Perhaps until we have a clear idea of what sorts of things are ineffable, we don't have a clear answer to the issues being discussed around ineffability. Trouble is, we don't have a way of saying what it is that is ineffable without the danger of thereby contradicting ourselves. — Banno

Your exploration of the high-C example is helpful. I know it was my own example, but I'm no longer happy with it because I don't think it's to the point of what Witt meant. What you write above puts it quite well -- words like "inexpressible" and "ineffable" and "indescribable" run a double risk. Not only are they like fly-paper for the flies of ambiguity, but there's a legitimate question whether even merely indicating or pointing to the inexpressible makes it no longer inexpressible.

Staying with that last point (which was the one I originally indicated doubt about), we still want an example. Two possible paths to take: We could try to state (try to!) what Witt himself had in mind when he referred to "that which cannot be spoken." I do not believe he was only making a formal point. I think he had a large range of such items in mind, having to do with values, God, and bedrock metaphysics. We could also take your suggestion about how such expressions are used in ordinary language. This dovetails with a theme that @Arcane Sandwich has taken up: whether ontology can be sensibly expressed in ordinary language.

I'd like to hear your thoughts about what might be "inexpressible in Wittgensteinese." And as an example of common usage, how about this: "We have a sense that life has a purpose, a meaning, that there is more to my existence than birth and death. But what that deeper sense may be, we find impossible to express -- not because it is incoherent, but because we don't know how to conceptualize what it is we are intuiting when we speak of 'the meaning of life.'" Might this be an example of something that's more or less describable, yet remains inexpressible?

This dovetails with a theme that Arcane Sandwich has taken up: whether ontology can be sensibly expressed in ordinary language. — J

My own view on that topic is actually far more extreme that what you said, and that's precisely why I'm suspicious of my own view. I shouldn't feel so strongly about this issue, but I do, and that makes me suspicious of myself, if that makes any sense. Anyways, here's what I would say: ordinary language is the only language in which ontology can be sensibly expressed. In other words, ontology cannot be done within the context of a formal language alone, be it math, logic, or a combination of both. You can utilize math and logic, you are free to do so because formal languages are mere tools, that's what they are to the professional physicist. Mathematicians and logicians do not automatically get the last word in matters of ontology "just because", without any reason.

In a debate with Richard Rorty, Umberto Eco tried to press the point that things cannot be pragmatism and convention "all the way down." A screwdriver, in some sense, shapes what we choose to do with it. Rorty disagreed and gave the unfortunate counter example that we could just as well scratch our ear with a screwdriver. Except we wouldn't, because of what a screwdriver is and what we are (or, if the point isn't clear enough, consider a razor sharp hunting knife). The world, and truth, imposes itself on how we deal with things — Count Timothy von Icarus

What we are using a thing for shapes how we perceive the constraints and affordances offered by that thing. If we understand what a computer is for , then we perceive the properties of that computer and how those properties shape what we can do with it in terms of speed, memory, screen brightness, quality of manufacturing, etc. If we have never heard of a computer, and find one on the side of the road, we will not consider the tower, screen, mouse and printer as even belonging to the same thing. We may then use the tower as a doorstop, and then it’s properties will appear to us in terms of its weight, ability to grip the surface it’s placed on, and other considerations relevant to effective doorstops.

A series of connected lines and curves made out of sticks doesn’t shape what we do with the this ‘object’ all by itself. What we do with it may involve interpreting it as a string of letters that form a meaningful sentence, if we read that language. Or if we don’t recognize that language, the stick objects may appear as random collection of shapes. In either case, what the object is and how it shapes us is a function of the role it plays for us a system of meaningful references tied to useful purposes. In order to decide that a screwdriver drives screws better than it scratches ears, we have to already know about not only the role of a screwdriver , but that of screws and the surfaces that screws fit together, the role of these fitted surfaces in a construction project, the role of the construction project in relation to a finished building or machine, the role of that building or machine in our activities, and so on. What makes the screwdriver a screwdriver for us is not inherent in the object all by itself but in this totality of chains of ‘in order to’s’ that belongs to and on the base of which it was invented.

Do the world, and truth, impose themselves on how we deal with things? Yes, but only in and through how we deal with things.

Yeah, that might be a little strong, but as a contrast to pure formalism, the point is useful. I realize that my own comments might lead one to think that I regard formalism as the only legitimate language for philosophy. I don't. Formalization is a brilliant tool, and often a necessary one, but we can certainly do many important philosophical tasks without it -- if not quite in genuinely "ordinary" language. No, my beef is with the term "existence", which I think we should retire from the field with all due honors. Same for "real". I believe we will learn a lot more about the concepts that those terms try to refer to, if we stop the endless, unresolvable bickering about them.

