Reply to Lawrence

I recently noticed Richard Lawrence had posted a rebuttal to my "Inconsistent Triad" essay on his website. In that essay, I had argued that three premises accepted by many Objectivists -- that there are prior causal conditions for every event, that time is not cyclical, and that there are no actual infinities -- were not mutually consistent. I find it a bit puzzling that Lawrence criticizes the essay for not doing things it never claimed to do. I did not claim that the three beliefs I cited were part of Objectivism, but rather that many Objectivists believed all three -- which is not the same thing. I still think the evidence is solid (though not conclusive) that Rand believed all three.

In any case, I suggest distinguishing the issues in this way:

1. Is the argument valid? That is, is it true that the three premises form an inconsistent triad?

2. Is Objectivism committed to the truth of the three premises? That is, does Objectivism either explicitly endorse each of them or is there something which is (uncontroversially) part of Objectivism that implies the premise in question?

3. Do many Objectivists accept all three premises? Note that this is not the same question as whether they should accept them, given their belief in Objectivism. Objectivists, like anyone else, can believe inconsistent things without realizing it, so Question 3 does not collapse into an application of Question 2.

I shall go through this more slowly, but quick answers can be given here. First, the argument is valid. The premises do form an inconsistent triad. Second, Objectivism is not committed to the truth of all three premises. (I never suggested that it was.) And third, many Objectivists do accept all three premises.

Evidence that many Objectivists believe all three can be found in the response to the article on various forums where it has been discussed. In particular, anyone who objects by raising questions about the validity of the argument without adding some qualification to the effect, "even if the argument were valid, it wouldn't upset my beliefs because I don't accept such-and-such a premise", is indicating that he does accept all the premises. Otherwise, why address validity alone? Further evidence that many Objectivists accept the premises comes from private e-mail responses I get about the article.

For more detailed discussion, I will begin with what Lawrence has to say about (3). He casts little doubt upon the claim that many Objectivists accept all the premises. First, I did not ever claim that "most Objectivists" believe them, though Lawrence used that phrase, in quotation marks as though it had come from me, to describe my claim. (I wonder why he should confuse "many" with "most".) Second, the only evidence he offers that most or many Objectivists do not hold the three beliefs is only tangentially relevant. He did not, for example, cite any polls of Objectivists. Instead, he claims that the three premises are either contrary to or not part of Objectivism. That would only count toward showing Objectivists do not hold the beliefs with the addition of some premise about how likely Objectivists are to believe things that are not part of or that are not consistent with Objectivism. Without some assumption like that, even a successful proof that every one of the three beliefs is inconsistent with Objectivism would not show that many Objectivists do not believe all three. In fact, however, despite some claims to that effect, Lawrence does not show that any of the beliefs is inconsistent with Objectivism, much less, all of them -- which is not surprising, since none of the three premises is inconsistent with Objectivism -- but more on that later. (And since none of the premises is inconsistent with Objectivism, the case against many Objectivists believing them is very weak.)

The existence of many Objectivists who believe all three, plus the validity of the argument, is all that is needed for the correctness of my essay.

Since many Objectivists do believe all three, let's consider the question of validity. This is fairly straightforward. It's comparable to the following argument about inter-defining words in a dictionary. At least one of the following must be true of the dictionary:

(1) It must contain some (at least one) entry ultimately defined in terms of itself, or
(2) It must contain some (at least one) undefined entry, or
(3) It must contain infinitely many entries.

Correspondingly, it cannot be true of the dictionary that

(1*) No entry is ultimately defined in terms of itself, and
(2*) It does not contain any undefined entry, and
(3*) It does not contain infinitely many entries.

The parallel should be obvious. Entries defined in terms of themselves correspond to cyclical time, undefined entries to events without prior causal conditions, and infinitely many entries to infinitely many events in the past. The argument is valid, whether applied to dictionaries or to sequences of causes stretching back into the past.

Lawrence raises only a single objection to the basic argument that may bear on its validity. He says, in effect, that an infinite chain of events leading up to the present does not count as an actual infinity in the sense in which one of the premises denied that there were actual infinities. In effect, he is charging the argument with committing a fallacy of equivocation, of changing the meaning of a crucial term in the course of the argument. The reason he gives is that

What Bass has postulated, however, is not an infinite number of things that exist in the present, or an infinite extent of any present quality. Rather, he has proposed that there is no countable end to the number of causes that existed in the past -- that is, no starting point for the series of causes. [This isn't quite right. I proposed that, given certain other conditions, the number of prior causes must be infinite. Some infinities are classified by mathematicians as countable (or denumerable) while others are not. Lawrence's slip on this point, however, makes no difference to the rest of the discussion. – RB] The difficulty for the argument Bass wants to make is that the past is no longer actual. The 'actual’ refers to entities as they exist in the present. Past causes are not present entities or qualities, and therefore are not 'actual.' So there is no clear contradiction between claiming that the sequence of causal conditions has no starting point, and also claiming that no actual, present-day entity is infinite.

