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)

So we still don't have any basis for determining that S followed a particular rule. We just treat certain circumstances as if she did. — frank

True.

If I'm understanding the argument: in place of truth-conditions Kripke resolves the sceptical problem with the sceptical solution that the community provides assertability-conditions. There's no fact which justifies the assertability-conditions, though.

Finally, the point just made in the last paragraph, that Wittgenstein's theory is one of assertability conditions, deserves emphasis. Wittgenstein's theory should not be confused with a theory that, for any m and n, the value of the function we mean by 'plus', is (by definition) the value that (nearly) all the linguistic community would give as the answer. Such a theory would be a theory of the truth conditions ofsuch assertions as "By 'plus' we mean such-andsuch a function," or "By 'plus' we mean a function, which, when applied to 68 and 57 as arguments,. yields 125 as value."

...

Wittgenstein thinks that these observations about sufficent conditions for justified assertion are enough to illuminate the role and utility in our lives of assertion about meaning and determination of new answers. What follows from these assertability conditions is not that the answer everyone gives to an addition problem is, by definition, the correct one, but rather the platitude that, if everyone agrees upon a certain answer, then no one will feel justified in calling the answer wrong.

But what would you look for in an extraterrestrial signal if you were assessing for rationality? You'd probably want to see intention, right? What tells you that an action was intentional?

Some would say we want to see some signs of judgement. For instance if we would take a sequence of constants as a sign of intelligence, that would tell us that the aliens consciously chose those numbers. Choice entails normativity. They picked this number over that one.

All of this is wrapped up in rule following, which is normativity at its most basic. To follow a rule means to choose the right action over the wrong ones.

If it turns out that there's no detectable rule following in the world, normativity starts to unravel and meaning along with it. Is that how you were assessing the stakes here? — frank

I want to post Kripke's summation of his own argument. On page 107-109:

Let me, then, summarize the 'private language argument' as it is presented in this essay. (I) We all suppose that our language expresses concepts - 'pain', 'plus', 'red' - in such a way that, once I 'grasp' the concept, all future applications of it are determined (in the sense of being uniquely justified by the
concept grasped). In fact, it seems that no matter what is in my mind at a given time, I am free in the future to interpret it in different ways - for example, I could follow the sceptic and interpret 'plus' as 'quus'. In particular, this point applies if I direct my attention to a sensation and name it; nothing I have done determines future applications (in the justificatory sense above). Wittgenstein's scepticism about the determination of future usage by the past contents of my mind is analogous to Hume's scepticism about the determination of the future by the past (causally and inferentially). (2) The paradox can be resolved only by a 'sceptical solution of these doubts', in Hume's classic sense. This means that we must give up the attempt to find any fact about me in virtue of which I mean 'plus' rather than 'quus', and must then go on in a certain way. Instead we must consider how we actually use: (i) the categorical assertion that an individual is following a given rule (that he means addition by 'plus'); (ii) the conditional assertion that "if an individual follows such-and-such a rule, he must do so-and-so on a given occasion" (e.g., "if he means addition by '+', his answer to '6S+ 57' should be '125"'). That is to say, we must look at the circumstances under which these assertions are introduced into discourse, and their role and utility in our lives. (3) As long as we consider a single individual in isolation, all we can say is this: An individual often does have the experience of being confident that he has 'got' a certain rule (sometimes that he has grasped it 'in a flash'). It is an empirical fact that, after that experience, individuals often are disposed to give responses in concrete cases with complete confidence that proceeding this way is 'what was intended'. We cannot, however, get any further in explaining on this basis the use of the conditionals in (ii) above. Of course, dispositionally speaking, the subject is indeed determined to respond in a certain way, say, to a given addition problem. Such a disposition, together with the appropriate 'feeling of confidence', could be present, however, even if he were not really following a rule at all, or even if he
were doing the 'wrong' thing. The justificatory element of our use of conditionals such as (ii) is unexplained. (4) If we take into account the fact that the individual is in a community, the picture changes and the role of (i) and (ii) above becomes apparent. When the community accepts a particular conditional (ii), it accepts its contraposed form: the failure of an individual to come up with the particular responses the community regards as right leads the community to suppose that he is not following the rule. On the other hand, if an individual passes enough tests, the community (endorsing assertions of the form (i)) accepts him as a rule follower, thus enabling him to engage in certain types of interactions with them that depend on their reliance on his responses. Note that this solution explains how the assertions in (i) and (ii) are introduced into language; it does not give conditions for these statements to be true. (5) The success of the practices in (J) depends on the brute empirical fact that we agree with each other in our responses. Given the sceptical argument in (I), this success cannot be explained by 'the fact that we all grasp the same concepts'. (6) Just as Hume thought he had demonstrated that the causal relation between two events is unintelligible unless they are subsumed under a regularity, so Wittgenstein thought that the considerations in (2) and (3) above showed that all talk of an individual following rules has reference to him as a member of a community, as in (J). In particular, for the conditionals of type (ii) to make sense, the community must be able to judge whether an individual is
indeed following a given rule in particular applications, i.e. whether his responses agree with their own. In the case of avowals of sensations, the way the community makes this judgement is by observing the individual's behavior and surrounding circumstances.

