My thought about this is that infinity exists in the same way 0 does, as an abstraction of the set. Hence the whole "some infinities are larger than others" thing. If 0 is nothing from the set, infinity is everything from the set. But I am not a mathematician.

But if something can't be said, it might be important to say why and surely philosophy has a role to play there. — Wayfarer

I . . . take [it] to be one of the main themes of the Investigations - that what cannot be said may be shown or done. — Banno

I just want to point out that these two views are not the same. You can indeed move on from inexpressibility to a demonstration or showing of what can't be expressed. But first (or conjointly) you can also say why, as Wayfarer suggests. Or would the claim be that inexpressibility itself can only be demonstrated, not justified?

What troubles me is the presumption to knowledge - justified true beliefs - in the absence of a coherent way of providing a justification.

Which of course leads into the discussion of what is to count as a justification... — Banno

I think when it comes to matters of faith personal experiences may serve as justifications for one's own (but certainly not anyone else's) beliefs — Janus

It seems to me that "I had an experience of God" may be both true and justified, in terms of my own (reasonable) standards. But the degree of justification -- the standards involved -- are quite different from those I would use if someone asked me to justify my belief that my cat is on the mat. Different degrees of certitude, in other words. Arguments for God based on personal experience are arguments to the best hypothesis. That's why it's unreasonable to expect anyone else to treat my belief as knowledge.

Yep. :up:
The intellectus/ratio distinction is something I focused on when I first arrived at TPF, for it seems to me the biggest error that basically everyone here makes, together.

Note too the way that all moderns tend to agree with Hume that no movement from ratio to intellectus is possible. For example:

Arguments [...] based on personal experience are arguments to the best hypothesis. — J

(The abandonment of intellectus is the abandonment of knowledge in favor of opinion and hypothesis.)

Arguments for God based on personal experience are arguments to the best hypothesis. That's why it's unreasonable to expect anyone else to treat my belief as knowledge. — J

Yes, and I'd also add that there are different generally socially accepted criteria for what counts as "best explanation" in different societies and times and milieus.

If something cannot be definitively said it just means it is beyond the limits of discursive language. What more couls added?

Arguments for God based on personal experience are arguments to the best hypothesis.

Yes, and I'd also add that there are different generally socially accepted criteria for what counts as "best explanation" in different societies and times and milieus.

How exactly does this differ from any empirical claims?

I just want to point out that these two views are not the same. You can indeed move on from inexpressibility to a demonstration or showing of what can't be expressed. But first (or conjointly) you can also say why, as Wayfarer suggests. Or would the claim be that inexpressibility itself can only be demonstrated, not justified?

It depends on what is meant by "justified." Plato, in Letter VII, says of "teaching" metaphysics that: There neither is nor ever will be a treatise of mine on the subject. For it does not admit of exposition like other branches of knowledge; but after much converse about the matter itself and a life lived together, suddenly a light, as it were, is kindled in one soul by a flame that leaps to it from another, and thereafter sustains itself.

But note, Plato does attempt to convey such things, and to justify them. Indeed, he produces a 2,000+ page corpus of exquisitely crafted dialogues to do so. St. Augustine has a similar view on metaphysics and a more dismal view of man's unaided reason, and yet he produced 35,000 pages of collected works, much of which deals with these same topics. Dante's Divine Comedy might be the greatest example in world literature of the attempt to convey what escapes language in image.

But if justification is taken to be synonymous with demonstration, (which is obviously a temptation if reason is just ratio) then obviously such efforts will involve "speaking where one ought to be silent." Or they would involve "art" primarily enjoyed for amusement, and not philosophy.

↪Tom Storm It's likes the arts— leads nowhere except to novel and perhaps inspiring experiences.

This denotes a very particular approach to the tradition Wayfarer is talking about though. One cannot take a Meister Eckhart, a Rumi, or a Dogen as simply conveying "novel and perhaps inspiring experiences" and take their claims seriously. Indeed, since such "experiences" generally involve the apprehension of truth, and so demand to be taken exclusively, this would be sort of a contradiction in terms. (Dante, for his part, doesn't even allow those who won't take a stand the dignity of a place in Hell; they will spend eternity following a banner that moves relentlessly and arbitrarily about the outskirts of Hell).

