Yes, like a brain use a finite number of molecules, and mechanism eventually only assumes the finite number 0, s(0), s(s(0)), …, which actually will be used to code the finite things we are interested in. But the meaning of those things are formalised by infinite structure, like the model (N, +, x), or like hide that a computable function associate any number to a number. The understanding of “red” should make you able to recognise *all* red things. With mechanism, such meaning are captured by nameable, and non nameable, number relations. All theories assumes such potential, phenomenological, infinities. The concept of understanding is itself infinite, and more or less well captured by the comprehension axiom in set theories, or the abstraction Operation in Lambda calculus. Compute science is concerned by the behaviour of finite entities confronted to finite or infinite entities. > > To have a theory that is composed of an infinite number of sentences is sort > of outside of their way of thinking. All theories contains an infinite set of sentences. Classical propositional logic contains as theorem “p -> p”, “p -> (p -> p)”, “p -> (p -> (p -> p)), etc. Elementary arithmetic contains infinite propositions: 1+1= 2, 2+2=4, 4+4=8, 8+8=16, etc. That is why we use variables to say generalities, like Ax(x=x), that is, for all x it is the case that x = x. Or we use scheme of axioms. No need to put any ontology on this, with mechanism we need only 0, s(0), … Mechanism explains, using only the laws of addition and multiplication (and succession) how finite numbers get able to hallucinate other numbers, and why some sheaves of hallucination can become persistent and associated to deep and complex lawful histories. I might disagree with you, everyone’s theory is infinite, but what you are perhaps saying is that at any moment of time, we consult only finite part of those theories, to figure out some reality we bet on. But that is not unlike the Turing machine, which consulte only finite portion of its tape, and asks only a finite number of query to some Oracle. F=ma assumes already many infinite theories. Infinite theories are far simpler to use than finite theories, due especially to the abundance of very similar types of things, like photons, electro, water molecules, but also numbers, functions, relations, space, etc. Digital Mechanism is a finitisme, not an ultrafinitism, to be clear. It also an indexical, it concerns your willingness to say yes to a digitalist doctor, or yes to a digital teleportation experience. I just show that in that case the mind-body problem reduce to a body illusion problem in arithmetic. It is more a problem asked in a theory of consciousness than in physics. Here the theory of consciousness is basically the whole theology of the universal machine, or the one common to all sound consistent extension of a little one like PA. PA assumes induction, which we can put already in the phenomenology. From the putself, we assume only RA(*). Bruno RA = Robinson’s Arithmetic (often called Q): 1) 0 ≠ s(x) 2) x ≠ y -> s(x) ≠ s(y) 3) x ≠ 0 -> Ey(x = s(y)) 4) x+0 = x 5) x+s(y) = s(x+y) 6) x*0=0 7) x*s(y)=(x*y)+x An even cuter TOE is (without logic!): 1) If A = B and A = C, then B = C 2) If A = B then AC = BC 3) If A = B then CA = CB 4) KAB = A 5) SABC = AC(BC) Both are finite theories, or can be easily viewed as shemes of proposition.. The second theory is purely equational. We cannot prove that SK = KI in that theory, but that is not needed in the ontology, where they are indeed different. Both theories emulate all Löbian machines, which you can define by any machine believing one of those axioms, + logic, + corresponding axioms of induction. They are the machines we can interview on the theology, and the key proper theological proposition, well they can communicate them only conditionally to the computationalist hypothesis (of course), and some “dangerous” self-soundness implicit assumption. It is here that there is a theological trap (consistent in claiming that G* would necessarily apply to us). 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