Why A=A (The Law of Identity) is still false. Pt. 2
Constructor and Assembly theory seem to say what I’ve been (unsuccessfully) struggling to say for over three decades.
For years, I’ve been arguing that the law of identity—A=A—is fundamentally false. I failed to express it clearly, and no one seemed to get what I was driving at. That’s on me. But recently, I stumbled onto Constructor Theory by David Deutsch and Chiara Marletto, and Assembly Theory by Sara Imari Walker, and I realized these frameworks articulate exactly what I’ve been trying to say all along.
A=A Is Not the Bedrock of Reality
In logic and mathematics, A=A works because we treat identity as pure and timeless, unaffected by physical reality. This is the Platonic ideal—the notion that abstract entities like numbers or concepts have fixed identities outside of time and space. But in the real universe, nothing remains static. As I’ve argued:
“Even abstract concepts lean on a shifting concrete substrate for their existence, meaning they too are in flux, never quite settling into a static identity.”
This is where constructor theory comes in. Instead of focusing on static identities, it’s about what transformations are possible within the laws of physics.
Identity isn’t fixed; it’s defined by what an object can do or become. So the claim that A=A is some unassailable truth about the universe falls apart. Identity is tied to what can be constructed or transformed, not to an eternal, unchanging essence.
Assembly theory supports this too. It shows that objects are the result of sequences—complex processes built over time. In the physical world, identity is always contingent on how something was assembled. There’s no static “A”; only a process that led to “A.”
Why This Matters
Because A=A is more than a tool in math and logic—it’s treated as a metaphysical foundation by systems like Rand’s objectivism and even Aristotelian logic. They use A=A as the bedrock for all kinds of claims about truth, ethics, and reality.
Rand built her entire philosophy on the idea that A=A is an irrefutable axiom, the cornerstone of objectivity. But if you’re a physicalist—and I am—A=A is necessarily false. In the physical world, nothing has a fixed identity outside of the processes that define and change it.
The issue isn’t just philosophical—it’s practical. Normative systems like laissez-faire capitalism or virtue ethics often derive their logical certainty from the assumed “truth” of A=A. We weaponize this expression to justify labeling people or reducing nuanced situations into simple ones, where we can then feel a fanatical certainty when we place judgements on others or engage with stories about them.
But if the most accurate premise is that A=A is false in a physical sense, then the systems built on it are standing on shaky ground. Sure, you can get far with A=A as a useful technique, but if we’re after truth, we ought to check our premises—just as Rand herself famously encouraged.
The idea that A=A is some unassailable, timeless truth needs to be reconsidered. It’s a cheat—useful in abstract logic, but false in the physical world. Both constructor and assembly theory make this clear: identity isn’t a static property but a result of physical processes and possibilities.
If truth is what we’re after, it’s time to start with a better premise than A=A. Use it if you want, but it’s a fiction like, say, libertarian free will, which is another truism put forth by Rand and prime example of Rand’s supreme cognitive dissonance.
Be wary of those you use such truisms to define you, or anything for that matter, in a simplistic way that doesn’t take into account how it got that way and where it might go next. Simplification in this way is a form of violence. And the law of identity is all about simplification. As Einstein approximately said, things should be made as simple as possible, but not simpler.