On the discussion between Rorty and Eco that @Count Timothy von Icarus contributed to the discussion on Mathematical Platonism, specifically in relation to infinitesimals:

I believe that @Banno has solved it. Infinitesimals exist if and only if Pegasus exists in the exact same sense. What we're debating now, at page 11 of this Thread, is what that "exact same sense" is. And my wager is that it cannot be solved in the language of first-order logic, or any other formal language, including mathematics.

The case I'm making here, folks, is a simple one. It's what's known in the literature as a "parity argument":

First Premise) There is no epistemic difference between the epistemic rights of professional physicists and the epistemic rights of professional philosophers.
Second Premise) If so, then: if professional physicists are within their epistemic rights to claim that math and logic are just mere tools, then professional philosophers are also within their epistemic rights to claim that math and logic are just mere tools.
Third Premise) Professional physicists are within their epistemic rights to claim that math and logic are just mere tools.
Conclusion) So, professional philosophers are also within their epistemic rights to claim that math and logic are just mere tools.

I claim that the preceding is a logically valid argument. I also claim that all of the premises are true, which means that the conclusion is necessarily true as well.

Does anyone wish to resist this argument, or do you agree with it?

EDIT: Here is the logical form of my argument, using Propositional Logic:

1) p
2) p → (q → r)
3) q
4) r

There are no restrictions on what a person can claim unless it's a religious environment and people are executed for saying the wrong thing.

There are no restrictions on what a person can claim unless it's a religious environment and people are executed for saying the wrong thing. — frank

What do you mean by that, @frank? I mean, in relation to the topic of Mathematical Platonism, formalism, and ontology? I don't get it. Can you explain it to me like I'm simple-minded?

There is no epistemic difference between the epistemic rights of professional physicists and the epistemic rights of professional philosophers. — Arcane Sandwich

This needs a lot of expansion. What exactly is at stake with this premise?

What do you mean by that, frank? I mean, in relation to the topic of Mathematical Platonism, formalism, and ontology? I don't get it. Can you explain it to me like I'm simple-minded? — Arcane Sandwich

I just meant physicists and philosophers can claim whatever they like. The idea of rights isn't needed.

This needs a lot of expansion. What exactly is at stake with this premise? — J

It means that it's an "all or nothing" deal, whatever we mean when we speak of "epistemic rights". Whatever they may be (the epistemic rights), there are only two options:

Option 1) Physicists and philosophers both have them, or
Option 2) Neither physicists nor philosophers have them.

There is no Option 3. At least not to my mind. And if you wish to deny the premise that you asked for expansion, you would have to argue that there is indeed an Option 3. What would that be? That there is an epistemic difference between physicists and philosophers.

(edited for clarity's sake)

I just meant physicists and philosophers can claim whatever they like. The idea of rights isn't needed. — frank

It is for my argument, frank. I would like to have a better argument, but I don't. I'm all ears, though, if you have a better idea.

Slow down thar, pardner! You say "Whatever they may be (the epistemic rights)" so let's start there. What are they meant to be?

Slow down thar, pardner! You say "Whatever they may be (the epistemic rights)" so let's start there. What are they meant to be? — J

They're meant to be rights. Letter of the Law versus Spirit of the Law and all that. Define them however you want. They're something that physicists and philosophers have in common, and it's what allows them both, to say, at the same time and in the same sense, that math and logic are just tools. They have no ontology built into them as formal languages. The existential quantifier doesn't really say anything about existence, just as the universal quantifier doesn't say anything about existence. You can even switch one for the other under certain conditions, as I've shown in my example about the "existence" of Pegasus.

"To be is to be the value of a variable"

just means (it seems to me)

"To avoid rabbit holes, do this: read 'there exists some x such that' as 'at least one of the x among the set of all that exist is such that' ".

I.e. the sentence (following) isn't about whether some particular thing exists but about some particular existent thing.

This might not be a perfect method of staying above ground, but replacing 'the set of all that exist' with anything else isn't following the method.

E.g. replacing it with 'the set of all elements of this or that fiction' is trashing the method.

Try

https://www.umsu.de/trees/#~6x~3((Gx~5Ax)~1(Ax~5Gx))

↪Arcane Sandwich

Try

https://www.umsu.de/trees/#~6x~3((Gx~5Ax)~1(Ax~5Gx)) — Banno

But then you reach a problem, mate. You can't deduce ¬Ga from ∀x¬((Gx→Ax)∧(Ax→Gx)). Here's your argument:

First premise: Gp
Second premise: ∀x¬((Gx→Ax)∧(Ax→Gx))
Conclusion: ¬Ga

But your two premises do not entail your conclusion. See for yourself: https://www.umsu.de/trees/#Gp,~6x~3((Gx~5Ax)~1(Ax~5Gx))|=~3Ga

