No! Not even close. I've been nervous to express myself because I feel like I'm in this in-between place: not directly involved in the conflict, but I know enough about the conflict that I know my country is involved. My sympathy comes from having met a guy who was born in Gaza. He lived in Wichita but would return to Gaza to visit family. One time he took me to a conference on the conflict with a group of Palestinian peace activists. That's where most of my knowledge of the history comes from -- these were peace activists in the US because they recognized how the US is involved in their struggle, and they did it through speaking about the history and talking about solutions, in spite of our darker impulses.

I agree with the quote, though I'm guilty of suggesting otherwise. There are lines in the sand here that are not easy to navigate, though being a USian I feel the compulsion to speak on them. As a citizen here I'm not directly involved, but I'm not indirectly involved either. My country acts on my behalf.

Another thought I've been struggling with is attempting to frame things in terms of numbers: I think it's important to note in the sense that we make these comparisons, but then there's this more absolutist side to me that believes there's no ethical justification for the act of killing, at least at bottom. Contingency, history, etc. gives us an excuse, but at bottom I'm skeptical that it follows.

Second, hierarchies are absolutely necessary to a functional society. This is simply too fundamental to argue. “Importantly, the organization of social groups into a hierarchy serves an adaptive function that benefits the group as a whole. When essential resources are limited, individual skills vary, and reproductive fitness determines survival, hierarchies are an efficient way to divide goods and labor among group members. Thus, an important function of the hierarchy may be to define social roles (Halevy et al., 2011) and allocate limited resources (Sapolsky, 2005).” - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5494206/#:~:text=Importantly%2C%20the%20organization%20of%20social,and%20labor%20among%20group%20members.

Societies must be organized in order to be functional. The hierarchy is the social organization of humans. Hierarchy is especially important in large societies, as there are more members of society to manage, more resources to distribute, and more social roles to be defined. — ButyDude

What is hierarchy, such that it's a necessity for all functional societies? (And notice how "functional" can beg the question -- it's a necessity for all societies you deem worthy of being functional, which could just mean "hierarchically organized").

What is a non-hierarchical society? In order to make the claim between hierarchy and function you have to define these things independently of one another. And it seems that you begin, from the outset, to define any society which exists to be hierarchical, which would indicate that there will be no examples of a non-hierarchical society -- but then how is it we're supposed to infer that non-hierarchy is not functional, if all societies are hierarchical?

Your https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5494206/#:~:text=Importantly%2C%20the%20organization%20of%20social,and%20labor%20among%20group%20members is of no help here. Let's begin with the abstract, rather than looking for sentences which might support our view one way or the other:

Social groups across species rapidly self-organize into hierarchies, where members vary in their level of power, influence, skill, or dominance. In this review we explore the nature of social hierarchies and the traits associated with status in both humans and nonhuman primates, and how status varies across development in humans. Our review finds that we can rapidly identify social status based on a wide range of cues. Like monkeys, we tend to use certain cues, like physical strength, to make status judgments, although layered on top of these more primitive perceptual cues are socio-cultural status cues like job titles and educational attainment. One's relative status has profound effects on attention, memory, and social interactions, as well as health and wellness. These effects can be particularly pernicious in children and adolescents. Developmental research on peer groups and social exclusion suggests teenagers may be particularly sensitive to social status information, but research focused specifically on status processing and associated brain areas is very limited. Recent evidence from neuroscience suggests there may be an underlying neural network, including regions involved in executive, emotional, and reward processing, that is sensitive to status information. We conclude with questions for future research as well as stressing the need to expand social neuroscience research on status processing to adolescents.

Hierarchies here aren't even cross-social, but cross-species -- it's a biological trait where members of a group have different "levels" (whatever that means) of power, influence, skill, or dominance. One of the things I'm suspicious of here is "levels" -- if we're speaking scientifically then what unit is common not just across all societies, but even across species? Is the unit of "power" identical between chimpanzees and homo sapiens? I don't think it's common between capitalism and feudalism, so I have reason to believe that homo sapien society doesn't even use the same units for "power" -- but rather it varies with what social organization is of interest -- giving me much less reason to believe that this review somehow managed to determine a unit to measure the "levels" of power across species.

At most your review states: we see some people rapidly doing what we believe they'd do anyways and our conclusion is this calls for further research. Yes, we can identify social status. We do it by how much property someone has access to. Sometimes we really admire a person for some deed or stance, but the rewards are financial or they are simply not seen as being a real reward -- the hierarchy we find ourselves organized around is the hierarchy of property, which in turn, through the law, is just the ability to enact ones will over more things which are tracked within the social organism.

But this doesn't say anything that you're saying about men and women, the necessity of hierarchy, or the relationship between hierarchy and function.

Moving onto your: https://ecorner.stanford.edu/articles/hierarchy-is-good-hierarchy-is-essential-and-less-isnt-always-better/

This is more or less a confessional, but it falls to the same problem I opened with. As it states in your article:

Gruenfeld and Tiedens conclude: “When scholars attempt to find an organization that is not characterized by hierarchy, they cannot.”

