Time, Causes and Infinity: A Rebuttal of "An Inconsistent Triad"

Last Updated: February 26, 2009¹

Background

In February 2000, Robert Bass, then a philosophy doctoral student, posted a short essay called "An Inconsistent Triad" to the (now-defunct) Atlantis mailing list. In the essay, Bass attributes three specific metaphysical claims to Objectivists, and then argues that all three cannot be simultaneously true. The essay now resides on his website, along with a number of other essays criticizing Objectivism. It is occasionally cited in other forums when someone asks for an example of problems with Objectivism. My essay below is based on a post I wrote to the newsgroup humanities.philosophy.objectivism, after someone had made such a reference. The essay presented below has been revised and expanded from the original posting.

The Triad

In his essay, "An Inconsistent Triad," Robert Bass has argued that Objectivists hold three views that "form a set that has the property that any two are consistent, but the addition of the third makes the set contradictory."² Specifically, the three views he attributes to Objectivists are the following:

"[T]ime is non-cyclical." By this, Bass means the commonplace view that time occurs in a linear fashion, with the present following the past and the future following the present.
"[E]very event has causal conditions. What that means is that for every event, there are some prior conditions such that, had they not occurred or been present, then the event in question either would not have occurred or else would have been different."
"[T]here are no actual infinities. This means that there are no sets or groups or collections with infinitely many actual or existing members and also that there are no properties of anything that actually exists that are present to an infinite degree."

Bass does not explicitly claim that these three positions are part of Objectivism, only that they are the beliefs of "many Objectivists," including "Rand herself almost certainly." However, his essay is normally taken as a criticism of Objectivism, and certainly Objectivism contains distinct positions regarding the nature of causality and the possibility of actual infinities. Moreover, if the explicit positions of Objectivism are different from what Bass describes, then it would be unlikely that many Objectivists³ believe as Bass says, and even more unlikely that Rand herself held such beliefs.⁴ Therefore, exactly what the claims of Objectivism are, and what they imply in conjunction with one another, is crucial to evaluating the argument Bass makes.

The Problems

Whether looked at as a criticism of Objectivism, or just of "many" Objectivists, there are problems with the arguments Bass offers:

Objectivism does not include the first claim Bass mentions (about non-cyclical time);
Bass does not accurately represent the Objectivist view of causality; and
Bass does not show that an infinite causal regress is inconsistent with the Objectivist theory of infinities.

I discuss each of these problems in detail below. Discussion of the third point raises an additional issue regarding the Objectivist view of time, which I also discuss.

1. Time

The first of the three legs of his "inconsistent triad" -- the claim that time is non-cyclical -- is a claim that is not formally a part of Objectivism. Nonetheless, I believe that Bass is correct in saying that this is the belief of most Objectivists, including Rand. The view that time is non-cyclical is the most common understanding of time in western culture, and Rand did not give any public indication of disagreeing with it.⁵

Still, insofar as Bass' argument is taken as a criticism of Objectivism, the fact that this particular position is not part of Objectivism per se is worth noting. Objectivism can be held to be entirely consistent, notwithstanding the rest of his argument, as long as it is acceptable within Objectivism for time to be cyclical. Individual Objectivists might be willing to change their beliefs about time if there were some reason to, and they could do so and still accurately describe themselves as Objectivists.

2. Causes⁶

For the second leg of his triad, Bass discusses beliefs Objectivists supposedly have about causality. But his description of causality is different than that provided by Objectivism, in a way that is important to his point. 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 part of its "causal condition."

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.⁷

Before bringing the Objectivist view of causality into the discussion, it is worth noting some differences in terminology. Bass uses the term 'causal condition' in a carefully limited way, and he distinguishes between a 'cause' and a 'causal condition.' He has explained this distinction as follows: "The cause of an event is what is sufficient for that event to occur in the circumstances. A causal condition of an event, however is something that is (causally) necessary for its occurrence."⁸ Rand and other Objectivists have not followed this particular distinction in terminology when expressing their views of causality. They refer to 'causes' and, when appropriate, would distinguish between a 'necessary cause' and a 'sufficient cause.' The former would be equivalent to Bass' 'causal condition,' while the latter would be his 'cause.' When the word 'cause' is used hereafter in this essay, it should be assumed that the term is being used as Objectivists use it, not as Bass would (except, of course, when presenting quotes from Bass). Because the Objectivist use of 'cause' is inclusive of what Bass calls 'causal conditions,' the difference in terminology does not affect the applicability of the rebuttal.