EDIT: Whoops, sorry, you do ineed reach your conclusion, which is not ¬Ga, but ¬Ap instead. Yep, you have a valid argument, mate: https://www.umsu.de/trees/#Gp,~6x~3((Gx~5Ax)~1(Ax~5Gx))|=~3Ap

Greek myth(Pegasus)
For all x, Greek Myth(x) ≢ Aztec myth(x)
Hence
~ Aztec myth(Pegasus) — Banno

It'd be

https://www.umsu.de/trees/#Gp,~6x~3((Gx~5Ax)~1(Ax~5Gx))|=~3Ap

@Banno Indeed, you have a solid argument on your hands. So what were we discussing in relation to that point? Why Bunge instead of Kripke on that specific point? Was that the question that you had?

You described Bung as introducing a relational operator for existence. I hope I shed some doubt on the necessity of doing so, by describing ontological commitment in terms of specifying the domain. That is, to say that something exists is little more than to talk about it. That's different to saying that it is a greek myth or a physical object or a number.

So, as I think you agreed, the answer to 's question is that infinitesimals can be the subject of a quantifier, and in that way, they exist; they can be in the domain of discourse. If there is something more to their existence, some "platonic" existence, then it's up to the advocates to set out what that amounts to.

You described Bung as introducing a relational operator for existence. I hope I shed some doubt on the necessity of doing so, — Banno

Indeed you have. I had been harboring suspicions about that part of Bunge's work myself (and about other parts of his work, but those are beside the point being discussed here). I'm not sure if I'm sold on the Kripkean-esque part of your proposal, though. I just don't know. I've done some experiments with treating individual constants (i.e., "p" for "Pegasus") as predicates (i.e. "P" for "is Pegasus"). If I say that there is an x, such that x "is Pegasus" in a predicative sense, like so:

∃xPx

what would I be committed to, exactly? Does that formula commit me to the claim that the symbol
∃ has ontological import? I don't think it does. All it means is "a particular thing, x, is Pegasus in a predicative sense). Now what does the predicate "is Pegasus" mean? Does it mean that x performs the act of "pegasizing"? I don't think that's a sound thing to say, so Quinenians will have to excuse me here.

to say that something exists is little more than to talk about it. — Banno

But I disagree with that for metaphysical reasons. To exist, in my opinion, is to have a spatiotemporal location. Pegasus does not have a spatiotemporal location. Where is it? Where is it located? Or, you could say that to exist is to have some kind or type of energy, such as potential energy or kinetic energy. Or thermal energy, or nuclear energy, or what have you. What kind of energy does Pegasus have, being a fictional object? I don't think it has any. So, I don't agree that existence is somehow a matter of words or even language more broadly. It's independent of language.

So, as I think you agreed, the answer to ↪Michael
's question is that infinitesimals can be the subject of a quantifier, and in that way, they exist; they can be in the domain of discourse. If there is something more to their existence, some "platonic" existence, then it's up to the advocates to set out what that amounts to. — Banno

Exactly, 100%, couldn't agree with you more on that point.

I'd like to hear your thoughts about what might be "inexpressible in Wittgensteinese." — J

You'd like me to set out what sort of things re inexpressible? To give reasons for the ineffable? To answer for Wittgenstein the question I asked you? :wink:

Well, why not. Trouble is, it'd be a thesis, not a post. Indeed, a series of theses.

I read the Tractatus as saying that things can't be said - It's propositions that are said, "the world is what is the case"; there are things only in so far as they are the subject of a proposition - a view few others seem to hold nowdays, but it fits his notion of logical atomism. Hence the extended discussion of proper names in the earlier part of the last century. That's probably salient to the nascent discussion of Bung and Kripke.

And values are not said, so much as enacted. Ethics is about what we do, which is why he has so little to say about it. Instead he worked as a hospital orderly and watched cheap crime thrillers.

Hinge propositions are said, but never quite rightly. "Here is a hand" isn't justified, at least not by other propositions. It's shown. "If you do know that here is one hand, we'll grant you all the rest".

So I keep coming back to PI §201. What's not expressible may nevertheless be enacted. Not just in following a rule, but in using language, deciding what to do, and generally in what he called a "form of life". You don't say it, you do it.

Any comments, @Sam26? I suspect this is an older reading of Wittgenstein than is popular now.

Infinitesimals can be the subject of a quantifier, and in that way, they exist; they can be in the domain of discourse. If there is something more to their existence, some "platonic" existence, then it's up to the advocates to set out what that amounts to. — Banno

That's good, as far as it goes. But the other kind of "more" that some philosophers (I think including @Arcane Sandwich?) want to claim is physical or spatio-temporal existence. I think we agree that quantification is agnostic about that, as it is about platonic existence. So is there a case that can be made for preserving the term "existence" for that sort of thing? I'm saying no -- that this is still trying to privilege a particular word and make it do something we don't need it to do. We understand the concept of "something in space-time" -- isn't that good enough? Why do we need to praise it by additionally saying it "exists" in some superior way -- so superior that it casts doubt on whether other non-spatio-temporal items exist at all?