But "hierarchy" here is so vague that it can be substituted with "pecking order", as it is throughout the essay, in which case it's not very surprising that the scholars couldn't find an organization that is not characterized by hierarchy -- they didn't bother to crisply define what they meant, and any sort of perceived difference between individuals would count as a hierarchy (a "pecking order"). That's just silly.

Funnily enough there's a naive view of hierarchy/non-hierarchy which I'd even agree with that I believe underlies that article. I've been in enough well-meaning management lead meetings which seem to attempt to pursue non-hierarchical relationships. The problem there is that a corporation just is a hierarchy -- it's like trying to construct an army on the basis of the social rules of a dinner party. It's a ruthless organization built on exploitation and maximizing exploitation.

But even here -- something to note -- neither of these deal with patriarchy or its necessity. You're several steps away from demonstrating what you seem to want to argue which has something to do with men and women, and how looking at history through the prism of power differentials is bad.

There is such a movement.

Good questions!

While this is surely not the whole story I think, partly, there is value to disagreement. Agreement allows us to proceed, but philosophy doesn't proceed; Or when philosophy agrees it stops being philosophy and becomes something else. This doesn't accord well with philosophical traditions, which seem to have a sort of progress to them that's a mixture of agreement and disagreement, so it's definitely not the whole story. Only I think it worth highlighting that rational disagreement is valuable, and so the elusiveness of rational agreement isn't necessarily a fault against philosophy.

I, for one, don't trust the United States government when it comes to talking about peace. It's just not what we're good at.

Now war? That's what we're good at. Recent USian handiwork in this area can be seen with Iraq and Afghanistan where we handily won the war, but were terrible at brokering peace after winning. Why on earth would I believe that the US is in Israel for peace among sectarian conflicts, given the outcomes there? And, even if we were, given the outcomes of Iraq and Afghanistan, what reason would I have to believe that we're even able to achieve it?

Seems to me that if peace is the actual objective then we're wasting billions of dollars on a failed project.

But my suspicion is that peace is not the objective, but rather is something which we'd like to have -- but it's not why we're there.

I'd feel a lot better if the United States stopped supporting Israel.

One reason the conflict continues is that one side is stronger than the other. And when you're stronger you don't have to listen to the weaker party -- you can just push them into submission, as has been Israel's tactic so far.

Then when the colonized inflict something back upon the innocents of the colonizers (which they certainly were -- just as has been the case for many innocent Palestinians) it all gets re-intepreted back into the more powerful's narratives: up to and including people wondering why Hamas didn't think about the electoral game of Israel (this is just what Netanyahu wants!), or wondering if this is a *truly* strategic choice because of the electoral optics, which is just an absurd belief in light of how much death is involved.

Maybe it wasn't, but hell if I know when it's the right time to stop talking even if I know what's going on "on the ground", which I surely do not know well enough here. That's not really the sort of decision I'd be able to feel good about even if I knew the full circumstances, much less so from my comfortable vantage.

But I certainly expect Israel to continue acting the bully as long as they continue to receive military support. Which is why I'd feel better if we'd stop supporting Israel. But even that is a fantasy. The United States will continue to support Israel because of its "special relationship" (strategic place within the world). And Israel will continue to colonize. Given those two truths then the Palestinian has these options: Emigrate, bow, or die. And often times "bowing" results in death -- in which case, barring emigration, one might as well die standing.

Which means the enjoyment angle is pretty much beside the point. I don’t know where that leaves this discussion :grin: — Jamal

:D -- my first thought was "well, I suppose I'd have to read the book at this point, but I'm not sure I should pile yet another project on"

But then today I thought of Videodrome. This is the Cronenberg flick I was thinking of when saying he crosses the lines at times. The movie sits in a very uncomfortable place for me because there are depictions of what I'd call snuff (except that we know we aren't watching real snuff) and so if you think about it at all you're like "this just is snuff" and it's disgusting. But then there are scenes through the movie which bend around the idea of snuff. It's a weird blend of phantasmagoria and this blunt reality of the possibility in human desire.

That's one I might revisit to check my intuitions, at least; it's artistic enough that I'd subject myself to it. There are things I enjoy about it. But then the subject matter and its expression make me uncomfortable and wonder why I'm watching this, of all the things in the world. But then, here I am talking about it. (Deadringers evokes similar feelings in me, but then I don't have a cognitive dislike of what's going on so it's not as bad, it's merely "oogie" to me but not a rational opposition... maybe this feeling is what you're talking about?)

what I’m talking about is the experience of a book or film etc. that would lead you to say, just after you’ve finished it, that it was a good experience. Many dark, harrowing and sad works would fit.

But Crash was not a good experience, and Salo was not a good experience for you. And yet later on, in my case Crash showed its power by making me think about stuff. — Jamal

I've been struggling to come up with a better example. Salo was not a good experience for me, but really all I learned was a lesson I knew and I still tell people "don't bother", so it's not exactly the same as what you mean either.

What makes this difficult to think through is I can almost always find something I enjoy in a work of art, but when I don't I also just move on. There can be a morbid curiosity that pushes me on, but that isn't the frustration you're describing. What you describe is a work of art that more or less invokes aesthetic analogues to pain which you suffer through, dislike, and then come to appreciate.

