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

- So for Griffiths and Paseau "logical monism" holds that there is one true formalization. I have not seen anyone on TPF hold this theory, and I certainly do not. He is also talking about consequence rather than inference. "Logical monism" does not look at all like the classical view.

Again, for Aristotle logic is the solution to the problem of the Meno. It is how discursive knowledge is achieved. It is primarily a matter of inference. Aristotle was quite clear that his formalization was not identical to logic in this fundamental sense.

If someone wants to argue for logical pluralism I would want to know exactly what they mean by that term, because it has been unhelpfully ambiguous all throughout this thread.

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. — Banno

No, not really. You really ought to read Rombout on the way that Frege and Wittgenstein mean different things by "logic." Your whole frame is mistaken. I am not a "logical monist," and I don't think Timothy is either. If every logic is on the same level, then pluralism must be true. Logical monism and logical pluralism strike me as equally silly.

You've made it plain that you don't accept Dialetheism, and will give no reason, so the point is moot. — Banno

You've made it plain that you won't offer any arguments, only assertions. Moliere tried and I answered his.

It's like "This sentence has six words" in some ways — Banno

"In some ways."

Unlike "...is false," "...has six words" does not require an assertion/claim.

(Moliere and yourself are doing what I would call Dialetheist apologetics. You've heard objections to the "Liar's paradox" and you are responding to those objections, regardless of the fact that my objection is quite different.)

I don't dislike formalism, I just think it is frequently called on to do things it is ill-suited for or retreated into to avoid difficulties that should rather be brought front and center. That said, I don't agree with the framing here (I haven't made it far anyhow), but it seems to me like it captures the intuition that monism is going to be about correct logics.

Their target is a natural language (or "cleaned up natural language"), or maximally, all natural and scientific languages. The analogy they draw is to physical geometry. The physicist is interested in physical geometry, not any and all geometries. They are only even potentially interested in a few of the geometries that might be dreamed up. Likewise, the applied logician is interested in logical consequence in the languages we actually use to discuss meaningful truths. Which I think is a useful analogy.

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'm sure they do in the second half, but I haven't made it that far (in part because I'm not sure about the project, but it's quite readable and got good reviews). The first half is objections to pluralism. They do foreshadow this a bit, because it is going to be a problem for pluralists too, since they generally don't want to say that all logics are legitimate either. Additionally, presumably pluralists will want to convince others to be pluralists by making a valid argument for pluralism. But they're going to likely to find this impossible to do in all the logics they accept as correct (at least per popular formulations of pluralism). Yet if they work with just one correct logic then inconsistency issues arise in the metalogic. That and the choice of a metalogic will be arbitrary (which Shapiro's account owns up to).

As they put it:

"In fact, it would be quite odd to suppose that there isn’t a single underlying argument for pluralism, but that it must be recast in different ways from different perspectives. By far the most natural thing to say is that if there is a good argument for pluralism, then that same argument should be frameable in any true logic—and so much the worse for any logic that does not allow for its expression."

Does the circumference of a (Euclidean) circle encircle space? Yes, two-dimensional space. — Leontiskos

You forgot that Euclid specifies a circle as a plane figure. I realise you're not going to accept that a great circle is not a Euclid circle, or that a circle in a plane at an angle isn't a Euclid circle without a repair of his definition - but please, trust someone who's wishy washy on logic that you're just wrong that Euclid's definition encompasses all circles.

I've been using the word "verbatim" to try to mean a couple of things:
A ) At face value.
B ) Using only the resources at hand in a symbolic system.

Thus Euclid's definition of a circle, verbatim, would exclude the great circle. And I keep bringing that up because it neatly illustrates the interplay between formalism and intuition and also a pluralism vs monism point.

But I never assented to any of these sorts of interpretations. — Leontiskos

And if you want to just talk about your intuitions without recourse to formalism, I don't know if this topic of debate is even something you should concern yourself with. You might not even be a logical monist in the OP's sense, since the kind of logic it's talking about is formal?

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. — Leontiskos

If you actually want my perspective on things, rather than trying to illustrate points from the paper: I'm very pragmatist toward truth. I prefer correct assertion as a concept over truth (in most circumstances) because different styles of description tend to evaluate claims differently. As a practical example, when I used to work studying people's eye movements, I would look at a pattern of fixation points on an image - places people were recorded to have rested their eyes for some time, and I would think "they saw this", and it would be correctly assertible. But I would also know that some subjects would not have had the focus of their vision on some single fixation points that I'd studied, and instead would have formed a coherent image over multiple ones, in which case they would not have "seen" the area associated with the fixation point principally, they would've seen some synthesis of it and neighbouring (in space and time) areas associated with fixation points (and other eye movements). So did they see it or didn't they?

