Petersen’s Failed Attempts to Refute Leonard Peikoff: Objection 1
The first entry in this series can be found here.
Dr. Peikoff’s statements in question can be found here.
Jason Petersen’s response to Peikoff can be found here.
In the present entry, I will examine Petersen’s interaction with Peikoff’s first objection to theism, which I will quote below.
Peikoff’s first objection is the following:
“For instance, God is infinite. Nothing can be infinite, according to the Law of Identity. Everything is what it is, and nothing else. It is limited in its qualities and in its quantity: it is this much, and no more. “Infinite” as applied to quantity does not mean “very large”: it means “larger than any specific quantity.” That means: no specific quantity—i.e., a quantity without identity. This is prohibited by the Law of Identity.”
Answer: Contrary to Peikoff’s assertion, the law of identity says absolutely nothing concerning whether or not anything can be infinite. All the Law of Identity says is that things are what they are.
First, notice that, in his statement, Peikoff is careful to clarify what he means by ‘infinite’. In the context of Peikoff’s point, ‘infinite’ means “larger than any specific quantity.” Petersen does not raise any objection to this understanding of ‘infinite’. Thus it seems safe to assume that Petersen agrees with Peikoff’s conception of ‘infinite’, for he had the opportunity to challenge it when he was composing his response to Peikoff, and he did not raise any objections to Peikoff’s definition of ‘infinite’. We will see below that this is significant.
Second, what is Petersen’s argument for his claim that “the law of identity says absolutely nothing concerning whether or not anything can be infinite”? He asserts (without any argument) that “all” that is denoted by the law of identity “is that things are what they are.” But is that truly “all” that the law of identity states?
Quoting from Ayn Rand’s Atlas Shrugged, we find the Objectivist conception of identity which at the very least Peikoff has in mind:
To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of a specific nature made of specific attributes. Centuries ago, the man who was—no matter what his errors—the greatest of your philosophers, has stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself.
Now contrast this with Peikoff’s conception of ‘infinite’ which he gives in the quoted transcription from his lecture series (and which Petersen himself does not contest):
“Infinite” as applied to quantity does not mean “very large”: it means “larger than any specific quantity.” That means: no specific quantity—i.e., a quantity without identity.
Moving on, Petersen interprets the law of identity to mean that “if God is omnipotent, then he is omnipotent. If God is God, then he is God.” Indeed, if “God” is merely imaginary, then “God” is merely imaginary. What’s unfortunately for Christianity is that there is no alternative but our imaginations as the means of “knowing” the Christian god. Petersen can tell me that his god is omnipotent, that it is infinite, that it is all-good, that it is all-knowing, that it is holy, just, loving, etc. But I have no alternative but to imagine such a god. I cannot acquire awareness of such a thing as Christians describe by looking outward at the world – meaning there is no objective evidence that the theist can point to in order to support his god-belief assertions, and we will find Petersen himself essentially confirming this.
What’s clear up to this point, however, is that Petersen is failing quite expressly to vindicate the assumption that an existent can be infinite. Running headlong on his sorely mistaken understanding, Petersen seeks to turn the tables on Peikoff in order to charge him (Peikoff) with an internal inconsistency.
Ironically, Objectivism holds that the universe is eternal. Thus, this view of the law of identity would entail the time that he universe has existed is infinite. Does this mean that there is no passage of time?
The universe is the total of that which exists—not merely the earth or the stars or the galaxies, but everything. Obviously then there can be no such thing as the “cause” of the universe…
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.” But when you get to the universe as a whole, obviously no standard is applicable. You cannot get outside the universe. The universe is eternal in the literal sense: non-temporal, out of time.
Moreover, given the nature of the meanings which Peikoff has clarified, it would be nonsensical to say that time exists “outside” the universe. And since the existence of the universe is preconditional to time, it could only be proper to agree that “the universe is eternal in the literal sense: non-temporal, out of time.”
It does not follow from any of the points Peikoff has affirmed that “this view of the law of identity would entail the time that he [sic] universe has existed is infinite.” Since time is a form of measurement, it has the potential to be extended indefinitely, like the number series, without implying that an “actual infinite” exists. So Petersen is proffering a non sequitur here.