With literature I'm struggling, though I can think of some examples from philosophy that are a lot like that -- start out frustrating and boring but then, upon pushing through, they become something better -- at the very least, worthwhile to have read. (and it's a curious experience because it's hard to describe to someone why you'd subject yourself to pain for the good of appreciating it, when usually people like creative works not in this sense but because it appeals rather than because it frustrates)

I wouldn’t personally put Eraserhead in the class of works that are unenjoyable but also good art, for the simple reason that I find it enjoyable. — Jamal

That's a good point. From my perspective I love it -- I just know I've tried showing it to people and have learned that it's a movie that doesn't appeal very widely. It's too weird for some.

Kubrick’s The Shining. Every time I watch it I wish I hadn’t, because it’s such a dark vision of never-ending abusive violence, cold and uncompromising and more disturbing than most horror movies, at least to me (even though they escape in the end). On the other hand, it definitely is entertaining so maybe it’s enjoyable after all. Yeah, not sure. — Jamal

That's a good choice I think. There's entertainment in the movie, but that aspect of it sort of ruins it. I loved The Shining when I first saw it as a horror movie that actually evoked fear in me. But when you start to put together how accurate the portrayal is, and how domestic violence continues on, it really takes out the enjoyment aspect.

Were you aware that Cronenberg made a film adaptation of the book? I wasn't aware that it even was a book, but I knew of the movie because I like Cronenberg (though I didn't see it, so I can't say how that particular movie is. Some Cronenberg crosses the line for me, and some doesn't)

On the topic of unenjoyable art, though: Salo fits for me. I had no idea what I was in for watching that film because it was just a friend who invited me over to watch another Criterion collection he got in the mail through a subscription service. We'd watch pretty much watch anything on the Criterion collection list, and I had no warning going in what the movie was about other than the title, and knowing who Passolini is from other nights like this.

It's so horrible that I recommend people not watch it. But the wiki gives the idea:

In the film, almost no background is given on the tortured subjects and, for the most part, they almost never speak.[16] Pasolini's depiction of the victims in such a manner was intended to demonstrate the physical body "as a commodity... the annulment of the personality of the Other."[17] Specifically, Pasolini intended to depict what he described as an "anarchy of power",[18] in which sex acts and physical abuse functioned as metaphor for the relationship between power and its subjects.[19] Aside from this theme, Pasolini also described the film as being about the "nonexistence of history" as it is seen from Western culture and Marxism.[20]

I kind of hated the film, but as the affect of it wore off I had to admit that it did the thing a movie has to do: not be boring. It wasn't in an enjoyable way, though.

This is just what came to mind because of your description of your experience of Crash kind of mirrors my experience of Salo. I'm wondering if there are other forms of unenjoyable art than these sort of grotesque depictions. There's something to be said for challenging work which goes over dark themes -- it's not exactly fun, but part of what makes art art is that it's in some sense appealing.

I'd put forward Eraserhead as a possible contender there. Just enough art to give it something more than just the subject matter as is, definitely moody and kind of insane, but it doesn't rely upon open depictions of depravity to do it (though it has its share of strange and grotesque imagery, too)

Some random thoughts:

I can sort of see how the cross and variables could represent various electrical components. One of the thoughts I had about re-entry was how, since he's dealing with a very large electrical system he kind of can get away with treating a part of the electrical system as being dependent upon another part of the system in such a way that it's like it's infinite. Or he can summarize a large network of components which are the same in form, but however-many times over (I have no idea what even the ballpark estimation would be) through re-entry rather than having to write out every individual component which would make for a technically accurate but difficult to use map. With re-entry you can summarize a large chunk of components.

And in Appendix 2, page 117 GSB makes a note of how he believes the marked state summarizes a large chunk of the Principia Mathematica -- so I believe it's correct to read him as trying to compress details into something more user-friendly so he can think through the problems of the network (but then he's a mathematician, so he's also developing a math).

Though

perhaps the answer to understanding chapter 11.. — wonderer1

That's not out of the question. And I'd go further and say it wouldn't undermine the text either. One of the stories from science I like to tell is about how the structure of Benzene was guessed at by Kukele, at least so he tells the story, when he had a very vivid day-dream of a snake eatings its own tail. The moral being for a science the inspiration isn't as important as whether the idea "works" (in Benzene's case, unified a number of observations into a single theory of its structure)

I don't see any reason to think that one is under an altered state of consciousness to then think that they are unable -- I'd prefer to say differently abled. There are people who see things without drugs, after all, though we also cannot substitute rigorous thinking with the possibly profound experiences people sometimes report hallucinogens having. On this topic I've always found Aldous Huxley's The Doors of Perception to be good. .


