I think it is right to say that the OP is not language, but I think @fdrake, @Baden, and perhaps @Srap Tasmaner are working with mistaken premises in drawing that conclusion.

It's the same type of mistake that would claim body language is language by the way. It's not. It's just communication. — Baden

Suppose, I am in an interview and I fold my arms to communicate my nervousness. That is an expression that communicates something, "discomfort", which is publicly interpretable and which is often described as "body language". But it is not language. Folding one's arms could conceivably be linguistic as part of a system of sign language, but in that case it could mean anything. — Baden

Why isn't it language? You used a sign intentionally to communicate something to others. You folded your arms "to communicate." This looks like a form of sign language or body language, in a non-metaphorical sense. The only quirk is that the interpreters may interpret the sign non-intentionally, in which case it would be more manipulation than language. But they may interpret the sign intentionally. They may know what it means and cognize its meaning, and they may even recognize that you are intending to communicate nervousness (or something else like reticence). If someone with a great deal of self knowledge folds their arms I am given to know that it is not unintentional.

Same question. Why not just say not all communication is linguistic? — Srap Tasmaner

If someone thinks in pictures is their thought process therefore non-linguistic? Part of this is definitions, but some definitions will fare better than others.

@fdrake seems stuck on non-necessary norms of interpretation, such as spacing and punctuation. I would suggest that he think about coded language, such as encryption or the hidden signs involved in a football game or military strategy, where the linguistic matter is supposed to be unrecognizable according to standard norms.

You really don't need fluency, or even much understanding. to detect the presence of units of meaning. — fdrake

"Салам, куыдтæ дæ?"

What are the distinct symbol groups in that? Clearly, "Салам", "куыдтæ" and "дæ". It has a question mark at the end, so presumably it is a question. — fdrake

Did you know that spaces and punctuation were a later addition to written language? Kinda blows up your whole theory about "units of meaning."

Even if we make mistakes, it's still clear what trying to split this stuff up would mean in terms of a language. I doubt you can say the same form Baggs' stimming. — fdrake

What's to prevent her actions from forming the material for a language? I don't think that's what she is doing, but there is no in-principle barrier to her actions being linguistic. It is not the material object that is non-linguistic. Anything can become linguistic, including running your hand under water. It is the non-linguistic intention behind her actions that is non-linguistic.

I wanted to avoid semiotic language since, taking Baggs at her word, her language is nonsignyfing. — fdrake

Is there a different definition of language other than the semiotic one which is underlying such critiques? Or is that the basis of the critiques even if it is unspoken?

Autism is a disability because the person has no choice in the matter. There is the opposite malady of being unable to "stim" and being limited to discursive reasoning. But a good example of someone who consciously undertakes such a practice is the monk who meditates. Is that language? Is it dialogue? Is it linguistic? Is it sub-linguistic? Super-linguistic? I think that presents a clearer case, which could then be extended to the autistic (or not).

They might be. I inferred that Baggs' were since she spoke of a dialogue with her environment. — fdrake

This seems like a matter of basic semiotics. There is sign use and then there is intentional sign use. Language is the latter, and it is uniquely human. A dog licking its paw is the former, and humans are of course immersed in this sort of unintentional sign use as well, but it is not language. It is Helen Keller's transition from water-as-stimulus to water-as-sign.

Perhaps interaction with environment can become dialogue if the environment is addressed as Buber's "Thou," but usually this is not happening, and it doesn't seem to be occurring in the OP. At best what we have here is a metaphorical sense of dialogue.

I think the person wants their actions to be seen as meaningful and valuable. They can be that, but I don't think they constitute the intentional sign use which is language. It is a kind of cathartic manifestation of potency, which is different from language.

(Site was hanging and somehow double-posted)

They might be. I inferred that Baggs' were since she spoke of a dialogue with her environment. — fdrake

This seems like a matter of basic semiotics. There is sign use and then there is intentional sign use. Language is the latter, and it is uniquely human. A dog licking its paw is the former, and humans are of course immersed in this sort of unintentional sign use as well, but it is not language. It is Helen Keller's transition from water-as-stimulus to water-as-sign.

Perhaps interaction with environment can become dialogue if the environment is addressed as Buber's "Thou," but usually this is not happening, and it doesn't seem to be occurring in the OP. At best what we have here is a metaphorical sense of dialogue.

I think the person wants their actions to be seen as meaningful and valuable. They can be that, but I don't think they constitute the intentional sign use which is language. It is a kind of cathartic manifestation of potency, which is different from language.

