But as noted at the outset, one of the characteristics of modern culture is the 'flattening' of ontology. — Wayfarer

I think you can have hierarchical organisation of predicates without being committed to reality degrees. Like everything which is red is coloured - the former is on a "lower rung", or "higher rung" on a ladder of predicates, than the latter. Much like plant is on a lower or higher rung than the mineral. Why equate the concepts?

That's certainly a perspective.

"wall" = w
"beige wall" = wall + beige

Walls have a higher degree of reality when painted beige? I suppose that just means some properties are privileged, because no one wants to believe that.

I don't understand why anyone would want to say "higher degree of reality" when they mean "has more characteristic predicates applying to it", could you spell that out for me? What makes a predicate make something it applies to more real?

Say as a crude example, that a delusional subject has an inadequate grip on reality. There are of course degrees, ranging from severe mental illness through to narcissistic personality disorder, for instance. I think in classical philosophy, there is at an least implicit principle that the philosopher is less subject to delusion than the untrained mind - the hoi polloi, if you like. They are more highly realised, they have a superior grip on reality. — Wayfarer

A deluded person's grip on reality is a property of them, not of the delusions. It would be the delusions that would need to admit of degrees of reality, rather than the degree of delusion of the subject. Paradigmatically though, delusions are that which are not real and we staunchly believe despite evidence.

IE that's an example of a predicate with an intensity parameter - a person's degree of grip on reality. And it's also not a degree of reality of what that person grasps.

It's very difficult for me to imagine what it might mean to have a degree of reality, in contrast to an existent which has a property of a given intensity. Like a remarkably red apple makes red "exist more" because its red is remarkable. But that's about the redness, not about the apple.

Degrees also seem like a quantitative concept - as if one thing can exist more than another, or exist harder in a given way. As opposed to a qualitative one - like an idea might exist in a different sense to a cup. The former corresponds to changes in degree of reality within a type, the latter corresponds to differences type. Compare heights and masses, two different quantitative axes, differences of degree. Ideality and materiality, two different seemingly binary properties, differences in kind.

What can you accomplish with different degrees of reality that you can't accomplish with a predicate with an intensity eg "Sally is 1m tall", or alternatively a standard predicate label, say "Sally is tall"? Open question.

If so then it seems the skeptic must at least admit of knowledge of time. — Moliere

We don't see the skeptic Sartre is responding to in the OP. I find it difficult to tell exactly what radical doubt he's responding to.

This is almost a troll reading, but I want to give it anyway - no further resources are needed to talk about the validity of "I think, therefore I am" than seeing if, in the circumstance of the utterance, predicating an entity entails it exists. In normal circumstances it does. Therefore the argument ought to be understood as valid by competent speakers of English.

What isn't a troll reading about it - Sartre's commentary is transcendental, a reading of the necessary preconditions of Descartes' ability to argue, judge, doubt ensuring the truth of the claim it seeks to demonstrate. That the doubter exists. The above account involves only norms of language, and specifically talks about predicability rather than any phenomenological, a-priori or transcendental structure.

If an account of the argument can be given without use of the specific transcendental concepts Sartre is using, how can we say his analysis of necessary preconditions follows? Since the argument can be conceived otherwise.

I mostly just wanted to throw this in the thread to see what happens.

but more because I wanted to see what a mild-mannered statistician saw in such a goofy unusual subject. — T Clark

Projects like that give you entire other ways of imagining everything. There isn't too much evidence for how we see the world at a base level, so it's nice to be able to view it from a remarkably alien perspective.

But at some point works like that became closer to how I see the world, in terms of worldview and metaphysics, than the everyday pretheoretical intuitions I live in. If whenever I open my mouth fairytales fall out, I may as well learn as many as possible.

I've been on a Cybernetic Culture Research Institute kick the last few months. I read:

Nihil Unbound by Ray Brassier through fully for the first time.
I went back to his dissertation Alien Theory. I didn't finish it because it would require a lot of further study for me to understand. Though I was surprised by how Brassier writes in it! He's usually very sardonic, and when he attacks a position you feel as though that position has been put firmly in its place, in this one there's a sense of catharsis in his critique. The dissertation just bulges with utter frustration at the navel gazing hermeneutic meta-game of continental philosophy and social science at the time.

