Thinking of all systems as univocal would appear to be putting unnecessary restrictions on the development of logic. — Banno

I suppose there's a distinction between "having the same underlying concepts of truth and meaning and law" and "having different laws", maybe all the systems we've created, despite proving different theorems, have proof and truth as analogous family-resemblance style concepts in them. Maybe they have a discoverable essence.

Not that I'm persuaded.

, The problem for logical monism is that if there is only one logic, then which one?

(I did read somewhere that modal logic could be "reduced" to first order logic...)

only one logic, — Banno

Only one type of logical law, all systems provide instances of? Only one type of truth, all systems provide instances of? I don't like it, or believe it, but it's possible.

It might not be a confusion, it could be an insistence on a unified metalanguage having a single truth concept in it which sublanguages, formal or informal, necessarily ape. — fdrake

A good move away from the strawmen. :up:

Historically logic is the thing by which (discursive) knowledge is produced. When I combine two or more pieces of knowledge to arrive at new knowledge I am by definition utilizing logic. — Leontiskos

Logic is that which reliably produces knowledge, via rational motion or inference. This is not limited to a single formal system - that is Banno's strawman. But knowledge and truth are one. There cannot simultaneously be knowledge both of X and ~X. Therefore logical pluralism is false.

Yep.

And again, there is the challenge set up by that very specification, to find a logic that does not meet it. Monism again restricts development.

There cannot simultaneously be knowledge both of X and ~X. — Leontiskos

And yet Dialetheism. You at least need to make a case, rather than an assertion.

And yet Dialetheism. You at least need to make a case, rather than an assertion. — Banno

Er, do you ever take your own advice?

Now in a given philosophy we'll want a particular logic, or particular logics for particular ends, but the logician need not adhere to one philosophy. — Moliere

Banno has so thoroughly poisoned the well that it becomes difficult. Here is what I said to this idea:

The idea that different formal logics can each yield sound arguments without contradicting one another is not in any way controversial, and I would not call it logical pluralism. — Leontiskos

-

It's the name for a sentence.

A name denotes an individual.

The individual is an English sentence.

The sentence is "This sentence is false"

(1) is a shorthand to make it clear what "This sentence" denotes. — Moliere

So again:

What do you mean by (1)? What are the conditions of its truth or falsity? What does it mean to say that it is true or false? All you've done is said, "This is false," without telling us what "this" refers to. If you don't know what it refers to, then you obviously can't say that it is false. You've strung a few words together, but you haven't yet said anything that makes sense. — Leontiskos

In order for a sentence to be true or false it must say something. That is what it means to be a sentence. "This sentence is false," does not say anything. It is not a sentence. It is no more coherent than, "This sentence is true," or, "This sentence is that."

One answer, which you've provided, is that the sentence means nothing.

It's not the only one though. — Moliere

If you think that answer is wrong then you'll have to tell us what the sentence means.

I suppose there's a distinction between "having the same underlying concepts of truth and meaning and law" and "having different laws", maybe all the systems we've created, despite proving different theorems, have proof and truth as analogous family-resemblance style concepts in them. Maybe they have a discoverable essence.

Not that I'm persuaded.

:up: This is what I was getting at with the reference to historical philosophy, although I think, in general, most thinkers I can think of would say that truth itself is the unifying and generating principle (genus vs species).

I suppose the flip-side would be that there is no relationship between concepts of truth. I can't help but think this would make truth arbitrary, or at least have major philosophical ramifications, maybe not.

I suppose the flip-side would be that there is no relationship between concepts of truth. I can't help but think this would make truth arbitrary, or at least have major philosophical ramifications, maybe not. — Count Timothy von Icarus

It is also another departure from natural language. We do not speak of truth as having various species with no relation to each other. Nor does the term "logics" jibe with the idea that the various logics have nothing in common.

Pick your poison. Your thesis is that there are true/correct logics with nothing in common, such that we cannot call their similarity logic in a singular sense, and we cannot apply a rational aspect under which they are the same. But the natural language itself betrays this, for simply calling them logics indicates that they belong to a singular genus. — Leontiskos

In order for a sentence to be true or false it must say something. That is what it means to be a sentence. "This sentence is false," does not say anything. It is not a sentence. It is no more coherent than, "This sentence is true," or, "This sentence is blue," or, "This sentence is that." — Leontiskos

If you think that answer is wrong then you'll have to tell us what the sentence means. — Leontiskos

What does it mean to "say something"?

I'll say more, though it's fair to ask what are the conditions you're after here -- what I have in mind is that English cannot refer to itself but must refer to objects. Is that so? Some sort of extensional theory of meaning?