Perhaps a better way of resituating language and communication is represented by Rowan Williams' recent review of Charles Taylor's new book, Poetry in the Age of Disenchantment, "Romantic Agenda." Williams' understanding of language is more robust in the way you might desire, and is more fully explicated in his Gifford Lectures, coalesced into his book, The Edge of Words: God and the Habits of Language. The lectures are available online.

(CC: @Srap Tasmaner)

- Good post. :up:

Common solutions: we introduce other toys so that everyone gets something (not an option in our example); no one gets it (not allowed in our example); they each get the whole thing because they will play with it together (not helpful for consumables, as in our example, which is why we split them); we divvy up not the toy but the time playing with it, take turns, and we can even measure the duration of those and make them equal-ish. — Srap Tasmaner

And are those constraints, empowerments, or both?

If physicalism is a metaphysical position, as you (and most everyone else) characterize it, then its only obligation to science is to be consistent with it and to not give it a priori constraints. — SophistiCat

I don't think the OP is ultimately about physicalism's obligation to science. I think it is about physicalism's claim to be a better (metaphysical) explanation, or at least a better scientific metaphysics.

But the strengthened liar's sentence persuaded me that there is at least an interesting formal concern. — Moliere

That's an interesting background explanation for why the "Liar's paradox" tempts you, but what I am hearing is that you are interested in playing a game that has nothing to do with reality. You have not answered the objections, and I don't see that Marx and Hegel have much at all to do with this issue. When you talk about "truth" and "falsity" you are not talking about truth and falsity; you are equivocating. We could play an arbitrary game and call the Liar's paradox "false," but we cannot call it false, and I have explained why.

I think this is all symptomatic of the decadence of contemporary philosophy, which is more a matter of novelties and entertaining oneself than actual philosophical engagement. On this point, there was a recent article about the filmmaker Terrence Malick and his encounter with droll contemporary philosophy, "Malick the Philosopher." This form of philosophy will be made to reckon with its own vacuity.

An afterthought -- in a way the pluralist is actually more anti-nihilist than the monist. The monist has to hold that contradictory statements cannot be logically comprehended which is, in a way, a baby nihilism: Here is the field of inquiry where no logical rules hold. — Moliere

Something like that. I would say that the so-called "monist" accepts that people can be wrong about things, and that that is probably at the pragmatic core of this thread. Truly, there is a mystery about how error can occur. But this was never a real thread. The people behind it were never interested in giving real arguments for their position, or even attempting to distinguish "monism" from "pluralism."

Edit: I realize this was curt, but I don't see the conversation going anywhere and so I am just setting out my view. I take it that Epictetus is much more interesting, substantial, and philosophical than the "Liar's paradox."

Coming back after being away for a few days… I think @Count Timothy von Icarus has successfully highlighted the fundamental problems in this thread and in Banno’s polemical approach. That aside, there are a few posts that deserve a response:

I disagree that that is what is going on. — fdrake

Whether or not it is what is going on, it is what is at stake, and that’s the point. Your construals avoid the problem of intent, and intent is the crucial aspect (e.g. when you talk about “verbatim” or “taking someone ‘exactly’ at their word”).

When someone stipulates a definition, they are committed to that definition insofar as it relates to the intended concept. — fdrake

I agree, but I really don’t think your approach in the discussion of square circles manifested anything like an attempt at close reading or an investigation of intended concepts. It was more an exercise in interpreting utterances as they suited your purpose (of arguing for square circles). Granted, it is no wonder that a polemical and insubstantial thread continued in polemics and lack of substance. You and I were just following Banno's lead in this, and it is why Banno should not be allowed to set the pace.

Which could equally mean "mind", "minds", "people"... — fdrake

And that was quite intentional on my part. When dealing with people prone to misrepresentation it is best to give a starting point which either makes them think or ask a question. If they do neither one then they show themselves to be uninterested in philosophical discussion. It is in no way surprising that Banno managed to do neither, and after dealing with this for long enough I’ve just put him on ignore. Indeed, my earlier definitions were more specific, and the later ones became more general in proportion to my realization that the instigators were not willing to look outside their paradigm.

-

Yes. I thought it went without saying. Some things people think of are more appropriate than others in some contexts, and strictly better by some metrics. Some fiction is more valuable than others. If a thingy works better than another thingy on every relevant facet, the first thingy is better than the second thingy.

How would you judge that for a given context? Well I suppose you'd look for examples, see what pans out, provide definitions of things to see if they capture the relevant phenomena... Maybe you'd refine your criteria for what counts as a good thing in a given context based on the what you've seen and what's been created, too. — fdrake

I’m still not seeing a straight answer. Why? Because you claim to be talking about metaphysics but then you qualify everything by words like “context,” “value,” and notions of artifice. Earlier when I asked if there is better and worse “fan-fiction” you again cleaved to the metaphor and gave examples of literal fan fiction.