Currently going through - I stress going through, not reading - Nick Land's Thirst For Annihilation, it's quite a book. The prose has a prophetic and thoroughly debased quality to it, though its coke fuelled rambling is marked by great self awareness:

What I offer is a web of half-choked ravings that vaunts its incompetence, exploiting the meticulous conceptual fabrications of positive knowledge as a resource for delirium, appealing only to the indolent, the maladapted, and the psychologically diseased. I would like to think that if due to some collective spiritual seism the natural sciences were to become strictly unintelligible to us, and were read instead as a poetics of the sacred, the consequence would resonate with the text that follows. At least disorder grows. — Thirst for Annihilation

and often there are fecund critical insights:

Kant’s great discovery—but one that he never admitted to—was that apodictic reason is incompatible with knowledge. Such reason must be ‘transcendental’. This is a word that has been propagated with enthusiasm, but only because Kant simultaneously provided a method of misreading it. To be transcendental is to be ‘free’ of reality. This is surely the most elegant euphemism in the history of Western philosophy.

The critical philosophy exposes the ‘truths of reason’ as fictions, but cunning ones, for they can never be exposed. They are ‘big lies’ to the scale of infinity; stories about an irreal world beyond all possibility of sensation, one which is absolutely incapable of entering into material communication with the human nervous system, however indirectly, a separated realm, a divine kingdom. This is the ghost landscape of metaphysics, crowded with divinities, souls, agents, perdurant subjectivities, entities with a zero potentiality for triggering excitations, and then the whole gothic confessional of guilt, responsibility, moral judgement, punishments and rewards...the sprawling priestly apparatus of psychological manipulation and subterranean power. The only problem for the metaphysicians is that this web of gloomy fictions is unco-ordinated, and comes into conflict with itself. Once the fervent irrationalism of inquisition and the stake begins to crumble, and the dogmatic authority of the church weakens to the point that it can no longer wholly constrain philosophy within the mould of theology, violent disputes— antinomies—begin to flourish. Due to the ‘internecine strife of the metaphysicians’ polyglot forces begin to be sucked into conflict, at first mobilized against particular systems of reason, fighting under the banner of another. But eventually a more generalized antagonism begins to emerge, various elements begin to throw off the authority of metaphysics as such, scepticism spreads, and the nomads begin to drift back, with renewed élan. — Thirst for Annihilation

the style of argument in it isn't what you would expect though. There are no syllogisms. There are no premises. There are scarcely conclusions. Where there is is a sustained and thorough attempt to get you to imagine everything around you differently. The book operates at the level of ideology without being propaganda, a surgery upon worldviews. It wrestles with intuitions that would make anyone imagine the world and its history of ideas in any way at all. All in the style of a candyflipper asking you to hold his snuffbox before running at a wall.

It is true that Knausgård wants to get into the deepest point of sadness and loneliness, but it is something I am looking for right now — javi2541997

Lemme know what you think when you're done please!

Was that list from ChatGPT?

A Death in the Family. My Struggle 1. by Karl Ove Knausgård. — javi2541997

I could not get along with this one. Knausgård has the most Norwegian man's narrative voice imaginable. He represents the ancestral urge to escape loneliness by living in the family's country hut in complete isolation.

You need to write an OP. I'll close the thread.

When I try to explain to friends why I do phil. — J

Madness.

Thank you for your welcome!! — KantRemember

I too welcome you! Great posts.

I want to return to this loose end. Am I right that we can avoid the conclusion in (8) by denying (4), the symmetry of relevance? — J

I believe so yes. I enjoyed your counterexample. Removing symmetry stops you from setting up a partition of things into that which is relevant and that which is not relevant to philosophy, on the basis of the relation, but you still end up having the sense of connection between ideas. As in, if X is relevant to Y, and Y is relevant to Z, then X is still relevant to Z. It's just you can't go "backwards" now.

I quite like the idea of dropping symmetry, since moves in disciplines tend to be autonomous of philosophy, whereas moves in philosophy do not tend to be autonomous of other disciplines. So things are relevant to philosophy, but philosophy is not always relevant to things.