So I like correctly assertible because it connotes there being norms to truth-telling, rather than truth being something the world just rawdogs into sentences regardless of how they're made. "There are 20kg of dust total in my house's carpet"... the world has apparently decided whether that's true or false already, and I find that odd. Because it's like I'm gambling when I whip that sentence out.

I apply the same kind of thought to maths objects, though they're far easier to build fortresses around because you can formalise the buggers. I'm gambling a lot less.

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. . — Leontiskos

I would agree that every quantification is into a domain, and I don't think there are context independent utterances. I do not think it follows that there is no metaphysics. I'm rather fond of it in fact, but the perspective I take on it is more like modelling than spelling out the Truth of Being. I think of metaphysics as, roughly, a manner of producing narratives that has the same relation to nonfiction that writing fanfiction has to fiction. You say stuff to get a better understanding of how things work in the abstract. That might be by clarifying how mental states work, how social structures work, or doing weird concept engineering like Deleuze does. It could even include coming up with systems that relate lots of ideas together into coherent wholes! Which it does in practice obv.

I do also agree that there are no square circles in Euclidean geometries as the terms are usually understood.

But we both know that there is no verbatim meaning of "square" and "circle," at least when subjected to this level of skepticism.

I think this goes too far, you can do your best to interpret someone accurately and what they say can still be too restrictive or too expansive. Good shit testing requires accurate close reading. This is how you come up with genuine counterexamples.

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 would have thought it clear how it relates to logical pluralism. If you model circles in Euclid's geometry, you don't see the great circle. But if you look for models of the statement "a collection of all coplanar points equidistant around a chosen point", you'll see great circles on balls (ie spheres, if you don't limit your entire geometry to the points on the sphere surface). They thus disagree on whether the great circles on balls are circles.

If you agree that both are adequate formalisations of circlehood in different circumstances, this is a clear case of logical pluralism.

As noted, the taxicab case involves equivocation, not substantial contradiction. — Leontiskos

The taxicab example is designed as a counterexample to the circle definition "a collection of all coplanar points equidistant around a chosen point", since the points on the edge of the square in Euclidean space are equidistant in the taxicab metric on that Euclidean space. It isn't so much an equivocation as highlighting an inherent ambiguity in a definition. And mathematicians can, and do, call those taxicab squares circles when they need to.

You can side with the thing as stated, or refine it to mean "a collection of all coplanar points Euclidean equidistant around a chosen point". Which would still fall pray to the great circle on the hollow sphere considered as is own object, since the point they're equidistant about is no longer part of the space.

The point isn't to say that we don't know what a circle is - that's sophistical - the point is to show that there are mutually contradictory but fruitful understandings of what a circle is. Which is a pluralist point par excellence.

Even going by @Count Timothy von Icarus's excellent reference:

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

The extensional difference between all of these different formalisms are the scope of what counts as a circle. A pluralist could claim that some definitions work for some purposes but not others, a monist could not.

To put it in super blunt terms, Euclid's theory would have as a consequence that the great circle on a ball is not a circle. The equidistant coplanar criterion would prove that the great circle on a ball is a circle. Those are two different theories - consequence sets - of meaningful statements. A pluralist would get to go "wow, cool!" and choose whatever suits their purposes, a monist would not.

I agree more with the second quote I provided (albeit the "mind and language independent" part is not unproblematic), but it's worth noting that G&P allow for multiple true logics, what they argue for is one logical consequence relationship consistent with natural language, and the justification of the "one true logic" will be broadly epistemic. The "one true logic," is in a sense the "least true logic," that covers logical consequence.

The reason I thought of it though is because I think their focus on application is likely to be relevant across many forms of monism. Of course, there are a dazzling number of systems to consider, but I think the intuition is that "truth in this system" sometimes has a status akin to fiction. It doesn't have to do with how we get true inferences at all.

@Count Timothy von Icarus

You might not even be a logical monist in the OP's sense, since the kind of logic it's talking about is formal? — fdrake

Just pulling this for context. The OP is three years old. The recent discussion is not about the OP. After frank bumped the thread Banno brought in an external conversation, and pigeon-holed the discussion into one of those interminable, internecine Analytic disputes (Pluralism vs. Monism).