Because it makes sense of your questions :D -- when I first read your questions I realized I just needed to do some of the homework. So far I've been arguing only that there is a skeptical problem or skeptical question that I see from your OP, and haven't gone so far as to offer a solution or response or even to draw out implications.

And I'm glad I did some of the homework. Kripke's mind is wild to ride along with. Look at all these incredible connections he's able to draw out, and look at how he's able to distinguish so many possible beliefs at once while maintaining a single thread of thought! It's impressive.

I think what I'd say is that there are ways of detecting if someone is following a rule, it's only that these ways are not a state of affairs in the world. Rather it's an acceptance by a community. At least this is the solution I see Kripkenstein offering. The conditions of assertability aren't in truth-conditions, but there are still conditions of assertability. You just have to learn what they are.

What Kripkenstein's skeptic points out is that our common belief that "1 + 1 = 2" doesn't have truth-conditions, but rather conditions of assertability, and in comparison with Hume's skepticism we learn the conditions of assertability through repetition and acceptance by a community of rule-followers: the force of habit reinforced by communal acceptance.

So not quite an undermining of all normativity, but possibly a re-adjustment on philosophical interpretations of meaning.

I don't believe arithmetic to be merely rule following, but I think it is something we get intuitively on account of its being naturally implicit in cognition. Some animals can do rudimentary counting, which means they must be aware of number.

So, it begins with recognition of difference and similarity, then gestalted objects, then counting of objects, and this basis is elaborated in the functions of addition, subtraction, multiplication and division. Mathematical symbols and the formulation of arithmetical rules then open up the possibility of endless elaboration and complexification. — Janus

How do you respond here to @Ludwig V's point?

Counting makes sense as a genesis of arithmetic. But is doesn't escape from the sceptical question. There is no fact of the matter that determines whether I have counted correctly - except the fact that others will agree with me. This reinforces me in my practice of counting, as my agreement with others about their counts reinforces their practice of counting. — Ludwig V

Here there's a few bases from which we could confuse one another: arithmetic as a practice, arithmetic as a part of our rational intuition, arithmetic as rule-following, arithmetic as it was in its genesis, and arithmetic as it is. It might depend on which we're thinking about in our assertions how we evaluate the skeptical position.

I hope that makes it clear how I see it. I'm happy for others to disagree, provided they disagree with things I actually think, and not some imagined position based on their misunderstanding. — Janus

Hard to attain, at times. All we can do is re-state, try again, and all that. I read you as taking an intuitionist stance, as in mathematics is a part of our natural intuition that's even shared with other creatures, and so the skeptic has no basis because the skeptic is framing arithmetic in terms of rule-following when there's more to arithmetic than rule-following, such as the intuitive use of mathematics, whereas the skeptic's use is derivative of that (and so is an illegitimate basis of their skepticism, considering that the skeptic is undermining their own position in the process)

Let me know if that's close or not.

The challenge is about rule following, specifically about rule following activity that's now in the past. It's not an epistemic problem. It's not about what a person knows about which rule they followed. It's that there's no fact (a situation existing in the world) even in terms of mental states that satisfies Kripke's criteria for a rule-following-fact.

The idea of quadition was just to convey the problem. Kripke wasn't trying to do philosophy of math, although there have apparently been philosophers of math who were interested in it. — frank

I'm not trying to do philosophy asof math. I don't think I'd reduce rationality to rule-following either.

I think what @Janus's position amounts to is that there is a kind of fact, namely the familiar rules of arithmetic, which is the natural way to believe a person to be thinking about the question "how many?"

I'm taking the position that this is not an adequate reply, and attempting to give examples, like modular arithmatic, that are actually used where the procedure is the similar to the philosopher's toy of quaddition. Just because quusing is a philosopher's toy in comparison to addition that doesn't mean we have a fact to the matter about which rule is being followed -- there are other, more "practical" operations of arithmetic which can serve the same function as quaddition in the set-up. So the familiar reply to the skeptic -- to ask the skeptic to justify their skepticism -- can be overcome because there are practical (natural) examples that look identical to addition that are not philosopher's toys.

My thoughts on it (so far) is that it fits pretty well with my belief that we aren't as rational in practice as we tend to think we are. I think some people would assume that means I end up a behaviorist, but I'd say they're making the same mistake again. They think their post hoc rationalizations are the way the world really is. It's not. — frank

Heh. I don't think I'm that deep. I see a question, but I don't see a resolution.

