Logical positivism was right, with respect to an ideal logical language.

Shawn

I will be as brief and concise as possible, without detracting from clarity...

If everything physical is Turning computable, then an ideal language consisting entirely of logical representations has the capacity to be an ideal language in perfect correspondence with reality, such as our own! I am relying heavily on the Church-Turing-Deutsch Principle.

Does this sound familiar to what Carnap or Russell and Frege, attempted, because it is. Namely, the caveat in this is that what the logical positivists didn't quite get right is that importance of not assuming that we have a criterion for epistemic knowledge about a ideal language. This sounds very similar to the problem of the criterion.

Actually, here is Irving Copi with a full explanation:

Even if a logically perfect language could be devised, the proposed program for investigating the ontological structure of the world by means of investigating the logical structure of an ideal language is impossible of fulfillment. For the project must have the following sequence: first, an ideal language must be set up, and then, through it, the metaphysical structure of the world is to be delivered. On this view, the construction of a logically perfect language is not an end in itself, but a means to the end of more general philosophical inquiry. I submit that this program cannot possibly be realized. — Language analysis and metaphysical inquiry.

Hence one can see the vicious circle, and even more vicious in light of Godel.

Yet, one has to step back and consider that an ideal language exists in the very medium from which you are reading this post from. A computer has the capacity to represent everything that is possible as having a representation in information. This, 'logical space' of a Central Processing Unit or CPU is utilized by an idealized formal language such as a computer to perform operations on logical schemata such as the CPU to perform decidable operations via idealized languages or software...

I'm no programmer or computer scientist; hence my jargon might sound terse or fallacious, but, I would like to ask other more adept at logic and computer science for their input. May, I ask @_db or @Nagase or @andrewk for their input about this?

andrewk

The concept of Turing Computability applies to functions between sets of words in a formal language. We cannot apply that concept to the physical universe, without first defining such a function. I cannot think of any natural candidate for such a function in relation to the physical universe.

I also note that, if we want the inputs to our function to include statements about the locations of objects in spacetime, and we assume spacetime to be a continuum, we cannot represent the position of most objects by a word in a formal language, which is a finite set of symbols from a countable alphabet. Why? Because almost all possible location coordinates will have non-repeating decimal expansions, requiring an infinite number of characters to represent them.

Jack Cummins

↪Shawn

I read a recent article in 'Philosophy Now' magazine which said how Ayer had a near death experience in hospital towards the end of life. He saw a 'divine being' and, afterwards, he said that he would have to revise his position on metaphysics. I found the story quite interesting, but, of course, Ayer didn't get the opportunity to write further books.

180 Proof

↪Shawn

See Max Tegmark's Mathematical Universe Hypothesis (re: the secondary Computational Universe Hypothesis imbedded within the MUH). This is more Leibnizian and set theoretical than logical positivist.

↪Jack Cummins

"Conversions", like other judgments or decisions made, under duress are dubious. Besides, 'logical positivism' is, in its own self-refuting terms, a metaphysical (i.e. "nonempirical, unverifiable") position and so it's not as great, or radical, a "leap" for Ayer to have found another metaphysics (re: "divine beings" (aka angels? greys?)) at or near the end of his long life.

Jack Cummins

↪180 Proof

I just found it to be an interesting story really. I am not saying that much should be read into it. If anything, it may be about conflicts between the unconscious and conscious. For example, I once had a friend who was very political and anti religion. He was sleeping on the floor while I was sitting on bed, writing a college essay. While he was asleep, he said, 'Jesus was a revolutionary. I wondered where that came from and when I told him what he said he was startled.

Of course, I am getting a bit psychoanalytical. But, that is a different language to logical positivism. Actually, I think that, 'Language, Truth and Logic', by Ayer is an extremely helpful book and I do think that most of metaphysics is only speculation ultimately.

180 Proof

↪Jack Cummins

I agree both with what you say about metaphysics and what your friend said about Jesus – neither, however, need be learned from Language, Truth and Logic. I'm sure I'd read Russell and Moore, Witty and Ryle, Peirce/Dewey and Popper, Quine and Goodman before I'd read Ayer and writings of the 'Vienna Circle' which I still find mostly tedious and redundant as well as 'unverifiable' (thus, self-refuting).

Shawn

The concept of Turing Computability applies to functions between sets of words in a formal language. We cannot apply that concept to the physical universe, without first defining such a function. I cannot think of any natural candidate for such a function in relation to the physical universe. — andrewk

May I ask if you agree with the Church–Turing–Deutsch principle, then? I mean, it states that:

In computer science and quantum physics, the Church–Turing–Deutsch principle (CTD principle) is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985.[1] The principle states that a universal computing device can simulate every physical process. — Church–Turing–Deutsch principle

If it is true (and that would be a discussion unto itself) that one can simulate every physical process, then wouldn't the implication be that with a robust enough theory one could, according to David Deutsch, be able to simulate all the workings of the universe inside a computer? With the logical positivists in mind, I assume that they might agree that the notion of such a possibility is that the logic system whence one could utilize such a universal computing device be possible too?

180 Proof

If it is true (and that would be a discussion unto itself) that one can simulate every physical process, then wouldn't the implication be that with a robust enough theory one could, according to David Deutsch, be able to simulate all the workings of the universe inside a computer? — Shawn

In principle, probably yes; but, assuming so, that '100% fidelity simulation' would require more computational resources (bytes, energy) than the universe within which it's running has (because the simulation would be doubling the simulated that supports it simulating). Anyway, I think Deutsch's point is that the universe itself is – physical laws are – quantum computable and therefore quantum Turing machines (by which simulations are possible) are themselves instantiations of fundamental physical laws.

andrewk

↪Shawn

I presume Deutsch means to restrict 'every physical process' to only processes for which the initial conditions can be encoded in a finite sequence of characters from a finite alphabet. Otherwise the computation cannot ever finish because there will always remain some inputs that the machine has not yet read.

That rules out simulation of the universe if the universe is infinite, as many cosmologists suspect.

I also think complications could arise if the Turing machine lay in the universe, as self-simulation, or self-reference more generally, often leads to problems. So I would require the Turing machine to be outside the universe in the sense of being unable to affect the universe in any way.

Subject to those two restrictions, the principle sounds plausible to me.

EDIT: I just realised the first restriction implies the second, since a Turing machine has an infinite tape and hence cannot lie in a finite universe.

Logical positivism was right, with respect to an ideal logical language.

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