You can see the difficulty of equivocating or refusing to elaborate on what the "truth" in "truth-preserving" means here. — Count Timothy von Icarus

Why does it matter?

Maybe @fdrake will explain what logical nihilism is?

In virtue of what is a logic "applicable"? — Count Timothy von Icarus

Come on. When it has a use.

why don't you explain to me why you think pluralism and nihilism are even different positions? — Count Timothy von Icarus

From the core article:
1) To be a law of logic, a principle must hold in complete generality.
2) No principles hold in complete generality.
3) There are no laws of logic.

Monists hold that (2) is false. Pluralists hold that (1) is false. Nihilists hold that the argument is sound. On this account pluralism is different from nihilism.

If the question is "have people created systems with different logical consequence relationships?" the answer is obviously yes. — Count Timothy von Icarus

So we are back to puzzling over whether there are principles that hold in complete generality.

Russell, to be sure, is in that article giving an account of how pluralism can be maintained in the face of nihilism. She is not a nihilist, so far as I can make out.

Come on. When it has a use.

Do some logics lack "a use?" Or do they all have one?

What does it mean to hold in generality?

On your understanding of this, why would monism remain the dominant position? It seems obviously false.

Because what it means to be "truth-preserving" and thus a "correct logic" will depend on what is being preserved.

Because what it means to be "truth-preserving" and thus a "correct logic" will depend on what is being preserved. — Count Timothy von Icarus

I think it's ok for people to add on whatever significance they like to the word truth in truth-preserving. In the same way, if you lean toward ontological realism or anti-realism, you can add that onto whatever shenanigans you're doing. It doesn't change the shenanigans either way.

Do some logics lack "a use?" — Count Timothy von Icarus

Perhaps. Although a logician's presenting a logic would be their making use of it.

What does it mean to hold in generality? — Count Timothy von Icarus

In all logical systems, presumably. But I would be happy to consider any other options you might offer.

why would monism remain the dominant position? — Count Timothy von Icarus

Appeal to popularity? So you are seeing the traction in the arguments here.

I've not seen any evidence one way or the other, although I suspect most logicians accept that there are a range of logics - that's pretty undeniable.

Appeal to popularity? So you are seeing the traction in the arguments here

No, I'm just trying to figure out your understanding of the topic.

Which is why I ask, what exactly do you think the monist is claiming? That every logical system people have created has the same entailment relation? Isn't this very obviously false? I'm mystified as to why you think this is a subject of controversy given your understanding.

Which is why I ask, what exactly do you think the monist is claiming? — Count Timothy von Icarus

Well, I've been trying to work out what you are claiming, on the presumption that you are advocating monism.

So again, a monist holds that there are logical laws that are common to every system of logic.

No, not that "every logical system people have created has the same entailment relation".

And so it is up to monists to show what it is that all logical systems have in common. I don't see that it can be done.

(edited)

1) To be a law of logic, a principle must hold in complete generality. — Banno

Its sound if complete generality is a thing. Does it follow that it must hold in partial specificity? If following things applies. Is obfuscation a system of logic?

Well, there are consistent and useful systems of logic.

This isn't an answer to the question though. What do you think is being meant by "correct logic" in these articles? — Count Timothy von Icarus

The idea of a correct logic is endemic to logical monism. I'm not sympathetic to monism, and so I'm not the one to ask this question of.

But presumably correct logic for a monist would be only those logics that make use of the general laws of logic, whatever they might be.

Does that help?

Right, it's had excellent branding for years. My question is rather is Russell making up a necessary rule here? Tossing in a strawman universal?Holding in qualified completeness is not holding in completeness. Its other than completeness.

My question is rather is Russell making up a necessary rule here. — Cheshire

Well, even "necessary" has differing interpretations depending on which logical system one chooses - S1 through S5 for a start. And we have logical systems that are incomplete. I'm not sure what to say.

Well, even "necessary" has differing interpretations depending on which logical system one chooses - S1 through S5 for a start. And we have logical systems that are incomplete. I'm not sure what to say. — Banno

It seems odd to define something as what it can't be. Like a 'law of aviation' can only exist if it applies to lead plane flight. There are no lead planes. There are no laws of aviation.