I still have the impression that you think of this is as an Objectively Correct vs Subjective-Relativist sense, and I don't want to accept the Subjective-Relativist role in the discussion since the proofs and refutations inspired epistemology of mathematics isn't relativist in the slightest, because its emphasis is on communities of people agreeing on what follows from what by following coordinating norms and demarcating those norms' contexts of application. Minimally then, it's intersubjective, and communities create knowledge about collectively understood subject matters. — fdrake

So then do you think intersubjective agreement is metaphysics? Is that the goal? To try to garner agreement? The democratization of science?

I’m perplexed at how impossibly difficult it is for folks on this forum to think about metaphysics and to escape modern immanentism. Truth has been so thoroughly deflated that folks around here can’t even recognize the notion of truth when it shows up at the party. “Communities of people agreeing on what follows,” is a very common substitute, but also a very bad substitute! When peer review and intersubjective consensus shifts from a helpful aid to truth, to truth itself, something very problematic and bizarre has occurred. What began as, “A number of instruments agree, therefore they are probably telling us the truth,” shifted to, “A number of instruments agree, and we’ll just define that as truth qua truth.” This is substituting truth with agreement; metaphysics with intersubjectivity. This is a significant misstep. Einstein’s physics is not superior to Newton’s physics because more people agree with Einstein. It is superior because it has more purchase on what is actually occurring in reality; because it is truer. Agreement is an epistemic criterion, not a metaphysical criterion.

The modern world is merely anthropocentric. We have made everything about ourselves, our desires, and our values, so that this is all that even exists. To talk about something beyond that is not allowed. Science, metaphysics, and truth are barred at the gate, even to the point that we cannot say what a woman is.

In an artificially bounded task like this — Srap Tasmaner

Hmm? I find your lack of bounds more artificial than the OP. It is not artificial to say that there are unbroken wholes, such as chickens. The notion that everything is infinitely divisible is much more contrived than the alternative.

Life is not like that. — Srap Tasmaner

Sure it is. That's the point of the OP: life is exactly like that. I go to my sister's house and there are three kids who want to play with the same toys. Toys are unbroken wholes. The OP is immediately relevant. I go to the car dealership and I am offered whole cars. They don't let me buy a half car for half the money. Life is exactly like this.

Either we find a creative way to complete this subtask (making do with rough equality ― 7 or 8 each, cutting the strawberries, if that's an option, or switching measures, say from units to weight, and so on) or we mark this path off in the search and backtrack until we find a path. — Srap Tasmaner

If the OP were saying that it is a great tragedy that we can't divide the 23 chickens equally then it would be a dumb OP, but I don't see it saying that. What the OP is illustrating is equally present in all of the cases you are presenting. The curious relation between mathematics and reality is equally present with strawberries, and weight, and measurements of time, etc.

Reality, sure, but mathematics is how we conceptualize our situation and can inform both our choice of action and our method. Mathematics is adverbial. — Srap Tasmaner

But to a large extent it's not. If you think the indivisibility of the 23 chickens is merely a conceptual problem, then provide a different conceptualization in which the chickens can be equally divided. Can you do that?

You want to talk about choosing a different course, but the mathematics precedes that pivot. We choose to weigh the chickens instead of count them because we can't divide them in a numerically equal way. This decision doesn't moot the point of the OP, it presupposes it. We decide to weigh them because mathematics is not merely "how we conceptualize our situation." When my low fuel light comes on I will be able to drive for about 70 miles without fueling, regardless of how I conceptualize my situation.

Anywhere you want to look, it is plain as can be that thinking and acting mathematically is empowering for humans, not some implacable constraint. — Srap Tasmaner

It seems to be both, no? "Empowering, not constraining," is a story you're telling, but mathematics constrains and empowers. Limiting it to either side is an ideological move.

But for the general distinction in approaches, which this little problem illustrates, the entire business world disagrees with you, the natural sciences disagree with you, the various branches of engineering disagree with you. — Srap Tasmaner

These are bold claims given how little I've said. You seem crabby and contentious. Are you whipping up bogies to fight against? The OP is about whether mathematical explanations are causal explanations. That shouldn't be a contentious topic.

Well, I know it's all off-topic for this thread, but that passage you quoted resonated with me. — Wayfarer

Great. And thinking about it again, "indivisible" is probably not a great way to describe it. But it is somewhat different from advaita, at least in the sense that the undividedness is applied to being itself, which includes beings (plural). I.e. beings are also unified in their separateness. But I have not studied this question in any great detail.

