Second-order logic. Reason and reason. Is the logic of logic possible?
Hello, dear Ladies and Gentlemen!The question is philosophical and the terms may not correspond to the generally accepted usage.In this case, by mind I mean the creative ability of a person to think. The mind re-invents the solution to the problem every time. But when the task is familiar, the mind is formed – a technical mind that can work according to the rules set or invented by the mind. The mind "rests" from creativity, the mind works, and the mind only controls.The most general such rules form formal logic, as a system of correct thinking. Let's call it first-order logic (not exactly the same division as in mathematical logic). We will also assign the first order to the mind. Its rules can be studied, it is formed from the regular work of the mind on this range of issues.Well, the mind itself – by what rules does it work? Is it possible to study them? In general, this may not be possible. But, perhaps, the mind, constantly creating intelligences (or: rules for a single intellect, rules of the first order), practicing creating such rules, will create a second-order intellect, which for the first-order intellect will play the role of reason (auxiliary), but the mind itself will control it in the same way as it controls the first-order intellect? Then the rules for this second-order understanding will themselves be second-order and form a second-order logic corresponding to them. And by these second-order rules, the second-order mind will generate first-order minds (or: first-order rules for a single first-order mind).Reason is above this reason, too. Perhaps this work of the mind repeats itself, and it will one day create a third-order mind and its corresponding logic, etc.Fantastic in a way. So far, we only know first-order logic (in this sense of the word). But what does artificial intelligence do? It generates first-order algorithms (ordinary programs), and thus has a second-order function. What rules does it follow? By megaton programs in C++?However, does artificial intelligence exist in the strict sense of the word? Or are these just attempts to approach it, but ultimately unsuccessful?If there is a second-order logic, what is it? Is it accessible for perception?In Soviet times, when dialectic was respected, it was given this place. However, it is now almost forgotten. Do you think dialectical logic can play such a role – the role of second-order logic?Unfortunately, apart from extensive discussions about the benefits of dialectics in Marxist textbooks, I have not found anything scientific (except for the theory of glass from V. I. Lenin, which is everywhere cited as the main example, but this is just an example, not a theory).What do you think should be the second-order logic? And if it is still, in your opinion, impossible, then how does the mind work? Can it be understood or is it irrational?
There is metalogy, as a philosophical discipline that studies the properties of logical systems. But the question, as far as I understand, is somewhat different.
Personally, I operate with the following theory regarding the work of thinking in relation to logic. Logic is a tool that we develop, adapting to solving problems of a certain variety. The mechanism sufficient for acquiring this adaptation is the ability to distinguish a solved problem from an unsolved one, the ability to feel something as correct. Here, guided by the appearance or disappearance of this feeling, we build logics, sifting out working from non-working ones. The feeling itself and how it works-this is already in the field of epistemology, it is a non-trivial question, with answers ranging from “god gave it to us in his goodness” to “evolution rejected all those who were wrong”.
“What does artificial intelligence do? It generates first-order algorithms (ordinary programs), and thus has a second-order function. What rules does it follow? By megaton programs in C++?”
Artificial Intelligence has not yet been created. And it is not clear whether it can be created at all. There is no scientific definition of AI either. Therefore, it is not clear what exactly needs to be created. The Turing test has already lost its validity: even computers can perform it.
Another candidate for the path leading to the AI neural network. For a start, you can read about them on Wikipedia, the article is quite suitable.
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I think it's actually much simpler than you might think. The human psyche as a whole works in such a way that, having received a task to solve at the input, it begins to sort through hundreds and thousands of options for solving it, and the same thing happens that we see in a dream – objects and events are combined in the most illogical and ridiculous combinations. At the same time, some other component of the psyche checks all these options for consistency, that is, for compliance with the properties of the surrounding world known from experience. When a match is obtained, a person realizes that he has received a solution, which is more beautifully called “closing the cognitive circuit” or something like that.
And “second-order logic” is something very dubious, because logic itself is a description of the fundamental properties of matter, such as regularity, unity, and knowability.