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. — Leontiskos

I never intended to say groups of symbols were necessary for something to count as language, I think it's essentially a sufficient condition to be able to recognise units of meaning. In the context of the discussion, I was showing a sufficient condition for recognising the presence of units of meaning without there being an understanding of the underlying language. Which was a counterpoint to the idea that one cannot hope to recognise whether something is a language unless one already speaks it.

;) I dare you to find the different particles in the word. And before you think of it: the ' symbol in the text is a normal letter in the Hebrew alphabet (Jod). You can find this and more examples on page 160 of the grammar I linked before. — KrisGl

All I meant was that there were recognisable units of meaning. The example you gave is a unit of meaning. I would have no idea wtf it means, there are still marks on the page. You even split it up into units of meaning for me.

There are plenty of examples like that, like making the sound iu-a'o in Lojban prior to saying an activity acts as an incredibly specific audible emoji. There isn't a translation of the attitude into English, or of the attitudinal indicator into English - it's still a unit of meaning!

You really don't need fluency, or even much understanding. to detect the presence of units of meaning. The fact that such a thing is so difficult for Baggs' stimming indicates that if it is a language, it is unlikely to be like any hitherto known one. It also will have only one "speaker".

Ok! And can you make the argument you intended to with the reference too?

I told you already that I don't think I can, because I do not speak that language. Take me by my word. I could make some elaborate counterargument now by introducing you to the nature of pre- and suffixes in the hebrew language and how you can cram a sentence into a whole word and how someone not familiar with that language would not be able to distinguish the different parts of one word that make up a whole sentence. I will not bore you with it. — KrisGl

You wouldn't bore me with it.

I don't speak this language. — KrisGl

You don't need to to try.

"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.



What are the distinct gestures in this ASL poem?

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. Can you do it?

Sometimes ticks include cursing. Would you know from the outside if my cursing is me cursing or me having a tick? — KrisGl

You can tell that over time. People who curse as the result of a tic do so in wildly variable circumstances and seemingly independently from them. For a single instance of cursing, you might not be able to.

What units exactly would be fine enough for you to consider something a language? — KrisGl

I don't know. Try going through her tap water scene and dividing it up into distinct events of qualitatively different character that might be used for expressing something! I'll respond further when you've tried something like this.

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. — Leontiskos

I wanted to avoid semiotic language since, taking Baggs at her word, her language is nonsignyfing. It doesn't have symbolic representation. You might think of that as a contradiction in terms, which would be another way to undermine its claim to be a language.

Why is that exactly? — KrisGl

Because AFAIK it's known that stimming is tightly linked with autistic people's emotional regulation. If you must suppress stimming, the self regulation goes out of whack. Another reason I want to think of it as autonomic is related to what you said here:

Whether or not there is intent or meaning(s) behind them ... we still don't know. — KrisGl

that likens her behaviour to stroking one's hair, scratching yourself, finger twiddling etc. None of which need be carried out with intent.

And how about the question if you would consider a sigh or a yawn part of language? — KrisGl

Someone can sigh in response to something, or at the end of a long day. A sigh in itself I wouldn't want to call an item of language in all circumstances, even though it is a sound that allows predictable expressions in some contexts. Like when it's a response to a request. But in others it isn't - like when you do it when frustrated. Compare the above to a word or a gesture in sign language. In contrast, "egg" is always "egg", an "a" sound is recognisably always an "a" sound. Can you say the same for Baggs' finger rubbing in the tap? Can you even say what this finger rub means vs that one? Can you even tell when one ends and one begins? There just aren't units of fine enough graduations to represent the continuum of behaviour she has.

A yawn is also something unintentional, but you "feel a yawn coming on", and can't suppress it. It's even unpleasant to try suppress. There's a sense of relief and normality afterwards. In that regard I think it's a better analogy for a stim than thinking of it as a language.

If you know an autistic person's stims, I think you can treat them as indicative of their mood sometimes. Some people have stims that only come out when very distressed, some people have stims that only come out when happy. If you knew what was what for a person, you can read it like a facial expression. Even though facial expressions aren't language either.

Okay. So language is something that can only happen when there are people agreeing on a standardized meaning of sentences, words, gestures? — KrisGl

Yes I think so. At the very least, something needs to be standardisable even if it isn't yet standardised. I don't believe Baggs' stimming is standardised, and I don't think it's standardisable in the same way as items of language are either. It's repetitive, there are patterns and types of things but... you can say the same of almost any process.

So "to individuate" stims means to be able to ascribe different meanings to each part of action within one stim (playing with the water)? — KrisGl

Yes. It is difficult to ascribe parts to the stimming. When her hand is moving back and forth in the water, should we just think that the first bit where she's relatively slow and the second bit where she's relatively fast count as distinct "units" which we could interpret as items of language? What about the variations in hand angle, which fingers feel the water etc within the units?