Because I'd say that just from a plain language sense "This sentence is false" is clear to a point that it can't be clarified further. "This sentence" is a pronoun being used to refer to the entire phrase which the pronoun is a part of. "... is false" is the sort of predicate we apply to statements.

"...is false" is the predicate which yields the value "true" for sentences which are false in a truth-functional sense, which seems to me to be pretty clear that this is the sort of background assumptions which are part of Russell's paper. (though what I'm advancing is different from Russell's, I'm in favor of her conclusion for logical pluralism)

But neither of these things rely upon truth-conditions or states-of-affairs.

And paraconsistent logic certainly seems to me to be a worthy candidate for being significantly different from bi-valent logic since it rejects the principle of explosion, and accepts dialethia.

Because I'd say that just from a plain language sense "This sentence is false" is clear to a point that it can't be clarified further. — Moliere

So be honest. When you say, "This sentence is true/false," do you think you are saying something meaningful? Would you actually use that phrase, speak it aloud, and expect to have said something meaningful?

What does it mean to "say something"? — Moliere

A sentence says something if it presents a comprehensible assertion. It says something if its claim is intelligible.

Now when you say, "X is false," I can think of X's that fit the bill. I might ask what you mean by X, and you might say, "2+2=5." That's fine. "...is false" applies to claims or assertions. If there is no claim or assertion then there is no place for "...is false." For example, "Duck is false," "2+3+4+5 is false," "This sentence is false."

There is an interesting question about the great circle, but the method which outright denies that the great circle is a circle can outright deny anything it likes. It is the floodgate to infinite skepticism. I think we need to be a bit more careful about the skeptical tools we are using. They backfire much more easily than one is led to suppose. — Leontiskos

Whether or not a sphere's line of circumference looks like a circle on an actual sphere presupposes a vantage point of origin. Sometimes it can and does. Other times, not. One can gradually change their own position relative to an actual sphere that has a visible line of circumference around it in such a way that the line of circumference only seems to change it's shape. It doesn't. That change is one of perspective(the way the line of circumference looks to the observer).

If all circles are located on 'perfectly flat' planes, that occupy no space at all, then the line of circumference around a sphere is not a circle. All lines of circumference encircle space. So, either something that does not occupy space can encircle space or the line of circumference is not equivalent to a circle...

...despite the fact that that line of circumference can look like a circle to an observer.

Is that wrong somehow?

Is that wrong somehow? — creativesoul

I don't see why one must accept this:

All lines of circumference encircle space. — creativesoul

Nevertheless, if the great circle is a torus—a three-dimensional object—then it is not a (Euclidean) circle. If it is not a torus then it may well be a circle. Yet perhaps it is not a torus but is nevertheless a set of coplanar points, falling on an implicit plane which possesses a spatial orientation. Is it a circle then? Not strictly speaking, because two-dimensional planes do have not a spatial orientation.

But what is the point here? Recall that @fdrake's desired conclusion was that there are square circles.

If logical monism is the view that all logical systems are commensurable, then there is presumably some notion of translation that works between them all.

I don't think this would be the way to put it. Presumably some systems are not commensurable unless we have some criteria for what will count as a correct logic.

From Griffiths and Paseau:

The intuitive concept of logical consequence has many different, incompatible, strands. One reaction to this situation is logical pluralism: roughly, the pluralist endorses different logics as capturing different precisifications of the rough intuitive conception. In this chapter, we define logical pluralism and its contrary logical monism.

The target notion is logical consequence in meaningful discourse and its possible extensions. But the model-theoretic definition is of course defined for formal languages. A crucial component of any account of logical consequence is therefore formalization: the process by which we move between meaningful and formal (meaningless) sentences and arguments. We define a logic as a true logic, roughly, when formalizations into it capture all and only consequences that obtain among meaningful sentences.
Logical monists claim that there is one true logic. Logical pluralists claim that there are many. We define logical pluralism more precisely as the claim that at least two logics provide extensionally different but equally acceptable accounts of consequence between meaningful statements. Logical monism, in contrast, claims that a single logic provides this account

But I think there are multiple forms here,

e.g. "McSweeney: ‘[T]he One True Logic is made true by the mind-and-language-independent world…[which]…makes it the case that the One True Logic is better than any other logic at capturing the structure of reality [2018, Abstract].’ So, the logical pluralist denies that any one consequence relation is metaphysically privileged,"

Cheers, Leon. Let me buy you a beer some time.

The idea that different formal logics can each yield sound arguments without contradicting one another is not in any way controversial, and I would not call it logical pluralism. — Leontiskos

Fair enough. Part of the issue here is whether pluralism can be set out clearly. As the SEP article sets out, the issue is as relevant to monism as for pluralism. The question is how the various logics relate. It remains that monism must give an account of which logic is correct. You've made it plain that you don't accept Dialetheism, and will give no reason, so the point is moot.