In the notes GSB notes his belief about the relationship between logic and mathematics is, on page 101-102:

What status, then, does logic bear in relation with mathematics? We may anticipate, for a moment, Appendix 2, from which we see that the arguments we used to justify the calculating forms (e.g. in the proofs of theorems) can themselves be justified by putting them in the form of the calculus. The process of justification can be thus seen to feed upon itself, an d this may comprise the strongest reason against believing that the codification of a proof procedure lends evidential support to the proofs in it. All it does is provide them with coherence. A theorem is no more proved by logic and computation than a sonnet is written by grammar and rhetoric, or than a sonata is composed by harmony and counterpoint, or a picture painted by balance and perspective. Logic and computation, grammar and rhetoric, harmony and counterpoint, balance and perspective, can be seen in the work after it is created, but these forms are, in the final analysis, parasitic on, they have no existence apart from, the creativity of the work itself. Thus the relation of logic to mathematics is seen to be that of an applied science to its pure ground, and all applied science is seen as drawing sustenance from a process of creation with which it can combine to give structure, but which it cannot appropriate

Which I find super interesting. It's kind of going into how math justifies itself, and in a way it seems GSB believes that logic is an applied mathematics, but that at bottom it all comes out of the void.

I actually don't. I had the thought, but then looking at his notes and what he did that just doesn't follow. I think he's drawing on his own intuitions about how he used the logic he developed more than he's being very explicit at this point in the book -- in a way he could have ended on Chapter 10 and called it a day, but instead he's trying to deal with the problems of self-reference.

There's something there, but in a way that reminds me of my old calculus professor: he certainly knew what he was talking about, but he found it hard to dumb it down for the rest of us. We managed to make it through, but it wasn't because the professor was good at communicating what he obviously knew.

And here the topic is very abstruse -- we don't even have the familiar things like number to rely upon in thinking through the calculus. But that's exactly what makes it interesting to me.

The marked state. So the waveform, trying this out, looks like this on page 66

¯¯|__|¯¯|__

and it becomes either:

¯¯¯¯|____

or

____|¯¯¯¯

And E4 is... not easy to render here, but the link to the book is on page 1 of this thread, and E4 is on book page number 66

Yeah, it's a bit of a stretch for me. I think at this point what would be best is for me to try and write out a synopsis of each chapter, summarizing the key ideas, while putting a little flag on Chapter 11 reading "needs further research"

Going back to the initial hook, I'd like to understand Chapter 8 a little better because of its relationship to your inference about the philosophy of philosophy being a reflection rather than a content.

That could very well be what's going on, actually. I said "smoothed out" because the example wave being fed into E4 is a series of marked-unmarked-marked-unmarked equally spaced out (where both the marked and unmarked square waves are equal in length), but then the output is a single wave which either starts unmarked-to-marked or marked-to-unmarked. Now that you mention adding it kind of does look like the output wave is equal in length to the input wave, it's just that the marked-unmarked-marked-unmarked wave became a long version of either marked-marked-unmarked-unmarked or unmarked-unmarked-marked-marked, depending upon E4's starting state.

So it could very well be addition! That appears addition-like. But to actually mean addition I'd have to be able to parse E4 better. I can see the input and the output, but I don't really understand how E4 operates on the input to obtain said output.

It wouldn't surprise me if you could relate this to radio wave-forms, though one thing that'd be different is that we're dealing with square waves, and my understanding of radiowaves is that they are not square waves. (but I do understand that electronic circuits use square waves sometimes -- but my understanding is not in a real, practical sense. Only I've seen square waves being used as examples while looking at websites while trying to make sense of the book)

And actually, now that you're here, I've started seeing how it might be possible to make counting more explicit -- which relates to the thread on Kripke's skepticism.

Heh, even reading the book I feel the same :D

There are gaps in my understanding of the book, still. I can say everything up to Chapter 11 mostly makes sense, now, but Chapter 11 is where the calculus suddenly changes -- and he spent 10 chapters making sense of the calculus before changing it all in one quick go.

For me it's mostly the logic that I find fascinating: it's a genuine logic that relies upon neither number or sentences (or truth!), and in the notes GSB even goes into connecting his logic to classical Boolean logic so there's even some sense in which we could say this is a "more primitive" logic. Or, at least, so the guess would go -- It'd be interesting if Boolean logic could, in turn, also derive GSB's LoF, giving a kind of "map" between both where you could simply choose which one you want to use.

So even if I don't quite grasp Chapter 11's operations, it's still pretty cool to be familiar with yet another example of a logic (as opposed to there being One True Logic, or some such).

Heh the morning routine has worked so far, but this morning I think I have an idea about E4, but GSB really is drawing on his extensive knowledge of electronics. I find myself going back to 's explanation of one-bit adders, and looking over electronics websites, but instead of bits E4 is changing the wave-form as it is "processed" through E4. E4 is also the first time GSB introduces re-entry from a deeper part of the expression to a more shallow part of the expression, where the prior example of demonstrating how markers work is the opposite. The task, for myself, is to see how the sentence immediately following E4 is true (and I'm not sure how to display a wave form here on the forum.): if I substitute the wave structure given for a then how is it that I can obtain either the marked-to-unmarked wave or the unmarked-to-marked wave at the end of the process? Somehow the two waves get "smoothed out", and I believe figure 4 goes some way to show how the crosses modulate pulses (as, I believe, we're meant to understand the statement following E4: a starts as marked or unmarked, and then the pulse is fed into E4 and somehow the pulse changes to a smoothed out marked-to-unmarked or unmarked-to-marked depending upon how it started -- which then, in turn, could be fed into a flip-flop. But here we're not dealing with memory, I don't believe; we're assuming memory and dealing with how expressions change waves)

But this is more or less me saying I think I need more homework to really work that out. My posts would just be guesses in the dark about rules I don't know, which would be even more confusing than the confusion I've already expressed :D

I'll pick through those videos from the previous conference to see if there are more worked out examples there. Else, LoF24 might be the best bet for understanding just how to operate on waves with the calculus.

