What do the Hangman Paradox, Epimenides Paradox, and the Chinese Room Argument have in common?

The underlying Symbol Grounding Problem common to all three is that from a purely quantitative perspective, a logical truth can only satisfy some explicitly defined condition. The expectation of truth itself being implicitly true, (i.e. that it is possible to doubt what is given) is not a condition of truth, it is a boundary condition beyond truth*. All computer malfunctions, we presume, are due to problems with the physical substrate, or the programmer’s code, and not incompetence or malice. The computer, its program, or binary logic in general cannot be blamed for trying to mislead anyone. Computation, therefore, has no truth quality, no expectation of validity or discernment between technical accuracy and the accuracy of its technique. The whole of logic is contained within the assumption that logic is valid automatically. It is an inverted mirror image of naive realism. Where a person can be childish in their truth evaluation, overextending their private world into the public domain, a computer is robotic in its truth evaluation, undersignifying privacy until it is altogether absent.

Because computers can only report a local fact (the position of a switch or token), they cannot lie intentionally. Lying involves extending a local fiction to be taken as a remote fact. When we lie, we know what a computer cannot guess – that information may not be ‘real’.

When we say that a computer makes an error, it is only because of a malfunction on the physical or programmatic level, therefore it is not false, but a true representation of the problem in the system which we receive as an error. It is only incorrect in some sense that is not local to the machine, but rather local to the user, who makes the mistake of believing that the output of the program is supposed to be grounded in their expectations for its function. It is the user who is mistaken.

It is for this same reason that computers cannot intend to tell the truth either. Telling the truth depends on an understanding of the possibility of fiction and the power to intentionally choose the extent to which the truth is revealed. The symbolic communication expressed is grounded strongly in the privacy of the subject as well as the public context, and only weakly grounded in the logic represented by the symbolic abstraction. With a computer, the hierarchy is inverted. A Turing Machine is independent of private intention and public physics, so it is grounded absolutely in its own simulacra. In Searle’s (much despised) Chinese Room Argument – the conceit of the decomposed translator exposes how the output of a program is only known to the program in its own narrow sensibility. The result of the mechanism is simply a true report of a local process of the machine which has no implicit connection to any presented truths beyond the machine…except for one: Arithmetic truth.

Arithmetic truth is not local to the machine, but it is local to all machines and all experiences of correct logical thought. This is an interesting symmetry, as the logic of mechanism is both absolutely local and instantaneous and absolutely universal and eternal, but nothing in between. Every computed result is unique to the particular instantiation of the machine or program, and universal as a Turing emulable template. What digital analogs are not is true or real any sense which relates expressly to real, experienced events in space time. This is the insight expressed in Korzybski’s famous maxim ‘The map is not the territory.’ and in the Use-Mention distinction, where using a word intentionally is understood to be distinct from merely mentioning the word as an object to be discussed. For a computer, there is no map-territory distinction. It’s all one invisible, intangible mapitory of disconnected digital events.

By contrast, a person has many ways to voluntarily discern territories and maps. They can be grouped together, such as when the acoustic territory of sound is mapped to the emotional-lyric territory of music, or the optical territory of light is mapped as the visual territory of color and image. They can be flipped so that the physics is mapped to the phenomenal as well, which is how we control the voluntary muscles of our body. For us, authenticity is important. We would rather win the lottery than just have a dream that we won the lottery. A computer does not know the difference. The dream and the reality are identical information.

Realism, then, is characterized by its opposition to the quantitative. Instead of being pegged to the polar austerity which is autonomous local + explicitly universal, consciousness ripens into the tropical fecundity of middle range. Physically real experience is in direct contrast to digital abstraction. It is semi-unique, semi-private, semi-spatiotemporal, semi-local, semi-specific, semi-universal. Arithmetic truth lacks any non-functional qualities, so that using arithmetic to falsify functionalism is inherently tautological. It is like asking an armless man to raise his hand if he thinks he has no arms.

Here’s some background stuff that relates:

The Hangman Paradox has been described as follows:

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the “surprise hanging” can’t be on Friday, as if he hasn’t been hanged by Thursday, there is only one day left – and so it won’t be a surprise if he’s hanged on Friday. Since the judge’s sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn’t been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.The next week, the executioner knocks on the prisoner’s door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.

Some thoughts on this: 1) The conclusion “I won’t be surprised to be hanged Friday if I am not hanged by Thursday” creates another proposition to be surprised about. By leaving the condition of ‘surprise’ open ended, it could include being surprised that the judge lied, or any number of other soft contingencies that could render an ‘unexpected’ outcome. The condition of expectation isn’t an objective phenomenon, it is a subjective inference. Objectively, there is no surprise since objects don’t anticipate anything. 2) If we want to close in tightly on the quantitative logic of whether deducibility can be deduced – given five coin flips and a certainty that one will be heads, each successive tails coin flip increases the odds that one the remaining flips will be heads. The fifth coin will either be 100% likely to be heads, or will prove that the certainty assumed was 100% wrong.

I think the paradox hinges on 1) the false inference of objectivity in the use of the word surprise and 2) the false assertion of omniscience by the judge. It’s like an Escher drawing. In real life, surprise cannot be predicted with certainty and the quality of unexpectedness it is not an objective thing, just as expectation is not an objective thing.

Connecting the dots, expectation, intention, realism, and truth are all rooted in the firmament of sensory-motive participation. To care about what happens cannot be divorced from our causally efficacious role in changing it. It’s not just a matter of being petulant or selfish. The ontological possibility of ‘caring’ requires letters that are not in the alphabet of determinism and computation. It is computation which acts as punctuation, spelling, and grammar, but not language itself. To a computer, every word or name is as generic as a number. They can store the string of characters that belong to what we call a name, but they have no way to really recognize who that name belongs to.

*I maintain that what is beyond truth is sense: direct phenomenological participation