That's an imprecise way of putting it, since the relevance relation is on assertions, but I hope that abuse doesn't do anything to what I'm saying.

The only way I see that we can get "relevance" to be symmetric here is to define it as such, so it means something like "possibility of making eventual connections." But that seems much too broad, and misses the interesting questions about why we care about relevance in the first place.

The possibility of making eventual connections seems to be the sense of relevance that iteratively asking a question as previously spelled out has, however. Which is to say, asking a series of relevant questions to a statement which must terminate somehow in philosophy would need a more precise demarcation of relevance to - and perhaps relevance of - philosophy to a claim or discipline of study. Otherwise I believe we're left the silly one I wrote down. At least, with reflexivity and transitivity intact.

First, just some housekeeping: We considered whether "Why?" was the actual recursive question, and raised some problems about that. But the way you've formulated it here is better, and still allows a robust sense of relevance, unlike the "What would Kant have thought of that?" example. So let's say that Q( X ) asks, "What is your justification for X?" — J

:up:

You point out the danger that we've done some definitional fast-footwork here. Philosophy (or the context Phil) is being construed as "the demarcation between a fixed set of Q and other sets." Does this mean that the fixed set of Q is only unique in this way? "Why does asking [the Q question] eventually lead to philosophy?" you want to know, and the suspicion is that is does so because we have defined it thus; there is no other reason. — J

Yes. It is quite probable that you end up setting up a question which forces you to terminate in philosophy. But with perhaps no good reason to assume that philosophy has this unique termination property. Like @Srap Tasmaner's psychoanalyst example shows. There needs to be something about the sequence of questions that renders each of them somehow relevant to what they're asked, and the answer to be informative to what it's asked of. That is, the question has to be a "good" question in a nebulous sense and the answer has to be a "good" answer in a nebulous sense.

Repeatedly asking "What is your justification for X?" might be seen as relevant to any claim, as the reasons motivating a claim are ideally articulable by someone who knows them - not that they always, or often, are known or said. The question would need a guarantee that one would always end up in philosophy when asking it.

One way of fleshing that out would mean at some point questions about justification always become philosophical. About the meaning of justification. Here is @Srap Tasmaner again with "I speak English", which you'd also need to parry - why isn't it a good answer? Why isn't it a relevant answer?

If you asked "What is your justification for "I speak English?"?, one could very well answer "I speak English" as a demonstration. But that's not a philosophical remark, it's a statement of fact about the person.

There's another thing to be mindful of when making the question related to justification - if we already come in with pretheoretical intuitions that justification is philosophical in nature and that philosophy concerns itself largely with justification, our pretheoretical intuitions will just make us note a few things. Firstly, we might reject off hand that the chain could terminate with something that looks like a bad justification, like repeating yourself might be - that's a no go, bad justification. Secondly that good justifications resemble explanations of logical principles. And in that case of course you're going to end up with a termination in philosophy, since you've pruned any answers that don't terminate in philosophical justification chit chat away.

Perhaps there are other terminations. If an experiment demonstrated a theory conclusively, you might end up saying "The experiment demonstrated the theory" - which may be the final relevant word on the matter of justifying the claim if "The experiment demonstrated the theory" is justified by the standards of the discipline. In that case asking "What is your justification for (The experiment demonstrated the theory)?" and expecting something on the nature of justification as the only type of relevant answer will just pop you out of the discipline's context and perhaps no longer be a good question.

Thus there seem to be profound and shitty terminations. Profound terminations say something about the relationship of philosophy to other disciplines and vice versa, and perhaps even about the nature of ideas themselves. Shitty terminations will occur when we've set it up the termination in philosophy through unarticulated, or trite, presuppositions regarding what counts as a good answer and what counts as a good question.

But we can perhaps toss away the "good question" thing for now, and grant that "What is your justification for X?" will always be "good" in the appropriate nebulous sense. To gesture in the direction of that nebulous sense, I'll say that a question is good when it reveals something about how what it is asked of is known or supplementary information about what it is asked of. And perhaps we should assume that the answerer plays nicely and just answers truthfully, directly and sincerely every time. No frame shifting on their part.

This thread appeared once before and immediately disappeared. I wonder why. — Vera Mont

It was deleted because.