I think this attempt to segregate the present, supposedly actual and finite, from a past series of causes, which is allowed to be infinite but non-actual, is untenable for at least three reasons.

First, there is the problem of spelling out the meaning of "things that exist in the present". It may be intutitive to suppose there there is some time which is the same throughout the universe -- so to speak, a universe-wide "now" or "present", in which everything exists at the same time -- but in the wake of Einstein, we have learned that the intuition is misleading and that simultaneity is not well-defined except with respect to frames of reference. Thus, apart from a specification of a frame of reference, it is unclear what is included or excluded from "things that exist in the present". Even if we ignore this difficulty, however, and suppose that there is some clear sense of "the present" to underwrite Lawrence's claims, there are further problems.

The second is that it is not obvious why not existing now (in time) is any more a reason for not counting the infinity envisaged as actual than not existing here (in space). Surely, not-now should be treated in parallel to not-here, but no denier of actual infinities would be consoled to be told that there were infinitely many stars, but only a finite number within any finite volume of space. He shouldn't be any more consoled to be told that there have been infinitely many events, but only a finite number within any finite stretch of time.

Third, "actual" is an adjective that qualifies "infinity", rather than an adjective that, together with "infinite", qualifies something else. To speak of an actual infinity of past events is not to speak of a collection of past events that is both infinite and actual, but rather to speak of the number of past events as being actually infinite. (To illustrate, if I speak of a purple, polka-dotted cow, I am not speaking of a cow that is purple and polka-dotted, but rather, of a cow with purple polka-dots.) The actual-infinity terminology originated to express a contrast with potential infinities, collections or series that could be indefinitely added to but were at any given time only finite, or to processes of division or subdivision that could in principle be extended for any number of steps, but had actually only been extended for some finite number of steps. The infinity of past events is not potential in either of these ways. It is not that there is a finite set of events which may be indefinitely augmented, nor that the past consists of something which can be progressively divided up. Given the other assumptions, there have certainly been infinitely many events in the past, so if the alternatives are that the infinity of past events is potential or actual, then it is an actual infinity.

This branch of the argument, then, is valid. If there are prior causal conditions for each event and time is non-circular, then there have been infinitely many events. Lawrence acknowledges this when he says:

According to Bass, 'if you suppose time to be non-cyclical and every event to require a causal condition, you can prove that any particular finite number suggested cannot be equal to the total number of events; there will have to be at least one more than any finite number to provide a causal condition for the earliest member or members of the set of events. Since that argument works for each finite number, the total number of events must not be finite.' This argument would be correct if the cause of each event had to involve a prior event.

The only thing wrong with Lawrence's remark here is that, at the point from which he quotes, I had already defined causal conditions as involving prior events, so his qualification is redundant. What he should have said is just: "This argument is correct."

The only point on which Lawrence has criticized the argument itself is over the matter of whether the infinitely many events thus proved count as an actual infinity. I've explained why they do. At least, if it is to be maintained that there is no actual infinity of past events, some better reason needs to be given than that the past is not actual.

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The argument is valid, and many Objectivists accept the three premises. Since that is what I claimed, I could stop here. Still, Lawrence raises or suggests some interesting questions that I'd like to address further. What I have to say about the third premise is to be found above; what is below addresses Lawrence's comments on the other two premises.

1. The first premise, that time is non-cyclical, Lawrwnce claims is not part of Objectivism, though probably believed by Rand and many other Objectivists. Surely, there is no explicit statement of it, but I think something can be said in favor of its being not just believed by many Objectivists but also being part of Objectivism.

I briefly alluded to this near the end of the webbed essay: "we typically take events in the past to be settled and (at least some) events in the future not to be settled yet. It is settled (say) that I had coffee this morning, but not yet settled whether I will have coffee tomorrow morning. But if time is cyclical, then either the future is just as settled as the past or else the past is just as unsettled as the future." If the past is settled, then we have no more choice about what will happen in the future than about what happened in the past. If the future is unsettled, if a person can decide whether or not to commit a crime, then, in principle at least, it should be possible to change whether a past crime has been committed. (Imagine the murderer's defense: "You don't know if it will continue to be true that I killed Smith! Maybe it will turn out that I never did!" -- and the court's response, "Maybe it will turn out that we never punished you!") Cyclical time appears to play havoc with notions of free will and responsibility that are essential to Objectivism. If non-cyclical time is necessary to preserve something essential to Objectivism, then it has as good a claim to be part of Objectivism as the other items it is called upon to preserve. In any case, it is too quick to move, without additional support, from "X is not explicitly part of Objectivism" to "X is not part of Objectivism".

