Thinking of all systems as univocal would appear to be putting unnecessary restrictions on the development of logic. — Banno
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
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
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. — Banno
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
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
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
One answer, which you've provided, is that the sentence means nothing.
It's not the only one though. — Moliere
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.
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
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
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
What does it mean to "say something"? — Moliere
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
Is that wrong somehow? — creativesoul
All lines of circumference encircle space. — creativesoul
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.
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
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.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
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.
I don't see why one must accept this:
All lines of circumference encircle space.
— creativesoul — Leontiskos
But what is the point here? — Leontiskos
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
there are square circles. — 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. — creativesoul
Just wondering if I've understood something. — creativesoul
My interest was piqued by the claim that a line of circumference around a sphere was a circle. — creativesoul
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
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
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
You've made it plain that you don't accept Dialetheism, and will give no reason, so the point is moot. — Banno
It's like "This sentence has six words" in some ways — Banno
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?
Does the circumference of a (Euclidean) circle encircle space? Yes, two-dimensional space. — Leontiskos
But I never assented to any of these sorts of interpretations. — Leontiskos
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
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
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
As noted, the taxicab case involves equivocation, not substantial contradiction. — Leontiskos
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
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
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
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.
You forgot that Euclid specifies a circle as a plane figure. — fdrake
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
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
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
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
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
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
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
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
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
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
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
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.