Isn’t a law of logic defined by its origin rather than by how general it is? In other words, a law of logic comes from Reason itself, not like a law that describes the behavior of physical things (a law of nature).

If that’s right, then there’s nothing in the concept of a law of logic that demands it must always apply universally. That just seems to be a characteristic these laws often exhibit, but it’s not essential to what they are. So, if it turns out that all proposed logical laws have exceptions, it doesn’t mean there are no laws of logic—only that they are more specific than we once thought.

Well to be clear, I don't think:

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.

this is what she is doing. To do this would be to ignore what the most popular pluralists (B&R) and what most monists say about their own positions. As fdrake says, if one is allowed to appeal to "every other logical apparatus in existence," and its self-defined capacity to produce valid inferences, then it is very easy to come up with "knock down arguments" demonstrating nihilism. But Russell is willing to admit that nihilism is a slim minority opinion that is often considered "absurd," which would be strange indeed if it was a position that is easily demonstrable. Hence the argument focuses on the plausibility and popularity of counterexamples, not their mere existence.

I don't really know what else to say here, SEP, IEP, the books I've referenced, and similar resources point out that this is not how the debate is defined; there is wide agreement that people have created logical systems that alternatively dispense with all of the "laws of logic" (or more accurately, would render the logical consequence relationship empty).

I feel like part of the confusion here is that this question is one of what holds for valid inference (true premises ensure a true conclusion) as a whole, across all logics, which in turn means that the common way of thinking of validity in a purely internal sense essentially begs the question here. (Russell doesn't do this BTW, although it seems this could have been made clear. Her intro on logical nihilism is clearer.)

Logical Monism holds that there is only one correct or true logic, meaning that a single set of logical rules or principles governs valid reasoning universally. Proponents believe that this one logic captures the essence of valid inference across all contexts. [Note, books making the case for monism I have seen generally focus on applied logic as the target for their argument. The analogy here would be the difference between trying to identify the physical geometry of the world versus the purely mathematical consideration of very many geometries.]

Logical Pluralism asserts that more than one logic can be correct, depending on the context or purpose. Different logical systems may be valid for different kinds of reasoning (e.g., classical logic for everyday reasoning, but other logics like intuitionistic or relevance logic in specialized cases). [The most common historical example here I can think of is the claim, arguably in Aristotle, that the Law of the Excluded Middle does not apply to statements about the future].

Logical Nihilism denies that there is any objective or true logic at all. It suggests that no logical system accurately captures reasoning or inference, and that the concept of "correct" logic may be meaningless or arbitrary. [Or, one way to put this more specifically, as Russell points out in a footnote, is idea that the logical consequence relationship in natural language (and so arguably scientific discourse as well) is actually empty. Of course, the nihilist may also recommended other ways to retrieve the concept of a "correct logic" as well.]

Part of the confusion is that just how one wants to define these might vary quite a bit, although they are generally not going to be defined in terms of "every logical apparatus in existence," since I think everyone is going to agree here making the debate a bit trivial.

So, if it turns out that all proposed logical laws have exceptions, it doesn’t mean there are no laws of logic—only that they are more specific than we once thought. — Clearbury

That's on the mark. appears to think this amounts to nihilism. It doesn't. Nihilism would have it that there are no laws of logic, that logic is at best a rhetorical device. That is not what Russell, or I think, @Clearbury, is claiming.

But Tim's view remains obscure to me. I don't see a confusion in Russell or SEP or IEP.

It seems to me that the idea that there are specific logics (specific entailment relations) for specific areas would be pluralism (at least as they define it.) Nihilism would reject this and claim that, depending on our goals and uses, we might use any logic in any setting. That is, there is, strictly speaking, no correct or singularly appropriate logic for any subject. In particular, there is no correct logic for modeling entailment in natural language.

I haven't even advocated for a position here, I have tried to clarify the monist position and how some arguments are poor responses for it. And I'd argue that if you're unable to understand the dominant position here (i.e., if it seems trivial to dispatch) then you really don't understand the debate at all.

I personally wouldn't consider myself a monist because the formalisms they advance are wholly inadequate for capturing natural language reasoning, particularly in the dimension of analogous predication, while also flattening out truth.

You keep claiming monism to be the "dominant" position. I see no evidence of that. Indeed, any logician will be aware that there are various logical systems.

Articles on this topic generally refer to it as such at any rate. B&R is normally brought up as the landmark case for pluralism and it is fairly recent. Shapiro is from 2014.

Indeed, any logician will be aware that there are various logical systems.

Yes, which maybe should make you question if you have any clue what the debate is about.

Yes, which maybe should make you question if you have any clue what the debate is about. — Count Timothy von Icarus

This comment makes me question if I know what the debate is about.

What's the debate about?

What's the debate about? — Moliere

It's about what "Logical Monism" is about. :wink:

O.

In that case, clearly stipulate-able.

And of course, if we have differing stipulations, the One True Stipulation will be correct.

Heh. I wouldn't go that far at least. I think @Leontiskos and @Count Timothy von Icarus would want us to come up with a notion of logical monism which is interesting enough for their concerns.

Thus far I've gathered that they both would like to relate to knowledge generation? I think?

This is what motived by earlier response about why the problem is interesting with respect to knowledge generation.

I havent been following this thread closely as it seems to me to be mostly boring. However I do remember someone asking whether there were any logical laws that applied to all forms of logic. How about validity and consistency? Or which is basically the same as far as I can tell—the law of non-contradiction?

