analyze causation in terms of events and, furthermore, its not quite clear that shifting categories from events to something else still won't commit the presentist to some kind of past existents.

Perhaps there's a fifth option: Deny that the truthmaker for "the past leaves causal traces on the present" requires positing real causal relations between past and present events. How so? Well, if we think of time like a presentist does, then what is real now (the present) is already pregnant with powers and propensities that will usher forth in a new reality, replacing the old one. Imagine that one of these powers is global in extent, fully reflexive, and at each new moment gives rise to a new state that retains a complete snapshot of the previous moment - kind of like a universal video recorder that, as reflexive, also records its own recording (and records its own recording of its own recording, etc.). If this is coherent, then maybe my proposed solution to the truthmaker objection (linked above) can also be pressed into service here.

I've argued that a presentist ought to be a theist, because the best (if not the only) way to solve the truthmaker objection is to ground truths about the past in God's memories. Given that God exists noncontingently, experiences time, and is omniscient, then God retains a perfect and complete memory of each successive moment of time. As omniscient, God's perspective fully reflexive and transparent such that in knowing P God knows that he knows P and knows that he knows that he knows P, etc., without the addition of any new facts. Hence, the truthmaker for "It was the case that P" is just God's remembering that P, and the truthmaker for "God remembers that P" is again just God's remembering that P. (Note: It is an established principle that one truthmaker can ground multiple truths.)

Is this a solution to Le Poidevin's challenge? I am inclined to think so. It does, however, suggest a way of thinking about causation that may be peculiar, namely, as the exfoliation of internal propensities through the exercise of some kind of 'active power' (to use Thomas Reid's phrase). I'll have to reflect more on that in a succeeding post.