Why a simple and seemingly private individualist mental life in the form of altered state of consciousness... has been represented and actualized in society to be aligned or opposed to a proper ethical way of life? — kudos

Some religions use psychoactive substances. Some religions condemn them. I'd say that if we're talking about an ethical impulse towards drugs then we're dealing with religious desires.

So the opposition to drugs is religious. In the Big sense the religious acceptance of drugs might also be religious (it's not like the religions which use drugs are recreational, any-time hedonists) -- but in the usual sense of most religious believers it's because of a religious impulse: it's just bad, and that's that.

Personally, I don't find walking enjoyable or conducive to thought and I am virtually indifferent to nature. I walk a lot in the city and when I visit other cities and towns. If I can be distracted by interesting people and architecture, I don't notice that I am walking. — Tom Storm

I love walking in cities and towns (most of my walking is there) but it's not to be distracted. I look about but there's something to the rhythm of it all that is conducive to thinking. It's just as much a part of nature as the woods, and at times our "home" is more terrifying and wonderous.

My point in indicating that everyone in the tread accepts it is to say that this burden is on you. To everyone in the thread it is accepted that we know our own actions in a more immediate way than we know others' actions, and if you disagree then you will have to provide an argument. The commonsensical idea is that when I see someone else flip a coin my knowledge is mediated by sense data; but when I flip a coin my knowledge that I am acting is in no way limited to sense data. Because I am the one effecting the act, therefore I know that the act is being effected. The mediation of the former is not present in the latter. — Leontiskos

Hrm! I don't know that I'd accept "we know our own actions in a more immediate way than we know others' actions" as a true sentence, but it'd be for boring reasons: I simply wouldn't use the predicate "...immediate" with respect to knowledge in general.

You could come up with a million absurd and arbitrary rules like quusing, and all I can say is "so what?". The logic of counting is inherent in cognition; even animals can do basic counting. And I see no reason not to think that basic arithmetic finds its genesis in counting. Give me a good reason not to think that and I will reconsider. — Janus

I'd say that basic arithmetic's genesis is in abstraction more than counting. But whether that's a good reason or not is up to you.

Mathematics is strange because there are no physical instantiations of it, really, and yet it's still true. It's always abstraction. With 0 you have to recognize something that isn't there. With 2 you have to look over the differences in physical objects to see what's the same between them. With 1 you have to individuate from the rest of the world: "this is an object distinct from the world as a whole. here we have a part"

I'd put mathematics on par with language as a whole rather than counting. Counting is an operation whereby we find the number. We don't even need things, as you've stated. You just go to the next number.

But what is the next number?

With modular arithmetic the number after 12 could be 1, or if we use military time the number after 24 is 1. Since we're in the domain of time this makes perfect physical sense. It's just a way of marking the day rather than the total time. Sometimes that's more important than a count "from the beginning of time".

Quaddition is certainly an arbitrary rule. (one might be tempted to say to the external world skeptic the same thing) It's a toy.

But the rub here is that addition is too -- it's just more useful than quaddition because of the world we happen to be referencing. But if we were referencing clocks then a different, modular arithmetic might be better suited.

So maybe a more plain-language way of putting the question @frank opened with (though I haven't read the text he's supplied, so I could be wrong): the skeptic might be asking how do you know the answer is not "the time is about 10:25" given that 125 divides into 12 10 times with a rough estimate of 25 minutes.

If you have four piles of four objects then you have sixteen objects, three piles of three objects then you have nine, two piles of two objects you have four. This obviously cannot work with two objects, so I'm not seeing the relevance to deciding whether addition, subtraction, multiplication and division are basically derivable from counting operations. — Janus

Well, if they're not derivable from counting then your argument against quusing isn't really talking about the same kind of thing since you've outlined a procedure for deciding if someone is quusing by pointing out that we can count beyond the quuser. But if it's not counting then that doesn't really demonstrate that a person is adding or quusing. The operations are distinct, rather than reducible to counting.

Of course I agree that arithmetic is more complicated than counting, all I've been saying is that it is basically counting. It is the symbolic language of mathematics that allows for the elaborations (complications) of basic principles. — Janus

I disagree that arithmetic is basically counting for the reasons I've stated: there are some numbers you cannot count to which you can get to within the arithmetic operations. This is an ancient problem, so I'm not sure how much the symbolic language matters. The symbols simplify and make things easier for us, but this is a problem that's not derived from the symbology: link on incommensurability (which should show why I keep harping on the square root of 2)

And I would also argue that it all finds its basis, its genesis, in dealing with actual objects, Thinking in terms of fractions, for example, probably started with materials that could be divided.

Probably, yes. But as the influential codger said:

There can be no doubt that all our cognition begins with experience...But even though all our cognitions starts with experience, that does not mean that all of it arises from experience — Kant