OK it's not much, but I'm sharing something that did click this morning: Figure 1 is a graphical representation of E3, and E3 is kind of the same as E1 when a and b are equal to n. E2 always has a solution regardless of where you're at in the iteration, but E3 is indeterminate at every odd-depthed iteration. The imaginary state is with respect to time because:

$\left. {\overline {\, p \,}}\! \right|p$

is using the form from before but to represent E3 instead of giving us an expression with a determinate value. The oscillator function is the solution to E3: it's both m and n, and by adding a dimension of time we're able to give a solution to E3 which goes back and forth, as Figure 1 shows. So now I'm seeing the square waves not as switches but as marks in time as E3 goes back and forth between its two values.

Also the bit on steps from Chapter 6 clicked this morning -- we can count steps but they don't cross a boundary so in a sense you can have as many steps as you want, and GSB uses that to generate the infinitely expanding functions of re-entry. But also because we're not crossing boundaries we're sort of in this place where, due to the dimension of time, we can begin to use steps in the process.... something like that. And now it's time for work, but I thought this worth sharing because most of what I've posted has been more confusing than elucidating, and for once I thought I had an elucidating thought.

We could say the same about classical monarchy, autocratic dictatorships, imperial dynasties, &c.

This is getting into the epistemological territory of identification. Is it communist because there is such a thing in-itself that is communist, or is it a mere descriptor that we apply to a phenomena because it fits sufficient relativistic criteria. — Merkwurdichliebe

I'd distinguish between ideology, nation, state, and party. Communism is an ideology, nations are historical claims on territory, states control nations, and parties compete to control states. I'd also point out that nations work differently from monarchies and dynasties: the nationalist cause is self-determination within the framework of a nation. If you don't even have a nation then it's an understandable demand because it's the basic framework of power in the modern world. One could be said to be without a politics if you don't even have a nation.

"Communism doesn't work" is not specific enough to evaluate. Doesn't work, for whom? The right-wing politician in the OP? Well, that's not a surprise. Doesn't work for China, with an actual Communist Party in charge adopting to new circumstances just as one would predict a Marxist ideology would? (but that's not *real* communism, some way) Doesn't work for radicals who want more out of an apathetic government claiming to be The One True Free Way For the World?

Communism "hasn't been tried" by some, and "has been tested and found wanting" by others -- but I'd suggest that ideologies don't work like this line of thinking is stating at all. Ideologies are big-picture thoughts that often times don't give a specific evaluation for the particular activities of politics. Even when they do they touch the day-to-day at a step removed from a particular law being debated or policy being enacted or action being taken. They are whole ways of understanding a political world or order.

For my part I prefer the warts-and-all approach. Communism has been tried, and it's done horrible things and good things -- just like liberal capitalist nations. I'd say the common there is in the structure of a nation. To build a nation requires violence, or at least that's been the most common and effective method so far. And to keep a nation in control also requires violence -- there's something to be said for the theory that the modern state has a claim to a monopoly on violence. It's what keeps the state in order.

But the way that you and I know communism "doesn't work" in the manner proposed in the OP? I pretty much think it follows by definition. The usual arguments have been trotted out here -- that we're too selfish, or some such. So we define communism in this way where it cannot be realized, refer to the human nature we all know, and call it a day. Not even a single look into a history book is needed!

Cool, that helps with what comes next in the reading too. I asked about the tunnel thing trying to understand Subversion (why doesn't Figure 2 already behave exactly like f in E1?) -- but if it's because 'f' cannot be substituted by mark/no-mark then what is allowed vs. what must be avoided has an understandable difference because in the first case we're burrying the function 'f" deeper, but in the second case we're bringing a variable deeper to the function. So there are times when we can use chapter 6 ConclusionsConsequences or even the initials of the calculus, but we have to be careful about when it's appropriate to do so.

EDIT: I say that but the next part is opaque to me this evening. Might have to poke around the conference website to see if they have already done work on this chapter. It's not explaining itself as well as the previous chapters have, or at least I feel stupider while reading it. ((Heh, OK, the journal they have set up doesn't have any issues in it. So maybe the conference will be the way to go: "Hey, uh, what's he talking about here and how do you check the oscillating functions?" -- seems they have some videos from the last conference that might be worth checking out if I can't guess through to a possible insight tomorrow morning: http://westdenhaag.nl/exhibitions/19_08_Alphabetum_3))

With Figure 2 on page 61 do you believe there are supposed to be two imaginary tunnels? One from a to b and one from a to outside b?

If you mean a fact that justifies the rule and/or justifies how the rule is applied. I sometimes think that the quickest way to state the problem is to point out that the rule cannot be a fact, because the rule has imperative force and no fact can do that - a version of the fact/value distinction. For the same reason, no fact can, of itself, justify the rule. — Ludwig V

That seems to be the easiest way to parse things, I agree. Imperatives do not fit the form, so they cannot be either true or false.