If these authors are simply conveying novel experiences to be surfed through, then they are, in some deep sense, fundamentally deluded. Which doesn't mean they cannot be interesting, but it does mean they cannot be right.

Well, isn't it reasonable to ask why it is? Granted, in some cases the answer will be obvious, but surely not always. The sorts of thing Wittgenstein had in mind as being inexpressible are hardly obviously so.

It depends on what is meant by "justified." — Count Timothy von Icarus

This is more complicated than I intended. By "justified," I just meant "explained" or "given an account of." Whereas a demonstration would be simply to show that it is the case, without further explanation why.

Example: A singer attempts to hit a high C, but is unable to do so after repeated attempts. She has thus demonstrated that the note is inexpressible by her. But the question "Why?" remains, and would be answered in terms of anatomy and acoustics. Similarly with philosophy. We may demonstrate that a particular thought is inexpressible, either by argument or some other way, as Wittgenstein claimed to do, and in addition offer an "account" (what I called an explanation) of why that is so. Such an account wouldn't merely repeat the demonstration; it would try to tell us why the result makes sense, or was to be expected.

How exactly does this differ from any empirical claims? — Count Timothy von Icarus

It depends on what you mean by "empirical claim". Direct observations are obviously corroborable, whereas claims to have experienced God are not

This denotes a very particular approach to the tradition Wayfarer is talking about though. One cannot take a Meister Eckhart, a Rumi, or a Dogen as simply conveying "novel and perhaps inspiring experiences" and take their claims seriously. — Count Timothy von Icarus

Why not? They are just men speaking about their ideas and experiences. What they say about their experiences, their ideas, their faith cannot be a definitive justification for anyone else to believe anything. Unless you are appealing to authority? I take their words as seriously as I would the words of any poet whose works I believed to be of high quality. I don't have to strictly believe what is being said in order to be affected, even inspired, by it.

Well, isn't it reasonable to ask why it is? Granted, in some cases the answer will be obvious, but surely not always. The sorts of thing Wittgenstein had in mind as being inexpressible are hardly obviously so. — J

I guess it depends on what you mean by "inexpressible". I take Wittgenstein to mean not expressible in a way that what is being said can be confirmed or disconfirmed. He applies this to ethics and aesthetics. For example, I can say that Beethoven was greater than Bach, but there is no determinable truth to that. So, do you think that by "inexpressible" he means "not truth apt"?


.

I guess it depends on what you mean by "inexpressible". I take Wittgenstein to mean not expressible in a way that what is being said can be confirmed or disconfirmed. He applies this to ethics and aesthetics. For example, I can say that Beethoven was greater than Bach, but there is no determinable truth to that. So, do you think that by "inexpressible" he means "not truth apt"? — Janus

Others on TPF know the Tractatus a lot better than I do, but I think he meant something more than merely "not truth apt" or "not confirmable." I think it's closer to "incoherent" or "illusory." And he wasn't just thinking of ethics and religion, but also of certain supposedly bedrock metaphysical truths. In any case, what I meant by "inexpressible" was more like "unsayable save by metaphor and indirection."

This denotes a very particular approach to the tradition Wayfarer is talking about though. One cannot take a Meister Eckhart, a Rumi, or a Dogen as simply conveying "novel and perhaps inspiring experiences" and take their claims seriously. Indeed, since such "experiences" generally involve the claim to the apprehension of truth, and so demand to be taken exclusively, this would be sort of a contradiction in terms. — Count Timothy von Icarus

I took the liberty of adding the bolded phrase, because leaving it out does make it appear that you're asserting that they succeeded in apprehending truth, which would beg the question.

I too think there's more to Eckhart et al. than "inspiring experiences" but again, let's be careful of the difference between "taking a claim seriously" and "believing it to be true on personal authority." I can be very impressed by a mystic's account without accepting it as somehow self-verifying.

