Implied Axioms
by Fred Seddon
“Existence exists—and the act of grasping that statement implies two corollary axioms: that something exists which one perceives and that one exists possessing consciousness, consciousness being the faculty of perceiving that which exists.” (Atlas Shrugged, p. 1015, emphasis added)
Part of my celebration of Rand’s hundredth birthday has been to reflect on some of her writings that are either central to Objectivism, or which have meant the most to me. This text fulfills both criteria. I was thinking about the "two corollaries" and came to realize that Rand could have added more axioms to this list.
Before I name some of them, I want to note something that has intrigued me about this sentence for a long time. Notice that it is not “existence exists” that implies the corollaries, but “the act of grasping that statement” that does the implying. And that is unique with Rand, I think. With most thinkers, it is the axioms themselves that imply either corollaries or theorems. Newton, for example, does not mention that someone must “grasp his axioms” (the three axioms of motion) in order for them to imply the six corollaries that follow in his text.
Does this mean that, for Rand, “existence exists” implies nothing? Do we need “graspers” in order for there to be implications? If the human race vanished for one hundred years and then reemerged, would those neo-humans be able to read Newton? Were those implications there during the hundred year absence of the human race? But enough of this; let me return to my topic. What else does “the act of grasping that statement” imply?
How about time? Could she have written, "Existence exists—and the act of grasping that statement implies that time exists, since it takes time for one to grasp anything?"
How about change? Could she have written, "Existence exists—and the act of grasping that statement implies that change exists, since no one can grasp anything without changing from a state of non-grasping to a state of grasping?"
How about space? Could she have written, "Existence exists—and the act of grasping that statement implies that space exists, since no one can grasp anything without some spatial separation from, in my case, the book of Atlas Shrugged and the eyes of one’s spatially extended head?"
After awhile I could pile up axiomatic corollaries at will. Maybe I was wrong to think this way. Wouldn’t it be nice if there were a test to make sure these were indeed corollary axioms? There is such a test, and Rand writes about it in Introduction to Objectivist Epistemology. Like Aristotle, she uses the "accept in order to reject" criterion for axioms. You can’t deny you are conscious without being conscious. You can’t deny that you exist unless you exist. So let’s look at the three I’ve listed above.
Can you deny that time exists? It will take time to do that. You would have to utter four words, namely, “time does not exist.” But that takes time. Sorry. You must accept time in order to reject time; therefore, time is axiomatic.
How about change? To utter the statement “there is no change” involves changing one’s lips and tongue in order to form the words.
How about space? To say, “there is no space” from nowhere is impossible. You have to be somewhere to say that ... somewhere with air to carry the sounds of your words. Corollary axioms abound, and all spring from the simple act of grasping that “existence exists.”
Maybe this is multiplying axioms beyond necessity. Nevertheless, they do seem to follow from “grasping the statement.” They seem to follow from grasping any statement!
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