However I do remember someone asking whether there were any logical laws that applied to all forms of logic. How about validity and consistency? Or which is basically the same as far as I can tell—the law of non-contradiction? — Janus

I'm a defender of dialetheism, thus far.

Which rules out the LNC.

Hence, the notion of pluralism -- at least so far no one has said that the logics which include the LNC are the same as the logics which exclude the LNC.

I'm a defender of dialetheism, thus far.

Which rules out the LNC. — Moliere

Can you explain how dialetheism rules out the LNC? My point was that within any valid logical argument of whatever stripe there must be consistency between the premises and the conclusion. If a premise contradicts another premise or the conclusion then the argument cannot be valid. That sort of thing.

My point was that within any valid logical argument of whatever stripe there must be consistency between the premises and the conclusion. If a premise contradicts another premise or the conclusion then the argument cannot be valid. That sort of thing. — Janus

Your choice of words here has me wondering if I can or not.

But I can give a straightforward answer to your question which may be aside from the point.

Can you explain how dialetheism rules out the LNC? — Janus

Quoting the SEP here:

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true. If falsity is assumed to be the truth of negation, a dialetheia is a sentence which is both true and false.

I've been advancing the argument that the LEM holds -- because there is nothing in between truth and falseness so we cannot choose some in-between or other -- but the liar's sentence is best treated as a dialetheia.

If one accepts that then the LNC cannot hold because the LNC says "A & ¬A" is false. Since ¬A and A, as a dialetheia, are both true and false, together, the LNC is rejected.

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true. If falsity is assumed to be the truth of negation, a dialetheia is a sentence which is both true and false.

Can you think of any examples of a sentence wherein both A and not-A are true in the same sense or context? For example I could be said to be both old or tall and not old or tall but not in the same senses or contexts.

Can you think of any examples of a sentence wherein both A and not-A are true in the same sense or context? For example I could be said to be both old or tall and not old or tall but not in the same senses or contexts. — Janus

The liar's sentence.

"This sentence is false" is the liar's sentence.

This doesn't fit your "for example", though, because it's not about a person, but a sentence.

Since the sentence can be said in any context, and it's basically about words and how we describe them, we can place them within the sense of logic.

The sense of logic can be informal or formal, and insofar as we understand one another well enough it need not be specified.

Though I'm wondering if I've just lost you at this point?

Someone the other day said of "The Selfish Gene" that it was most influential amongst those who had read only the title.

I wonder if that is true to some extent here, too. — Banno

Though I'm wondering if I've just lost you at this point? — Moliere

Not lost. For me the liar sentence is neither true nor false, not both true and false.

M'kay. Then my example would not convince you of dialetheism, and at this point in the debate I'd ask -- if dialetheism were somehow justified would that then justify logical pluralism?

For me the liar sentence is neither true nor false, — Janus

So it's para-consistent?

M'kay. Then my example would not convince you of dialetheism, and at this point in the debate I'd ask -- if dialetheism were somehow justified would that then justify logical pluralism? — Moliere

I would only consider dialetheism to be justified if I could think of an example of a sentence which is demonstrably true and false in the same sense and context. That said if it were somehow justified I guess that might justify logical pluralism.

Perhaps. What do you think?

You've suggested a third truth-value - neither true nor false. Is that right?

I guess I have. Apart from the 'liar' sentence and the 'barber' paradox I can't think of any coherent sentences which are demonstrably neither true nor false. When I said the liar is neither true nor false that is only because if it is taken to be true it is false and vice versa. Apart from that I would not claim to be clear on what it could mean for it to be neither true nor false. Perhaps it is incoherent, from which I guess it would follow that it is neither true nor false. I think the difficulty would be to come up with a clearly coherent sentence which is neither true nor false, not to speak of one which is both true and false.

Paraconsistent logic includes the study of logics with other than two truth values. Such logics might include those that are valid yet inconsistent, or inconsistent yet valid. If they are allowed, then there are valid inconsistent logics as well as invalid consistent logics.

That there are such logics makes it difficult to maintain that all logics must be valid and consistent.

And these logics do have some uses.

I think of validity and consistency being inseparable. I could say the liar sentence is inconsistent insofar as it asserts that it is both true and false. In other words it inconsistently and contradictorily asserts that it is true that it is false. I don't know whether it is para-consistent (unless) the para in that context means 'beyond' in a similar sense as it does in 'paranormal'. I count it as inconsistent and thus invalid and neither true nor false.

I don't know much about formal logic and perhaps there are formal ways of making invalid consistent and valid inconsistent logical posits work and even do work. I am interested only in what can be parsed in ordinary language.

I think of validity and consistency being inseparable. — Janus

Then presumably you conclude that paraconsistent logic is not logic proper? And isn’t the liar in ordinary language?

All this simply to show what the interest here is.

Then presumably you conclude that paraconsistent logic is not logic proper? And isn’t the liar in ordinary language? — Banno

Right it seems that is what my position entails. The liar is in ordinary language and as I said for me it is implicitly self-contradictory from which it follows that it is inconsistent and invalid and neither true nor false.

Can you think of a propositional sentence in ordinary language which is not self-contradictory that is both true and false or neither true nor false?

I doubt it and thus conclude the LNC holds in all valid logics.

OK.

Logic is supposed to describe the structure of thought, so pluralism is basically saying there are multiple ways to think instead of just one. Nihilism is saying there is no "way" that we think? Structure is applied post hoc?