I mean ... we can certainly individuate the different stims (playing with water, moving hands in the air) and the different actions within one stim (moving slowly one second, then faster the next), right?'

Absolutely. It's just that you can't split the stims up from within them easily. Do all the bits of her humming have the same meaning? Does her humming change meaning when her hands flap? What about when she rocks? What about when she paces back and forth? Is she saying one thing or two things? Is her rocking and her humming one unit and her flapping another?

We just are not sure about the meanings these actions have or if they have meaning at all.

I think the situation is even more ambiguous. If we take her at her word, and that she's in a constant state of reciprocal connection with the environment, it would be really weird if we could only ascribe meaning so broadly. She spent a long time humming, and we'd have to reduce that to "her humming".

Whereas eg I've spent a long time typing this, and you can see where the letters are, where they end, which marks count as what words etc. You can tell that I'm doing certain things with the words - like elaborating, like answering questions, like making arguments, like analysing concepts etc. What I'm doing is language, and I'm also using language to do stuff.

If you were an anthropologist 6000 years from now and discovered this post, it would be recognisably language even if you didn't know what it meant at all - because you can see language's hallmarks.

I don't think you can say any of this about Baggs' stimming.

Frankly, though this is a bit off topic, I also think interpreting Baggs' stimming as language has the opposite of its intended life affirming/depathologising effect for autistic people. It's framed as a response to her being believed to be inferior because she has a speech disability. But it addresses this by framing her stimming as a language, thus undermining the speech disability claim. There doesn't have to be anything pathological about being disabled. Though I appreciate that calling her stimming a language can normalise that aspect of autism in some contexts.

I do wish that stimming was understood more like yawning than like language. Something autonomic.

What exactly distinguishes language-action from other forms of action? — KrisGl

I would say that an item of language needs to be standardised, or at the very least standardisable. Like words have wrong ways to pronounce them, sentences have grammatical errors, words can be misspelled, some gestures are seen as displaying an emotion in some contexts - like getting in someone's face, and it would not be seen as intimate. There needs to be something in the action that allows it to be standardised in order for it to count as an item of language in some context.

And I don't think her stims can be standardised in the above way. They probably can't even be individuated - can you tell the difference in significance of the water, or Beggs' relationship with her environment, when she changes the speed her fingers move against the water's current? When she's splashing or following the flow?

I assume you consider stims to be an action as a response to an emotion. — KrisGl

They might be. I inferred that Baggs' were since she spoke of a dialogue with her environment. Though some of them might not be about enacting some part of her mental state - eg when she seems to be pitch matching background noises with her humming.

Broadly speaking I thought that stimming was a response to an emotion - but in the sense that stimming is part of self regulation for autistic folks. Stims can be like sighs. They can also be like yawns.

I assume that, because you paralleled rubbing the face on a toy with someone going for a run when they are sad before. Is that correct?

In the context of what I wrote, I was trying to infer "her side" of the dialogue, the parts of her environment-person relationship that she was experiencing and what was structuring her intentions. And I found it difficult to imagine that such things make sense as items of language, they seemed much more like singular sensations and feelings, or like shifting on your feet to balance.

Do you believe what Baggs is doing counts as language?

And language is definitely not something like ... let's call it an "action" (going for a run when sad). — KrisGl

I think language is a subset of action. Just there are some actions which aren't instances of language.

Could you maybe explain what you mean with "phenomenology" of the two different rubbing stims here? — KrisGl

By phenomenology I mean the qualitative character of the experience and that experience's elements' significance in the life of the person who is having it. The felt stuff and its structure. As opposed to the performed stuff, the gestures and movements and sounds.

In the context of my post, I meant the reference to phenomenology in a certain conditional way. That if the states associated with her stimming were instances of communication, they would need to communicate some aspect of the state through gesture. Which would be difficult, if not impossible to do, if we take the Mel Baggs at her word that she is in a state of "dialogue" with the felt character of the environment.

For an example - what can you infer about Mel Baggs' state of mind from the section of the video in which she's stimming with the tap water? Is that state of mind what she's presenting?
Can you say that she's saying anything with it? Or does the motion have some intimate and singular significance to her? I think it's more accurate to think of Mel Baggs behaviour as a series of stims rather than as a language or as communication.

I don't think it makes sense to think of it as communication. Since there is no message, only receptivity and exploration. It also doesn't make sense to think of it as a language, since there's nothing like syntax arranging language items, there are only repetitious behaviours.

Consider the face rubbing stim. You can rub your face on two different soft toys in the same way, the phenomenology of those acts can differ radically even if the rubbing stim is the same. Thinking of the stim as a language item, it must have a reproducible content of some sort, and since the phenomenologies differ so much it would difficult to call the content of the stim state reproducible.

