Your yearly dose of is-the-universe-a-simulation

Look at a thing on your desk. You are having a sensation of light and colour. Kant calls this raw pixel level sense data "sensibility".

Now as well as just seeing pixels you can distinguish the thing you are looking at as an individual object, with certain dimensions and in a certain location. Kant calls this processed spatiotemporal data "intuition".

Now you may also recognise the object you are looking at as being "a stapler" and you may recognise it as being on your desk and as belonging to your friend who's lent it to you. Kant calls this abstract data "concept" (also called "idea" as in the OP).

Now. If you're doing Science then you'd better have intuitions corresponding with all your concepts otherwise you're just making stuff up without actually looking at the world. But unfortunately there's a limit to how much we can observe in the world and we are greedy so we start coming up with judgements about concepts that do not correspond to any intuitions. E.g. "The universe is a simulation". In the Critique of Pure reason the central question is how any such judgements can be true (hint we think that some are true: Pythagoras's theorem is a judgement about all triangles, and so we think it is true for some triangles we have never seen). If you think this is a worthwhile question you might like to read Kant.

A Kantian reply to the blog post linked above would be that if the universe is a simulation then we can't even be sure that the laws of mathematics or geometry hold outside of it, because these laws are added by our brains when we turn "sensibility" into "intuition".

If it seems silly to you that the laws of mathematics or geometry might be all in our heads, then you are what Kant calls a "Transcendental Realist". If it seems natural to you that the laws of mathematics and geometry are all in our heads and that this is what allows those laws to be true of every object we see, then you are what Kant calls "a Transcendental Idealist".

If we're being Transcendental Realists then it makes sense to collect empirical data to settle whether the universe is a simulation or not. If we're being Transcendental Idealists, then the empirical data we collect has absolutely no bearing on the question.

It doesn't follow that all of these possibilities are equally likely, so I do not buy this line of reasoning

In fact, the argument was refuted in print before Lucas ever published it, in a nice paper called "Minds and machines" by Hilary Putnam.

Exactly where it fails depends on exactly how it's stated, but here's a sketch:

Goedel proved that a formal system powerful enough to talk about mathematics either is inconsistent or else cannot prove its own consistency. Lucas and his followers claim that human mathematicians have no such limits; presented with such a system they can just see that it's consistent. In Lucas's version we look at some particular candidate system that might implement a human being, and just see it's consistent. In Penrose's version we look at mathematics as a whole and just know it's consistent.

But this is all nonsense. Real human mathematicians don't look at the sort of system that might implement a human being (still less, the totality of all mathematicians working together) and "just see" it's consistent. They don't even look at the nice streamlined formal systems they've made specifically for doing formalized mathematics in and "just see" that. Frege's system was inconsistent and he didn't notice after writing two volumes on it. (Russell famously pointed out an inconsistency.) Quine's ML was inconsistent and he didn't notice until Wang pointed it out. For all we know there might be some inconsistency lurking in ZF; it seems like a very good guess that there isn't, but that's all.

And, I repeat, those are highly streamlined systems that don't attempt to do anything nearly so complicated as describing the complete behaviour of an actual mathematician's mind.

We do sometimes attempt to study computer hardware and software -- systems a bit more like actual human minds, but still orders of magnitude simpler -- using formal methods. Sometimes we try to prove them correct. These proofs are also often wrong, which is why hardware and software have bugs. (In some cases we're pretty confident about relatively large systems; guess what?, the correctness proofs for those are done by computer and there's no "just seeing" about them.)

The idea that a human being could look at a formal system representing the entirety of what their brain does and "just know" that it's consistent is not just wrong, it's one of the wrongest things any otherwise intelligent human being has ever suggested. But that is (part of) what it would take to show that the formal system didn't really model them perfectly.

This is far from being the only major error in the Lucas-Penrose argument, but it's the worst one.

You are a Transcendental Realist if you think this "view" of an apple comes from a system, your brain, which itself is based 100% in reality...the reality that contains "real" apples, perhaps on a table at work, which can be confirmed by consensus of coworkers. The consensus and coworkers are also 100% based in reality, if you believe this way. This theory is based on what Kant called a posteriori knowledge, or knowledge after observation.

If you are a Transcendental Idealist, you will know that the internal, mind's eye view of the apple makes it real. You will also know other "things" in your "real world" view have little or no bearing on your internal view. Things out here in the real world are mutable, in other words, and are undergoing a constant change by everyone's view (or just your view, in some variations) of their/your internal realities. i.e. all of this stuff is just brought into being by your consciousness. This "ability" is a priori knowledge, or knowledge that comes from reasoning.

I would propose this reality is actually a mix of the two, where both work in union, in a decidedly meta a priori way, to render reality as we see it. It is not a simulation and it is simulation-like at times, in other words. It's a hybrid consciousness!

Random, and irrational, but figured I'd share.

That's where the postulation stops and I just go with "turtles all the way down" after that.