-

I think @J's OP is interesting. It is something like: if mathematical necessity is not self-supporting, then whence is the necessity derived? There is an understandable temptation among some in the thread to grow impatient and fast-forward to the end instead of watching the whole movie. And that further question is a difficult one, having to do with such things as the transcendental of unum.

But the very idea that mathematical necessity is not self-supporting is important, even before we get to the further question. Mathematics seems to dominate logic, thinking, and philosophy in every age. We have a very strong intuition that mathematical necessity is necessity par excellence, and that it should be the model for thinking and reasoning. It is not obvious, historically or culturally, that mathematical necessity is not self-supporting or self-sufficient, and much could be gained by recognizing this.

I think what's strange about this problem is that the setup makes human beings helpless before the implacable necessity of mathematics, and that's the wrong story to tell. — Srap Tasmaner

That seems a rather strange way to express it, but what is your alternative? "If we are smart we will foresee that the chickens cannot be evenly divided, and therefore we will not try and will not be thwarted?" Either way the math/reality constrains our options.

In real life, a case like this is more likely to play out this way: you've got these 23 thingamabobs, and there's talk of splitting them three ways. You say, "Won't work," and someone less numerate than you says, "Well, let's just try." As they fail, with a puzzled look, they say, "Wait, I messed up somewhere. Let me start over." You will want to explain to them that it's impossible, because 23 is not only not a multiple of 3, it's a frickin' prime.

What's of primary interest here is that you, because of your relative expertise in mathematics, understand the situation better than the person who, even after trying and failing several times, still believes it might be possible. — Srap Tasmaner

I think that is a large part of the point, yes. Mathematics provides us with a grasp of reality even though it is not necessary in the strict way that we tend to conceive of it. But looked at from a different angle, there is very little difference between the less numerate and the more numerate. The less numerate just takes a few more minutes to recognize that something cannot be done. And it's not as if the more numerate recognizes this a priori, in no time at all.

But I am not sure it is a useful standard in this context since it seems to allow for refuting the dominant position(s) in terms in which its advocates wouldn't recognize it. — Count Timothy von Icarus

Sider calls this "hostile translation." From the QV/Sider thread:

This is what Sider refers to as a "hostile translation" on page 14. It is interpreting or translating someone's utterance in a way that they themselves reject. — Leontiskos

@fdrake wants to talk about "good counterexamples," and he relies on notions of "verbatim" or "taking someone exactly at their word" (even in a way that they themselves reject). The problem is that if these are still hostile translations then they haven't managed to do what they are supposed to be doing: they haven't managed to produce good counterexamples.

I have to say, I love the cheekiness of the cover. — Count Timothy von Icarus

Medhurst's Moses

https://commons.wikimedia.org/wiki/File:The_Phillip_Medhurst_Picture_Torah_457._Moses_breaks_the_tables_of_the_Law._Exodus_cap_32_v_19._after_Parmagiano.jpg

This is the principle that animates all living beings, from the most simple up to and including humans. it is why, for instance, all of the cells in a living body develop so as to serve the overall purpose of the organism. So the 'one-ness' of individual beings is like a microcosmic instantiation of 'the One'. — Wayfarer

Yes, and it's hard to say exactly how the animate and the inanimate relate on this score, but the convertibility of being and unum goes beyond animate realities. A rock, a molecule of H2O, a drop of water, a road, a river, a country, etc., are all one. They all possess a unitariness, so to speak, both as concept and reality.

Trying to get out of this thread, but...

a stipulated logical monist of a certain sort, that there is only one entailment relation which all of these logics ape. — fdrake

I called the pluralism/monism debate an internecine debate between Analytics because they are all univocalists. Your word "ape" here is doing a lot of work, but it seems that for both pluralists and monists such an entailment relation will be purely univocally predicable. This is why the whole game is so boring. The interesting question is an adjudication between two different paradigms, and folks like Banno and probably G. Russell are eternally stuck in a single paradigm, interpreting the other paradigm in their own terms.

My definition of logic via the Meno is something like, "That which creates discursive knowledge" (or perhaps just knowledge). Now is knowledge or discursive knowledge a univocal concept? I don't think so, and therefore there can be no univocal "entailment" relation that holds for all knowledge. For the univocalist this means that each kind of knowledge and each accompanying entailment relation are hermetically separate from every other kind, and that is precisely what analogical predication denies. This is probably something like Wittgenstein's "family resemblances," although I am not overly familiar with Wittgenstein. (And note again how drastically this univocal analysis deviates from natural language use.)