We must keep in mind the fact that time is measured between two points, one prior to the other: e.g., between the time I was born and today (which I can measure in terms of years), or between the time I woke up this morning and the time I took a shower (which can be measured in terms of minutes). We can even measure the time between today and the days of ancient Greece (which we can measure in terms of (millennia). Even larger units of time can be used to measure between greater quantities of time. But if we take away one of those points, then we are no longer measuring anything, so the concept of time no longer applies. So again, Petersen’s attempt to find an internal inconsistency on Peikoff’s part (and consequently within Objectivism proper) fails.
Also, it should be noted that the idea of an eternal universe in no way implies the existence of an actual infinite. The concepts ‘eternal’ and ‘infinite’ do not mean the same thing. Peikoff makes it clear that he does not mean that the universe is infinite:
Is the universe then unlimited in size? No. Everything which exists is finite, including the universe. What then, you ask, is outside the universe, if it is finite? This question is invalid. The phrase “outside the universe” has no referent. The universe is everything. “Outside the universe” stands for “that which is where everything isn’t.” There is no such place. There isn’t even nothing “out there”: there is no “out there.”
Petersen quotes Peikoff:
To grasp the axiom that existence exists, means to grasp the fact that nature, i.e., the universe as a whole, cannot be created or annihilated, that it cannot come into or go out of existence.
This is an exercise of special pleading by objectivists. They wish to say that God cannot be infinite, yet they wish to assert that the universe has never been created and will never be annihilated. This entails an infinite passage of time.
Also - and this is important, the notion of a “passage of time” does not denote an entity, which is what the law of identity is primarily concerned with. Objectivism does not reject the notion that a series can be extended indefinitely (such as the number series), so long as it is understood that such a notion does not imply the existence of an ‘actual infinite’ (which it doesn’t). A “passage of time” could only have meaning in the context of measuring, which is what time does: it measures distance between two points given an objective standard, e.g., a year ago today until today constituting a full revolution of the earth around the sun. So even if Petersen wants to focus on the notion of a “passage of time,” which Petersen himself does not define, he’s already missing crucially important points about the meaning of the law of identity as Peikoff is applying it (since the notion of a “God” is supposed to denote an entity, not a potential like the ability to continue extending a series indefinitely).
A further difficulty for Petersen is in how he measures temporal units. For however he measures these, they would have to imply an actual infinite once they’re added together in order to have any hope of bringing a sustainable objection against Peikoff’s position. But this is akin to the problem of counting ‘events’. Summing up the number of events that happen in a given time period, such as today (October 12, 2014), runs into the “problem” (for Petersen, anyway) that whatever sum is reached, we will have a finite quantity. So if N- number of events happened today and M- number of events happened the day before, and L- number of events happened the day before, and so on, in each case we have a finite number (indeed, the notion of a ‘finite number’ is a redundancy). If we add two finite numbers, we have yet another finite number as their sum. If we add 40 billion finite numbers, we still have a finite sum. At best, all that Petersen can do is point to the potential that we can continue adding finite sums together, in which case we can happily say: Congratulations! You’re (hopefully) catching on!
Petersen goes on:
If Peikoff were consistent with his own philosophy of objectivism, he would have to conclude that the universe shouldn’t be eternal, for it would entail an that [sic] the universe is eternal, and thus, the passage of time is infinite.
So Peikoff is entirely consistent with his own worldview’s definitions and positions in affirming the eternality of the universe. Only by smuggling in non-Objectivist notions and inserting them into Peikoff’s mouth can Petersen and other detractors of rational philosophy attempt to find some problem here, but in doing so they would no longer be executing an internal critique. It simply becomes more ignorance-laded misrepresentation at that point, and that is essentially all that Petersen has given us throughout his paper.
But Petersen doesn’t want to let go. He continues:
Objectivists accept that there is a passage of time, but according to Peikoff’s view of infinity, there can be no passage of time because according to his metaphysic, the passage of time is infinite.