Bass has an event-based view of causality -- that is, he believes the cause of one event is another event. On such a view, it is necessary that the "causal condition" of any event must include other events. In contrast, the Objectivist view of causality is that events are caused by entities, not other events. As Rand put it, "The law of causality is the law of identity applied to action. All actions are caused by entities."⁹. Leonard Peikoff affirms that this means that actions do not cause one another: "[T]he causal link does not relate to two actions. ... The law of causality states that entities are the cause of actions ..., not that the cause of an action is action, but that the cause of action is entities."¹⁰ In short, the Objectivist theory of causality is entity-based, not event-based.¹¹

The difference between the understanding of causality held by Bass and what Objectivists believe is a crucial problem for his "triad" argument. Since in the Objectivist view the cause of an event is an entity, it is possible that there could be an end to the series causes, because an entity is not required to have any prior causal conditions. In the Objectivist view, in some cases an entity might (indeed, some entities do) initiate an event without any necessary cause other than itself. This type of self-generated action is impossible in the event-based view of causality. As Nathaniel Branden notes, "The premise that every action is only a reaction to an antecedent action, rules out ... the existence of self-generated ... action." This "premise" is one that Branden decries.¹² In contrast, on an entity-based view, an action can be self-generated by an entity. Therefore, an event can be without any prior cause other than the existence of the entity that caused it.

To put it another way, an Objectivist would say that if Bass could trace a particular causal chain backwards, he might come to a first event that was caused simply by the nature of the universe, by the bare fact of the universe's existence, with no prior events to be counted. He would therefore not have an infinite sequence. This situation would be perfectly compatible with Objectivist beliefs about causality. Since the Objectivist view of causality does not require an infinite sequence of causes, Bass has not shown an inconsistency within the beliefs of Objectivists.

In a reply to an earlier version of this essay, Bass admits that "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." My own argument has always been that the Objectivist view of causality allows for "the denial that there must be prior (event-including) causal conditions for every event." As to arguing against event-based causality, while this might be an interesting topic in its own right, it is not relevant to the "triad" argument offered by Bass. Regardless of what Bass thinks of entity-based theories of causality, such beliefs are held by Objectivists. If Bass is going to show an inconsistency in the beliefs of Objectivists, he will have to base his argument on what they actually believe, not on whether he agrees with those beliefs. (Alternatively, he could abandon his claim of inconsistency, and focus instead on arguments against entity-based causality.) Later in his reply, Bass claims that "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." He seems to not grasp that the claim that "there is some event that occurs without causal conditions" (using his particular meaning for 'causal conditions') is exactly one of the positions that I have said is acceptable for Objectivists, and is therefore most definitely a "way out" of his claim that their beliefs are inconsistent.¹³

3. Infinity

Point (2) notwithstanding, Bass also fails to show precisely how a proposed infinite regression of causal conditions would contradict the Objectivist position on infinities. The Objectivist position on infinities is described by Leonard Peikoff:

Every entity, accordingly, is finite; it is limited in the number of its qualities and in their extent; this applies to the universe as well. ... For example, one can continually subdivide a line; but however many segments one has reached at a given point, there are only that many and no more. The actual is always finite.¹⁴

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. 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.

Since this point sometimes causes confusion, it is worth looking at from another perspective as well. The problem with infinities lies in the finite identities of things that exist, which is why Peikoff refers specifically to entities. Peikoff states that, "Every entity ... is limited in the number of its qualities and in their extent; this applies to the universe as well." So the question of an infinite sequence of causes can be analyzed by asking whether it implies a lack of limits on any of the items Peikoff says must be limited. If there was an infinite past sequence of causes, then:

What quality of an entity would exist in an infinite extent? None. An infinite sequence of causes does not require that any particular entity have any infinite quality.
What quality of the universe would exist in an infinite extent? None. The obvious claim for Bass to make in this regard would be that "age" is the quality¹⁵ that would be infinite, since an infinite sequence of causes would require that time be unbounded in the past. However, as I discuss in the next section, the Objectivist view is that the concept of age applies only to particular entities, not to the universe as a whole.
Would there exist an infinite number of qualities for any entity? No.

