I think your problem with UD (argument 1, in your second link) arises entirely from the way you choose to think about possible worlds. You built on a bad foundation, discovered the foundation was shaky, and so abandoned the original plan. But the problem was just the foundation, not the plan.
Both common sense and physics talk about the world as consisting of things-with-states. This remains true for possible worlds. Possible worlds defined using everyday concepts (e.g. worlds where “McCain defeated Obama in 2008”) or using some exact physical theory (e.g. a billiard-ball world) still have this attribute. If you were to talk about all the possible billiard-ball worlds, there’s no problem telling them apart, and it’s easy to ask whether there’s a natural measure on the set of such worlds.
But at your second link you write
There is an infinite number of universal Turing machines, so there
is an infinite number of UD. If we want to use one UD as an objective
measure, there has to be a universal Turing machine that is somehow uniquely
suitable for this purpose. Why that UTM and not some other? We don’t even
know what that justification might look like.
So you’ve adopted a concept of possible world which is something like “possible program for a universal Turing machine”. But the problem here is arising entirely from your idiosyncratic concept of possible world.
What does a universal Turing machine look like, from the things-with-states perspective? Consider the primordial example of a UTM, Turing’s example of a tape moving back and forth through a read-write head. There are two things with states: the head and the tape. They undergo causal interaction and change states as a result.
Originally Turing was thinking of physical machines like the ones around him, made of metal and electronics and so forth. But suppose we try to take the UTM he described to be a universe in itself. How far can we go in that direction? Again, we can do it, thinking in terms of things-with-states and their interactions. We can think in terms of fundamental entities which have states and which can also be joined to each other in some sense. The tape is a one-dimensional string of entities joined side by side. The head is another entity which interacts with the entities making up the “tape”, and whose join relations are also dynamical—it moves up and down the tape.
This all describes a type of possible world, just as the “billard-ball world” of elastically colliding impenetrable spheres in n-dimensional space is also a meaningful type of possible world. The dynamical rules for the Turing tape are the “laws of physics” for this world, each set of initial conditions gives rise to a possible history, and so on.
Now suppose you consider a different set of laws for the Turing-tape world. It still has the same structure, but the states and how they change are different. Is this mysterious? No, you’ve just defined a different class or subclass of possible worlds. Both classes of world are “computationally universal”, but that doesn’t mean that the world from one class which performs a particular computation is the same world as the world from the other class which performs that computation.
Yet this is what you’re assuming, more or less, when you talk about having to pick a UTM as the UTM, in terms of which possible worlds will be defined. You’re treating a possible world as a second-order abstraction (equivalence class of computations) and trying to do without a thing-with-states foundation. If you insist on having such a foundation, this problem goes away. You still have the very formidable problem of trying to enumerate all possible forms of interactions among things-with-states. There is still the even larger problem of identifying and justifying the broadest notion of possible world you are willing to consider. What about worlds where there’s no time? What about worlds where there’s no “physical law”—changes happen, but for no reason? But your particular problem is an artefact of computational idealism, where reality is supposed to consist of computational or mathematical “entities” which exist independently of anything like “things” or “substances”.
I think your problem with UD (argument 1, in your second link) arises entirely from the way you choose to think about possible worlds. You built on a bad foundation, discovered the foundation was shaky, and so abandoned the original plan. But the problem was just the foundation, not the plan.
Both common sense and physics talk about the world as consisting of things-with-states. This remains true for possible worlds. Possible worlds defined using everyday concepts (e.g. worlds where “McCain defeated Obama in 2008”) or using some exact physical theory (e.g. a billiard-ball world) still have this attribute. If you were to talk about all the possible billiard-ball worlds, there’s no problem telling them apart, and it’s easy to ask whether there’s a natural measure on the set of such worlds.
But at your second link you write
So you’ve adopted a concept of possible world which is something like “possible program for a universal Turing machine”. But the problem here is arising entirely from your idiosyncratic concept of possible world.
What does a universal Turing machine look like, from the things-with-states perspective? Consider the primordial example of a UTM, Turing’s example of a tape moving back and forth through a read-write head. There are two things with states: the head and the tape. They undergo causal interaction and change states as a result.
Originally Turing was thinking of physical machines like the ones around him, made of metal and electronics and so forth. But suppose we try to take the UTM he described to be a universe in itself. How far can we go in that direction? Again, we can do it, thinking in terms of things-with-states and their interactions. We can think in terms of fundamental entities which have states and which can also be joined to each other in some sense. The tape is a one-dimensional string of entities joined side by side. The head is another entity which interacts with the entities making up the “tape”, and whose join relations are also dynamical—it moves up and down the tape.
This all describes a type of possible world, just as the “billard-ball world” of elastically colliding impenetrable spheres in n-dimensional space is also a meaningful type of possible world. The dynamical rules for the Turing tape are the “laws of physics” for this world, each set of initial conditions gives rise to a possible history, and so on.
Now suppose you consider a different set of laws for the Turing-tape world. It still has the same structure, but the states and how they change are different. Is this mysterious? No, you’ve just defined a different class or subclass of possible worlds. Both classes of world are “computationally universal”, but that doesn’t mean that the world from one class which performs a particular computation is the same world as the world from the other class which performs that computation.
Yet this is what you’re assuming, more or less, when you talk about having to pick a UTM as the UTM, in terms of which possible worlds will be defined. You’re treating a possible world as a second-order abstraction (equivalence class of computations) and trying to do without a thing-with-states foundation. If you insist on having such a foundation, this problem goes away. You still have the very formidable problem of trying to enumerate all possible forms of interactions among things-with-states. There is still the even larger problem of identifying and justifying the broadest notion of possible world you are willing to consider. What about worlds where there’s no time? What about worlds where there’s no “physical law”—changes happen, but for no reason? But your particular problem is an artefact of computational idealism, where reality is supposed to consist of computational or mathematical “entities” which exist independently of anything like “things” or “substances”.