2. The second premise was that every event has prior causal conditions. Lawrence objected that

Bass has offered an event-based view of causality, in which events cause other events. He attributes this view of causality to Objectivists. But in fact, the Objectivist view of causality is that events are caused by entities, not other events.

This isn't quite right, though I think an event-based view is correct. What's not right about it is that I didn't attribute an event-based view to anyone. The claim that every event has prior causal conditions that include at least one other event is compatible with the claim that every case of causation also involves or is the action of an entity. I simply didn't make the mistake Lawrence charges me with. Nor is it correct to assert, as he does elsewhere, that

As a criticism of Objectivists, it still fails, because the second leg of his triad (the belief that all events have prior events as their causal conditions) is not in fact the belief of Objectivists -- it actually contradicts the explicit Objectivist view of causality.

I didn't attribute the belief that "all events have prior events as their causal conditions" to Objectivists or to anyone. I didn't even claim to believe it myself (and I don't). What I did say was that many Objectivists believe that every event has at least one prior event among its causal conditions. Lawrence actually quoted the passage where I said this and immediately misinterpreted it in his next sentence:

Bass states that, 'for every event, there will be at least one before it to be or to be part of its causal condition.' That is, there will be at least one other event before each event, to be its 'causal condition.'

To add emphasis in the right place, "for every event, there will be at least one before it to be or to be part of its causal condition." That does not contradict the Objectivist view of causality, because it neither identifies the causal condition with some prior event, nor denies that there must be at least one entity, also as part of the causal condition, to cause the event in question. Further, since the premise I attributed to Objectivists is compatible with an entity-based account of causality, appeal to the entity-based theory is, by itself, no reason (not that it ever was much) for saying Objectivists do not accept the premise.

Nevertheless, it is true that in terms of an entity-based view of causality, it is possible to make sense of the denial that there must be prior (event-including) causal conditions for every event. Given that, any further argument shifts to a different level -- that is, to questions about the defensibility of entity-based accounts of causation.

That's what I addressed in the footnote Lawrence cited. What I said was:

[T]he causal conditions for an event must themselves include at least one event. For suppose that the causal conditions need not include any event. That is, suppose that there is some event, E, and that, before the occurrence of E, there is a complete set of its causal conditions, C, which includes no event. How then does E arise from C? Isn't that an event -- C giving rise to E -- that is distinct from both C and E, but, contrary to the supposition, a causal condition of E?

His comment was that "causation is a relationship between an effect and its causes, not a separate event in its own right, so this argument is also flawed." I'm not quite sure what is meant by "not a separate event in its own right", but I shall not pursue that. I think there's a good point here, and I shall suppose, what I think is meant, that the "event" of C-causing-E is a kind of artifact, created by linguistic convention between any cause and its effect. There need not be a real event there, any more than there needs to be an entity to be the subject indicated by the pronoun in "It is raining".

If that is granted, the picture we have is that there is some set of causal conditions, C, which do not include any event, and there is the effect, E, which is an event (or action or occurrence, etc.). For simplicity, we can assume that the set of causal conditions is a single entity. Somehow, there is a causal relation between C and E, but this is not to be described as a distinguishable event of C giving rise to E. Since C is supposed to be a complete set of E's causal conditions, there are two possibilities. Either C is sufficient for E or it is not.

Let us suppose for the moment that C is sufficient for E. Then, E must occur as soon as C exists. If C comes into being in stages or through some process of development, then E must occur no later than when the process of development is complete. If any version of those is true, then E does have an event as a causal condition after all, namely, the coming into being or sufficient development of C. The same applies if it is said that what is sufficient for E is C being in a certain state or being present under certain conditions, for then the event will be that C has arrived at that state or has come to be under those conditions. There's one loophole, to which I'll return.

Suppose, alternatively, that C is not sufficient for E. That cannot mean that C plus something else is sufficient for E -- not in the current context. That's because it was already assumed that C comprises or includes the complete set of E's causal conditions. So, if the complete set of E's conditions is to be provided by C, while C is not sufficient for E, that must be because there is no sufficient condition for E. Neither C nor anything else nor anything in combination with C is sufficient for the occurrence of E. The presence of C can only raise the probability of E above zero. (If, apart from C, the probability of E is already above zero, then, contrary to the hypothesis, C does not include the complete set of E's causal conditions, since there would then be some chance of the occurrence of E, even without the existence of C.) This may seem favorable for C being an eventless causal condition of E. Given that C is present, there is some probability of E, greater than zero and less than one hundred percent. That chance comes off, and so we have the occurrence of E without any events among its causal conditions. But there's a problem: What about the existence of C? If C came into being, then the origination or coming into being of C is a causal condition of E, since without C, the probability of E was zero.