Based on the analysis above there is no incompatibility between a supposed infinite prior sequence of causes and the position Peikoff describes with regard to infinities.¹⁶

4. And Time Again

In the previous section I mentioned that Objectivists do not believe that the concept of age can be applied to the universe as a whole. This claim deserves further discussion, since it may be unfamiliar to many readers. The Objectivist view of time is described by Leonard Peikoff:

Time is a measurement of motion; as such it is a type of relationship. Time applies only within the universe, when you define a standard -- such as the motion of the earth around the sun. If you take that as a unit, you can say: "This person has a certain relationship to that motion; he has existed for three revolutions; he is three years old."¹⁷

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.

To return to the original topic of discussion, then, the relationship between a possible infinite sequence of causes and the boundedness of time is as follows: if there was an infinite sequence of past causes, then time is not bounded in the past. However, the implication does not go in the other direction. If there was not an infinite sequence of past causes, one cannot infer whether or not time is bounded in the past. The reason one cannot make this inference is that although any given causal chain may be finite, there may have been prior causal chains, so that while all causal chains are finite, time is not bounded in the past.¹⁸

Conclusions

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 part of 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 part of their causal conditions) is not in fact the belief of many Objectivists. 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. In effect, this means that his interpretation of the third premise is not a belief of many Objectivists, even though there is a common Objectivist belief that uses similar terminology.

One aspect of the discussion above is that my objections from sections (2) and (3) are compossible -- that is, they might both be true at the same time. It is conceivable that while an infinite series of past causes is consistent with Objectivist theory on infinities, there was not in fact an infinite series of past causes. However, since problems (2) and (3) are fatal to the argument Bass presents in his essay either separately or in combination, a rebuttal of Bass does not require that both be true. Either one will do to refute his argument.¹⁷

Notes

¹ This essay is based on a post I wrote to the newsgroup humanities.philosophy.objectivism in April 2002. When I placed it on the web, I revised and expanded it from the original posting, and added footnotes. In the spring of 2004, Bass posted a response to the first web version of this essay on his own website. In 2005, I further revised my own essay to take his additional comments into account. In 2008, I had to update the page to fix technical items (such as URLs that had changed). At that time I took the opportunity to make additional minor changes that did not alter any of the core arguments. For reference, the version of my essay that Bass responded to is archived here.

In an email exchange with a blogger in 2008 (which I was not aware of until later), Bass revealed that he knew about my revision of this essay, but had chosen not to respond to it. He characterized my replies to his arguments as not being "satisfactory," but declined to elaborate. Bass has a habit of going beyond counterargument to reveal his overall negative evaluations of my criticisms of him (see note 19 below). Except in this case he skipped the arguments and just announced his evaluation. Since he is hardly an unbiased judge on the matter, I can only wonder what significance he expects anyone to attribute to such comments. Anyhow, in early 2009 I updated this footnote to mention his apparent final words on the subject.

² Robert Bass, "An Inconsistent Triad," >. Unless otherwise cited, all quotes are from this essay by Bass, as it appeared on his website in April 2002 (last verified in June 2008).

³ In the original version of this essay, I accidentally wrote "most Objectivists" instead of "many Objectivists." Bass seized on this mistake to reply that he never claimed that most Objectivists held these beliefs, only many of them, leaving 'many' completely unspecified as to number or proportion. It is unclear why he couched the essay as a critique of Objectivists at all, or placed it on his website among a list of essays commenting on Objectivism, if he does not think the majority of Objectivists hold these views.

⁴ In a reply to me, Bass argues that I have not offered sufficient evidence that the beliefs he describes are not held by many Objectivists. For example, he says that I have not cited any polls of Objectivists. Such a response seems disingenuous. Since Bass is the one making positive claims about what people believe, one would expect that he would be the one offering such polls. Instead, the only evidence he offers is that "the response to the article on various forums where it has been discussed" and "private e-mail responses" show that the respondents hold these beliefs. Note that such responses could not be the basis for his original claim, since by definition they could only have come after he circulated his essay. Moreover, he does not cite any actual endorsements of the premises in these responses, but rather characterizes them as having an absence of explicit denials of his premises. Apparently, if a respondent does not expressly deny a premise, Bass counts that as agreement. Even setting aside that dubious approach to interpretation, I also have other serious doubts about his characterization of the responses. Although I do not have access to his private email, I have reviewed the responses on two public forums (the Atlantis email list and the newsgroup humanities.philosophy.objectivism). In both groups, objections to his premises were expressed. In fact, there were few responses that did not question or explicitly deny at least one of the premises.

