. If one is genuinely trying to instill a sense of duty for a good, substantial reason, then no. — ToothyMaw

I think that's pretty much what a noble lie amounts to: it's technically a lie, but it's for a good, substantial reason of drawing the people towards what's good. Since your account asks leaders to instill goodness in others through manipulation it seemed to fit.

A cynical exploitation would not be a noble lie, but just a lie.

These concepts can be real to one person and not another and it doesn't diminish the importance of duty to those who are attuned to it. — ToothyMaw

I'm going to try and do a little philosophy with this sentence, if you don't mind.

Something that's confusing to me here is "concepts can be real" -- not the relativism, but just that sentence alone. My guess is you're saying duty is not a noble lie because duty is real, in some sense. So duty is real for some people, and not real for others. Is that correct?

I'm calling out the leaders, not the people. And yes, I do maintain that duty is the most powerful motivator, as it can override just about any other consideration if the human is manipulated correctly. Remember the Third Wave experiment? In that instance it was used to harm, but such manipulations can be used for good. Many, if not most, of us have grown complacent, and good leaders with the peoples' best interests at heart need to intervene - before a nasty, fascistic one does. — ToothyMaw

Nowhere do I say that duty is what one "ought" to do, but rather is a subjective motivator that can be manipulated by good leaders to good ends - which is what I'm actually advocating for here. — ToothyMaw

So duty is a kind of noble lie, then?

There are so many inspiring stories in the history of labor. Thanks for sharing, I didn't know that one.

Yeees... only... Well, let's say both the political and economic landscape of the future are as yet unmapped. But I think that speculation belongs elsewhere. — Vera Mont

Heh, yes.

Well, it is interesting to see that mafia trade unions share the same industry/commerce: trucks and transportation. To understand how poisonous can a trade union be, we have to look at Jimmy Hoffa's story. Hoffa became involved with organized crime from the early years of his Teamsters work, a connection that continued until his disappearance in 1975. He was convicted of jury tampering, attempted bribery, conspiracy, and mail and wire fraud in 1964 in two separate trials. He was imprisoned in 1967 and sentenced to 13 years. In mid-1971. — javi2541997

The one I was thinking of was learned of in passing, and I rather like my legs.

It takes a lot of bravery to organize on a shop floor, or youthful anger (as others have already pointed out). It takes even more bravery to try to organize the honest way if the mafia is involved. Some organizers have done that, but not me. But because some organizers have done that this is how I know they still exist (and that the answer is always organizing).

But it's a rare case. I mentioned it as an obvious example of when unions can go bad. I don't think anyone should just blindly believe that because there's a union it's a good thing. It could be a bad union. There are examples of that.

The thing is: you can either leave your job, or organize. Sometimes the fight is too much for some people, and I understand that. Human beings are frail and weak. Duty is something that's a bit out of reach for most of us, though it can be inspiring.

I just don't think you can frame scabbing, in particular, as a dutiful action. It really is as selfish as I described: you're picking your own family over the families of your coworkers. A lot of people have sympathy for that position, but think on the categorical imperative: if everyone scabs then there's no strike to scab and everyone is back at work. I understand that duty need not follow the CI, but it's a pretty well worked out example of a philosophical theory of duty at least. So I have my doubts.

I think it's time to ditch all the old forms. — Vera Mont

:D

A saying after my heart. But I've mellowed out. Union structures work to give some semblance of power to working people. The old forms stick around because they still work better than nothing, and also because the old form of capital is still around. It hasn't changed that much, except to grow larger and become better at divide and conquer.

But I'm afraid I have to say one should think in terms of bosses and workers, when looking at political economy. Or at least the bourgeoisie, if not the lieutenants of capital. As a socialist surely you agree here? Automation can give us good things if used well, but to be used well the workers need to have a say in political economy?

Right, I understand. I just mean -- look at the 1800's. The hours were longer, automation caused there to be a labor reserve army, and there were fewer laws in place.

I don't think the working class has disappeared, though it's not a topic for USian political parties. Like you say, it's all middle-class based talking points.