It depends on what you mean by "empirical claim". Direct observations are obviously corroborable, whereas claims to have experienced God are not

That depends on the experience. The most famous theophanies, the Incarnation (and events related to it, such as the Resurrection, Transfiguration, and various miracles) as well as the Pillar of Fire over the Tent of Meeting all involved appearances to multiple individuals (in the latter case, an entire community). Hence, for those involved, they were corroborable.

They aren't corroborable for us, at least not in the direct sense that we can go back in time to the Sinai and see the Pillar of Fire traveling alongside the Hebrews and the Glory of the LORD filling their tent. At the same time, this is also true for virtually all historical facts. One cannot go back to 1492 to see if Columbus really did "sail the ocean blue," and we certainly cannot run multiple independent experiments to confirm this fact. Corroboration always involves piecing together signs and testimony.

Why not?

Why not what? Read them that way? Well, I suppose that if they are right, then one is missing out on something terribly important if one reads them in that sort of detached manner. Indeed, according to them what is most important.

If the question is: "why can't we take them seriously if we disregard what they are saying as being true in the sense in which they claim it is?" then IDK, that seems like the definition of not taking them seriously. When the Patristics claim that we are deluded and enslaved to sin until we turn our mind to God, that this alone is our true telos, etc. etc., it doesn't seem possible to say "well that's just a sentiment for their times," and still be "taking them seriously."

One need not be a Sufi to take Rumi seriously, but it hardly seems like one can be an atheist. Likewise, an atheist might find much to enjoy in Dante or Plotinus, but they have to at least allow them the courtesy of being deluded and wrong in order to take them seriously.

Others on TPF know the Tractatus a lot better than I do, but I think he meant something more than merely "not truth apt" or "not confirmable." I think it's closer to "incoherent" or "illusory." And he wasn't just thinking of ethics and religion, but also of certain supposedly bedrock metaphysical truths. In any case, what I meant by "inexpressible" was more like "unsayable save by metaphor and indirection." — J

I am no expert either, but I understood that in the Tractatus Wittgenstein was concerned to make a distinction between what can be propositionally claimed and what cannot. I think that for him a coherent proposition just is a proposition which is truth-apt.

Hence, for those involved, they were corroborable. — Count Timothy von Icarus

We don't know if the reports of those events are reliable, so for us they are not corroborable.

They aren't corroborable for us, at least not in the direct sense that we can go back in time to the Sinai and see the Pillar of Fire traveling alongside the Hebrews and the Glory of the LORD filling their tent. At the same time, this is also true for virtually all historical facts. — Count Timothy von Icarus

Strictly speaking that is true. But we think the gospels were written many years after the events, which would make them less reliable than many historical documents, especially in cases where there are multiple accounts of, and cross references, to events.

If the question is: "why can't we take them seriously if we disregard what they are saying as being true in the sense in which they claim it is?" then IDK, that seems like the definition of not taking them seriously. — Count Timothy von Icarus

We can take works seriously as poetry, as allegory, as being revelatory of more or less universal aspects of the human condition, and hence as being inspiring, insightful. Think about Dante's Divine Comedy, for example, or Homer's Odyssey—can we not take those works seriously without believing that the events described therein are accurate descriptions of real events? What about the whole Greek mythical pantheon?

When the Patristics claim that we are deluded and enslaved to sin until we turn our mind to God, that this alone is our true telos, etc. etc., it doesn't seem possible to say "well that's just a sentiment for their times," and still be "taking them seriously." — Count Timothy von Icarus

Apart from taking them seriously in terms of their literary merit. we can take such worldviews seriously in acknowledging that they felt real and important for those who held them, without believing them to be true ourselves. I'm not seeing the problem you apparently do.

One need not be a Sufi to take Rumi seriously, but it hardly seems like one can be an atheist. Likewise, an atheist might find much to enjoy in Dante or Plotinus, but they have to at least allow them the courtesy of being deluded and wrong in order to take them seriously. — Count Timothy von Icarus

The point is that we don't and can't know whether any of these claims are true or false because they are not empirically or logically confirmable. If I feel drawn to such claims and feel in my heart that they are true, that's fine for me, but it's never going to be sort of thing that must be compelling for any unbiased judge.

