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People use logic to determine what's possible within our worlds, but is there a field of study that studies what's possible within a logical system? So instead of using logic to determine what's possible outside of logic, using another type of logic to determine what's possible within logic itself? I am saying another type of logic, because I don't know if we can use logic to determine what's possible within logic itself.

So in summary:

(??? or pre-logic or logic) > logic > physical world

So what is the ??? that comes before everything?

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    Are you talking about metalogic?
    – Conifold
    Commented Mar 29 at 3:58
  • I guess you could call it "... being a rational sapient human..."? Logic can be thought of as formalized rationality. Plurality of logics implies that many alternate formalizations are possible
    – Rushi
    Commented Mar 29 at 4:05
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    Mathematical Logic is usually just concerned with what is possible within Logic, rather than being concerned with how to apply logic to derive things in the "Real World". More specifically, meta-logic, Provability Theory, Model Theory, are specific areas which are concerned with those kind of questions. Classically, Gödels Completeness and Incompleteness theorems are focused on these topics as well. Note: Often when we allow a syntax to talk about itself we open ourselves to contradictions, so we use meta-logic to talk about logic. Commented Mar 29 at 16:33
  • Perhaps your pre-logic designation has to start from what're different possibilities to designate the starting foundational axioms or inference rules within a logic system, a big part of it can be traced to how to designate truth or whatever pre-theoretic notion such as information or relevance as similarly asked by today's another post... Commented Mar 29 at 19:06

2 Answers 2

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People who study logic are called logicians. There are also set theorists, mathematicians, philosophers, logic linguists and meta-logicians, who will all potentially have something to say on the topic of studying logic.

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There are definitely some domains of thought that could be called “pre-logic”, and if nobody has tried to gather them and synthesize them into a named field, I believe somebody should. It would take me a little time to gather a list of examples of what such a field would contain, but this is one interesting example. Another would be this.

This is the best I can do right now to try to delineate it. I think possibly one of the (less obvious) unifying principles in most approaches to logic is foundationalism. But foundationalism gives rise to no shortage of further philosophical critiques. This is perhaps the entry-point - even if not much of a descriptor - of pre-logic. Many, many of the core assumptions one is told in a mainstream class on logic are deeply embedded assumptions on which the field stands. Treating each of those as a main object of study leads to tons of interesting new ideas.

One that I personally grapple with the most is something I have almost turned into a kind of personal slogan: “information requires a medium of expression”. The historical tendency of the field to accept graphemic “symbols” as some kind of acceptable representation of “pure abstraction” is an illusion. It presupposes at minimum a two-dimensional visual field. This relationship could be reversed, where the structure of human graphemic systems of order could be projected into any other ontological domain.

In my opinion, a deeper problem than logic is that of information. Basically, as a student of logic, I study foundationalism, but from the beginning I have felt the longterm goal is something more like coherentism/infinitism. I think Quine’s ontological relativism may have had the right premises (meaning embedded in a complex network) but the wrong conclusions (that there is no unifying principle for these different networks).

I personally think there is something pretty deep about the “semiotic triad”. At minimum, in order for “meaning” or “information” to exist, requires a network of at least 3 things, which mutually give information to one another.

I don’t think highly of my own answer to your question, but I do hope it can kick off some conversation, since I think it’s a really good question.

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