But it's not like the house of commons during Marx's time was the most progressive force, either. It took organizing then, and it took organizing during the 1900's to maintain those victories which brought about a kind of golden age of labor, and that's what it would take today. And really it'll depend upon the workers. Not my little opinions on the matter.

It might have to get worse before people want to make it better, though. Most workers are not fighters. They just want the best for them and their family, and fear is an effective motivator.

I know something about the history of trade union movements and labour parties. The present is pretty dim, especially in the US, but other countries, too, where a succession of governments have been systematically kneecapping unions.

But what of their future? Given the state of automation and collar-bleaching... I wonder. Teachers, librarians, nurses, yes. Who else is, or can be organized into, a progressive political force? — Vera Mont

I'm out of the game, and I broke my crystal ball awhile ago, but my sympathy for the future of labor has always been the service sector. But as long as there's a money-flow within a firm and a group of people who depend upon a wage from the firm then there's lies the possibility to unionize: call centers, food chains, delivery drivers, uber/lyft drivers, amazon, wal-mart, target, alphabet workers, public sector workers, migrant farmers, transit workers, baristas, catering companies, hotels, non-profits...

When people talk about the dimness of labor I note how the golden age of labor was something of a fluke, and it only came about due to fights under arguably worse circumstances (sometimes the same, in the most extreme cases -- migrant farmers come to mind here particularly). What worked then is what would work now, if people decided to stop living in their little family-bubble.

And that's why I think the scenario, as posited, is basically reactionary: it's the scabs prayer.

I've been in unions at various points in their life-cycle, including an attempt to form a brand new one. That was defeated, and two years later, the same workers opted to join one of big, powerful unions, in which they would be an insignificant cog. Not a great outcome, but a rational choice that resulted in better pay for my ex-colleagues. By then, I was working elsewhere as a member of one of the big, powerful unions - which served us very well, as it happens, and deserved our support. — Vera Mont

I started as an organizer on my own shop floor and then eventually became a staffer for a different union in another life. But not so much union activity now that I'm doing the sciences -- scientists, among other professionals, have a hard time seeing themselves as "workers". The images of the factory are still strong, even though there's no need for a factory to have a union that works -- all you need is solidarity. Also I've had my fill of fighting. Being an organizer is a stressful, thankless job where everyone blames you for everything and most of what you do is run around putting out fires for less than the members you service make ;).

There are definitely flaws in unions which are worth noting and learning from. They're human organizations. And from a Marxist perspective it's generally viewed that unions can't be strong enough to compete with capital, so there are even political reasons to criticize unions from the left.

I guess I just don't see the scenario as presenting the flaws and how to learn from them as much as giving us a very common image that the boss uses: the image of the poor, benighted worker who has two bosses, the union boss and the company boss, and he's just trying to feed his family.

The OP example was questionable, so I questioned it. Is that not why we're here? — Vera Mont

It is. But I thought @Banno had a good point. There's a very rich history, and I thought the scenario was kind of highlighting the worst aspects of a union without really getting at how people have actually overcome (or failed to) these sorts of things. So I suppose I'm just questioning the question. The annoying philosophy thing.

As presented in the example, the call to strike seems irrational. — Vera Mont

That's because it's meant to ;).

At least so I'm maintaining, while maintaining that it's not possible to make the argument from duties to scab.

But it is just an example, a hypothetical.

The example I used the strike was for equal pay for women. They didn't win in the first strike, but they got some victories, and then some odd 15 years later the original demand was met with a longer strike.

This is why I wanted to know if there is a possibility for a worker to disengage from this structure. When I read papers and news related to this issue, I figured out that a "scab" is badly seen among workers and most of them end up disowned. Yet, I was curious to understand the purposes of a scab and then some delicate situations like my OP could exist. Even, the trade unions can act aggressively towards the workers and threaten them. Acting like a gang, as you explained. — javi2541997

When I said "mafia laundering" I wasn't making a metaphor. I mean there exist legal entities in the United States which are registered as unions but are operated by the actual mafia as a money laundering operation. They don't really service their contracts very well, and they don't even bother to fight for a better one. They'll just re-up the contract for as long as they can so they can keep the structure, and for the most part the contracts are hardly enforced anyways.