I can't make sense of what is being asked. — Vera Mont

It's very dense word salad.

@EdwardC - please put more detail into your points and questions. I'm going to close the thread. You can remake something on the topic but please try to make it readable.

unless fdrake or his evil twin were to come along and claim that this is the only way of understanding the issue I raised in the OP. — J

The only way of understanding anything is to assign symbols to bits of it. Paying no attention to the silent process of individuation which allows the symbol to refer to a target. It worries me, but I think I'm joking.

I don't believe they are. I stipulated them based on my intuitions. It captures a sense of relevance, but you might prefer to think of relevance differently. Like if relevance was thought of causally, you might want to relax symmetry (since if X is a cause of Y, then Y cannot be a cause of X, perhaps). — fdrake

@Leontiskos

That gives you two choices about how disciplines are organised based on relevance. Either philosophy is related to all domains, and thus co-extensive with each of them it is related to. Or philosophy is not relevant to some domains - that is, philosophy is of no relevance to any claim in them.

But we don't get to decide which is which, based purely on the notion of relevance. If you can show that some claim is related to some claim which is relevant to philosophy, you would show that it is thereby relevant to philosophy assuming relevance is an equivalence relation. — fdrake

I don't think your sentence here is grammatically coherent. Not sure what it is supposed to mean. Same with your argument given earlier. — Leontiskos

Equality is transitive.

A) 2=1+1
B ) 1+1=4/2
C) Therefore 2 = 4/2

Similarly, when relevance is transitive.

A) X is relevant to Y
B) Y is relevant to Z
C) Therefore X is relevant to Z

Assume X isn't relevant to any claim whose context is philosophy, then X cannot be relevant to any Y which is related to a Z whose context is philosophy, since then X would be relevant to that Z through transitivity.

That is it. Are you not familiar with equivalence relations?

Interesting. What must not happen, or at any rate what we don't want to happen on pain of triviality, is the "flippant repetition" version. I think we need to be more precise. Did you mean your repeated "Why?" to be shorthand for "Why is what you just said a justification for what you said before that (eventually recurring back to X)"? Or does the "Why?" question change its character and possibly its reference depending on where we are in the chain of reason-giving? I'm trying to figure out if we're absolutely stuck with what we might call the "2-year-old's version" of "Why?" I think this makes a difference, but say more about how you were using the repeated why's. — J

Interrogating the question which can be asked repeatedly. What I was saying is that there should be a guarantee that the question preserves relevance of what it is asked of to its answer. That is, as much as an answer to it must be a good answer, the question must be a good question. What would make a good question to iterate is that it can be asked in any domain and makes sense in that domain.

"Why?" works because it always makes sense. But that doesn't have a clear termination in philosophy, like "How do you justify what you just asserted?" may.

Consider that if we can vary the questions asked, something must block our philosopher stereotype from doing this:

Person: 2+2=4
Philosopher: What would Kant have thought of that?

Which just trivialises the exercise, surely. The conceptual content of the philosopher's response does not seem to relate to the conceptual content of 2+2=4, it shifts the domain from without. It thus seems there needs to be a special sort of connection between the statement's content, the question's content and the answer's content in order to flesh out the idea that there will always exist a series of questions that terminates assertions in philosophy. Consider that people, like @Srap Tasmaner highlights, ardently resist what appears to be strictly philosophical probing IRL. Even if what they're saying is philosophical anyway.

IE, there must be something in the nature of questioning itself which allows it to alchemize any input into relevant philosophical concepts. And we'd need to put that in as a constraint on the series of questions to ensure the termination. What would it be?

There should also be a rejoinder to the claim that if a question takes an assertion to a strictly philosophical context, it should thus be seen as irrelevant to what it is asked of, like my example above. You might want to do that by expanding the scope of philosophy to cover all domains - and see my comment here about possible wrinkles with that prohibition.

Well, not quite that bad, but I think we have good reason to want to draw back from this conclusion. Before I talk about that, could you say whether your premises concerning relevance relations (3 - 7) are accepted logical truths? I don't know alternative logics well enough myself. — J

I don't believe they are. I stipulated them based on my intuitions. It captures a sense of relevance, but you might prefer to think of relevance differently. Like if relevance was thought of causally, you might want to relax symmetry (since if X is a cause of Y, then Y cannot be a cause of X, perhaps).