By reproducible X, I mean that something which counts as X could be done again. I think you only get her stims type identified - face rubbing soft toy stims are face rubbing soft toy stims, rather than "this state at this time type items", like you'd be able to get with "the dog I walked today".

There'll be some autobiographical detail which would allow an intent on her part to be inferred, which would form some reproducible context around the act - maybe she rubs her face on one toy in one circumstance, and one in another. But there's nothing to distinguish the latter from, say, someone going for a run when they feel sad - which isn't a language.

I thus thing it's a bad idea to call her stimming a language because it misses necessary properties of language - reproducible and structured presentation - and also that if it were language, it makes something like going for a run when sad language, which definitely is not language. I also don't think it's right to call it communication, since there's no reproducible message.

What is in the video? — I like sushi

It's only 8 minutes long.

Welcome to the forum!

Spitballing here.

Spite is an underrated motivator. But I don't think it's healthy to be the unique motivator in your life. If I'm motivated to do something, I think I'll experience that motivation as a result of one of the following drives or causes:

• A sense of need - this might be for food or social contact or routine tasks.
• A sensation of nervous energy - this might be for a deadline or deescalating a fight.
• A sense of duty - doing what I perceive is right regardless of any circumstance to the contrary.
• A sensation of pleasure - it just feels good to do the thing or to keep going.
• A sense of purpose - the task satisfies a deeply held belief or desire.
• A belief that it would be funny.
• A belief that the behaviour would be transgressive in a satisfying way.
• A feeling of anger - at injustice or a perceived wound/slight.

I'm sure there are many others.

Some of these states are sustainable, if often used, and some of them are not. The sense of need for food, social contact or routine tasks is something that can come and go without much effort, and can thus always serve its purpose. The sensation of nervous energy has contexts in which it is helpful and contexts in which it is unhelpful - the stress of nervous energy will impact you if it is sustained. Being bound by duty regardless of your other principles is taxing - often so taxing that a person's preferences will change to match their duties. The sensation of pleasure is sustainable, but the body quickly adapts to it and the sensation reduces. Humour and transgression are circumstantial, even if the attitude which sustains them is a facet of personality and thus always possible as motivations. Anger comes and goes quickly.

Of these drives, only duty, purpose, humour and transgression are things which can be cultivated through trying to improve one's resilience and insight. If a person can combine them, as you might with transgression through spite to act in accordance with a higher purpose, perhaps the motivation is heightened and easier to reinforce.

However, perhaps one needs to be careful that sustainable motivations are only mixed with sustainable motivations when trying to cultivate drive. Transgressive spite with a sense of purpose, that is a humorous lifestyle of a sort in which one's passions are exercised, transgressive spite with a sense of purpose and anger will make you persist in a state of stress if called on as one's principal drive.

Thus a person has to be careful how they mix their states and projects to cultivate their drive, else you end up poisoning yourself against your own nature over time.

↪fdrake Is that much different to ↪TonesInDeepFreeze or ↪Banno or to ↪Michael? Looks as if we have broad agreement. Always cause for concern. — Banno

It isn't much different no.

~G→~(P→A)
~P
G — Banno

Mostly spitballing.

The offending equivalence (this is logically valid).

(¬G→¬(P→A))↔((P→A)→G)

The latter: "If a prayer is answered by god, then that god exists"
The former: "If there is no god, then if something is a prayer then that prayer will be unanswered by that god."

Then you introduce ~P into the mix.

(((¬G→¬(P→A))∧(¬P))↔((P→A)→G)∧(¬P))

Those are still equivalent, you just conjoin ~P to both sides. If you encountered ((P→A)→G)∧(¬P)) out in the wild, you'd think "if something is a prayer, then it is an answered prayer, and that implication being true implied god existed" + "something isn't a prayer", you'd wonder why the hell anyone would be talking about something not being a prayer when it'd need to be an answered prayer to be relevant. It's a bit like trying to test a cat at the vet for a dog's illnesses.

Another thought regarding it is that the concept which makes the argument work is that if some prayers are answered by God, then God exists... Which looks a bit like (A→G). Rather than (P→A)→G. The equivalence between those two parsings isn't valid:

(((P→(A→G))∧(¬P))↔((P→A)→G)∧(¬P))

since its countermodels are P false, A false, G false - IE no prayers, no answered prayers, no gods. The fact that A false G false is part of a countermodel to the equivalence and are also the facts which made the OP's argument seem paradoxical makes me believe that translating the natural language into (((¬G→¬(P→A)) makes us think we've translated (((P→(A→G))∧(¬P)) into formal language, when we haven't. Which translation is of the two is not, in this instance, an innocuous choice.