Bit suspect is all.

A law of aviation would presumably apply to all flight, and a law of logic to all logics.

Right, so what's with complete generality? Why not say all logics.

Perhaps it was a stylistic decision, in order to keep more options open for the monist. I don't know. I don't see much hanging off it. The monist says there is something common to logic of any sort, by virtue of which it is to count as logic. The Nihilist says (perhaps) there is no logic. The Pluralist says there are logics, but they don't necessarily have a commonality. This does not make presumptions as to the nature of that commonality.

But presumably correct logic for a monist would be only those logic s that make use of the general laws of logic, whatever they might be.

Doesn't that sound a bit tautological to you? If correct logics are just those logics that utilize the general laws then monism is true by definition.

Your understanding of each of the positions seems to make them trivial rather than controversial.

If correct logics are just those logics that utilize the general laws then monism is true by definition. — Count Timothy von Icarus

If there are general laws...

That's the issue.

Your understanding of each of the positions seems to make them trivial rather than controversial. — Count Timothy von Icarus

How so?

Well, in virtue of what would a law be considered a "general law?" The monist says the general laws are those which hold in "correct logics," which is why they aren't forced to abandon their position on, say, LNC, due the mere existence of dialthiest systems.

If their position is that the general laws are those which hold in "correct logics" and that "correct logics" are those that use general laws... they have a circularity issue.

Your understanding of each of the positions seems to make them trivial rather than controversial. — Count Timothy von Icarus

Great posts. :up:

There are two questions with this pluralism/monism debate: What the heck is the thesis supposed to be, and Who has the burden of proof in addressing it? The answers seem to be, respectively, "Who knows?" and "The other guy!" :lol: — Leontiskos

Right, which is why their position is generally something like G&P's, which is that correct logics are those which capture the logical consequence relationship at work in natural language and scientific discourse, or perhaps "preserves-truth" relative to some metaphysical notion of truth, etc.

But you have acted like this is unfathomable, so I'm not really sure what you think this debate is about. Feel free to describe what you think the difference between the three views would even be in your view.

There are two questions with this pluralism/monism debate: What the heck is the thesis supposed to be, and Who has the burden of proof in addressing it? The answers seem to be, respectively, "Who knows?" and "The other guy!" :lol: — Leontiskos

But we have plenty of criteria and that's what matters.

I think it's ok for people to add on whatever significance they like to the word truth in truth-preserving. In the same way, if you lean toward ontological realism or anti-realism, you can add that onto whatever shenanigans you're doing. It doesn't change the shenanigans either way.

A pluralist will say that there is a certain type of logical consequence that is appropriate for a particular context. A nihilist will deny this.

A monist will claim there is only one logical consequence relationship, though no doubt they are aware that consistent logics have been constructed with other consequence relationships.

So why do you think there is any controversy here?

...which is why their position is generally something like G&P's, which is that correct logics are those which capture the logical consequence relationship at work in natural language and scientific discourse, — Count Timothy von Icarus

So you call a logic "correct" when I might call it "applicable". And Paraconsistent logic is for you "correct" when used for processing images and signals, while Lambda Calculus is "correct" when used for cryptography or AI.

A monist will claim there is only one logical consequence relationship — Count Timothy von Icarus

What one? Set it out.

Right, so what's with complete generality? Why not say all logics. — Cheshire

The impression I got was that "complete generality" doesn't commit you to quantifying over logics. A principle holding in complete generality, being understood as the entailment relation being the same for all logics, would need to contend with the fact that you can arbitrarily make systems that prove a claim and corollary systems that prove its negation when they share the same set of symbols.

So you can come up with a logic where modus ponens holds, and come up with a logic where modus ponens does not hold. Which would mean that if you wanted to find The Logic Of All and Only Common Principles (tm), you'd need to jettison modus ponens. Since it is not a common principle, since two logics disagree on whether it is a theorem.

The paper gives lots of strategies for coming up with schematic counter examples to many, many things. You can come up with scenarios where even elementary things like "A & B... lets you derive A" don't hold. So much would need to be jettisoned, thus, if The Logic Of All and Only Common Principles was taken exactly at its word, in the sense of intersecting the theorems proved by different logics.