The external conversation revolves around this post from Srap:

So we have (1) the primary phenomena, everyday language use and reasoning.

Then there's (2) the way logic schematizes these.

And there's the further claim that in carrying out (2), we see (3) the deep structure of everyday language and reasoning, the underlying logical form.

My claim was that we can talk about (2), whether (3) is true or not, and even without considering whether (3) is true or not.

It's the same thing I've been saying all along, that (2) doesn't entail (3). — Srap Tasmaner

This was Srap's attempt to frame it, but we went on to ask whether that framing was neutral or not.

I tried to continue the conversation in that thread, but Banno insisted on bringing it here. If Srap had continued the conversation in that thread I would have simply ignored Banno's transplant, given how insubstantial it was bound to become.

My position has never been logical monism's program of a single true formalization. That's just something Banno falsely pinned on me. For example:

Each time you state the problem in terms of artifice or invention you fail to capture a neutral (2). Do you see this? To call logic an invention of artifice, or a schematization or formalization, is to have begged the question. If that's all logic is then the answer to (3) is foreclosed. — Leontiskos

The extensional difference between all of these different formalisms are the scope of what counts as a circle. A pluralist could claim that some definitions work for some purposes but not others, a monist could not.

Do we need different accounts of logical consequence to have different geometries, etc.? Wouldn't pluralism be more something like: "we start with Euclid's postulates and end up with differing geometric propositions that can be deduced as true?"

You forgot that Euclid specifies a circle as a plane figure. — fdrake

No I didn't.

I realise you're not going to accept that a great circle is not a Euclid circle, or that a circle in a plane at an angle isn't a Euclid circle without a repair of his definition — fdrake

See:

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. — Leontiskos

I've been using the word "verbatim" to try to mean a couple of things:
A ) At face value.
B ) Using only the resources at hand in a symbolic system.

Thus Euclid's definition of a circle, verbatim, would exclude the great circle. — fdrake

But it is here illustrative that I am not familiar with the concept "great circle," especially as to its specific geometrical properties, and I did query you about the picture you posted. You thought there was a verbatim sense of "great circle," but you were mistaken. You would have to explain what you mean by it in order to achieve your contradiction, because "great circle" says very little, verbatim.

And if you want to just talk about your intuitions without recourse to formalism, I don't know if this topic of debate is even something you should concern yourself with. — fdrake

I think you're moving too fast. Formalisms have limits. What are the specific properties of lines, points, circles, great circles, two-dimensional planes, three-dimensional planes, etc.? How do they relate to each other? For example, can points be deleted or not? Is the great circle a torus, and if not is it three-dimensional at all? You're making a bunch of assumptions in all of this and drawing a fast conclusion.

But the deeper issue is that I don't see you driving anywhere. I don't particularly care whether the great circle is a Euclidean circle. If you have some property in your mind, some definition of "great circle" which excludes Euclidean circles, then your definition of a great circle excludes Euclidean circles. Who cares? Where is this getting us?

If you actually want my perspective on things, rather than trying to illustrate points from the paper: I'm very pragmatist toward truth. I prefer correct assertion as a concept over truth (in most circumstances) because different styles of description tend to evaluate claims differently. As a practical example, when I used to work studying people's eye movements, I would look at a pattern of fixation points on an image - places people were recorded to have rested their eyes for some time, and I would think "they saw this", and it would be correctly assertible. But I would also know that some subjects would not have had the focus of their vision on some single fixation points that I'd studied, and instead would have formed a coherent image over multiple ones, in which case they would not have "seen" the area associated with the fixation point principally, they would've seen some synthesis of it and neighbouring (in space and time) areas associated with fixation points (and other eye movements). So did they see it or didn't they?

So I like correctly assertible because it connotes there being norms to truth-telling, rather than truth being something the world just rawdogs into sentences regardless of how they're made. "There are 20kg of dust total in my house's carpet"... the world has apparently decided whether that's true or false already, and I find that odd. Because it's like I'm gambling when I whip that sentence out. — fdrake

Okay, thanks. And I agree with this. I am interested in knowledge—including justification—as opposed to just truth. Very often justified knowledge is precisely that which has been (correctly) logically inferred. I would define logic as that thing that gets you to (discursive) knowledge, or at least to justified assertion.