Aye. It's an argument that if you make philosophy the most expansive and the most foundational discipline, you end up making philosophy able to be done without philosophical reasoning and also have its foundations refuted by non-philosophical reasoning.

Equivalence relations work like equality. If you knew that x = 2, and that 2 = y, then you know x = y. Imagine that X is relevant to Y and that Y is relevant to some philosophical claim P, then X is relevant to Y, Y is relevant to P, then X is relevant to P. Y was arbitrary, so anything which is relevant to X cannot be relevant to philosophy.

Does this have to be an argument, if I can put it this way, that philosophical maximalism is equivalent to philosophical minimalism?

Does it also function as an argument that no boundary between philosophy and the sciences (and possibly other empirical disciplines, and possibly the arts, ...) is definable much less enforceable? — Srap Tasmaner

Yes. Yes.

And also that the top paragraph and bottom paragraph are equivalent.

Here is another spanner.

Assume that if philosophy is the strictly the most expansive discipline, every claim should have philosophical importance, but not every philosophical claim would have domain specific import.

1 ) Take a philosophical claim X which does not have relevance to a claim in any discipline.
2 ) Take the collection of statements of which X has relevance to and call it Q.
3 ) Relevance is transitive, if X is relevant to Y, and Y is relevant to Z, then X is relevant to Z.
4 ) Relevance is symmetric, that is if X is relevant to Y, then Y is relevant to X.
5 ) Relevance is reflexive, X is relevant to X.
6 ) Relevance is an equivalence relation.
7 ) Then anything relevant to X cannot be relevant to any philosophical claim.
8 ) Then all of Q is not relevant to philosophy.

That gives you two choices about how disciplines are organised based on relevance. Either philosophy is related to all domains, and thus co-extensive with each of them it is related to. Or philosophy is not relevant to some domains - that is, philosophy is of no relevance to any claim in them.

But we don't get to decide which is which, based purely on the notion of relevance. If you can show that some claim is related to some claim which is relevant to philosophy, you would show that it is thereby relevant to philosophy assuming relevance is an equivalence relation.

Asking why X is justified gives you a good candidate for finding a claim relevant to the questioned claim which is relevant to philosophy, and thus showing X is relevant to philosophy.

However despite philosophy perhaps containing every discipline, it cannot uniquely constrain their content. Assume that a system of philosophy entails that some claim in some domain is true, then the falsehood of the latter claim entails the falsehood of some statement, or invalidity of argument, in the philosophical system through modus tollens impact.

If ever you end up strengthening philosophy's import to a discipline, that discipline can take a refutational revenge. It seems, then, that if one makes inferences within any domain which are not philosophical, and some philosophical inferences constrain those inferences, then the domain inferences also place constraints on philosophy. IE, one can impact what is true or false in philosophy without reasoning philosophically at all.

If we take the assumption that every discipline is a subdiscipline of philosophy, and grant that inquiry within discipline need not be done using philosophical reasoning... then every part of philosophy is saturated by nonphilosophy's refutational impact on philosophy.

The situation may even worsen for philosophy. If we assume that every philosophical claim is relevant to every other philosophical claim, then every claim in the subdisciplines is relevant to any claim in philosophy.

Just at the moment philosophy becomes the core of human inquiry, it balances on that inquiry's fine edge. Philosophy's nature turns on a dime without any philosopher lifting a finger.

I'm not opposed to that, but what I said was the opposite. — Leontiskos

You mean that you claim that if X is a subdomain of Y, then studying X is also studying Y?

The two latter studies are co-implicative with the former. — Leontiskos

The analogy of course limps given the sui generis character of being. — Leontiskos

Alright. Several claims at work. All of them inequivalent.

The first is that the study of the totality of some domain X entails substudies of subdomains of X. The study of deer in toto is at least the study of deer movement plus the study of deer longevity. I think that's fine. That's ultimately a combinatorial thing. Notably the deer is fixed. That's of one of the following forms:

A ) If X is a subdomain of Y, then studying Y is studying X.

B ) If X is a subdomain of Y, then the subject matter of Y is a superset of the subject matter of X.

