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[twenty twenty-four day thirty-three]: roll the bones

centaur 0

As both Ayn Rand and Noam Chomsky have both said in slightly different ways, concepts and language are primarily tools of thought, not communication. But cognitive science has demonstrated that our access to the contents of our thought are actually relatively poor – we often have an image of what is in our head which is markedly different from the reality, as in the case where we’re convinced we remember a friend’s phone number but actually have it wrong, or have forgotten it completely.

One of the great things about writing is that it forces you to turn these abstract ideas about our ideas into concrete realizations – that is, you may think you know what you think, but even if you think about it a lot, you don’t really know the difference between your internal mental judgments about your thoughts and their actual reality. The perfect example is a mathematical proof: you may think you’ve proved a theorem, but until you write it down and check your work, there’s no guarantee that you actually HAVE a proof.

So my recent article on problems with Ayn Rand’s philosophy is a good example. I stand by it completely, but I think that many of my points could be refined considerably. I view Ayn Rand’s work with regards to philosophy the way that I do Euclid for mathematics or Newton for physics: it’s not an accurate model of the world, but it is a stage in our understanding of the world which we need to go through, and which remains profitable even once we go on to more advanced models like non-Euclidean geometry or general relativity. Entire books are written on Newtonian approximations to relativity, and one useful mathematical tool is a “Lie algebra”, which enables us to examine even esoteric mathematical objects by looking at the locally at the Euclidean tangent space generated around a particular point.

So it’s important to not throw the baby out with the bathwater with regards to Ayn Rand, and to be carefully specific about where her ideas work and where they fail. For example, there are many, many problems with her approach to the law of identity – the conceptual idea that things are what they are, or A is A – but the basic idea is sound. One would say that it almost approaches tautological except for the fact that many people seem to ignore it. However, you cannot fake reality in any way whatever – and you cannot make physical extrapolations about reality through philosophical analysis of a conceptual entity like identity.

Narrowing in on a super specific example, Rand tries to derive the law of causality from the law of identity – and it works well, right up unto the point where she tries to draw conclusions about it. Her argument goes like this: every existent has a unique nature due to the law of identity: A is A, or things are what they are, or a given existent has a specific nature. What happens to an existent over time – the action of that entity – is THE action of THAT entity, and is therefore determined by the nature of that entity. So far, so good.

But then Rand and Peikoff go off the rails: “In any given set of circumstances, therefore, there is only one action possible to an entity, the action expressive of its identity.” It is difficult to grasp the level of evasion which might produce such a confusion of ideas: to make such a statement, one must throw out not just the tools of physics, mathematics and philosophy, but also personal experience with objects as simple as dice.

First, the evasion of personal experience, and how it plays out through mathematics and physics. Our world is filled with entities which may produce one action out of many – not just entities like dice, but even from Rand and Peikoff’s own examples, a rattle makes a different sound every time you rattle it. We have developed an entire mathematical formalism to help understand the behavior of such entities: we call them stochastic and treat them with the tools of probability. As our understanding has grown, physicists have found that this stochastic nature is fundamental to the nature of reality: the rules of quantum mechanics essentially say that EVERY action of an entity is drawn from a probability distribution, but for most macroscopic actions this probabilistic nature gets washed out.

Next, the evasion of validated philosophical methods. Now, one might imagine Rand and Peikoff saying, “well, the roll of the dice is only apparently stochastic: in actuality, the dice when you throw it is in a given state, which determines the single action that it will take.” But this is a projective hypothesis about reality: it is taking a set of concepts, determining their implications, and then stating how we expect those implications to play out in reality. Reality, however, is not required to oblige us. This form of philosophical thinking goes back to the Greeks: the notion that if you begin with true premises and proceed through true inference rules, you will end up with a true conclusion. But this kind of philosophical thinking is invalid – does not work in reality – because any one of these elements – your concepts, your inference rules, or your mapping between conclusions and states – may be specious: appearing to be true without actually reflecting the nuance of reality. To fix this problem, the major achievement of the scientific method is to replace “if you reach a contradiction, check your premises” with “if you reach a conclusion, check your work” – or, in the words of Richard Feynman, “The sole test of any idea is experiment.”

Let’s get really concrete about this. Rand and Peikoff argue “If, under the same circumstances, several actions were possible – e.g., a balloon could rise or fall (or start to emit music like a radio, or turn into a pumpkin), everything else remaining the same – such incompatible outcomes would have to derive from incompatible (contradictory) aspects of the entity’s nature.” This statement is wrong on at least two levels, physical and philosophical – and much of the load-bearing work is in the suspicious final dash.

First, physical: we actually do indeed live in a world where several actions are possible for an entity – this is one of the basic premises of quantum mechanics, which is one of the most well-tested scientific theories in history. For each entity in a given state, a set of actions are possible, governed by a probability amplitude over those states: when the entity interacts with another entity in a destructive way the probability amplitude collapses into a probability distribution over the actions, one of which is “observed”. In Rand’s example, the balloon’s probability amplitude for rising is high, falling is small, emitting radio sounds is still smaller, and turning into a pumpkin is near zero (due to the vast violation of conservation of mass).