I guess here we have to ask: is the reduction of addition to an imperative enough to satisfy the skeptic?

Can we state the imperative?

Is "68+57=?" a command? For the student it is, but when we are using the arithmetic it seems like we're actually asking something even if it's about numbers rather than some units of something (and perhaps this is what gives rise to the credulity Kripke's skeptic is pointing at). Perhaps we could rephrase all such instances as "If I were to perform addition on the constants a and b then what is constant c which all adders would agree to?"

Perhaps in general we could reformulate all arithmetical commands as "given this set of constants, and this set of operations, and this set of ordering the operations, find the correct constant"; which kind of highlights its game-like nature in that we have to have several stated "givens" before we're able to derive necessary conclusions.

In modern lexicon doesn't communism not work more or less by definition?

The empirical record on the whole phenomena is all over the place, just as it is with capitalist liberal democracy.

But the reason we know communism doesn't work is that's how the word works. If something worked then it wouldn't be communism.

OK I think all that GSB is saying in that paragraph, in simplified terms, is that re-entry doesn't allow us to use the arithmetic to solve for the value of an expression because re-entry creates an infinite sequence which doesn't allow us to substitute the marked or unmarked state for all cases within an expression (given that the expression is infinite). The part that makes that confusing to me is that the proofs for the Conclusions in Chapter 6 rely upon that same move -- the only way this makes sense is that we can use the initials for the parts of an expression which are "presented", but re-entry indicates a "...and so on" which is unspecified and so it becomes impossible to simply substitute for all cases of a particular variable the marked or unmarked state. E1 in Chapter 11 shows there is at least one case where an expression with re-entry simplifies to either the marked or unmarked state while attempting to utilize the arithmetic in this way to substitute and simplify, and so re-entry denies Chapter 8 as a set of theorems that rely upon being able to specify where one is at in the form.

I'm still a little confused about why this doesn't effect Chapter 6, but I think I understand why Chapter 8 is denied at least. And I'm ready to push on as well.

So the flip-flop circuit gives us a reason to posit imaginary values -- at this point I think "imaginary" is a bit of a term of art. So far the mathematics presented have been reliant upon forms and their inter-substitutibility. But here we have a form that, just like imaginary numbers in our everyday algebra, demands another number. (or, in this case, form, since numbers aren't really a part of the domain of interest) -- in a way we have to look at "p" in Figure 1 as having both the marked and unmarked state, and so we introduce imaginary values to indicate "the value of this expression is dependent upon the value of a function, and the value of a function depends upon time -- it is either the marked or unmarked state, but the calculus (with the assistance of the arithmetic, at least) cannot give you the answer at this point"

Also I think I understand what GSB is on about with respect to the oscillator function -- in p-cross-p if p is marked then the function is marked, and if p is unmarked then the function is unmarked. So there are some functions which even as they oscillate they are still continuously valued.

.... well, and that's as far as I got this evening. :D

Looking at E4 at this point I think we have to be able to follow along with a given expression's oscillation patterns, sort of like what I did with p-cross-p in the above, such that we can tell, over time, how often it will be marked or how often it will be unmarked or if it will always be one or the other.

Maybe we should distinguish between what brings the rule into effect (I chose that word carefully because after it becomes effective it is correct to say that there is a rule that ...) Can we see conditions of assertability as comparable to the licence conditions for someone to perform a wedding? If so, laying down a rule is or at least is comparable to, a speech act. We then have to explain that in some cases, the rule is not formally laid down, but informally put into effect (as when language changes, and "wicked" comes to mean the opposite of what it meant before). Once the rule is in effect, there is a fact of the matter, as when your king is in check or 68+57=125. — Ludwig V

I'm inclined to say there is a fact, but that it's not the fact which justifies, say, the license conditions for someone to perform a wedding. The rule is in effect, and in some sense then it produces facts -- but the production of facts is not justified by the facts so produced. The rule itself has no factual justification, though we could only judge if a person knows how to add if we know the fact we'd obtain by performing the rule. (at least, in my way of speaking where facts are true sentences. this could very well be me bringing in an inconsistency, though, whereas Kripke wouldn't bother with this notion of facts being true sentences. I'm not sure there)

Or, at least, I can't help but think that there has to be some distance between rules and facts for Kripke in order for the position to be philosophically interesting. The skeptic has to be pointing out that we're inclined to believe there's a fact where there is none in order for the skeptic to have a point at all, or else we're more or less just stating that the skeptic does not succeed in pointing out a skeptical problem.

From Chapter 8, p43-44:

A consequence is acceptable because we decided the rules.
All we need to show is that it follows through them.

But demonstrations of any but the simplest consequences
in the content of the primary arithmetic are repetitive and
tedious, and we can contract the procedure by using theorems,
which are about, or in the image of, the primary arithmetic.
For example, instead of demonstrating the consequence above,
we can use T2.

T2 is a statement that all expressions of a certain kind, which
it describes without enumeration, and of which the expression
above can be recognized as an example, indicate the marked
state. Its proof may be regarded as a simultaneous demonstration
of all the simplifications of expressions of the kind it
describes.