And that's kind of a knock down argument, when you consider X is true in system Y extensionally at any rate (which is AFAIK the standard thing to do)

Phrasing it in terms of "complete generality" thus gives a whole lot of wiggle room regarding what it would mean for a principle to hold in complete generality, like you might be able to insist somehow that any logic worth its salt must have LEM, or any logic worth its salt must have modus ponens as a theorem. So that sense of "complete generality" (NOT completeness of a logic) might mean "in every style of reasoning", so it would let you think of some logics as styles of reasoning and some as not.

You also have the opportunity to think of informal logical principles as holding in "complete generality", as eg if someone believes that the No True Scotsman fallacy is fallacious in some sense, an argument definitively establishing its fallaciousness might be considered a theorem of The Logic of All and Only Common Principles, even though No True Scotsman doesn't admit an easy formalisation. Next paragraph is just extra detail supporting that it doesn't have an easy formalisation.

Just for extra detail, No True Scotsman doesn't admit of an easy formalisation in terms of predicate logic because deductively it kind of works. If x is always p( x ), and someone provides an example of x such that ~p( x ), it should be taken as a refutation. But the fallacy corresponds to interpreting the person providing the counterexample as instead providing an example of someone for whom some distinct property q( x ) holds where q( x ) != ~p( x ). Which isn't exactly a fallacy, it's a reinterpretation, and sometimes it's a good thing to do when arguing - sometimes people make bad counterexamples. But what makes it a fallacy is somehow that the suggested q( x ) only has irrelevant distinctions from ~p( x ), like a true Scotsman is just a Scotsman. You could also read it like the the asserter that x is always p( x ), upon receiving the counterexample, clarifies their position to some predicate q( x ) such that the counterexample given does not apply to it while still using the same predicate label ("Scotsman"). In that case the fallacy consists of revising the content of the claim to "just" exclude counterexample for no other reason, which deductively is without problem, but provides another irrelevant distinction. In either case, the sense of irrelevance of distinction is the thing which is so norm ladened and contextually situated that you're not going to be able to put it into a logic without (unknown to me) profound insight about logical form in natural language.

So if you wanted to have the fact that No True Scotsman is a fallacy as a "theorem" of The Logic Of All and Only Common Principles, maybe your whole logic needs to be informal to begin with.

:up: :up: :up:

Thank you, I am glad someone else also seems to understand what the topics is about and why there is even debate. I felt like I was going insane here lol.

It is interesting that you bring up the No True Scotsman because I think the monist can often be accused of something like this.

Anyhow, this is why I think avoiding any trace of metaphysics entirely seems impossible here. The CD paper uses counterexamples that involve abstract objects almost exclusively (occasionally propositions about proofs), and people's willingness to accept these as strong counterexamples seems linked to the sense in which they can be said to "exist." CD seems to suppose that if they exist in any formalization that they "exist" in a univocal sense. I imagine monists are generally going to just deny this, because monism is about logical consequence relative to some non-arbitrary context (although which one varies).

Maybe no "metaphysical" notion is needed and we just speak in terms of "plausibility" and "usefulness" but these seem to easily become even murkier notions. The two most common versions of pluralism (Beall and Restall and Shapiro) cited have very different notions of which logics should "count" for instance.

So you can come up with a logic where modus ponens holds, and come up with a logic where modus ponens does not hold. Which would mean that if you wanted to find The Logic Of All and Only Common Principles (tm), you'd need to jettison modus ponens. Since it is not a common principle, since two logics disagree on whether it is a theorem. — fdrake

Just for extra detail - how easy it is to come up with logics that disagree on theorems is a good argument for nihilism if you agree, with a stipulated logical monist of a certain sort, that there is only one entailment relation which all of these logics ape.

The cases approach allows us to say more about what logical nihilism amounts to: it is the view that for any set of premises Γ and conclusion φ whatsoever, there is a case in which every member of Γ is true, but φ is not. — Russell

I underlined "any" and "there is a case" above to highlight something about their scope of quantification. What collection is being quantified over? It must generically include arbitrary cases, premises, conclusions etc. IE, "complete generality" in a manner that allows the arbitrary representation of statements in formal languages. It's thus a metalinguistic notion with respect to any object formalism, it lays beyond and out with them.