In the realm of circles we are asking about the relation between the pretheoretical grasp or notion of a circle and the formalization. We could say that the formalizations "ape" that pretheoretical notion, but the scrutiny here is entirely on the manner of aping. Yet in the case of knowledge there is something more concrete and even practical at stake in the question.

No True Scotsman doesn't admit of an easy formalisation in terms of predicate logic — fdrake

Yep.

I imagine monists are generally going to just deny this, because monism is about logical consequence relative to some non-arbitrary context — Count Timothy von Icarus

I think this is part of it too.

I'd also want to liken the relationship of formalisms to their intended objects, or intended conceptual content — fdrake

That is the big equivocation for me. Is it a relation to a non-mental reality or merely a conceptual content? Timothy's point about non-arbitrary contexts hinges on the answer.

My intuition is also that there are other principles that set up relations between the practice of mathematics and logic and how stuff (including mathematics) works, which is where the metaphysics and epistemology comes in. But I would be very suspicious if someone started from a basis of metaphysics in order to inform the conceptual content of their formalisms, and then started deciding which logics are good or bad on that basis. That seems like losing your keys in a dark street and only looking for them under street lamps. — fdrake

Sure, and I don't think this is controversial. But I don't think you've given a straight answer to the other side of the coin: are some formalisms truer than others? Is there better and worse metaphysical fan fiction? That's the nub. (And some grandchild of logical positivism is operative here, because the formalists are liable to say, "This question is not formally adjudicable, therefore there is no better or worse metaphysical fan fiction.")

(This central topic has been sidestepped in all sorts of ways. Wanting to talk about modeling or "correctly assertible" rather than truth is one of those ways. If some metaphysical fan fiction is better than others, then it is truer than others, and there is (non-deflationary) truth to be had.)

Unum in the same sense as in non-dualism, advaita, non divided. — Wayfarer

Or perhaps indivisible, and that seems to be a bit different. A chicken is indivisible. To divide it is to lose your chicken.

In your other thread we touched on the Scholastic transcendentals or convertibles. Another transcendental besides being and truth is oneness (unum). — Leontiskos

In this vein, this paper looks interesting, "being without one: deleuze and the medievals on transcendental unum."

There was consensus among the scholastics on both the convertibility of being and unity, and on the meaning of this ‘unity’—in all cases, it was taken to mean an entity’s intrinsic indivision or undividedness. [19] In this, the tradition was continuing and affirming a definition first proposed by Aristotle in the Metaphysics. [20] This undividedness, in the words of Aquinas in his Commentary on the Sentences, is said to lie “closest to being.”[21] For the most part, ens and unum were distinguished by these thinkers only logically or conceptually—unum adding nothing real to being, or more properly, adding only negation, only a privation of actual division.[22] It was common practice in medieval philosophy to distinguish the transcendental sense of unum, running through all of the categories, from the mathematical sense of unum, restricted to the category of quantity. These two ‘ones’ are each in their own way opposed to ‘multiplicity.’[23] Aquinas offers a succinct account of this in his Summa Theologiae (Ia. q. 11, art. 2).[24] The ‘one’ of quantity is the principle of number; it is that which, by being repeated, comprises the sum (the multiple).[25] Aquinas says that there is a direct opposition between ‘one’ and ‘many’ arithmetically, because they stand as measure to thing measured, as just-one to many-ones. Likewise, transcendental unity is opposed to multiplicity, but in this case not directly. Its opposition is not to the many-ones per se, but rather to the division essentially presupposed in and formal with respect to the multiplication of actual multiplicity. This tracks with a consistent distinction in Aquinas between division and plurality in which division is seen as ontologically and logically prior.[26] Transcendental unity then, has a certain priority to its predicamental counterpart.

We will return below to the consequences for contemporary ontology that follow upon this fact that, in its developed form, it was division, not plurality, that was taken by the classical tradition to be the precise contrary to transcendental unity. . . — Being without One, by Lucas Carroll, 121-2

If your prayers are answered you assume it was God who did the answering. — Metaphysician Undercover

And you think that one should still pray even if God doesn't exist?

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

Great posts. :up:

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

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. — Leontiskos

It seems to me that Sider's thread is the better place for this, but what you describe here doesn't really sound like metaphysics at all. The only point that sounds like metaphysics is the fanfiction metaphor, but if the fanfiction cannot be good or bad then one cannot be doing metaphysics, and are you willing to say that the fanfiction can be good or bad?

- Good to know.

- Good points.

One of the great things about producing formalisms is that they're coordinative. — fdrake

Coordination, cooperation, intersubjective agreement, etc., really tends to be the goal and limit of contemporary thinking. I think such things are useful, but I also think that at some point we have to venture out beyond the bay and into the open sea.

Seems right.