But what would this even mean? Clearly Petersen has imported a non-Objectivist conception of time, treating time as though it were an entity of sorts (rather than a form of measurement requiring an objective standard), in order to try to find some internal inconsistency among Peikoff’s affirmations. But Petersen has not consulted Peikoff’s statements about what time is according to Objectivism. If he had, perhaps he might have been able to catch his own errors before presenting them to the world (though I’m coming to doubt that he has such ability). That Objectivism clashes with other worldviews which do not share its definitions, is conceded. But so what? We already know this. This does not automatically make Objectivism wrong. Moreover, by importing non-Objectivist notions into his critique, Petersen has abandoned his own task of trying to produce an internal critique of Objectivism. Petersen’s entire case against Peikoff (not to mention Objectivism proper) is falling to pieces here.
And yes, Objectivists do in fact “accept that there is a passage of time” in the sense that they agree that activity can be measured in reference to an objective standard – such as the earth’s motion around the sun. But this in no way implies the existence of an actual infinite. If Petersen thinks he’s secured such an implication, he is sorely mistaken.
Since the passage of time is infinite, it cannot, according to Peikoff, have any specific quanity. [sic]
The proper implication for Peikoff’s argument for God [sic] is that there is no passage of time.
Also, Peikoff’s objections to the notion of a god in no way imply that “there is no passage of time” if by “passage of time” one means activity which can be measured against a specific standard, such as the motion of the earth around the sun. (If Petersen means something else here, he needs to spell it out, but so far he hasn’t. Why?) Objectivism affirms that entities both exist and act. These are the metaphysical preconditions of time. Epistemologically, one needs both a standard for temporal measurement (e.g., the earth moving around the sun) and two points that can be measured against that standard (e.g., my daughter was born six and a half revolutions of the earth around the sun – from the date of her birth to today). All these points fly right over Petersen’s head.
Therefore, his argument against God contradicts his own objectivist metaphysic. From this contradiction, a proper implication can be drawn that the idea of an eternal universe is nonsensical. The law of identiy [sic], according to Peikoff’s own logic, actually contradicts objectivist metaphysics.
Petersen threw in some last-minute confusion on the matter:
An objectivist such as Peikoff might respond by saying that time is an abstraction, but the fatal flaw in this response is that it doesn’t recognize that with the passage of time, the universe expands. Thus, the size of the universe is increasing, the age of the universe is increasing, their [sic] is no finite quantity to the universe because it is expanding in size and in age. By Peikoff’s logic, the universe cannot exist because it is of no specific quantity. Rather, the universe is in constant change for better or for worse. Perhaps according to Peikoff’s logic, existence does not exist.
1. Since time is a form of measurement, it is essentially epistemological rather than metaphysical;
2. What time measures – namely motion, activity, action – is metaphysical and must exist in order to be measurable;
3. Existence, i.e., the universe as a whole, then, is metaphysically preconditional to time;
4. Therefore, that the universe is literally eternal – i.e., outside of time – is the only position logically compatible with the facts;
5. To say that “size of the universe is increasing” because the universe is expanding, is at best misleading. The quantity of what exists is not what’s expanding; it is the distribution of what exists that is expanding: things are moving away from each other. This does not mean that new material is being added to the universe;
6. To say that the age of the universe is increasing because its inflation (“expansion”) is increasing, is also misleading at best. What is increasing in age is not the universe as a whole, but its expansion. These are two different things that Petersen has failed to distinguish and has conflated for apologetic purposes;
7. No scientific discovery that I am aware of, either about the inflationary expansion of the universe or its rate, contradicts the essence of what Objectivism teaches. Even in the case of the so-called “big bang,” if its proponents are saying that the entire contents of the universe were compressed into some tiny particle the size of a proton and spontaneously exploded into what we find today, then they’re still starting with existence and thus tacitly affirming the eternality of the universe; they would not be saying “something from nothing” in such a case. What has changed is only the arrangement of the universe’s contents – from being compressed into tiny particle to the continually inflating distribution of stars, planets, and galaxies that we see today in the night sky.
For some fascinating information on these matters from an Objectivist perspective, I highly recommend David Harriman’s two interviews on Gnostic Media Research & Publishing, which can be found here:
All of this points to a fundamental distinction between my worldview and Petersen’s: Objectivism begins with what exists, with what is real, while Christianity starts with what is imaginary. The two could not be more at odds with each other.
Petersen raised three more objections against Peikoff’s comments about the existence of a god. I will review each in separate upcoming entries on my blog.
by Dawson Bethrick