1. Computation is just the manipulation of arbitrary formal symbols, according to rules (algorithms) applied to the symbols’ shapes, not their interpretations (if any).

2. The symbol-manipulations have to be done by some sort of physical hardware, but the physical composition of the hardware is irrelevant, as long as it executes the right symbol manipulation rules.

3. Although the symbols need not be interpretable as meaning anything – there can be a Turing Machine that executes a program that is absolutely meaningless, like Hesse’s “Glass Bead Game” – but computationalists are  mostly interested in interpretable algorithms that do can be given a coherent systematic interpretation by the user.

4. The Weak Church/Turing Thesis is that computation (symbol manipulation, like a Turing Machine) is what mathematicians do: symbol manipulations that are systematically interpretable as the truths  and proofs of mathematics.

5. The Strong Church/Turing Thesis (SCTT)  is that almost everything in the universe can be simulated (modelled) computationally.

6. A computational simulation is the execution of symbol-manipulations by hardware in which the symbols and manipulations are systematically interpretable by users as the properties of a real object in the real world (e.g., the simulation of a pendulum or an atom or a neuron or our solar system).

7. Computation can simulate only “almost” everything in the world, because  — symbols and computations being digital — computer simulations of real-world objects can only be approximate. Computation is merely discrete and finite, hence it cannot encode every possible property of the real-world object. But the approximation can be tightened as closely as we wish, given enough hardware capacity and an accurate enough computational model.

8. One of the pieces of evidence for the truth of the SCTT is the fact that it is possible to connect the hardware that is doing the simulation of an object to another kind of hardware (not digital but “analog”), namely, Virtual Reality (VR) peripherals (e.g., real goggles and gloves) which are worn by real, biological human beings.

9. Hence the accuracy of a computational simulation of a coconut can be tested in two ways: (1) by systematically interpreting the symbols as the properties of a coconut and testing whether they correctly correspond to and predict the properties of a real coconut or (2) by connecting the computer simulation to a VR simulator in a pair of goggles and gloves, so that a real human being wearing them can manipulate the simulated coconut.

10. One could, of course, again on the basis of the SCTT, computationally simulate not only the coconut, but the goggles, the gloves, and the human user wearing them — but that would be just computer simulation and not VR!

11. And there we have arrived at the fundamental conflation (between computational simulation and VR) that is made by sci-fi enthusiasts (like the makers and viewers of Matrix and the like, and, apparently, David Chalmers). 

12. Those who fall into this conflation have misunderstood the nature of computation (and the SCTT).

13.  Nor have they understood the distinction between appearance and reality – the one that’s missed by those who, instead of just worrying that someone else might be a figment of their imagination, worry that they themselves might be a figment of someone else’s imagination.

14. Neither a computationally simulated coconut nor a VR coconot is a coconut, let alone a pumpkin in another world.

15. Computation is just semantically-interpretable symbol-manipulation (Searle’s “squiggles and squiggles”); a symbolic oracle. The symbol manipulation can be done by a computer, and the interpretation can be done in a person’s head — or it can be transmitted (causally linked) to dedicated (non-computational) hardware, such as a desk-calculator or a computer screen or to VR peripherals, allowing users’ brains to perceive them through their senses rather than just through their thoughts and language.

16. In the context of the Symbol Grounding Problem and Searle’s Chinese-Room Argument against “Strong AI,” to conflate interpretable symbols with reality is to get lost in a hermeneutic hall of mirrors. (That’s the locus of Chalmers’s “Reality.”)

Exercise for the reader: Does Turing make the same conflation in implying that everything is a Turing Machine (rather than just that everything can be simulated symbolically by a Turing Machine)?