There is also a really odd thing that happens constantly on TPF (and it usually happens with SEP). Someone will champion a position like logical pluralism or dialetheism or something like that, but when it comes down to the question of what exactly they are promoting they are at a loss for words. They don't have any clear definition of, say, logical pluralism.

So we go to a secondary source like SEP or Griffiths and Paseau. But as soon as the content of the position is being taken from SEP and not from the TPFer we are no longer engaging/arguing with that TPFer. The TPFer had superficially identified with logical pluralism without being able to say what logical pluralism is, or what they mean by it, and when one flies over to SEP they have overlooked the crucial nature of this conundrum. SEP is not going to tell us what the TPFer thinks; it is only going to tell us what the author of SEP thinks. The thread becomes the discussion of a position that no one in particular holds, and that no one in particular has a stake in. In my opinion this outlines one of many misuses of SEP on TPF. Yet there is a fascination in our contemporary culture with labeling and labels!

...And to be specific, after this thread was necro-bumped Banno did the thing, "Yay for logical pluralism! Boo for Leontiskos and his logical monism!" What did Banno mean by logical pluralism? He had no real idea. Why did he think I was committed to logical monism? Again, probably no idea, although everyone took him at his word (!). It was a half-baked thought meant to stir up controversy, and that is the heart of the problem. Bringing in something like SEP is not going to make that initial move impressive or substantive.

- So apparently if you didn't get a good look at the guy who hit you, you would just assume it was Tyson. I still don't see how you would write him a letter if you don't believe he exists.

But again, virtually no one wants to claim that truth should be both deflated and allowed to be defined arbitrarily. So we still have the question (even in the permissive case of Shapiro) about what constitutes a "correct logic." The orthodox position is that this question is answered in terms of the preservation of "actual truth." But we also see it defined in terms of "being interesting" (e.g. Shapiro). Either way, we are right back to an ambiguous metric for determining "correct logics," hence to common appeals to popular opinion in these papers. — Count Timothy von Icarus

Right. As I said earlier, a basic challenge for the pluralist is to show which logics are acceptable/correct and which are not. I haven't seen anyone in the thread attempt such a feat, and if that can't be done then I'm not sure a serious position is being put forward. The same could be said for nihilism or monism, but no one has claimed such positions.

That reads disingenuously to me. Your use of "roundness" previously read as a completely discursive notion. If you would've said "I think of a circle as a closed curve of constant curvature" when prompted for a definition, and didn't give Euclid's inequivalent definition, we would've had a much different discussion. I just don't get why you'd throw out Euclid's if you actually thought of the intrinsic curvature definition... It seems much more likely to me that you're equating the definition with your previous thought now that you've seen it. — fdrake

I gave that option before giving Euclid's. You are the one who brought up Euclid in the first place, but I really don't see the two descriptions as competing.

The latter of which is fair, but that isn't a point in the favour of pretheoretical reasoning, because constant roundness isn't a concept applicable to a circle in Euclid's geometry, is it? Roundness isn't quantified... — fdrake

Pretheoretical or intuitive reasoning need not be quantified, does it? In making that comment I was making the point that pretheoretical reasoning represents the same basic idea as the calculus definition you gave. "...In calculus [consistent roundness] cashes out as a derivative, but folks do not need calculus to understand circles. Calculus just provides one way of conceptualizing a circle."

Mathematical concepts tend to be expressible as mathematical formalisms, yeah. And if they can't, it's odd to even think of them as mathematical concepts. It would be like thinking of addition without the possibility of representing it as +. — fdrake

Well then I would ask whether the intuitive concept that is the intended concept is a mathematical concept. When a child learns to place circle-shaped blocks in circle-shaped holes they are not involved in formal geometry.

And therein lies a relevant distinction. Formalisms aren't prepackaged at all. In fact I believe you can think of producing formalisms as producing discursive knowledge! — fdrake

Or rather, producing a thing that can produce discursive knowledge. And knowing a true logical system is a kind of knowledge, which is probably discursive. I think that's right. But they are prepackaged in a very relevant sense, particularly for those of us who are not their inventors.

But I also don't think a logic like Frege's is merely a model, nor that it could be. To invent a logical system is to attempt to capture a (or the?) bridge to discursive knowledge, and I don't know that any success or failure is complete.

But you also seem to think the context you have in mind for any question that arises is the only context it can possibly arise in. — Srap Tasmaner

Rather, if the context is different then the geometrical response is different, and I have no dog in the fight over the question of "family resemblances" as applied to geometrical abstractions. I have claimed that there are not square circles, not that "circle" can only ever be utilized within a single context.