The funny thing here is that the solution is still the same. It's not disengagement, but engagement: you organize. Else you just let the mafia run the show. Same goes for if you disagree with leadership: you organize.

Participation is what keeps a democratic organization alive. A worker can disengage with the structure, sure, but I think you'd have a hard time making the case that it's a duty to do so unless a worker's duty is only to themself and their family. (which others have basically said so far -- so if you take that extra step then you can even be secure in yourself and know you've done your duty)

Now insofar that democratic structures are gang-like then a union can act like a gang. But this is more of a reaction to having to deal with social structures and a desire to be independent than it is engaging with the reality of trade unionism: The next job, contra @ssu, will have similar structures in place. The cowboys of the world, as I call them, are entirely selfish as I set it out: they're there for themselves and their family, and that's that.

But the union movement benefits them even if they decide to hamper it. That's why it'd be hard to make the case that it's a duty -- if you're a worker then you're already indebted to a long history of struggle. There are the cowboys who want to be individuals, but by that they're making the choice I said: they're choosing their own family over the families of others.

And that's true even if human nature is basically bad, and so unions, too, are of course corruptable. But that's not what they are, and that's kind of the vibe that your scenario presents: it would be naive to believe that every union is a shining beacon of goodness, or something along those lines. I don't even think "goodness" enters the picture -- it's about power, simple as. But it's similarly foolish to judge unions on the basis of the single scariest thing that a worker might have to do. That's not even most of what a union does. Most unions try to avoid strikes.

That's an assumption not always borne out by results. The strikers are not necessarily represented by the union leadership; they may be incorrect in their assessment of the situation; this particular worker may be aware that the strike is futile.
If he makes his decision on nothing more than loyalty to the union, it's just another case of blind obedience, not a moral or ethical one. — Vera Mont

When does scabbing not hurt strikers?

"The strike is futile" is fear, as I said. So that worker is picking on the basis of their fear, because they believe the boss will win so they're hedging their bets and helping the boss break the strike. It's not "nothing but loyalty", but an awareness of how the world works -- if you help the boss break the strike then you're putting your family ahead of the other families that are also risking themselves. That's the choice being made.

The real choice... eh, we're not in a union drive here so it's a bit idle to talk about "the real choice", unless we're going to use historical examples.

Either way I don't think you can make the case that scabbing is following a duty, which is what the original scenario is speaking in terms of, unless the only duty you have is to yourself and your family. (which, in truth, is where a lot of people reside in terms of willfully chosen duties -- duty to union, outside of union families, is often seen as a naive position. But it's not. It's the only reason workers have what they have today, and it's the reason why they're losing more of it too)

I mean, there is always one specific person who, for whatever reason, is in a worse position than the rest. — javi2541997

Yup.

But here's where history can serve as a better guide to understanding the problems and decisions a worker faces. Union drives have succeeded and failed, unions have been successful in one generation and fade away with future generations, or experience resurgences. That's the ebb and flow of historical reality. (One might be tempted to call it dialectical ;) )

For instance, unions cross the anglosphere -- they are organized all across the world, across different ethnicities and language-groups. Some of the most inspiring stories of strikes come from overcoming differences in language, culture, and expectations. Unions thrived prior to women becoming more prominent within the workforce as well, to speak to another point you brought up.

And sometimes trade unions aren't even as effective as a political lobby. Sometimes they're a money laundering operation for the mafia, and the contracts they service won't protect anything, nor are they actually run on democratic principles.

All these possibilities are explored in the history of labor.

I'd echo @Banno's sentiments here. A particular worker is in a particular time and place. The scenario is already abstract from the outset: it's a deontological problem of choice. For particulars we should look to history.

But there's no choice in the abstract. If you're a worker then, like it or not, scabbing will hurt strikers. Even if the worker really wants to scab that will occur, and that's not really defensible on ethical, deontic grounds. It falls pretty easily to the first formulation of the categorical imperative because not everyone can scab -- if they did then there'd be no strike and they'd all be back at work.

One of the things missing from the abstract problem is that unions are democratic organizations. So there's already social responsibility in the mix which isn't represented by the problem.