But the theorem itself is not a consequence. Its proof does
not proceed according to the rules of the arithmetic, but follows,
instead, through ideas and rules of reasoning and counting
which, at this stage, we have done nothing to justify.

Thus if any person will not accept a proof, we can do no
better than try another. A theorem is acceptable because what
it states is evident, but we do not as a rule consider it worth
recording if its evidence does not need, in some way, to be
made evident. This rule is excepted in the case of an axiom,
which may appear evident without further guidance. Both
axioms and theorems are more or less simple statements about
the ground on which we have chosen to reside.

Since the initial steps in the algebra were taken to represent
theorems about the arithmetic, it depends on our point of view
whether we regard an equation with variables as expressing a
consequence in the algebra or a theorem about the arithmetic.
Any demonstrable consequence is alternatively provable as
a theorem, and this fact may be of use where the sequence of
steps is difficult to find.

Perhaps a way to put it, and to go back to an earlier distinction: Theorems are statements in the meta-language about what we can do in the object-language, and consequences are demonstrations within the object-language.

And the statement of GSB's I'm trying to understand:

But we are denied the procedure (outlined
in Chapter 8) of referring to the arithmetic to confirm a demonstration
of any such equation, since the excursion to infinity
undertaken to produce it has denied us our former access to a
complete knowledge of where we are in the form.

To use arithmetic we have to have a complete knowledge of where we are in the form, it seems, but the calculus manages fine because, well, we are dealing with variables at that point?

Something subtle in there that I'm not fully picking up.

heh. OK I've seen this before. But still good to watch again.

Yeah, this is the first time I've come across that too.

This is cool though. Thanks for sharing.

Heh. It gets worse. You reminded me of the album so I decided to cue it up in YouTube as a playlist, and I have to do the same for every song :rofl:

lol I had to click through 2 warnings about how harmful that song is to see what it was.

This is the one I'm listening to tonight:

I'm still crawling my way there. This morning I didn't have time to do my little bit of philosophy to warm up the mind. Hopefully with two of us we can guess our way through.

I get that distinction. Indeed, arguably an assessment whether the knower is in a position, or has the capacity, to know p is appropriate in assessing any claim to knowledge. And I can see that final truth will often be distinct from any such assessment. (The jury has a perfect right to find the prisoner guilty or not. Yet miscarriages of justice do happen - and proving that is different from proving whether the prisoner is guilty or not. (A miscarriage might have reached the right result.)) But I still feel that the distinction is quite complicated. After all, the truth would be the best assertability condition of all, wouldn't it? And the assertability conditions would themselves be facts, wouldn't they? Of course, they need not be the same facts as the truth conditions. — Ludwig V

Yeah, I'll admit it's complicated. Or at least vague. I don't know if the truth is the best assertability condition, though, because here we have truths that we arrive at because of the conditions of assertability -- at least this seems to make sense of Kripke's position as an interesting position. If it all came back to truth then what's the deal with pointing out that there's no fact to the matter?

Also I think Kripke takes us to this place in his essay, but then doesn't say much more. I'm still uncertain that I have the exact right interpretation of Kripke here, too -- this is just what comes to mind when I attempt to make sense of Kripke's arguments.

There's something queer for myself at least in holding that facts are true sentences, that mathematical sentences are true, and yet they are not true in virtue of truth-conditions. It would seem that under this interpretation that I'm committed to some way of coming to know true sentences aside from truth-conditions. Given that we're talking about meaning that seems to be where I'd have to go. And there's a historical precedent there in the analytic/synthetic distinction, but I wouldn't want to rely upon that distinction because I pretty much agree with Quine on it being fuzzy.

So, yes, to hold to my interpretation of Kripke's conclusion along with some of my other beliefs and defend them I'd have to do some work on what these conditions of assertability are.

I am a moth jumping from light to light, but I usually come back around.

This morning I find myself going back. In particular as I proceeded I started to pick up on a pattern in the writing: between theorems and conclusions.

Going to Chapter 4: Theorems are general patterns which can be seen through formal considerations of the Initials. Also axioms are used. In going back to get a better feel for the distinctions between these terms I'm also picking up on that Canon is never formally defined -- it's like a Catholic Canon in its function. Also I'm picking up on why identity is the 5th theorem -- if the calculus was inconsistent then you could come up with x =/= x. And, going back over, I'm starting to see the significance of theorem 7 -- it's what let's us build a calculus through substitution, which theorem's 8 and 9 provide the initials for that calculus in chapter 5.

This is all inspired by the paragraph immediately where I left off:

We may take the evident degree of this indeterminacy to
classify the equation in which such expressions are equated.
Equations of expressions with no re-entry, and thus with no
unresolvable indeterminacy, will be called equations of the
first degree, those of expressions with one re-entry will be called
of the second degree, and so on.
It is evident that Jl and J2 hold for all equations, whatever
their degree. It is thus possible to use the ordinary procedure
of demonstration (outlined in Chapter 6) to verify an equation
of degree > 1. But we are denied the procedure (outlined
in Chapter 8) of referring to the arithmetic to confirm a demonstration
of any such equation, since the excursion to infinity
undertaken to produce it has denied us our former access to a
complete knowledge of where we are in the form. Hence it
was necessary to extract, before departing, the rule of demonstration,
for this now becomes, with the rule of dominance,
a guiding principle by which we can still find our way.