There will be Euclid circles in that space which are not Aristotle circles too, I believe. — fdrake

Sure.

I believe "A closed curve of constant positive curvature" is the one the differential geometry man from above would've said — fdrake

Yes, or:

We could say that a circle is a [closed] figure whose roundness is perfectly consistent.* There is no part of it which is more or less round than any other. — Leontiskos

The discussion about capturing the intended concept is relevant here. The interplay between coming up with formal criteria to count as a circle and ensuring that the criteria created count the right things as the circle. That will tell us what a circle is - or in my terms, what's correctly assertible of circles (simpliciter).

That's the kind of quibble we've been having, right? Which of these definitions captures the intended object of a circle... And honestly none of the ones we've talked about work generically. I believe "A closed curve of constant positive curvature" is the one the differential geometry man from above would've said, but that doesn't let you tell "placements" of the circle apart - which might be a feature rather than a bug. — fdrake

But what is the "intended concept"? Presumably it is an intuitive concept, and are intuitive concepts mathematical formalisms? I wouldn't think so. So:

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

Why think that the intended concept is a formalism, a mathematical equation? Similarly, why think that logic is a formalism, a logical system? Perhaps logic is as I've said: that which produces discursive knowledge. It is a natural or anthropological reality, not a prepackaged formalism.

- Fair enough. Or I suppose the person could respond to the quibbler, "If the center was deleted—per impossibile—then there would only be an Aristotelian Circle."

Perhaps you can see my complaint. Given that the sort of mathematics we are engaged in is in an important sense limited only by our imaginations, so too quibbles are limited only by our imaginations. For example:

Edit: And why can't a quibbler say that R^3 and even R^2 spaces are not Euclidean? What's to stop him? When is a disagreement more than a quibble? — Leontiskos

The flip side of this is that mathematical concepts seem to become purely stipulative and imaginary when viewed in such a way. In that case the ground rules for something like propositional logic lose all coherence and plausibility—as do all concepts—once we have dispensed with the notion of the true or useful. It then becomes nothing more than Banno's "symbol manipulation." That's why I keep asking things like this:

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? — Leontiskos

Gonna call it for tonight and rethink stuff, though obviously not in your favor :D — Moliere

Fair enough. :wink:

I'd appreciate you answering my question about whether or not paraconsistent logic would count as a plural logic insofar that we accept both paraconsistent logic and classical logic. — Moliere

Yes, I didn't really understand it, and it seems like neither you nor I have a firm grasp on what it means for something to be a paraconsistent logic. Like probably everyone on TPF, I have read about paraconsistent logic as I read about animals in a far off land, but I have never worked with it or made use of it. They seem to be used mostly in the way that Aldous Huxley used his encyclopedia entries.

Are you asking me whether I think that accepting both paraconsistent and explosive logic results in the robust kind of logical pluralism? My guess is that I would answer 'no.' Paraconsistency does not entail Dialetheism. And paraconsistent logic is often used informally in everyday life (if that counts). I also haven't seen anyone in this thread who favors logical pluralism embrace Dialetheism - other than yourself, of course. They seem to be mostly Augustinians, "Lord, give me logical pluralism, but not yet!"

Because every Aristotle Circle can be shown to be a Euclid Circle and vice versa. — fdrake

Suppose the quibbler has "deleted" the center, and therefore it can only be shown to be an Aristotle Circle?

Then we're using Euclidean space differently. To me a Euclidean space is a space like R^3, or R^2. If you push me, I might also say that their interpoint distances must obey the Euclidean metric too. Neither of these are Euclid's definition of the plane. "A surface which lies evenly with straight lines upon itself" - R^2 isn't exactly a surface, it's an infinite expanse... But it's nice to think of it as the place all of Euclid's maths lives in. R^3 definitely is not a surface, but it is a Euclidean space. — fdrake

Okay, so R^3 is a Euclidean space and R^2 is the place where all of Euclid's mathematics lives. I mean, your early insistence on locating Euclidean circles in R^2 is why I am thinking of R^2 as Euclidean space. Apparently you are making the "...ean" of Euclidean do a lot of work here.

Edit: And why can't a quibbler say that R^3 and even R^2 spaces are not Euclidean? What's to stop him? When is a disagreement more than a quibble?

You also disagree with him strongly if you like Euclid or Aristotle's definition of a circle. I actually prefer his, since you can think of the car wheels as its own manifold, and the one he would give works for the great circle on a hollow sphere too. I think in that respect the one he would give is the best circle definition I know. Even though it individuates circles differently from Aristotle and Euclid. — fdrake

None of this matters much to me. I only took Euclid's definition as a point of departure or something I would be comfortable with. But I view Euclid's definition as describing a relative property of a continuous curved line that forms an enclosed shape, which is probably why I don't think the center can be "deleted."