C ) If X is a subdomain of Y, then the rules which Y are studied with are a superset of the rules which X is studied with.

Every one of these asks if a different predicate distributes over the subset relation - or if you wanted, ratio. That is, does X subset Y imply D( X ) subset D( Y ).

The argument from analogy you gave smacks of ( B ), whereas the rules that constitute how something is grasped involve both B and C, and moreover the broader rules of study are only encapsulated in A. In that regard the argument from analogy doesn't get at the crux of it, since it leaves unexamined how context would need to distribute over the nesting of contexts. Which is, I reckon, the principle manner in which @J's iterative questioning results in all inquiry "converging to philosophy".

Why does the study of being qua motion (physics) implicate the study of being qua being (metaphysics)? Because motion is a kind of being. — Leontiskos

Yeah that's the inference I want you to flesh out. You have:

1 ) X is a subset of Y
2 ) Study of X is a subset of study of Y.

Why does 1 entail 2?

But the study of being qua being will be implicated in every other study of being (qua X). — Leontiskos

Why though?

I say that the dialogue would go differently. After the first reply of “I read it in the book,” the next recursion is not “Why?” but rather, “Tell me how reading it in the book justifies your answer.” The interlocutor would then need to give an account of fictional realities, and how they may relate to truth and justification, etc. etc. More philosophy, and very interesting philosophy at that. So it’s not just reading comprehension. What it “says in the book” is far from a concluding moment in the dialectic. — J

Broadly speaking I wanted to use the Frodo example to highlight some challenging properties of the question sequence that would need to be in place for the "termination in philosophy" to behave as you seem to want it to. But I wasn't explicit about it, because I hadn't thought those constraints through. Here is my attempt to highlight what was merely implicit in the Frodo example.

I think this is presumptive in a way the set up of the problem hasn't specified. It could very well be that the "right" answer to Q in that instance is as you say, but that elides the nature of a criterion by which the right answer could be specified.

I have bolded "would" there since it seems modal. But in my view it's the wrong modality for the question - I think the dialogue must go differently than I suggested in order for it not to count as an counter example. So we'd be left requiring an account of why the flippant repetition cannot count as an answer. It strikes me that it could count as one, even if it is a bad one.

Roughly, you'd need to constrain which answers are accessible from a start point by iterating Q.

Another wrinkle is that Q would need to be a specific question with one variable in it. It would need to behave very much like "Why is X justified?", where X is the prior assertion. I think you've given yourself a freedom to change at least the exact wording of the question in that paragraph. Which would be fine, but then there's a similar question to above regarding which questions are accessible from which other questions in this context. How do you ensure the content is preserved? Does the content need to be preserved? Or is the thesis a bit different?

Is it now more: "For every initial statement X, there exists a series of questions Q1, Q2, ... , Qn such that when Q1 is asked of X, and Q2 is asked of the answer of Q1 to X... the context of the answer of Qn is Philosophy"?

I’m suggesting that this be downrated to an argumentative pinnacle because of a particular characteristic it reveals: The philosopher can automatically trump any card played against them. Suppose some surly neo-Freudian interrupts me at the point where I assert that “there’s nowhere else to go.” Nonsense, he says. “I’ll give you a psychological-slash-reductive explanation of why philosophers do what they do, and this explanation will have nothing to do with ‛ideas’ or ‛reasoning,’ and everything to do with culturally determined modes of expression mixed with individual depth psychology.” Ah, but I can reply, “Indeed? And what is your justification for asserting that such an explanation is true?” We see where this has to go: We’re back to doing philosophy. My surly interlocutor has been trumped. My question doesn’t arise out of any real insight or depth, but he can’t very well deny that it’s reasonable and meaningful. And nor can he claim that it has an answer within his discipline. — J

I don't think it follows that one discipline is more primordial/foundational than another based on the "what is your justification for this?" question's recursive nature. I will spell out why.

Asking the question "What's your justification for this this?" is recursive. Call asking that question of an assertion X the function Q( X ), which I'll just assume maps to another assertion X'. Every assertion occurs in a context, and call the mapping from an assertion of X to its context C( X ). I'm going to leave 'context' undefined for now, and just assume that every assertion has a context of utterance that makes it understandable, and some rules that characterise that context.