The latter translation is also suspect - you can read it like "if I pray then all prayers answered are answered by god".

I prefer the latter analysis, an ambiguity between A->(B->C) and (A->B)->C that we don't notice much. But I get the impression that you could design other paradoxes to slip through this latter analysis.

Is there better and worse metaphysical fan fiction? That's the nub. — Leontiskos

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.

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.

If you read through Proofs and Refutations, which is an amazing book, the most clear cut resolution and associated proof of the book's central topic is offered using an entirely separate formalism than what had been considered up until that point. It was a substantial theoretical innovation and reframing that cleared away the old problems, but was nascent within them. Lakatos' approach has a dialectical flavour in that regard.

It is interpreting or translating someone's utterance in a way that they themselves reject. — Leontiskos

I disagree that that is what is going on. When someone stipulates a definition, they are committed to that definition insofar as it relates to the intended concept. Rejecting a criticism of a definition on the grounds that the criticism doesn't portray your intents is a fine thing, so long as it isn't pointing out something which your stated commitments entail. Isn't this a basic idea in reasoning itself, playing out in how people codify ideas?

Indeed, you offered an alternative informal definition of logic:

"That which creates discursive knowledge" (or perhaps just knowledge) — Leontiskos

Which could equally mean "mind", "minds", "people", "institutions", "thought processes", "scientific experiments", "scientific theory", "perceptions", "deductive reasoning", "deductive reasoning using formalisms" and so on. Which are perhaps in the intended scope, and perhaps not.

But something like a research institution creates knowledge in a sense, and I doubt that is in the scope. And we could play the same game as we played with the formalisms out in natural language. What would make a research institution fail to be logic?

The book "Sophie's World" is a good starting place. I recently picked up "Plato and a Platypus Walk Into a Bar...", which is a bunch of introductory snippets on various parts of philosophy but illustrated with jokes.

Both of these give you a taste of various topics without having to do too much work. I think it would be a good idea for you to find out something you're interested in in it so that you know what you read next. At least gives you some key terms to google.

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

Thanks. It looks a little bit like a Chuck Tingle cover.

For instance, G&P frame the position they want to argue against as: "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." — Count Timothy von Icarus

Can you link me this paper please? If it hasn't been done already.

Maybe no "metaphysical" notion is needed and we just speak in terms of "plausibility" and "usefulness" but these seem to easily become even murkier notions. The two most common versions of pluralism (Beall and Restall and Shapiro) cited have very different notions of which logics should "count" for instance. — Count Timothy von Icarus

My intuition is that the rules which bind coming up with mathematical formalisms are the same as those which govern writing fiction. They're in general loose, murky, descriptive, but you can tell a good description from a bad one. I'd also want to liken the relationship of formalisms to their intended objects, or intended conceptual content, to the relationship some writers have with their characters. They don't always know what the character wants, how the character would react, but they'd be able to work through how they'd feel and act if they put them in a scenario. That lets them write in a manner true to the character. I think formalisms have a similar "true to the character" expressive flavour, and the concept of an interpretation lets you come up with "scenarios" and "story beats" to flesh out the understanding of the concepts and what's written about them. Interpreting your own symbols in that extensional sense is a way of finding the meaning of what you've written. And just like writing fiction, you can find the conceptual content very resistive to your expression. A theorem may escape you just like how to put a scene.

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.

No worries. I do think your insistence that the extensional understanding of truth is deflationary in this context is imprecise. If I understand correctly, you're using "deflationary" to mean restricting the interpretations of a theory to all and only the ones which are syntactically appropriate and clearly within the logic's intended subject matter. Like propositional logic and non-self referential statements. Effectively removing everything that could be seen as contentious from the "ground" of those systems. Which would then ensure the match of their conceptual content with whatever objects they seek to model, (seemingly/allegedly) regardless of the principles used to form them. Which 'deflates' truth into unanalysable, but jury rigged, coincidence.

By contrast, correspondence would consider truth as a relation between the conceptual content of a theory and its intended object.

So you can come up with a logic where modus ponens holds, and come up with a logic where modus ponens does not hold. Which would mean that if you wanted to find The Logic Of All and Only Common Principles (tm), you'd need to jettison modus ponens. Since it is not a common principle, since two logics disagree on whether it is a theorem. — fdrake

Just for extra detail - how easy it is to come up with logics that disagree on theorems is a good argument for nihilism if you agree, with a stipulated logical monist of a certain sort, that there is only one entailment relation which all of these logics ape.