It would be much better to look at historical cases, the miners and Thatcher, perhaps. — Banno

I agree here. Historical cases demonstrate how people have overcome various problems, or failed at overcoming various problems. What they lack in conceptual clarity they gain in fidelity to the vagaries of political action.

https://en.wikipedia.org/wiki/Ford_sewing_machinists_strike_of_1968 is a good example because it also has a movie you can watch which I found satisfying. I like that it depicts strikes as scary things, because they are scary. You don't know the outcome of your actions, and you have the real possibility of losing.

But progress has only come from normal people being willing to do scary things.

But keep in mind that the worker of the example has problems in his family: the wife is already unemployed, one kid is sick and the other goes to college. Maybe the rest of the workers are covered up thanks to the incomes of their respective families... — javi2541997

Families are rarely in a state of perpetual comfort. There's always something to take care of. This is the common mantra of the scab: "I understand what you're doing, but I have to take care of my family" -- which is fear. The scab believes the boss is going to win, so the scab chooses the boss's side. This is to the detriment of the strikers, whose families are similarly unstable, have needs, and so forth. It's not a neutral act of duty, it's a person actively sabotaging the efforts of strikers in the name of their family: Family over Union.

A common act of social grace is to say something along the lines of "The spouse wouldn't allow it" or "My kid is at home sick", and I understand them to be bowing out of whatever it is we're doing. But they're usually speaking for themself, and sometimes the kid is at school and the parent just needs some time to themself and the only excuse people accept is some duty or other.

But when you're talking union the "my family" excuse is out the door -- buddy, we all have families. That's what we're doing this for.

Workers do face difficult decisions in supporting a union drive, becoming active in the union, and in striking, especially when the employer is hostile. The risks are not a pretense. Strikes do not always succeed, and a failed strike can leave the union members broke and out in the cold. — BC

I agree.

That's why I thought that duty doesn't leave a choice.

You may have a family. But do you think that the other strikers don't? They're already risking exactly what the OP sets up. Some cave to fear, or selfishness, and think of their own family in the moment. It's particularly difficult because a person has these connections, and that's a struggle.

But philosophically speaking the duty is clear: the strikers are risking their families already. You should do the same. Don't blame your fellow workers who are just asking for fairness to be able to take care of their families, blame the boss for not doing what's right!

Which should point out the importance of looking at, even if I'm wrong, fear and anger.

With that being said: I really like the last chapter because it's close to what I was writing out, once upon a time, when attempting to invent a purely spacial logic (that didn't work out, and so I threw it away as nonsense). Also I enjoyed working through a calculus that isn't the same as all the others, though there are parts I'm still uncertain about. And I enjoyed GSB's fusion of poetry with math, which is something I have a soft spot for. (EDIT: Might be a bit of a surprise given my approach so far -- but I wanted to treat the book as a logic in addition to its poetic value, and thought maybe that was the part I could contribute to for understanding the text)

Good recommendation @unenlightened, and thanks for the prodding and motivation. I would not have finished the book without your help.

Empathy. You see what happened to someone, you understand that you could have been the one, and so you leave something nice because that's what you'd like to be done if it were you.

Typing out the ending, because it's probably the most interesting philosophical part:

An observer, since he distinguishes the space he occupies, is also a mark.

In the experiments above, imagine the circles to be forms and their circumferences to be the distinctions shaping the spaces of these forms.

In this conception a distinction drawn in any space is a mark distinguishing the space. Equally and conversely, any mark in a space draws a distinction.

We see now that the first distinction, the mark, and the observer are not only interchangeable, but, in the form, identical

While I've admitted ignorance to certain parts of GSB's demonstration, I'm not sure about the conclusion here. Not that it's wrong, only that I'm uncertain that it's earned.

Observers and such haven't really shown up until this point. He's asking us to interpret ourselves as an "m" outside of a circle where the circle is the forms around us. But this would be the simple subject, if it can be reduced to an "m"? Or no? It's not clear, because "observer" shows up at the very end.