Some contexts will have properties that make their rules philosophical. If a context is characterised by rules of philosophy - again stipulate that such rules are comprehensible and recognisable -, say that that context has the property Phil.

The quote says that for every statement X, there exists a number of recursions of Q^n ( X ), mapping an assertion to its justification, such that Q^n( X ) has a context C characterised by Phil. You can grant that, but you might wonder why such a thing would render philosophy the "top level". Roughly what this claim states is that asking for justification eventually terminates in philosophy, but there's no particular argument for the uniqueness of the termination. The statement in the quote construes Phil as the demarcation between a fixed set of Q and other sets. There's a question about the uniqueness of the fixed set - why does asking that question eventually lead to philosophy?

When Hegel compares this image to the way a philosophical idea develops, he points out that nature must exist in time, so this development is necessarily time-sequential. But he emphasizes that, again, being last in a sequence is not what he means by “highest” or “last” philosophy. We are speaking of a dialectical process in which each stage retains or “sublates” the former one. Ideas reveal themselves as a theoretical unity, they do not grow or develop in time, like a plant. That would be like saying that 3 “comes before” 4 according to a clock measurement. This coming-before is surely not temporal. Rather, we perceive the sequence in one glance, so to speak, and can recognize that what is last has to be last, but not in the way that events in time are last. — J

The iteration of Q also induces an order on contexts. If you consider the sequence X, Q( X ), Q^2 ( X ) ..., Q^n ( X ) and so on, you could treat that as defining an order on the contexts. Which would just be C( X ), C(Q( X ) ), C(Q^2 ( X ) ), each context has its place in the order given by the number of recursions of Q it is evaluated of.

If you showed that for every initial X there existed an n such that C(Q^n ( X ) ) = Phil, you would have some kind of "termination in philosophy".

At this point, if we want to, we can shrug our shoulders and declare nothing of interest here. Or we could keep the Hegelian glasses on and speculate that philosophy is “last” or “concluding” because it represents a true limit of something beyond mere argumentation. If we go full-on Hegelian, we would describe this something as Idea, or Spirit. But we could also say, more modestly, that the limits of inquiry may also show us the limits of being. As mentioned earlier, this requires a monistic turn, a suspicion that what is true of thought must be true of being as well. We have all read Irad Kimhi by now ( :joke: ) so we know how complicated this can get. But, again more modestly, all I’m pointing to is this: If there is an important connection between what can be thought and what exists, then it must include a thesis about self-reflection, and the limits of inquiry, and how these limits are related to what exists. — J

But the relationship between the termination of the sequence of contexts in Phil and any properties of the recursive function Q remains unspecified. Why Q has the (alleged?) properties it has is something hitherto unexamined.

I do notice a bit of a landmine in this discussion, however. There is a presumption that Q can be meaningfully applied to any assertion X which is reached by some application of Q. Roughly this means that any assertion is in the domain of Q. Why would this be the case, when we know that questions generically also occur in contexts that determine their conditions of meaningful answer?

A ) For example, if you have 2+2=4, and someone asks why, you better give a mathematical answer.
B ) If you ask why Frodo had to bear the ring, you better give an answer in terms of Lord of the Rings.

In both cases, if you ceased talking in the initial context of assertion, you would no longer be providing relevant information about the question. That isn't necessarily a bad thing, since contexts tend to relate to each other even if they are distinct (but have fuzzy boundaries). What I suspect is producing the termination in Phil, if it indeed happens, is that it is a property of Q itself rather than any of the assertions it is applied to.

Here's an example of a chain that doesn't terminate in philosophy. So if X is "Frodo bears the ring", Q( X ) would be the answer to "How do you justify that Frodo bears the ring?", which would be "I read it in the book"... And someone asks you why... And you assert you read it in the book. And someone asks you why. And you assert you read it in the book. Which, I hope we can agree, is not a termination in philosophy. It's about basic reading comprehension.

It thus seems to me to be a big extrapolation to imagine that every image of Q's context tends more and more to philosophy. What ensures that Q( X ) has this convergent property? And what ensures the convergence always goes to philosophy? How do you argue that the convergence goes to philosophy without already arguing that philosophy interrogates the context of all contexts.