The cases approach allows us to say more about what logical nihilism amounts to: it is the view that for any set of premises Γ and conclusion φ whatsoever, there is a case in which every member of Γ is true, but φ is not. — Russell

I underlined "any" and "there is a case" above to highlight something about their scope of quantification. What collection is being quantified over? It must generically include arbitrary cases, premises, conclusions etc. IE, "complete generality" in a manner that allows the arbitrary representation of statements in formal languages. It's thus a metalinguistic notion with respect to any object formalism, it lays beyond and out with them.

It's, furthermore, a semantic notion:

Henceforth I’ll assume the interpretations approach to logical consequence, on
which logical nihilism is the view that for every principle of the form Γ |= φ there is an interpretation of the non-logical expressions in Γ and φ such that every member of Γ comes out true but φ does not. Such an interpretation would be a counterexample to the principle. If it turns out that there are no such counterexamples, and that on every interpretation of those non-logical expressions on which each member of Γ is true, φ is also true, then the principle will be a logical law, and nihilism will be false.

The turnstile with two lines above means that Russell wants to find counterexamples to principles through interpreting the logic, which is a way of finding a "syntactically appropriate" mappings from its symbols to other objects - like propositions to truth values - to see in what conditions the proposed principle holds. Mucking about with interpretations like that is what makes the kind of logical nihilism she's playing with a semantic argument.

On the interpretations view Γ|=φ is true iff whatever (syntactically appropriate) interpretation is given to the non-logical expressions in Γ and φ, if every member of Γ is true, then so is φ. For example, if our argument is P a, a = b P b, then the interpretations approach says that the argument is valid iff there is no interpretation of P, a and b (assuming we are treating = as logical) such that P a and a = b are true, but P b is not. Models are understood as offering us different interpretations of the non-logical expressions, and hence if we find a model in which P a and a = b is true but P b is not, the principle is not true. On the interpretations conception then, logical nihilism is the view that for every argument, Γ φ, there are interpretations of the non-logical expressions in Γ and φ which would make every member of Γ true, but φ not true

So what Russell is doing, when she's finding counterexamples, is taking "syntactically appropriate" expressions, throwing them into a formalism, then evaluating them in that formalism through an interpretation. If she can find an expression and an evaluation that fit the rules of the logic that is also a counterexample to one of its candidate principles, then it's not a principle of the logic for all expressions in it - and so is not a logical law.

So the sense of "complete generality" also allows Russell to consider variations over interpretations and the relationship of interpretations with syntactical elements of languages - it's thus a highly metalinguistic notion. Which is not surprising, as the Logic Of All And Only Universal Principles would need to have its laws apply in complete generality, and thus talk about every other logical apparatus in existence.

Which is an incredibly, incredibly strong thing to want. It's practically alchemical, one must have in mind a procedure in which the complexities and ambiguities of natural language, every inference, can be stripped, dissolved, distilled into gold. The true atoms of rationality. The story hooks in the book of divine law. In some respects it's even stronger than the petty desire to take the intersection of all logics, at least that has a precedent in each logic. And you need to claim that this holy book of divine order is spoken in one voice, the true semantical derivation symbol of the cosmos, that admits no quibbling, sophistry or perversion.

Or you could refuse the above notion and take the path Russell does, by applying metalinguistic restrictions to the space of interpretations of a theory. As in, "yes, we know the Liar blows this logic up, so let's just say for all bivalent φ", hence the method from proofs and refutations, lemma incorporation, in which a system is mapped to another system with an additional lemma in order to constrain its space of syntactically valid interpretations.

In formal terms, the latter is what distinguishes @Leontiskos's sophist from someone who finds good counterexamples, someone who finds good counterexamples ensures that they are syntactically valid - that is, obeys all and only the stipulated rules, both intended and written. If you can jam something between the intention and the written word, while playing by all the rules stipulated, you've shown that the conceptual content of the formalism does not reflect the intended object. Or alternatively the intended object is the wrongly represented in the formalism, conceived in a confusing or inopportune manner etc.

Right, so what's with complete generality? Why not say all logics. — Cheshire

The impression I got was that "complete generality" doesn't commit you to quantifying over logics. A principle holding in complete generality, being understood as the entailment relation being the same for all logics, would need to contend with the fact that you can arbitrarily make systems that prove a claim and corollary systems that prove its negation when they share the same set of symbols.

So you can come up with a logic where modus ponens holds, and come up with a logic where modus ponens does not hold. Which would mean that if you wanted to find The Logic Of All and Only Common Principles (tm), you'd need to jettison modus ponens. Since it is not a common principle, since two logics disagree on whether it is a theorem.

The paper gives lots of strategies for coming up with schematic counter examples to many, many things. You can come up with scenarios where even elementary things like "A & B... lets you derive A" don't hold. So much would need to be jettisoned, thus, if The Logic Of All and Only Common Principles was taken exactly at its word, in the sense of intersecting the theorems proved by different logics.