If one accepts this basic physical fact about our world – that entities that are not observed exist in a superposition of states governed by probability amplitudes, and that observations involve probabilistically selecting a next state from the resulting distribution – one can create amazing technological instruments and extraordinary scientific predictions – lasers and integrated circuits and quantum tunneling and prediction of physical variables with a precision of twelve orders of magnitude – a little bit like measuring the distance between New York and Los Angeles with an error less than a thousandth of an inch.

But Rand’s statement is also philosophically wrong, and it gets clearer if we take out that distracting example: “If, under the same circumstances, several actions were possible, such incompatible outcomes would have to derive from incompatible aspects of the entity’s nature.” What’s wrong with this? There’s no warrant to this argument. A warrant is the thing that connects the links in a reasoning chain – an inference rule in a formal system, or a more detailed explanation of the reasoning step in question.

But there is no warrant possible in this case, only a false lurking premise. The erroneous statement is that “such incompatible outcomes would have to derive from incompatible aspects of the entity’s nature.” Why? Why can’t an entity’s nature be to emit one of a set of possible actions, as in a tossed coin or a die? Answer: Blank out. There is no good answer to this question, because there are ready counterexamples from human experience, which we have processed through mathematics, and ultimately determined through the tools of science that, yes, it is the nature of every entity to produce one of a set of possible outcomes, based on a probability distribution, which itself is completely lawlike and based entirely on the entity’s nature.

You cannot fake reality any way whatever: this IS the nature of entities, to produce one of a set of actions. This is not a statement that they are “contradictory” in any way: this is how they behave. This is not a statement that they are “uncaused” in any way: the probability amplitude must be non-zero in a space in order for an action to be observed, and it is a real physical entity with energy content, not merely a mathematical convenience, that leads to the observation. And it’s very likely not sweeping under the rug some hidden mechanism that actually causes it: while the jury is still out on whether quantum mechanics is a final view of reality, we do know due to Bell’s theorem that there are no “hidden variables” behind the curtain (a theorem that had been experimentally validated as of the time of Peikoff’s book).

So reality is stochastic. What’s wrong with that? Imagine a correct version of Ayn Rand’s earlier statement: “In any given set of circumstances, therefore, there is only one type of behavior possible for an entity, the behavior expressive of its entity. This behavior may result in one of several outcomes, as in the rolling of a die, but the probability distribution over those set of outcomes is the distribution that is caused and necessitated by the entity’s nature.” Why didn’t Peikoff and Rand write something like that?

We have a hint in the next few paragraphs: “Cause and effect, therefore, is a universal law of reality. Every action has a cause (the cause is the nature of the entity that acts); and the same cause leads to the same effect (the same entity, under the same circumstances, will perform the same action). The above is not to be taken as a proof of the law of cause and effect. I have merely made explicit what is known implicitly in the perceptual grasp of reality.” That sounds great … but let’s run the chain backwards, shall we?

“We know implicitly in the perceptual grasp of reality a law which we might explicitly call cause and effect. We cannot prove this law, but we can state that the same entity in the same circumstances will perform the same action – that is, the same cause leads to the same effect. Causes are the nature of the entities that act, and every action has a cause. Therefore, cause and effect is a universal law of reality.”

I hope you can see what’s wrong with this, but if you don’t, I’m agonna tell you, because I don’t believe in the Socratic method as a teaching tool. First and foremost, our perceptual grasp of reality is very shaky: massive amounts of research in cognitive science reveal a nearly endless list of biases and errors, and the history of physics has been one of replacing erroneous perceptions with better laws of reality. One CANNOT go directly from the implicit knowledge of perceptual reality to any actual laws, much less universal ones: we need experiment and the tools of physics and cognitive science to do that.

But even from a Randian perspective this is wrong, because it is an argument from the primacy of consciousness. One of the fundamental principles of Objectivist philosophy is the primacy of existence over consciousness: the notion that thinking a thing does not make it so. Now, this is worth a takedown of its own – it is attempting to draw an empirically verifiable physical conclusion from a conceptual philosophical argument, which is invalid – but, more or less, I think Rand is basically right that existence is primary over consciousness. Yet above, Rand and Peikoff purport to derive a universal law from perceptual intuition. They may try to call it “implicit knowledge” but perception literally doesn’t work that way.

If they admit physics into their understanding of the law of causality, they have to admit you cannot directly go from a conceptual analysis of the axioms to universally valid laws, but must subject all their so-called philosophical arguments to empirical validation. But that is precisely what you have to do if you are working in ontology or epistemology: you MUST learn the relevant physics and cognitive science before you attempt to philosophize, or you end up pretending to invent universal laws that are directly contradicted by human experience.

Put another way, whether you’re building a bridge or a philosophy, you can’t fake reality in any way whatsoever, or, sooner or later, the whole thing will come falling down.

-the Centaur

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