I just want to point out that these two views are not the same. You can indeed move on from inexpressibility to a demonstration or showing of what can't be expressed. But first (or conjointly) you can also say why, as Wayfarer suggests. Or would the claim be that inexpressibility itself can only be demonstrated, not justified? — J

If something is inexpressible, then by that very fact one cannot say why... Doing so would be to give expression to the inexpressible.

In the end, past all the justification and discussion, there is the act. Any justification becomes besides the point.

And this applies to ritual, ethics and maths:

What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call "obeying the rule" and "going against it" in actual cases. — PI §201

This is the answer offered to the problems of rule following, and it's the only one that works - that in the end, it's just what we do.

And in so far as it is just what we do, the rationalisations, arguments and justifications are almost irrelevant, mere superstructure or appendix.

So while "it might be important to say why" (@Wayfarer) it remains that "what cannot be said may be shown or done" (Banno)

So we still have, from the Tractatus, "The world is all that is the case" and "What we cannot speak about we must pass over in silence", both quite so. And then we go to the next step, which is that nevertheless, we must act, and be part of that world.

When Moore holds up a hand and says "Here is a hand" he is performing an act, making a declaration; here he cannot be wrong.

Hi, can I jump in here? I'll just go for it, apologies if I'm intruding.

I'd like to quote a passage from the book After Finitude, by Quentin Meillassoux. There he says:

"(...) the Tractatus maintains that the logical form of the world cannot be stated in the way in which facts in the world can be; it can only be 'shown', that is to say, indicated in accordance with a discursive register that cannot be bound by the categories of science or logic. Consequently, it is the very fact that the world is sayable (that is to say, liable to formulation according to a logical syntax) that cannot be bound by logical discourse. Whence proposition 6.522: 'There are indeed things that cannot be put into words. They make themselves manifest. They are what is mystical.' But the mystical does not consist in other-worldly knowledge -it is the indication of science's inability to think the fact that there is a world. Hence proposition 6.44: 'It is not how things are in the world that is mystical, but that it exists. (...)" (Meillassoux, After Finitude)

What do you folks make of that? Does any of that make sense to you, or not? Not sure if I'm actually helping here, in the sense of being collaborative. If not, then I'll excuse myself out.

If something is inexpressible, then by that very fact one cannot say why... Doing so would be to give expression to the inexpressible. — Banno

That's what I'm not sure about. I don't think I'm asking for the inexpressible itself (call it P) to be expressed; that would indeed be impossible. Rather, I want to know why P is inexpressible. Call that explanation Q. Does it really follow that, if P is inexpressible, Q must be as well?

In a certain sense, I agree with you (and Witt) that justification becomes pointless when what we do is interpreted as rule-following. Nor am I disagreeing that, often, rule-following is a good way to think about what we do. But I'm not convinced that this entire situation is opaque to explanation, or at least to elucidation.

Probably this all depends on whether one considers the Tractatus to be a demonstration or an explanation. Some of both, surely? I know Witt said very austere things about how not-philosophy his approach was, but I see a lot of explaining and justifying going on nonetheless.

No need to apologize. We all jump in as the spirit moves us. And sure, the passage you quote is very germane.

But if something can't be said, it might be important to say why and surely philosophy has a role to play there.
— Wayfarer

I . . . take [it] to be one of the main themes of the Investigations - that what cannot be said may be shown or done.
— Banno

I just want to point out that these two views are not the same. You can indeed move on from inexpressibility to a demonstration or showing of what can't be expressed. But first (or conjointly) you can also say why, as Wayfarer suggests. Or would the claim be that inexpressibility itself can only be demonstrated, not justified? — J

Thanks for picking up on that. I was saying, Wittgenstein's famous 'that of which we cannot speak....' is often used as a fireblanket to suppress discussion of the mystical, which I feel is one facet of philosophy. I peruse the Tractatus (which I've never studied formally or read in full), there are aphorisms which ring true, and many others I don't understand at all. The one that I always recall is 6.41:

The sense of the world must lie outside the world. In the world everything is as it is and happens as it does happen. In it there is no value—and if there were, it would be of no value.