I would agree that every quantification is into a domain, and I don't think there are context independent utterances. I do not think it follows that there is no metaphysics. I'm rather fond of it in fact, but the perspective I take on it is more like modelling than spelling out the Truth of Being. I think of metaphysics as, roughly, a manner of producing narratives that has the same relation to nonfiction that writing fanfiction has to fiction. You say stuff to get a better understanding of how things work in the abstract. That might be by clarifying how mental states work, how social structures work, or doing weird concept engineering like Deleuze does. It could even include coming up with systems that relate lots of ideas together into coherent wholes! Which it does in practice obv. — fdrake

And this sounds a lot like Srap's approach. I was encouraging him to write a new thread on the topic.

Plato's phrase, "carving nature at it's joints," seems appropriate here. I would say more but in this I would prefer a new or different thread (in the Kimhi thread I proposed resuscitating the QV/Sider thread if we didn't make a new one). I don't find the OP of this thread helpful as a context for these discussions touching on metaphysics.

I would have thought it clear how it relates to logical pluralism. If you model circles in Euclid's geometry, you don't see the great circle. But if you look for models of the statement "a collection of all coplanar points equidistant around a chosen point", you'll see great circles on balls (ie spheres, if you don't limit your entire geometry to the points on the sphere surface). They thus disagree on whether the great circles on balls are circles.

If you agree that both are adequate formalisations of circlehood in different circumstances, this is a clear case of logical pluralism. — fdrake

So:

Let's suppose it is a countermodel. How does the logical pluralism arise? I can only see it arising if we say that a "circle" means both Euclid's definition and the great circle countermodel, and that these two models are incompatible. Is that what you hold? — Leontiskos

For the univocalist the two definitions are incommensurably different. For the analogical thinker there is an analogy between a great circle and a circle. I think both adhere to the definition, "A set of coplanar points equidistant around a single point," but this also involves analogical equivocity between 2D planes and 3D planes.

That also lines up just fine with my view of logic. If logical pluralism means there are incommensurably different logics which are true/correct, then I disagree. If it means there are analogically similar logics which are true/correct, then I agree. But I don't think that all true logics are isomorphic. "Incommensurably" is meant as strong incommensurability, in the sense of excluding analogical equivocity.

The taxicab example is designed as a counterexample to the circle definition "a collection of all coplanar points equidistant around a chosen point", since the points on the edge of the square in Euclidean space are equidistant in the taxicab metric on that Euclidean space. It isn't so much an equivocation as highlighting an inherent ambiguity in a definition. — fdrake

Again, I think there is an equivocation on "distant." Equidistant qua circularity pertains to straight lines. The taxicab circle is premised on an extreme redefinition of "distance" - an equivocation.

The extensional difference between all of these different formalisms are the scope of what counts as a circle. A pluralist could claim that some definitions work for some purposes but not others, a monist could not. — fdrake

Although I don't hold to logical monism, this doesn't seem right. You are claiming that for the logical monist a token such as 'circle' can mean only one thing. I don't think that's right.

The Analytic dispute between logical pluralism and monism strikes me as a superficial dispute. The deeper question is univocal vs. analogical predication. That source abandons the more interesting question as soon as it limits itself to, a "model-theoretic definition." Pluralism looks like a poor man's analogicity, like trying to draw a perfect circle with pixels. My guess is that most versions of soft pluralism and monism are not even differentiable, unless there is some precise concept of "equally correct" logics or arguments (which I highly doubt).

To put it in super blunt terms, Euclid's theory would have as a consequence that the great circle on a ball is not a circle. The equidistant coplanar criterion would prove that the great circle on a ball is a circle. Those are two different theories - consequence sets - of meaningful statements. A pluralist would get to go "wow, cool!" and choose whatever suits their purposes, a monist would not. — fdrake

If they are different theories then they define different things, i.e. different "circles." The monist can have Euclidean circles and non-Euclidean circles. He is in no way forced to say that the token "circle" can be attached to only one concept.

To put it in super blunt terms, Euclid's theory would have as a consequence that the great circle on a ball is not a circle. The equidistant coplanar criterion would prove that the great circle on a ball is a circle. Those are two different theories - consequence sets - of meaningful statements. A pluralist would get to go "wow, cool!" and choose whatever suits their purposes, a monist would not. — fdrake

Nice. Now we are getting to an interesting bit, that the difference is not about the nature of logic but about logical method.

Have a quick look at What is Logical Monism?. I suspect you would enjoy it, since it draws on the parallels with mathematics that you are using here.