Hinge propositions are said, but never quite rightly. "Here is a hand" isn't justified, at least not by other propositions. It's shown. "If you do know that here is one hand, we'll grant you all the rest". — Banno

Let's lean into that a little. "Here is a hand" is certainly expressible. It's a proposition that states a fact about the world. You now say of it, "But it isn't justified by other propositions." Fair enough. Have we reached inexpressibility -- what "can't be spoken"? How, exactly? Is it the alleged justification that is supposed to be inexpressible? That doesn't sound quite right. I would have thought the (propositional) justification was simply absent or non-existent, rather than inexpressible.

Or is this a blind alley? I may not yet be quite seeing the expressibility problem here.

But the other kind of "more" that some philosophers (I think including Arcane Sandwich?) want to claim is physical or spatio-temporal existence. — J

Yes, that is indeed the case. And I will say something even more extreme: there is no other existence than spatiotemporal existence. To exist is to exist at some place, and at some time. Does it have to be a precise, clear-cut spatiotemporal location? No, not at all, since you need to take tiny quantum objects into consideration, and it's a bit of a tough thing to do to pinpoint the exact location of those tiny "jiggly-things".

But yeah, to exist is to be somewhere at some time, like this rock on the floor. Is that a fallacy of appealing to a rock? To me that's just good common sense.

That's good, as far as it goes. — J

@Arcane Sandwich has agreed with a part of what I had to say. He focused on that we can treat them as individuals in virtue of being able to quantify over them. I also suggested that numbers are more something we do rather than individuals, although we can treat them as individuals. See . So I agree that they are not physical, and add that we can show how they nevertheless come to be treated as individuals by quantification. It's a "counts as..." thing, an act performed in language. These are of course things that exist but are not physical. Money and property and so on.

Let's lean into that a little. — J

Asking someone to justify "Here is a hand" is inane in that it misunderstands what is going on in the illocution. In a way "This is a hand" is like "This counts as a hand", it's not part of the language game so much as setting up the language game. But Moore wanted to go a step further, wanting to use the illocution to demonstrate that the world exists. This is the step too far that Wittgenstein examines. Moore takes himself to having proved that there is a world, but rather, that there is a world is already supposed by his demonstration. It's not that Moore has proved the existence of a hand, but that treating this as a hand is what we do. And that doing is not expressible, but, to paraphrase PI§201, "What this shews is that there is a way to grasp that this is a hand which is not a conclusion, but which is exhibited in what we do in actual cases"

And that is not expressed, but performed. Ineffable, yet understood.

How's that?

But Moore wanted to go a step further, wanting to use the illocution to demonstrate that the world exists. — Banno

And he succeeded, in my honest opinion. Like, what more do you want? Good common sense is suddenly not a respectable epistemic framework? Well I mean you should take a look a the amount of bullshit that passes around these days as far as "respectable" epistemic frameworks go, and they're nowhere nearly as good, as sound, and as reasonable as common sense. Like, philosophers begin with a completely demented question (i.e., "How do you know that you're not a disembodied brain in a vat that is hallucinating?") but they expect, nay, demand a reasonable answer to their demented question. Like, here's a hand mate, what are you talking about? Why should I take your nonsense seriously to begin with?

And he succeeded — Arcane Sandwich

Well, he wasn't wrong.

Well, he wasn't wrong. — Banno

Then what are we even arguing about? I mean, let's keep this on track, we're talking about quantities and numbers. Do they exist? As in, did you learn this stuff in school? Sure mate, they exist in that sense. I can imagine the number 3. That doesn't mean that they exist in the same sense that this rock on the floor does, and if the fallacy of appealing to a stone is such a sin, then by God send me straight to Hell for all Eternity, because what you call "appeal to the stone" I call good common sense.

Phew... I really should chill out.

Then what are we even arguing about? — Arcane Sandwich

Are we arguing? I thought we were agreeing.

Oh man, this one is brutal for me. I get so worked up over this. Sometimes I hate being a philosopher. That's an odd thing to say. Hmmm...

Well, if you want disagreement, then I'll disagree with this:

To exist is to exist at some place, and at some time. — Arcane Sandwich

Numbers exist. 2 is a number, therefore there are numbers. But it is difficult to make sense of the idea of 2 existing only at some place and some time.

I'll grant, at least provisionally, that to be physical is to exist at some place and some time. As good a definition as any. But there is a difference between existing and being physical.