, "This sentence is false" is about that sentence. It says that it is false. It's like "This sentence has six words" in some ways, and "That sentence is false" in others. There is no obvious reason to think it meaningless.

Not all paraconsistent logics accept dialetheism, but dialethiests are pretty much obligated to accept paraconsistent logic.

A crucial component of any account of logical consequence is therefore formalization: the process by which we move between meaningful and formal (meaningless) sentences and arguments. We define a logic as a true logic, roughly, when formalizations into it capture all and only consequences that obtain among meaningful sentences.

Interesting. Thanks for this. I'm a bit surprised by you referring to this, since I had taken it that you had a dislike for formalism.

But taking it at face value, how can we be sure that only one logic will "capture all and only consequences that obtain among meaningful sentences." If one logic has "Γ ⊨ φ" and another has Γ' ⊭ φ, what is our basis for choosing which is the One, True? Not either Γ or Γ', without circularity. Some third logic? And again, Which? Does the monograph address this? Are we faced with an explosion of logics?

I don't see why one must accept this:

All lines of circumference encircle space.
— creativesoul — Leontiskos

Point well-made and taken. That should have been further qualified as all spherical lines of circumference. That's what I meant. That's what I was thinking. Evidently a few synapses misfired.

But what is the point here? — Leontiskos

Just wondering if I've understood something.

Nevertheless, if the great circle is a torus—a three-dimensional object—then it is not a (Euclidean) circle. If it is not a torus then it may well be a circle. — Leontiskos

My interest was piqued by the claim that a line of circumference around a sphere was a circle. The shame of this all is that the term "circle" can mean whatever we decide. Then we can equivocate. Sorry for the interruption. Have at it.

there are square circles. — Leontiskos

My position was that there are circumstances in which it makes sense to say there are square circles, perhaps even that there are circumstances in which one can correctly assert that there are square circles, not "there are square circles" with an unrestricted quantification in "there are". Quantifying into an undifferentiated, uncircumscribed domain is a loaded move in this game. I do not imagine myself hacking into the mainframe of being to view the source code.

Absolutely crystal quote, thank you.

Point well-made and taken. That should have been further qualified as all spherical lines of circumference. That's what I meant. That's what I was thinking. Evidently a few synapses misfired. — creativesoul

Well, one might accept it. I don't see any of these objections as straightforward. I don't think there is a "verbatim" meaning, to use @fdrake's word.

Does the circumference of a (Euclidean) circle encircle space? Yes, two-dimensional space. But then does the great circle's encompassing space make it a non-circle? Apparently not. Unless what we mean is that the great circle encompasses three-dimensional space, in which case this does make it a non-circle.

Just wondering if I've understood something. — creativesoul

Fair enough, and I meant to ask in a broader way and include fdrake.

My interest was piqued by the claim that a line of circumference around a sphere was a circle. — creativesoul

I am quite fine with that claim. Apparently I think the coplanar points of the great circle contain a circle (and a two-dimensional plane).

fdrake effectively puts words in my mouth in declaring victory, "Ah, when you say 'great circle' you mean something which does not contain a two-dimensional plane, therefore when you say 'great circle' you don't mean a Euclidean circle." But I never assented to any of these sorts of interpretations.

---

My position was that there are circumstances in which it makes sense to say there are square circles, perhaps even that there are circumstances in which one can correctly assert that there are square circles, not "there are square circles" with an unrestricted quantification in "there are". — fdrake

So you are ("perhaps") willing to say that there are circumstances in which one can correctly assert that there are square circles, but you won't commit yourself to there being square circles. This is odd.

The idea behind this sort of thinking seems to be that every utterance is limited by an implicit context, and that there are no context-independent utterances. There is no unrestricted quantification. There is no metaphysics. I take it that this is not an uncontroversial theory. Here is an example of a statement with no implicit formal context, "There are no Euclidean square circles." You would presumably agree. But then to be wary of the claim that there are no square circles, you are apparently only wary of ambiguity in the terms. You might say, "Well, maybe someone would say that without thinking of Euclidean geometry." But we both know that there is no verbatim meaning of "square" and "circle," at least when subjected to this level of skepticism. This is a nominal dispute, but it won't touch on things like logical pluralism, for that question has to do with concepts and not just names. A new definition of "circle" will not move the needle one way or another with respect to the question of logical pluralism. As noted, the taxicab case involves equivocation, not substantial contradiction.

I am still wondering:

I'm not really sure what you are arguing, fdrake. It doesn't sound like you hold to logical nihilism or logical pluralism in any strong or interesting sense. Am I wrong in that? — Leontiskos