If there is a value which is of value, it must lie outside all happening and being-so. For all happening and being-so is accidental.

What makes it non-accidental cannot lie in the world, for otherwise this would again be accidental.

It must lie outside the world.

I'd like to ask, 'Why is that?'

Is the answer 'Shuddup already' :rage: ?

he here cannot be wrong. — Banno

But he can be jejune.

"For it does not admit of exposition like other branches of knowledge; but after much converse about the matter itself and a life lived together, suddenly a light, as it were, is kindled in one soul by a flame that leaps to it from another, and thereafter sustains itself" ~ Plato, VII Letter — Count Timothy von Icarus

That resonates with the legendary origin of Ch'an Buddhism, namely, the Flower Sermon, wherein the Buddha's insight is transmitted worldlessly to one Mahakasyapa, the only monk to smile when the Buddha gazes at a flower, and the origin of what is thereafter designated a 'special transmission outside the scriptures' - notwithstanding that this tradition also generated a vast corpus of written texts about what supposedly could not be transmitted by them. Something similar is also discernable in the 'doctrine of divine illumination', associated with Augustine, and about which there's an article on SEP.

Having said that, I also understand that the mystical is something which engenders vastly different responses in people. It resonates for some, and not at all for others, and it is also a fertile source of both exploitation and delusion. I've always felt an affinity for it and I do think that properly grasped, there are self-validating elements in such teachings, but only if they are properly grasped. That is what it 'has to be done' refers to: they're dynamic principles that have to realised in both sense of made real, and understood properly.

That seems to be pretty much what I have been arguing.

That's what I'm not sure about. I don't think I'm asking for the inexpressible itself (call it P) to be expressed; that would indeed be impossible. Rather, I want to know why P is inexpressible. Call that explanation Q. Does it really follow that, if P is inexpressible, Q must be as well? — J

So we might proceed by looking at examples.

But your high "C" will not do, becasue the singer being unable to reach it is not inexpressible; we know what note they are trying to reach, and that they cannot reach it.

So give an example of something that is inexpressible...

See the problem?

Is the only answer 'Shuddup already' — Wayfarer

Yep.

But that's not to stop you from doing.

Shut up and calculate. :wink:

Yeah, the high-C example has problems with equivocation on "expressible" -- we can express the fact that she cannot express the note. I'll see if I can come up with a better example . . . tomorrow. (And yes, I perceive the fiendish trap that awaits me as I try to somehow denominate or refer to what I also claim is inexpressible! :wink: )

When Moore holds up a hand and says "Here is a hand" he is performing an act, making a declaration

One that requires having a hand no doubt.

I wonder what sound one hand makes? :chin:

:wink:

What and are proposing is important - but it is also just froth.

Speaking from a purely personal POV, I think that Natural numbers might objectively exist, and perhaps Real numbers as well. But when you get to stuff like the set of Complex numbers, things just don't make sense anymore. Like, if I look at the four apples on my table, I understand that each of them is a unit (and hence, I can represent that with the Natural Number 1. I can also count them as Four apples). I understand that if I cut an apple in half, I have two half apples, I have two 1/2 apples in total. I get that. But if I ask you "What physical, ordinary object in the world, can be accurately referenced by the number that stands for the square root of minus one?" There is no such object. Imaginary numbers have no correlate in the external world. Or do they?

Q. How many Wittgensteinians does it take to change a light bulb? A. Shut up and screw!

I have a friend who's legs were removed curtesy of the US military using an old cluster bomb. He sometimes finds himself, on waking, checking that they are not there. Not so jejune, .

"What physical, ordinary object in the world, can be accurately referenced by the number that stands for the square root of minus one."? There is no such object. — Arcane Sandwich

https://www.geeksforgeeks.org/applications-of-imaginary-numbers-in-real-life/

@Banno But that's kinda my point, there's no "ordinary" object that one can pinpoint to have a more "common sense picture" of what the imaginary number "i" stands for. Like, it's something that's used in very technical, specialized fields, like electrical engineering and quantum physics. But if you had to explain the concept of an imaginary number to me, using an ordinary object like an apple, how would you do it? Sorry if I'm being rude.