And that's kind of a knock down argument, when you consider X is true in system Y extensionally at any rate (which is AFAIK the standard thing to do)

Phrasing it in terms of "complete generality" thus gives a whole lot of wiggle room regarding what it would mean for a principle to hold in complete generality, like you might be able to insist somehow that any logic worth its salt must have LEM, or any logic worth its salt must have modus ponens as a theorem. So that sense of "complete generality" (NOT completeness of a logic) might mean "in every style of reasoning", so it would let you think of some logics as styles of reasoning and some as not.

You also have the opportunity to think of informal logical principles as holding in "complete generality", as eg if someone believes that the No True Scotsman fallacy is fallacious in some sense, an argument definitively establishing its fallaciousness might be considered a theorem of The Logic of All and Only Common Principles, even though No True Scotsman doesn't admit an easy formalisation. Next paragraph is just extra detail supporting that it doesn't have an easy formalisation.

Just for extra detail, No True Scotsman doesn't admit of an easy formalisation in terms of predicate logic because deductively it kind of works. If x is always p( x ), and someone provides an example of x such that ~p( x ), it should be taken as a refutation. But the fallacy corresponds to interpreting the person providing the counterexample as instead providing an example of someone for whom some distinct property q( x ) holds where q( x ) != ~p( x ). Which isn't exactly a fallacy, it's a reinterpretation, and sometimes it's a good thing to do when arguing - sometimes people make bad counterexamples. But what makes it a fallacy is somehow that the suggested q( x ) only has irrelevant distinctions from ~p( x ), like a true Scotsman is just a Scotsman. You could also read it like the the asserter that x is always p( x ), upon receiving the counterexample, clarifies their position to some predicate q( x ) such that the counterexample given does not apply to it while still using the same predicate label ("Scotsman"). In that case the fallacy consists of revising the content of the claim to "just" exclude counterexample for no other reason, which deductively is without problem, but provides another irrelevant distinction. In either case, the sense of irrelevance of distinction is the thing which is so norm ladened and contextually situated that you're not going to be able to put it into a logic without (unknown to me) profound insight about logical form in natural language.

So if you wanted to have the fact that No True Scotsman is a fallacy as a "theorem" of The Logic Of All and Only Common Principles, maybe your whole logic needs to be informal to begin with.

and are you willing to say that the fanfiction can be good or bad? — Leontiskos

Yes. Harry Potter and the Methods of Rationality is definitely better written than My Immortal.

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. — Leontiskos

I do enjoy the open sea, I just tend to think its openness is necessary. If you'll forgive me the excess of portraying metaphysical intuition through vagueness.

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. — Leontiskos

I would be pretty happy to defend logical nihilism as set out in Russell's paper.

You are the one who brought up Euclid in the first place, but I really don't see the two descriptions as competing. — Leontiskos

Ah. That's unfortunate. Euclid's definition makes the great circle not a circle. The closed curve one makes it a circle.

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." — Leontiskos

It's the same basic idea, yeah. When understood in the context of a circle. You can think of curvature as a more general concept than roundness, since curvature's also "pinchiness" and "pointiness". and "flatness" etc all rolled into one. So it's sort of like roundness is to curvature as apples are to fruit.

Or rather, producing 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. — Leontiskos

It's both innit. Getting the definitions right is one thing - yay, you have found the commonality between circles. Using the definitions to produce even more knowledge is another.

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.

I don't think any of the examples we've discussed so far is "merely" a model, since the different frameworks place much different commitments and demands on the behaviour of people that use them.

One of the great things about producing formalisms is that they're coordinative. If you and I operated on the constant curvature definition, we'd be committed to the same beliefs about circles. The same with the Euclid one. When you add that to our ability to mathematise abstractions expressively in a common language, you end up being able to write down the mathematical rules one must follow when dealing with an abstraction - just in case you have successfully defined it in the symbols. At that point, whether it is the right abstraction for the job seems a different issue.

I certainly wouldn't tell my students that a circle is a closed curve of constant curvature, I'd show them examples of circles and just say "like this". Roll them about. Measure them. I wouldn't even show them Euclid, or try to define the shape. For a lot of things you can get an okay idea of what they are without a formalism, but that loses its charm when you need to explore things that have less straightforward intuitions associated with them.

Like the example I gave of continuous functions vs Darboux functions (functions with the intermediate value property). Mathematicians thought those were equivalent for a long time based on pretheoretical notions.

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

That reads disingenuously to me. Your use of "roundness" previously read as a completely discursive+pretheoretical 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.

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...

Presumably it is an intuitive concept, and are intuitive concepts mathematical formalisms? — Leontiskos

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 +.

not a prepackaged formalism. — Leontiskos

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!