I'm not familiar with Aristotle's definition of a circle at all. I might not even understand it. Though, if I understand it, I think the two definitions are equivalent in the plane. So there's no disagreement between them. Which one's right? Well, is it right to pronounce tomato as tomato or tomato? — fdrake

But why couldn't a quibbler say that their definitions disagree on account of the formal differences between them?

- If you write a letter to Mike Tyson asking him to punch you in the face, and the next day a random guy on the street punches you in the face, has your petition been granted? Would you still await a response from Tyson?

The restricted sense of "pray" is just an accident of contemporary English. The concept traditionally has to do with petition:

early 13c., preien, "ask earnestly, beg (someone)," also (c. 1300) in a religious sense, "pray to a god or saint," from Old French preier "to pray" (c. 900, Modern French prier), from Vulgar Latin *precare (also source of Italian pregare), from Latin precari "ask earnestly, beg, entreat," from *prex (plural preces, genitive precis) "prayer, request, entreaty," from PIE root *prek- "to ask, request, entreat."

From early 14c. as "to invite." The deferential parenthetical expression I pray you, "please, if you will," attested from late 14c. (from c. 1300 as I pray thee), was contracted to pray in 16c. Related: Prayed; praying. — Pray Etymology

And as such, prayer is not restricted to God, worship (latria) is.

An incline plane in a Euclidean space is definitely a Euclidean plane. An incline plane can't contain a circle just rawdogging Euclid's definition of a circle, since an incline plane is in a relevant sense 3D object - it varies over x and y and z coordinates - and is thus subsets of it are not 'planar figure's in some sense. — fdrake

I agree, but that's why I would not say that an incline plane in a Euclidean space is definitely a Euclidean plane. I don't see that there are incline planes in Euclidean space.

However, for a clarified definition of plane that lets you treat a plane that is at an incline as a standard flat 0 gradient plane, the "clearly a circle" thing you draw in it would be a circle. — fdrake

But here too, I would say that you are confusing a "flat" plane with a Euclidean plane. A Euclidean plane is not a "0 gradient plane," it is a plane without any gradient dimension whatsoever. I have been overlooking these sorts of errors, but if you are going to be persnickety about what you see as my errors then I suppose I should return the favor, especially given that you haven't shown interest in trying to mete out the question of why/when we should disagree.

I have had a similar experience to this. It was a discussion about rotating an object 90 degrees in space, and having to consider it as a different object in some respects because it is described by a different equation. One of the people I spoke about it with got quite frustrated, rightly, because their conception of shape was based on intrinsic properties in differential geometry. I believe their exact words were "they're only different if you've not gotten rid of the ridiculous idea of an embedding space". IE, this mathematician was so ascended that everything they imagine to be an object is defined without reference to coordinates. So for him, circles didn't even need centres. If you drop a hoop on the ground in the NW corner of a room, or the SE, they're the same circle, since they'd be the same hoop, even though they have different centres. — fdrake

Yep, I sympathize with him.

Which might mean that a car has a single wheel, since shapes aren't individuated if they are isomorphic, but what do I know. Perhaps the set of four identical wheels is a different, nonconnected, manifold. — fdrake

People really will say that they have four of the same tires.

But the same question about Euclid's Circle vs. Aristotle's Circle is arising here. If there is no right answer to these questions then there are no real questions, and in that case I don't know why we're arguing.

I can't tell if you're just being flippant here (which is fine, I enjoyed the razz), or if you actually believe that something really being the case is impossible to demonstrate in maths (or logic). Because that would go against how I've been reading you all thread. — fdrake

I'm being flippant, but not "just." :wink:

But no, I take it that your "correctly assertible" means something like "justifiably assertible," and on that reading I think it is correctly assertible that the cross-section contains a Euclidean circle. At the same time, I think the phrase "correctly assertible" is only a placeholder for further explication, because justification doesn't have food to eat unless there is a truth of the matter, at least on the horizon.

Do we get a referendum on what topics we have a referendum on? — unenlightened

:lol:

Are mathematical truths necessary if mathematics is grounded in the contingency of the world?

So where are abstractions taken from? I suggest "the world" is a sensible answer, and one that explains the "mystery" rather well. — unenlightened

But you said:

If you have 23 objects you have already mathematicised them by counting — unenlightened

Apparently you should have said, "If you have mathematized objects you have already had recourse to the 'pre-mathematical' world."

If the abstraction of mathematics is derived from the world, then the indivisibility of the 23 is more than a merely mathematical fact.