There's one loophole here, too -- and it is the same as when C was considered as a sufficient condition for E -- that C did not come into being. The only way that C can include or comprise a complete set of causal conditions for E, without itself including any events, is if C did not come into being. At minimum, C must have existed as long as the universe. Though it is only one of the possibilities, I shall assume for simplicity that C is the universe itself. Then, the question presents itself: Is the history of the universe infinite? That is, is it true that for every finite phase or stage in its history, there has been some earlier stage or phase? If so, then we have an actual infinity by way of a different argument.

If not, then there is some phase or stage for which there was no prior phase. On the other hand, if it is not true that every finite phase or stage has a predecessor, then there must be a first phase, stage or event of the universe's history -- which is to say that the universe came into being. But since we were identifying C with the universe, C must have come into being after all. Once again, we have an event -- in this case, the origin of the universe -- as a causal condition of E. Of course, this contradicts the initial assumption that C includes the complete set of E's causal conditions but does not include any event. But even if we give up that initial assumption, since the origin of the universe (understood as including everything that exists) cannot have anything else as a causal condition, there must be at least one event that has occurred without any causal conditions.

In other words, the entity-based theory of causality provides no way out. Even if we assume it, we will find ourselves having to reject at least one of the three theses of the inconsistent triad: Either there's an actual infinity (whether proven by old arguments or new) or there is some event that occurs without causal conditions (such as the origin of the universe) or time is cyclical. There is no escape from the inconsistency of that triad, certainly not any that Lawrence has provided.

In his comments, Lawrence objects to speaking of the universe as having originated, but his reasons for doing so are not made clear. What he says (quoting Peikoff) is "Time is a measurement of motion; as such it is a type of relationship. Time applies only within the universe," and (in his own voice):

According to Objectivism, the universe itself cannot be measured in temporal terms. It is "eternal" -- outside the scope of the concept of time.

It is important to understand that this conception of the universe as eternal does not mean that time extends infinitely into the past or future. Rather, it means that even if time is bounded -- that is, even if there was a first measurable time or will be a last measurable time -- one cannot coherently speak of this boundary as marking the "beginning" or "end" of the universe itself. Time-based concepts are not applicable to the universe as a whole. So, for example, to say that the "age of the universe" is 15 billion years (or whatever) is an inaccurate use of the concept of age. It would be more accurate to speak of the earliest known event having occurred 15 billion years ago. Specific events can be placed in time. The universe itself cannot.

The problem here is with understanding why the application of time only within the universe is any barrier at all to speaking about the origin of the universe. Setting aside cyclical time, the origin of the universe, if there was one, was a specific event which can be placed in time. That's applying time as a relationship within the history of the universe -- between the present and a (say) fifteen-billion-years-earlier origin. The only problem I see here is in the suggestion that there was something before the origination-event -- that because we can speak about a beginning 15 billion years ago, we can also talk about 16 or 20 billion years ago. Plainly, going back before the origin will be ruled out on any view that treats time as a relation between events. But the way to handle that is just to firmly deny that you are allowing inferences to "times before the beginning". That's entirely consistent with saying that there have been 15 billion years since the beginning.

Talking about "eternity" is not an intelligible alternative. Either there was some first event or stage in the history of our universe, some finite period ago ... or there was not. If there was, the universe originated, however long ago that first event or stage was. If not, the universe has an infinite history.

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Lawrence's performance here has not been impressive. He concludes his rebuttal this way:

The argument Bass offers is fatally flawed. As a criticism of Objectivism, it fails because two of the beliefs he discusses (that time is non-cyclical and that all events have prior events as their causal conditions) are not in fact part of Objectivism. As a criticism of Objectivists, it still fails, because the second leg of his triad (the belief that all events have prior events as their causal conditions) is not in fact the belief of Objectivists -- it actually contradicts the explicit Objectivist view of causality. And on either interpretation of his argument, it suffers because the third belief he discusses (that there are no actual infinities) is a part of Objectivism and a belief of Objectivists, but he has misunderstood its application to past events.

The "fatal flaws" are creatures of Lawrence's imagination, as is the incompatibility of the premises I employed with Objectivism. As he did throughout, he attributes to me claims I never made. Even where he correctly reports what I said -- on the issue of the non-existence of actual infinities -- it is he who has misunderstood the application to past events.