Finally, Bass fails to defend one important part of his claim: that not only do "many Objectivists" hold these beliefs, but "Rand herself almost certainly" held them as well. He does aver that "the evidence is solid (though not conclusive) that Rand believed all three," but does not present this evidence. The question of what "many" Objectivists believe is probably unresolvable at present, due in part to the absence of standards for what constitutes "many" or even "Objectivists." Determining the views of Ayn Rand, a published author and public speaker, should be much easier. Nonetheless, Bass presents no evidence whatsoever that Rand held any of the beliefs he describes. He also does not identify any other well-known Objectivist who holds them. Since it is possible that "many" people believe all sorts of inconsistent things, I can only wonder what historical or philosophical significance Bass attributes to this triad of views that apparently belong to an unnamed minority of obscure Objectivists who only reveal their existence by sending Bass private email replies to his essay.

⁵ In an essay that touches on some of the same topics as this present one, Alex Silverman states that

Dr. Harry Binswanger mentions in the first question period of his lecture Selected Topics in the Philosophy of Science that Miss Rand had a theory that she called "circular time," which Dr. Binswanger said he unfortunately did not learn very much about.

Given the limited nature of this reference, I do not know whether the theory alluded to is anything like the cyclical time discussed by Bass. In any case, Rand's discussion of this theory does not appear to have been public, so the point made above stands. However, this reference does raise the interesting possibility that, contrary to my earlier conclusions, Bass might actually be wrong about all three premises, at least in regard to Rand personally. (I should also mention that I have serious reservations about some of the arguments made in Silverman's essay, and it should not be taken as representative of my own positions, similarities on some points notwithstanding.)

⁶ In consideration of several criticisms Bass makes in his reply to an earlier version of this essay, I have made several revisions to this section. Therefore, someone reading his reply would see a number of criticisms of statements that do not exist in the current version or which have been revised. For reference, the version of my essay that Bass responded to is archived here.

⁷ In his reply to me, Bass quotes this paragraph of my essay and declares,

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."

However, it is not true that Bass defined causal conditions as involving prior events. He describes causal conditions as "some prior conditions such that, had they not occurred or been present, then the event in question either would not have occurred or else would have been different." This description (I hesitate to call it a "definition," since Bass did not identify it as such) makes no mention of events. In a footnote, he argues that the causal conditions must involve events, but this is not explained as part of the definition of what a causal condition is. Moreover, elsewhere in his reply Bass effectively rebuts his own footnote, and allows that, if the conclusion of another argument (which Bass seems to accept) is granted, there could be "some set of causal conditions ... which do not include any event." Such a reply would be inconsistent with defining causal conditions as involving events. Therefore, I take my paragraph to be exactly correct as originally stated.

⁸ Robert Bass, "Re: Contradictions within Objectivism ...?," posted to humanities.philosophy.objectivism, April 4, 2002.

⁹ Ayn Rand, Atlas Shrugged, p. 954. All quotes from the works of Ayn Rand and Leonard Peikoff in this essay, unless otherwise noted, are taken from The Objectivism Research CD-ROM, edited by Phil Oliver, and cite the pagination used therein for each particular work.

¹⁰ Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand, p. 16. That Objectivists believe causation is entity-based, and not event-based, is affirmed by other commentators on Objectivism, including Allan Gotthelf (On Ayn Rand, pp. 44-45), Paul Lepanto (Return to Reason, p. 16), John W. Robbins (Without a Prayer, pp. 102-103), and Chris Matthew Sciabarra (Ayn Rand: The Russian Radical, pp. 142-143).

¹¹ In discussions related to his essay, Bass has stated that he denies causation is entity-based, calling that theory "barely intelligible" (cf. the newsgroup posting cited in note 8 above). Why it is barely intelligible is not specified. A footnote appended to the webbed version of his essay implicitly criticizes the idea of entity-based causality. The footnote argues that if a non-event cause ('C') led to an effect ('E'), there would still be an event involved -- specifically, the event of C causing E. However, causation is a relationship between an effect and its causes, not a separate event in its own right, so this argument is also flawed. (Bass poses the claim that C causing E is an event as a question, but the question is clearly intended to be rhetorical.) In his later reply to me, he appears to discard the argument offered in his footnote, but offers additional criticisms of event-based causality.