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

Oh. Because the definition of a Euclidean space, in the modern sense, includes both. They're infinite expanses of points whose interpoint distances are given by straight line distance. In the old sense, in Euclid's sense, only R^2 could be, since R^3 isn't a surface.

"If the center was deleted—per impossibile—then there would only be an Aristotelian Circle." — Leontiskos

It's interesting really. Since deleting the point from the plane impacts lots of possible circles. There will be Euclid circles in that space which are not Aristotle circles too, I believe. Though I'm not totally convinced.

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

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.

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

Interesting. But yes.

You stipulated that we've got to understand them in the plane in Euclid's sense, which I'll assume is R^2, and that has every point in it. So the "deletion" doesn't provide a counter model, this is similar to the "for all bivalent" thing from the paper. If we understand the definitions both to apply to the whole of R^2, if you deleted a point from R^2 we're just not dealing with R^2.

If you take the definitions and apply them on arbitrary sets, they can disagree. So, you'd begin the proof of their equivalence like "In R^2, consider...".

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

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

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. — Leontiskos

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.

Yep, I sympathize with him. — Leontiskos

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.

Do Euclid and Aristotle disagree on what a circle is? That sort of question is what I think lurks behind much of our disagreement, such as the deletion of points. If two people draw something differently, can they both have drawn a circle? — Leontiskos

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?

Now does such a cross-section really contain a Euclidean circle? Trying to gain a great deal of precision on the answer to this question seems futile, but it seems to me that it is "correctly assertible" that it does (whatever your "correctly assertible" is exactly meant to mean :razz:). — Leontiskos

I think it contains a circle. It's just that the contraption you use to show that it contains a circle also means you need to go beyond Euclid's definition. 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 thus subsets of it are not 'planar figure's in some sense. However, for a clarified definition of plane that lets you treat a plane that is at an incline as a standard flat 0 gradient 2D plane, the "clearly a circle" thing you draw in it would be a circle.

I mean, what would a university math professor think if they saw someone arguing that they can delete the point in the center of a circle and make it a non-circle? I think they would call it sophistry. They might say something like, "Technically one can redefine the set of points in the domain under consideration, but doing this in an ad hoc manner to try to score points in an argument is really just sophistry, not mathematics." — Leontiskos

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.

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.

Now does such a cross-section really contain a Euclidean circle? Trying to gain a great deal of precision on the answer to this question seems futile, but it seems to me that it is "correctly assertible" that it does (whatever your "correctly assertible" is exactly meant to mean :razz:). — Leontiskos

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.

It is petitio principii to simply insist that, say, an inclined plane is not reducible to a Euclidean plane qua circles. — Leontiskos

Can you give me a lot more words on the phrase "an incline plane is reducible to a Euclidean plane qua circles"? I'd really like to understand the predicate:

X is reducible to Y qua Z

There's not much point continuing this if you feel like it's the same thing over and over.

Thank you!

So are there rational norms or aren't there? What does it mean to "correctly understand a stipulated object"? One minute you're all about sublanguages and quantification requiring formal contexts, and the next minute you are strongly implying that there is some reason to reject some sublanguages and accept others. I suggest ironing that out. — Leontiskos

I'm saying that one can understand a language without being committed to whether it is a "correct language", and be able to say whether a given statement in it is correct or incorrect. Because the norms of the sublanguage are fixed. Like all the statements in propositional logic are bivalent, the LEM holds etc.

Where this breaks down is the intuition that propositional logic "ought" apply to all meaningful sentences. Hence the Liar and indeterminate truth values now serving as "counterexamples" in this context. They can be understood as counterexamples when one expects propositional logic to work for all meaningful sentences. This was analogised with our circle discussion.

We were talking about circles as a concept, and they have associated formalisms, we've now seen that there are different formalisms for it in different contexts, and sometimes they disagree. How can you insist that one is more correct than another? Which one is baked in the metaphysics? I don't really need you to know the final answer on it, I just want to know how you'd go about deciding it even in principle.

I've had plenty of university math. You strike me as someone who is so sunk in axiomatic stipulations that you can no longer tell left from right, and when you realize that you've left yourself no rational recourse, you resort to mockery in lieu of argument. — Leontiskos

Alright. It just surprises me that you survived all of these different things to do with maths concepts with a strong intuition remaining that there's ultimately one right way of doing things in maths and in logic, and that understanding is baked right into the true metaphysics of the world. And also seem to align this understanding with Aristotle?

Maybe "propositional logic" is as slippery as "circle." — Leontiskos

Neither of them is particularly slippery. The slippery thing is a pretheoretical conception of logic, or circles, which might be better exemplified in some ways by some theories and in other ways by others. There's wide agreement on what the theorems are in propositional logic, how it's used etc. I don't believe it makes sense to say something is slippery when the norms of its use are so well enshrined that it's taught to people the world over.