All the same I think I like "a distinction drawn in any space is a mark distinguishing the space" -- to mark a space one must mark. Even "the unmarked state" has been used so far as equal to variables, and so works, in a sense, as a marked space would (in a different way from the way space pervades expressions)

But I'd say that GSB sees something I don't, at the end. And I suspect it's because he's an idealist. He can see that the first distinction makes the observer interchangeable with the mark because he believes that, at base, this is all mind-stuff and the forms we see are mentally constructed? Or something along those lines.

But all I see is a mark, and a man who wants to be that mark.

I said I'd wait but I'm not :P :D -- I finished the book today. But that chapter on time isn't clicking.

I'm tempted at this point to just grant chapter 7. I checked T10 through the proof by example of J2 and it works out, but since I didn't get to C9 the same as GSB, and it looks close enough for me, I'm fine with just allowing it and moving on. After working through those examples the text is reading a lot easier and I can kind of see how it's good enough for me. :D -- it was fun to work through the nitty gritty puzzles, but I'm starting to think "OK, I'm ready for a point now"

Seventh Cannon is what made me think the above -- it pretty much lays out what we've been doing in the demonstrations, but allows you to use the algebra now.

The bits on time: we get the conclusion I was thinking of, which is interesting to me!, that there are undecidable expressions (now that we have functions that go to infinity).

One thing I'm thinking is you could just posit another space-dimension to accommodate GSB's "cross in a plane", but I'm ok with saying this is space-time instead.

The oscillator function makes me want to take back what I said earlier about negation. It seems like we're close to negation with it because of the relationship between the two spaces inverts, but it's never named.

But I can say I've officially lost the plot at page 62's "Time in finite expression" -- I don't understand Figure 3, or most of the figures after that. The only one I get right now is page 65's rendition of E1.

But also I kind of continued past when I normally would just because I was hooked. I've officially finished the book now, but without as much math ;). Still chewing on the ending.

The boss's weapon is fear, the union's weapon is anger.

I prefer anger to fear. But many prefer fear. I don't think it comes down to duties as much as these two emotions -- which one a person lets rule them is how they'll decide to strike or scab. Or, if I were to put it in terms of duties, I'd say there isn't even a choice. But I doubt that's surprising ;).

And let's see if I can finish it out now...


(C9.12) from above shows how C2 can be used to obtain C9.3 more easily.

Let C2's a= unmarked state, and b= r for the right-hand expression in C9.12

$\left. {\overline {\, ab \,}}\! \right|b$ = $\left. {\overline {\, a \,}}\! \right|b$ (C2)

Plugging the right hand expression of C9.12 into the right-hand side of C2, while keeping $\left. {\overline {\, xy \,}}\! \right|$ as is...

$\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|r$-->$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right| \,}}\! \right|r \,}}\! \right|$ (C9.13)

We remove the double cross with C1 and put back into the original expression to get C9.3:

$\left. {\overline {\, ba\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|\left. {\overline {\, rxy \,}}\! \right|$ (C9.3)

Looking at the differences between C9.3 and C9.4 I thought that only the left-hand cross was involved in the transformation, but then saw that we're using C2 and the only way to get r-x-y-cross underneath that cross is by setting C2's b = r-x-y-cross, and a is everything else underneath the left-hand cross. It's a transformation from the right-hand-side of C2 to the left-hand-side.

$\left. {\overline {\, ba\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|\left. {\overline {\, rxy \,}}\! \right| \,}}\! \right|\left. {\overline {\, rxy \,}}\! \right|$ (C9.4)


This last step took some guesses for me. What worked was using C7. I could see that we really just want to get rid of some of the terms underneath the left-hand cross of C9.4. I pretty much just guess-and-checked my way to a solution.

C7, but inverted to show the direction of transformation:

$\left. {\overline {\, ac \,}}\! \right|\left. {\overline {\, \left. {\overline {\, b \,}}\! \right|c \,}}\! \right|$ = $\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, a \,}}\! \right|b \,}}\! \right|c \,}}\! \right|$

Let C7's a =xy, b =xy, and c = r. Ignoring, from C9.4, and maintaining b and a from C9.4 (but erasing the cross that all of this is contained in to make it less bulky)

$\left. {\overline {\, ab\left. {\overline {\, xyr \,}}\! \right|\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|\,}}\! \right|$ --> $\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|xy \,}}\! \right|r \,}}\! \right|ab \,}}\! \right|$ (C9.5)

Which is close to where we want to get to, we just want to remove the redundant part at depth 3 and 4.

