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In my understanding, when a computer program is written, a syntax is a legal statement in the sense that tokens supplied are in expected relative positions. Whether or not that makes "semantic" sense to a given computation or a human is generally regarded as a separate issue.

My question is why is it that semantics is not just a hidden layer of more syntax that isn't obvious in a local scope like that of a single syntactical statement let a = 10, but is a collective "syntax" of a given context. An algorithm to sort a list of numbers would then be a semantic, given a particular algorithm. Clearly there is no one semantic general syntax of the entire algorithm, as different programmers may use different syntactic statements to solve the problem in essentially the same spirit as the original algorithm intended it. What matters is the end result of the computation, and the computation itself, behaved in generally the same way.

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  • Semantic is about meaning: meaning is about language used to communicate between humans or, at least, social being. The computing operations performed by the machine running the program that implements the algorithm (the computer program is a piece of code, while the algorithm is a "procedure" that has meaning for humans) produce a "final state" of the machine that has meaning for we humans that read it and are able to understand it as the result of the operations.
    – Mauro ALLEGRANZA
    Commented Feb 25, 2020 at 10:46
  • There is no semantic without language, and there is no language without "someone" using it to communicate with "someone other". The issue with AI can be: is the machine running the software "communicating" with us ?
    – Mauro ALLEGRANZA
    Commented Feb 25, 2020 at 10:48
  • So the algorithm is a statement of observer-dependent meaning. I can agree on that. But my problem is, why isn't the human, the algorithm implementing person, also reducible to syntax. In this case, the "program" of being a human which was naturally selected by evolution?
    – Weezy
    Commented Feb 25, 2020 at 11:00
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    Formal semantics is reducible to syntax. One could analogize natural semantics to "informal syntax" (Wittgenstein called it "grammar"), but this "syntax" is neither precise nor algorithmic. Humans are analog devices, modeling them by digital computers does not work so well. Nonetheless, Rapaport advocates interpreting natural language semantics as a sort of syntax in Syntactic Semantics, with an eye toward developing semantics for AI.
    – Conifold
    Commented Feb 25, 2020 at 12:31
  • @Conifold thanks for that. I was looking for something similar. I'll get to it.
    – Weezy
    Commented Feb 25, 2020 at 13:02

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A beam of gazillions of photons collapsing on one of both eyes of a specific person in a specific period of time can be reduced to a unique image interpreted by his brain.

The photons behavior, the eyes behavior, the brain behavior (all of them equivalent to the syntax) are not the image (equivalent to the semantics). That's what you're suggesting.

Yes, strictly, a specific instance of the aforementioned system (emitter, photons, eyes, brain) corresponds to an image (meaning), but it is useless to appreciate it as such. When you think of an image, you don't think of the behavioral rules of photons. You think on the meaning.

From a different but coherent perspective, the syntax is usually applied from a reductionist approach (it is applied to the subsystems of a whole). The semantics, on the other hand, are applied from a holistic perspective, that is, to the whole.

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  • The way I see this, the perception of an image, in the eye of the beholder can be regarded as a thing interacting with another thing, thus we are talking about a new kind of syntax that emerged from the sum of their parts. The human element and the sight of an object.
    – Weezy
    Commented Feb 28, 2020 at 15:44

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