Neither of us disagree on what Euclidean, taxicab or great circles are at this point, I think. So they're not "slippery", their norms of use are well understood. The thing which is not understood is how they relate to the, well I suppose your, intuition of a circle. I seem to have a spectrum of intuitions about circles that apply in different contexts. Maybe you don't?

I am getting the impression that you have quite an all or nothing perspective on this - either there is a single unified objective system or there is a sea of unrestrained relativism and mere subjectivity over what theorems are provable in what circumstances. I would suggest that people can agree on what theorems are provable in what circumstances without an opinion about whether they're the "right" theorems. It seems to be knowing what theorems something should satisfy and having the right formalism to prove them are inextricably related in mathematical creativity and reasoning - eg:

If I had the theorems I should find the proofs easily enough. — Riemann

Which brings us onto understanding a stipulated object.

What does it mean to "correctly understand a stipulated object"? — Leontiskos

I would say that someone correctly understands a mathematical object when they can tell you roughly what theorems it should satisfy, give some examples of it, and has ideas about proof sketches for theorems about it. That means they know how it behaves and what contexts it dwells in. They know how it ought to be written down and how to write it. They know how what they imagine is captured by how they write it down, and that what's written down captures all it should capture about the object.

That's also quite contextually demarcated - eg I would say I understand differentiable bijections in terms of real analysis objects but my understanding of their role in differential geometry is much much worse, despite their major role in the latter context.

There's a bit of graph theory I work on in my spare time, regarding random fields on graphs with an associated collection of quotient graphs, and I have an idea of what I want that contraption to do, but I've yet to find a good formalism for it. Every time I've come up with one it ends up either proving something which is insane, and I reject it, or I realise that the formalism doesn't have enough in it to prove what I need to. Occasionally I've had the misfortunate of making assumptions so silly I can prove a contradiction, then have to go back to almost square one. I wouldn't say I understand the object well yet, nor what theorems it needs to satisfy, but I have a series of mental images and operations which I'm trying to be able to capture with a formalism. I would call this object "slippery", but that's because I haven't put it in a cage of the right shape yet. Because I don't have the words or the insight yet. Perhaps I never will!

Terence Tao has a blogpost on stages of mathematical comprehension in a domain of competence, if you're interested I can dig it up.

I also don't want to say that all objects are "merely" stipulated, like a differential equation has a physical interpretation, so some objects seem to have a privileged flavour of relation to how things are, even if there's no unique way of writing that down and generating predictions. I had an old thread on that, which was not engaged with due to poor writing and technical detail, called "Quantitative Skepticism and Mixtures". It's just a recipe for making largely useless models that produce the same predictions as useful ones, but have pathological properties. And the empirics aren't going to distinguish them if you choose the numbers right.

A final comment I have is that we should probably talk about the development of formalism also changing what counts as a pretheoretical intuition - cf the way of reading general relativity that undermines Kant's transcendental aesthetic, since noneuclidean geometries aren't just intelligible, they're baked into the reality of things. Also people who overdose on topology come out changed.

We seem to think about mathematics very differently. You think that a point can be deleted; that a set of coplanar points might not lie on a plane, etc. Those strike me as the more crucial disagreements. — Leontiskos

I don't know what to tell you other than you learn that stuff in final year highschool or first year university maths. If you're not willing to take that you can do those things for granted I don't know if we're even talking about maths.

A set of coplanar points could have a plane drawn through them if you had the ability to form a set in that space which was a plane... and contained them. So they wouldn't even be coplanar if you couldn't draw the plane, no? Like how would coplanarity even work if you've just got three points {1,2,3}, {4,5,6} and {7,8,9} embedded in no space.

Maybe we're talking about Leontiskos-maths, a new system. How does this one work? :P

At the heart of this thread seems to be the question of whether we can actually say that someone is wrong. — Leontiskos

Of course you can. If someone tells you that modus ponens doesn't work in propositional logic, they're wrong.

our notion of "correctly assertible" seems to be something like a subjective consistency condition, in the sense that it only examines whether someone is subjectively consistent with their own views and intentions. — Leontiskos

More normative. It's not correct to assert that modus ponens fails in propositional logic because how propositional logic works has been established. And modus ponens works in it.

Okay, but I still don't understand why you are calling this "shit testing." Why does it have that name? It sounds like you want to give counterexamples that highlight subjective inconsistencies. Fine, but why is it called "shit testing?" — Leontiskos

I used it as a joke and then ran with it. And they aren't subjective inconsistencies, they're norms of comprehension, and intimately tied up with what it means to correctly understand those objects.

Counterexamples that I've been giving don't just refute stuff, they mark sites for theoretical innovation and clarification.