But we are talking about SI. An SI isn’t making English statements. What is true of a GPT is not necessarily true of an SI.
The instructions in a programme executed by an SI have semantics related to programme operations, but not to the outside world, because all machine code does. Machine code instructions do things like “Add 1 to register A”. You would have to look at thousands or millions of such low level instructions to infer what kind of kind high level maths—vector spaces , or non Euclidean geometry—the programme is executing.
And it’s hard to see how you know with certainty that SI is describing an uncomputable or random universe. If it is using limited precision floating point calculations, is that an approximate representation of unlimited precision real number calculations taking place in the territory? Or should it be taken literally? if it uses pseudo-random number generation, does it believe that there is real indeterminism in the territory? Human scientists are also limited in the kind of maths they can use, but again, can communicate verbally what it is supposed to mean, how exact it is, and so on.
The same way a human can? GPT-4 can state “suppose the world is non computable” for example.
But we are talking about SI. An SI isn’t making English statements. What is true of a GPT is not necessarily true of an SI.
The instructions in a programme executed by an SI have semantics related to programme operations, but not to the outside world, because all machine code does. Machine code instructions do things like “Add 1 to register A”. You would have to look at thousands or millions of such low level instructions to infer what kind of kind high level maths—vector spaces , or non Euclidean geometry—the programme is executing.
And it’s hard to see how you know with certainty that SI is describing an uncomputable or random universe. If it is using limited precision floating point calculations, is that an approximate representation of unlimited precision real number calculations taking place in the territory? Or should it be taken literally? if it uses pseudo-random number generation, does it believe that there is real indeterminism in the territory? Human scientists are also limited in the kind of maths they can use, but again, can communicate verbally what it is supposed to mean, how exact it is, and so on.