I'm not interested in discussing it with them at all, I just remarked that the decision to ban him has nothing to do with the forum being left-leaning or censorship as is being implied. But rather that he showed a failure to behave respectfully. — Christoffer

:up:

Take the discussion about the excesses of reactive left wing culture elsewhere @Leontiskos @Swanty , @Christoffer . It is an interesting topic for a thread but it's not for this one. If you have further comments related to Lio's banning, say them.

It is difficult to have any charitable interpretation of his remarks, in particular, given that he'd used a white supremacist organisation as a source and lied about it. There was plenty of other mod relevant behaviour which we did not provide warnings for, but serves as additional context. "Sodomy" and "george floydism" should be interpreted as pejorative given his past behaviour, some of which probably went unnoticed except through mod work. Making an explicit troll thread at the same time as that remark also didn't help - I deleted it.

Suffice to say it isn't just his current remark which got him banned, it's a whole history.

I don't have the background to think through this unfortunately.

Isn't formal language a part of natural language? — Banno

Not transparently so, to me? Consistent systems capable of first order arithmetic can't contain their own truth predicate, so we don't put the predicate in. But natural language does contain its own truth predicate and behaves... well it doesn't disintegrate. That's at the very least a type distinction between consistent formal systems and natural language - one can contain its own truth predicate without being crap, one cannot.

Don't know what you're driving at. — TonesInDeepFreeze

I imagined Srap and I were talking about how the formalism in mathematics doesn't start at its "grounds", in the axioms. I imagine Srap and I are reacting to an imagined enemy of a formalist who thinks that mathematics is somehow "just" symbol manipulation. Or alternatively just awed at how the root of the formalism is in as something as messy as natural language, despite how set in stone - settable in stone - the concepts of mathematics seem to be.

because there is nothing anyone can say to explain it. — Srap Tasmaner

You can give a few token examples of... collections... using blocks, hands of cards, sweeties, square of chocolate, desks in their class, and just hope that the kid can educe the idea of a collection through analogy. Eventually.

Though it is incredibly hard if someone struggles with analogies and abstractions.

There's your foundations, all in box, instead of logic coming from outside mathematics ― that's what I was questioning, am questioning. (I suppose, as an alternative to reducing it to something acknowledged as being part of mathematics, which I admit doesn't seem doable.) — Srap Tasmaner

Eventually the metalanguages terminate in predicates applied to undefined primitives and natural language statements. At some point that always happens. Even though such statements have clear conceptual content - though one might need to flesh that content out by derivation.

What does mathematics get out of pretending it's importing logic from elsewhere? — Srap Tasmaner

Someplace to start writing without having to explain yourself. I honestly think that's it.

What about division by 0? This stuff got me so confused in calculus — Shawn

Yes! Following that thread leads you either to ill definition or infinity, neither of which maths teachers are expected to teach.

One of my students gave the ingenious answer: 16/0 = 0, because the number of steps you can apply the iterated subtraction for division algorithm (finding division with remainder) to 16 with 0 as the divisor is 0 since you can't do it at all. Which is, again, quite cromulent.

I agree somewhat with the "required pace", but you and I know that in post-K12 math and related subjects it takes effort and time to accumulate a background necessary to advance or apply knowledge even a bit. In my years of teaching college math I have encountered only one such individual - an older student who dropped out to support himself as a poker player. He had taken my course in complex variables, and I recall speaking with him informally in the math office in which he brought up a really interesting and unusual notion on the subject, spur of the moment. Like a light bulb burning bright. I was unable to convince him to continue the curriculum. — jgill

I think our bar for profundity is different. Kids trip up on stuff like:

a ) x+1 = 2, solve
b ) x+1 = 3, solve

because they think that x in the context ( a ) is the same as x in the context of ( b ). Which is a very good reason to be stuck.

They also get tripped up on stuff like addition in the integers being commutative, but subtraction in the naturals not being.

Sometimes they even do things like 1-2 = 0, which isn't "wrong", per se, it's a sense of subtraction that removes instances from collections of stuff - like scoring off bags of pasta from a shopping list. You then have to tell them that it's "wrong", in some sense, to say 1-2=0 even when such subtraction is perfectly cromulent.