¹² Nathaniel Branden, "Volition and the Law of Causality" in The Objectivist, 5:3 (March 1966), p. 44. Branden's and Peikoff's use of the term 'action' in the quotes used above, and their use of the term 'motion' in some other contexts in the cited works, is equivalent to my use of the term 'event' in this essay.

¹³ I do not personally claim to know whether there was a first event or not; I consider this a scientific question. From the perspective of the Objectivist philosophy (which is what Bass is implicitly criticizing, his defensive remarks about "many Objectivists" notwithstanding), either answer should be acceptable. Various Objectivists have adopted different positions on this issue, with some arguing for a first event, and others arguing that there is not first event and time therefore is unbounded. For additional explanation of how the latter belief is compatible with Objectivism, see my discussion of the third problem with Bass' argument.

¹⁴ Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand, pp. 31-32, emphasis in original.

¹⁵ Technically, Objectivists do not consider time to be a quality at all. Rather, it is a relationship. See the next section for further discussion.

¹⁶ In his reply to me, Bass gives an extended critique of a portion of my response, while ignoring the essence of my rebuttal to him: that the Objectivist position as stated in widely-read Objectivist literature is not incompatible with a supposed infinite prior sequence of causes. He even goes so far as to parse the grammar of the phrase "actual infinities," without acknowledging the point-by-point comparison I made to Peikoff's description of the Objectivist view. If a belief in an infinite prior sequence of causes does not correspond to any of the criteria listed by Peikoff, then it does not trigger the Objectivist objection to infinities, regardless of how Bass parses the words in my reply. If Bass wants to interpret the objection to "actual infinities" as being something other than the objections articulated by Peikoff, then he should offer some evidence that Objectivists have beliefs that match this alternative interpretation.

¹⁷ Leonard Peikoff, "The Philosophy of Objectivism" lecture series (1976), Lecture 2 question period. Quoted in The Objectivist Lexicon, edited by Harry Binswanger, p. 503. That the concept of time as motion was also Rand's is affirmed by her comments on the subject in a letter to John Hospers in Letters of Ayn Rand, p. 530.

¹⁸ In comments he makes in the "Intellectual Ammunition Department" column of The Objectivist Newsletter (May 1962, p. 19), Nathaniel Branden indicates that there has not been "an infinite series of antecedent causes." Since Rand was co-owner of the magazine and provided its direction on philosophical issues, the implication is that this was her view as well. However, as discussed above, such a statement does not directly address the question of whether time is bounded or not.

¹⁹ Since the original discussion that prompted this essay, Bass has made some updates to his essay in the form of an addendum and two footnotes, and he has issued a reply to an earlier version of my essay. Most of my reaction to his reply is incorporated into the essay and notes above. Bass characterizes my essay as "unimpressive," to which I can only respond that I have a similar attitude towards his reply. He manages to ignore some of my key points, a deficiency which I consider far more significant than any of the flaws Bass identifies with the earlier version of my essay.

As to the footnotes and addendum, these only serve to dig deeper holes for him to climb out of. In the addendum, he discusses "several [arguments] that have been used at one time or other" to claim that there are no actual infinities. Interestingly, his list does not mention the specific Objectivist argument given by Peikoff (as quoted in my essay above). This omission, in combination with his earlier arguments, suggests that Bass is not actually familiar with what the Objectivist argument is. He appears to know that Objectivists have some objection to actual infinities, presumably due to discussions he has had on the internet or elsewhere, but perhaps he never bothered to track down the specifics of the objection. His reply to me continues to disregard these specifics, even though I quote them in the body of my essay.

In his first footnote, Bass argues that every event must have at least one other event among its causal conditions:

[S]uppose 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?

Aside from committing the category error of considering causation to be an event (as discussed in my note 11 above), this argument has other problems. If this argument is correct, and C giving rise to E is an event (call it E2), then there must be another event (E3) which consists of something giving rise to E2, etc. The implication is that there must be an infinite number of events, not just in the entire past, but in the immediate causation of any one event. However, in the main body of the essay, Bass ventured that it is "somewhat more likely that not every event has a causal condition than that there are actual infinities." However, as mentioned in note 7 above, Bass effectively admits in his reply to me that the argument in this footnote is flawed, so perhaps this concern should be set aside.

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