It's, furthermore, a semantic notion:

Henceforth I’ll assume the interpretations approach to logical consequence, on
which logical nihilism is the view that for every principle of the form Γ |= φ there is an interpretation of the non-logical expressions in Γ and φ such that every member of Γ comes out true but φ does not. Such an interpretation would be a counterexample to the principle. If it turns out that there are no such counterexamples, and that on every interpretation of those non-logical expressions on which each member of Γ is true, φ is also true, then the principle will be a logical law, and nihilism will be false.

The turnstile with two lines above means that Russell wants to find counterexamples to principles through interpreting the logic, which is a way of finding a "syntactically appropriate" mappings from its symbols to other objects - like propositions to truth values - to see in what conditions the proposed principle holds. Mucking about with interpretations like that is what makes the kind of logical nihilism she's playing with a semantic argument.

On the interpretations view Γ|=φ is true iff whatever (syntactically appropriate) interpretation is given to the non-logical expressions in Γ and φ, if every member of Γ is true, then so is φ. For example, if our argument is P a, a = b P b, then the interpretations approach says that the argument is valid iff there is no interpretation of P, a and b (assuming we are treating = as logical) such that P a and a = b are true, but P b is not. Models are understood as offering us different interpretations of the non-logical expressions, and hence if we find a model in which P a and a = b is true but P b is not, the principle is not true. On the interpretations conception then, logical nihilism is the view that for every argument, Γ φ, there are interpretations of the non-logical expressions in Γ and φ which would make every member of Γ true, but φ not true

So what Russell is doing, when she's finding counterexamples, is taking "syntactically appropriate" expressions, throwing them into a formalism, then evaluating them in that formalism through an interpretation. If she can find an expression and an evaluation that fit the rules of the logic that is also a counterexample to one of its candidate principles, then it's not a principle of the logic for all expressions in it - and so is not a logical law.

So the sense of "complete generality" also allows Russell to consider variations over interpretations and the relationship of interpretations with syntactical elements of languages - it's thus a highly metalinguistic notion. Which is not surprising, as the Logic Of All And Only Universal Principles would need to have its laws apply in complete generality, and thus talk about every other logical apparatus in existence.

Which is an incredibly, incredibly strong thing to want. It's practically alchemical, one must have in mind a procedure in which the complexities and ambiguities of natural language, every inference, can be stripped, dissolved, distilled into gold. The true atoms of rationality. The story hooks in the book of divine law. In some respects it's even stronger than the petty desire to take the intersection of all logics, at least that has a precedent in each logic. And you need to claim that this holy book of divine order is spoken in one voice, the true semantical derivation symbol of the cosmos, that admits no quibbling, sophistry or perversion.

Or you could refuse the above notion and take the path Russell does, by applying metalinguistic restrictions to the space of interpretations of a theory. As in, "yes, we know the Liar blows this logic up, so let's just say for all bivalent φ", hence the method from proofs and refutations, lemma incorporation, in which a system is mapped to another system with an additional lemma in order to constrain its space of syntactically valid interpretations.

In formal terms, the latter is what distinguishes @Leontiskos's sophist from someone who finds good counterexamples, someone who finds good counterexamples ensures that they are syntactically valid - that is, obeys all and only the stipulated rules, both intended and written. If you can jam something between the intention and the written word, while playing by all the rules stipulated, you've shown that the conceptual content of the formalism does not reflect the intended object. Or alternatively the intended object is the wrongly represented in the formalism, conceived in a confusing or inopportune manner etc.

No worries. I do think your insistence that the extensional understanding of truth is deflationary in this context is imprecise. If I understand correctly, you're using "deflationary" to mean restricting the interpretations of a theory to all and only the ones which are syntactically appropriate and clearly within the logic's intended subject matter. Like propositional logic and non-self referential statements. Effectively removing everything that could be seen as contentious from the "ground" of those systems. Which would then ensure the match of their conceptual content with whatever objects they seek to model, (seemingly/allegedly) regardless of the principles used to form them. Which 'deflates' truth into unanalysable, but jury rigged, coincidence.

By contrast, correspondence would consider truth as a relation between the conceptual content of a theory and its intended object.