And reviewing back up to Chapter 5 is about as far as I got this morning. I'm attempting to disentangle the procedures of Chapter 6 from Chapter 8 to give myself a better understanding of what's missing and needed to understand the next bits in Chapter 11.  

Forgive me, I don't really understand what "conditions of assertability" are as opposed to "truth-conditions". Are they facts? In which case, we may be no further forward. — Ludwig V

I think it'd depend upon how we're trying to judge if someone knows something or not. With arithmetic those conditions are spelled out in books and habit and embodied within a community of arithmetic speakers. I'm thinking that it has more to do with a community's process of acceptance than facts.

So the teacher has a handful of representative problems which if the student is able to do without aid we then accept them as part of the community of arithmetic speakers.

Same goes for accepting whether a person knows the meaning of such-and-such for particular topics, or whether they know a language: the meaning isn't a fact as much as what you have to do in order to be accepted within a community of languagers.

Kripke's mistake (assuming I am recalling his position correctly), was phrasing the skepticism as a circular question to a mathematician where he asked to defend the validity of his judgements, as in

"How do you know that your present usage of "plus" is in accordance with your previous usage of "plus" ?"

That question is easily viewed as nonsensical, since it is easily interpreted as asking a person to question their own sanity. Similarly bad phrasing, leading to pointlessly circular discussion is found throughout the philosophy literature on private language arguments. — sime

Today we're talking in the meta-language about the object-language of yesterday, or right now we're talking in the meta-language about the object-language of addition. What, in the object-language, is the fact that we're adding at all? Would you say that this version of the question is easily viewed as nonsensical?

One of the things that I keep thinking on is how I tend to think of facts not as things but rather as true sentences. So in reading the essay, to make it make sense, I'd probably put it that -- rather than there is no fact to the matter -- there are no truth-conditions which make 68+57 equal 125. It's true because that's the answer we should obtain according to the conditions of assertability, but there are no truth-conditions that make it true.

In saying that much -- the question begins to make a kind of sense because mathematics is abstraction. So, in a way, there shouldn't be truth-conditions of addition. If there's a physical unit involved then there are possibly truth-conditions, but that's not the question. It's much more a question about meaning because of the abstraction. (at least, as I'm understanding it so far)

Keeping the analogy between Hume and Kripke's sceptic:

Hume's questioning of the place of causation doesn't yield reliably workable results. Scepticism isn't as much about reliable workable results as truth.

Quaddition's workability isn't really at issue. I think the sceptic would say "no, that's not useable for engineering. But what's the fact you can point to that lets us know the engineer is using addition?" Quaddition is there as a conceptual contrast to addition to help in understanding the question "What's the fact I can point to that justifies my belief that I'm adding?"

To make a similar function to quaddition that'd be easier to accept in light of engineering: Instead of Quaddition we could posit Googol-ition -- where the rules of arithmetic are the same up to a googol. If you find an example of an engineer whose used a number that high, then you can raise the googol to the power of a googol, and posit the googol^googol-ition. What's being asked after is a fact which demonstrates that we're performing addition, and googol-ition is there to give a conceptual contrast (and highlight that there's no factual difference, or at least make that challenge).

And the sceptic believes there is no fact at all -- there's a rule being followed rather than a truth being stated.

Does that make the question make sense?

I've been trying to think of a good response @Janus but have been unable, so perhaps this will do better. I believe this expression may be close to what you've been getting at?

You see, in both cases, the fundamental issue isn't resolved. Answering "habit" doesn't create rule-following facts for us. As with the problem of induction, we still have the gaping hole where we expected empirical data to support our assertions. Obviously, since Hume's problem attracted Kant's approach, we might expect that Kripke's problem would do something similar. Meaning isn't based on objective rule following, so maybe there's something innate about it. Maybe this innateness is a touchstone that meets each episode of communication, including this one. — frank

"innate" with respect to meaning is something I wouldn't deny as true, but only as unsatisfactory. It may be the case that innateness of meaning is the touchstone that allows you and I to communicate. When it comes to poetry, especially, that's where I gravitate towards -- asking for more words to explain words.

However we'd like to know more about something than "this is just what it means". This is getting back to a question I don't know how to answer: what do I want from a theory of meaning? To disappoint, I don't know what I want from a theory of meaning. Somehow I just ended up here with these questions, probably because I like to ask after seemingly silly things ;)

I think I'm tempted to simply accept the conclusion: there are no rule-following facts. Same with Hume and causation, though I really do admire Kant's attempt to overcome Hume's skepticism towards causation.

Fair point about the target audience. I'm asking about the speaker of the essay. If Kripke isn't offering a resolution, then I'm asking: what about these resolution-like looking paragraphs at the end? Who is offering them? That's what I mean. Who is the speaker?

The way that makes sense to me is to read the essay as presenting Kripkenstein's views, rather than Kripke's. Is that how you're reading it? (which, to be fair, that's how he starts out the essay -- saying it's an essay not on his view as much as an impression of his while reading Witti)