Like Aristotle, Rand believes that logic is inseparable from reality and knowledge. She states: “If logic has nothing to do with reality, it means the Law of Identity is inapplicable to reality.” But, as Peikoff explains: “The Law of Contradiction … is a necessary and ontological truth which can be learned empirically.” … [For Rand,] logic is certainly a law of thought, insofar as it is “the art of non-contradictory identification.” But logic is true in thought only because contradictions cannot exist in reality. Rand writes: “An atom is itself, and so is the universe; neither can contradict its own identity; nor can a part contradict the whole.” [Ayn Rand: The Russian Radical, 139-140]
What on earth does it mean to say that contradictions cannot exist in reality? What kind of processes or events is this supposed to rule out? What would a “contradiction in reality” look like? What does it mean, in empirical terms, to say that an atom cannot be a non-atom? Or is it merely that we simply cannot conceive such “contradictions in reality”? But if we cannot conceive what a “contradiction in reality” might be, what is the point of saying such a phenomena cannot exist? If we cannot even imagine its existence, it has no relevance, either as an error or a falsehood. So again, what is this mythical gremlin, the “contradiction in reality,” and why should we bother our heads with it?
Rand’s confusion here runs deep, and stems from confusing different aspects or realms of existence and trying to assume that logic, in order to be cognitively useful, must be valid in every domain or realm of existence. The philosophers George Santayana and Karl Popper, working entirely independent of one another, distinguished at least three realms or “worlds”:
- Realm of Matter/World 1: the physical world, the world of matter existing in time and space.
- Realm of Spirit/World 2: consciousness, the world of mental objects and events.
- Realm of Essence/World 3: the world of ideas, meanings, theories, problems, etc.
While Santayana’s realms of matter and spirit are largely identical to Popper’s worlds 1 and 2, there are important difference between the Santayana’s realm of essence and Popper’s world 3. Santayana’s realm of essence includes all possible meanings, whether anyone has experienced them or not. Popper, on the other hand, tends to confine his world 3 to those ideas or meanings produced by the human mind. These differences are not important for the points I will be trying to make about logic and reality in this post.
Now where does logic actually hold true? Does it hold true in all three realms/worlds? Or in only one or two of them? Or in none of them? Well, let’ s take a look, first, at the realm of matter. Does it hold true for that? No, it doesn’t. This is demonstrated by an experiment proposed by Karl Popper. Popper begins by noting that when a logical statement such as 2+2=4 is applied to reality (as when someone puts 2+2 apples in basket),
it becomes a physical theory, rather than a logical one; and as a consequence, we cannot be sure whether it remains universally true. As a matter of fact, it does not. It may hold for apples, but it hardly holds for rabbits. If you put 2+2 rabbits in a basket, you may soon find 7 or 8 in it. Nor is it applicable to such things as drops. If you put 2+2 drops in a dry flask, you will never get four out of it. If you answer that these examples are not fair because something has happened to the rabbits and the drops, and because the equation ‘2+2=4’ only applies to objects in which nothing happens, then my answer is that, if you interpret it in this way, then it does not hold for ‘reality’ (for in ‘reality’ something happens all the time), but only for an abstract world of distinct objects in which nothing happens. To the extent, it is clear, to which our real world resembles such an abstract world, for example, to the extent to which our apples do not rot, or rot only very slowly, or to which our rabbits or crocodiles do not happen to breed; to the extent, in other words, to which physical conditions resemble pure logical or arithmetical operation of addition, to the same extent does arithmetic remain applicable. But this statement is trivial.” [Conjectures and Refutations, 212]
So logic does not in all respects hold good for the physical world. What about the mental world? Here I draw on Santayana’s testimony:
Now as a matter of fact there is a psychological sphere to which logic and mathematics do not apply. There, the truth is dramatic. That 2+2=4 is not true of ideas. One idea added to another, in actual intuition [i.e., in conscious experience], makes still only one idea, or it makes three: for the combination, with the relations perceived, forms one complex essence, and yet the original essences remain distinct, as elements in this new whole. This holds true of all moral, aesthetic, and historical units: they are merged and reconstituted with every act of apperception. [Realm of Truth, 410]
Where, then, is logic fully applicable? According to Popper, “Logical necessity exists only in world 3. Logical connection, logical relations, logical necessities, logical incompatibility — all that exists only in world 3. So it exists in our theories about nature. In nature this does not exist, there is no such thing.” [Knowledge and the Body-Mind Problem, 41]
Santayana regards logic to be “merely a parabolic excursion in the realm of essence.” If a logical construction is true, this truth derives, not from logic, but from conformity to the order of nature.
The only serious value of … logical explorations would lie in their possible relevance to the accidents of existence. It is only in that relation and in that measure that mathematical science would cease to be mere play with ideas and would become true: that is, in a serious sense, would become knowledge. Now the seriousness of mathematics comes precisely of its remarkable and exact relevance to material facts, both familiar and remote. And this in surprising measure. For when once any essence falls within the sphere of truth, all its essential relations do so too: and the necessity of these relations will, on that hypothesis, form a necessary complement to a proposition that happens to be true. This same necessity, however, would have nothing to do with truth if the terms it connects were not exemplified in existence. In this way mathematical calculations far outrunning experiment often [but not always!] turn out to be true of the physical world, as if, per impossible, they could be true a priori. [ibid, 409]
In other words, when a logical proposition turns out to be true, the truth of that statement arises, not from its logic, but by the fact that it is exemplified by the real world. It is the real world, not logic, which makes a thing true. Facts, nature, reality constitute the standard of truth, not logic. I would also note that, while there exists an infinite number of logical expressions (after all, every mathematic equation is a logical expression, and there are an infinite number of such expressions), only a small fraction of those will find exemplification in existence. Logical validity is therefore no warrant of truth.
If existence were actually logical, as conceived by Objectivists, then reality would have to be a system of ideal relations, like we find imagined in the idealist reveries of Plato and Hegel. In other words, this view only makes sense on idealist assumptions. But on realist assumptions, reality may be anything it pleases. It is not for the mind to determine how reality must be. On the contrary, the mind must accept whatever it finds. And since we have not experienced every possible fact of nature, all theories about facts are ultimately conjectural, and must be revised or overthrown if a fact is discovered that contradicts them. Facts, therefore, for all practical intents, are contingent — which effectively means, alogical and "unnecessary." If a fact contradicts one of our theories about reality, it is the theory that has to go, not the fact.
I suspect there will be Rand apologists who will protest that Objectivism denies no facts. Well, that’s not so clear, as we shall see in my next post.