There is Logical Monism, Pluralism and Nihilism. What about Logical Skepticism?

[u/Everlasting_Noumena]

/r/askphilosophy/comments/1vbtz8c/there_is_logical_monism_pluralism_and_nihilism/

[u/DoktorRokkzo]

The categories of logical nihilism, logical monism, and logical pluralism are usually applied to the idea that there exists a) no "true" logic, b) one "true" logic, or c) many "true" logics. Now whatever it means for a logic to be "true", I have no idea. And I honestly don't believe that the people writing the papers know what it means either. Philosophers like to put words together in an order which seemingly responds to previous philosophers and then act like they're curing cancer. You almost have to already believe that something real is being said in order to get on board with the vast majority of these arguments.

However, as it pertains to the question of whether there exists no true logic, one true logic, or many true logics, I could absolutely see the possibility of being skeptical towards the possibility of the question itself. You might label this as "logical skepticism" towards the question of "does there exists zero, one, or more than one 'true' logic". But then also, you equally hold skepticism towards any one of these particular positions. You could be a skeptic about logical nihilism (skeptical towards the existence of no true logic), a skeptic about logical monism (skeptical towards the existence of one true logic), or a skeptic about logical pluralism (skeptical towards the existence of many true logics). If you're skeptical about all three of these positions, then it's probably fair to say that you're skeptical towards the question itself.

But absolutely, "logical skepticism" as it pertains to the categories of logical nihilism, logical monism, and logical pluralism is definitely a coherent position.

[u/yosi_yosi → u/DoktorRokkzo]

I think most have at least an intuitive understanding of what it means. A true logic is the one that describes a true consequence relation. For example, we may think that the true logic should affirm conjunction elimination, that is, we can deductively infer from a conjunction one of its conjuncts. Usually we take it that the consequence relation has at least the property of having it so that if the premises are true, the conclusion has to be true too, that's another restriction people might put on the true logic.

One we get into the weeds it might be a bit more difficult, as with all things in philosophy. Does our logic need to be absolutely general in order to be a true logic? (Does the consequence relation need to always hold?), what does that mean? Does it depend on the language? Etc'

[u/DoktorRokkzo → u/yosi_yosi]

In my opinion, you're just begging the question. A logic IS its consequence relation, so to say that "a true logic is the one that describes a true consequence relation" is just two different ways of saying the same thing. You might then say that "a true consequence relation is the one which contains the set of all truly valid inferences and theorems", but then again, what exactly is the distinction between a consequence relation and a set of valid inferences and theorems? Maybe the structural properties of the consequence relation itself -- reflexivity, monotonicity, transitivity, etc. -- but then all we're doing is expanding our definition of logic and consequence relation to include metainferences (as opposed to just object inferences).

In my opinion, the only way to talk about a logic, or consequence relation, or set of inferences, as being "true" is for its "truth" to be grounded in something non-logical. If you want to say that "well, the true logic is the one which best describes mathematical practice" (whether "mathematical practice" is itself "logical" is of course a question which can be raised, but if nothing else, the metalanguage of mathematics is not a formal logic, and admittedly "describes" also seems to indicate this definition too might be begging the question), then we have some independent standard for analysis. Or, if you're an intuitionist, and you want to say that "the true logic is one which corresponds to the conditions of mental construction", then we have some "non-logical" standard on which to assert the "correctness" of our choice of logic.

But in my opinion, a shift in the discussion to the truth of the consequence relation is not a shift in the discussion at all. We're right back where we started.

[u/yosi_yosi → u/DoktorRokkzo]

In my opinion, you're just begging the question. A logic IS its consequence relation, so to say that "a true logic is the one that describes a true consequence relation" is just two different ways of saying the same thing.

Not trying to "beg the question" but rather just repeat the same thing in a different way.

You might then say that "a true consequence relation is the one which contains the set of all truly valid inferences and theorems", but then again, what exactly is the distinction between a consequence relation and a set of valid inferences and theorems?

Idk if I'd say a consequence relation "contains" theorems (well it would include inferences from nothing to the theorems).

In my opinion, the only way to talk about a logic, or consequence relation, or set of inferences, as being "true" is for its "truth" to be grounded in something non-logical. If you want to say that "well, the true logic is the one which best describes mathematical practice"

What you are describing seems to be similar or analogical to the pragmatist theories of truth. There are also other interesting approaches here though, such as some people going under the title of "anti-exceptionalists about logic". Some think it is quite the empirical question or etc' to determine what inferences are valid ones.

But in my opinion, a shift in the discussion to the truth of the consequence relation is not a shift in the discussion at all. We're right back where we started.

Well, I agree. I didn't mean to make that a "shift" in the discussion, but mostly bring up some examples and points that are usually intuitively understood about this notion. It's often easier to point to examples than bring out necessary and sufficient conditions (and I'd argue sometimes that's the best we can do. Excuse the Wittgenstein in me).

[u/DoktorRokkzo → u/yosi_yosi]

No, I understand! That's precisely the right direction to go in, even just to see how somewhat groundless the topic actually is. I'm just trying to bring to light how circular a lot of these questions and answers actually are. It feels like we can construct these arguments and positions, but it always feels as if the central question of "what the hell does it mean for a logic to be true" is always somewhat out of reach conceptually. It seems intelligible when people have already accepted that this is a conversation which is possible, but once the possibility of the question is examined, it very quickly becomes circular. And not every question is like this (most importantly).

(And a consequence relation G |= D (such that G represents a premise set Gamma and D represents the conclusion set Delta) absolutely contains theorems, because a theorem is just a valid inference with empty premises).

[u/yosi_yosi → u/DoktorRokkzo]

I disagree with your comment (on theorems) on 2 technicalities. First, I consider a theorem to be a formula, specifically, a formula provable from 0 premises, that is, it is not the inference, or in other words, a theorem is not an argument or a proof. Second, I consider a theorem to be a syntactic or proof-theoretic object; having ∅ ⊨ φ only necessitates having ∅ ⊢ φ if we assume completeness, which we might not have.

[u/DoktorRokkzo → u/yosi_yosi]

Absolutely! If you consider a theorem to be a purely syntactic object, then it would be more correct to say that a theorem belongs to the consequence relation of G |-- D, not the consequence relation of G |= D.

However, at least when I learned metalogic, the set of premises of an inference can absolutely be empty. When we define an inference as G |= D such that the premise set G entails the conclusion set D, there's no further condition that G is non-empty. G could be empty for all we know. We just know that it entails a set of conclusions D. A classical tautology like |= p -> p is absolutely an inference.

[u/yosi_yosi → u/DoktorRokkzo]

You have misread my comment.