For that I went to C2:

$\left. {\overline {\, ab \,}}\! \right|b$ = $\left. {\overline {\, a \,}}\! \right|b$

Taking just the expression:

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

Let C2's a = unmarked state
Let C2's b = xy

It becomes

$\left. {\overline {\, * \,}}\! \right|xy$ (C9.6)

Then take this expression into C3:

$\left. {\overline {\, * \,}}\! \right|a$ = $\left. {\overline {\, * \,}}\! \right|$

Let C3's a = xy and C9.6 reduces to a single cross.

Plug C9.6 reduced back into C9.5:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, \left. {\overline {\, * \,}}\! \right| \,}}\! \right|r \,}}\! \right|ab \,}}\! \right|$

Using C1 we reduce the double crosses over the unmarked state and plug this back into C9.4 and rearrange we obtain C9's conclusion:

$\left. {\overline {\, \left. {\overline {\, r \,}}\! \right|ab \,}}\! \right|\left. {\overline {\, rxy \,}}\! \right|$

And so we have C9:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, b \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, x \,}}\! \right|r \,}}\! \right|\left. {\overline {\, \left. {\overline {\, y \,}}\! \right|r \,}}\! \right| \,}}\! \right|$ = $\left. {\overline {\, \left. {\overline {\, r \,}}\! \right|ab \,}}\! \right|\left. {\overline {\, rxy \,}}\! \right|$ (C9)

Which, yup, I can get the conclusion, but it certainly didn't involve using C6 -- and I tried to do it that way a few times but concluded it couldn't be used because there's just not that form present in the expression of interest. So a bit of a guess-and-check based on what we're trying to obtain got me through the demonstrations.

There's something odd about letting b = xy and a = xy, but I don't really see a reason within the logic presented so far to not allow two different variables to be assigned to similar names at different parts of an expression so I just went with it. But it does seem kind of funny. (Also noting how Theorem 12 states that I should use T10 in place of J2, and I didn't really use J2... I was just looking for a way to make the equation work. So that derivation may be wrong, or at least wasn't what GSB had in mind -- but it seems to follow still)

I have now figured out what he meant by "integration". I missed that C3 was named integration, and so this is him pulling out one of the sub-steps in the demonstration of C3 and calling it "integration".

That leaves the bit where he says "Thus if we consider the equivalence of steps..." which I'm still scratching me head on. I understand that the steps have an order to them, and so reduce depending upon the order of transformations. But his conclusion that "therefore the unmarked state is equivalent to a step" doesn't make sense to me. He demonstrated that taking steps is inconsistent and so he concludes that the unmarked state is a step rather than not putting steps into the calculus -- which is what I'd do since steps had never been introduced as a member of the calculus. We've been working through the marked state, the unmarked state, equivalence, and transformation through substitution. The steps are semi-arbitrary in that we can set any part of an expression equal some other conclusion as long as the forms match up. Why on earth would I take a step as a part of the calculus and set it equal to the unmarked state?

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, b \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|$ (C9.1)

Noticing that the form closely matches C8... (Note, I thought I had it in typing it out but then noticed I'm making a mistake, so the first part is a failed attempt at demonstrating this step, but after the break I figured out my mistake and demonstrate the step from C9.1 to C9.2)

Let C8's...

a = $\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|$

Because that's the only expression which appears under both crosses in C8's transformation to the right-hand-side.

b = $\left. {\overline {\, b \,}}\! \right|$

c = $\left. {\overline {\, a \,}}\! \right|$

r = $\left. {\overline {\, r \,}}\! \right|$

Then plugging these values into the right hand side of C8 we get:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, b \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, a \,}}\! \right| \,}}\! \right| \,}}\! \right|$$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, r \,}}\! \right| \,}}\! \right| \,}}\! \right|$

And then we remove the double brackets using C1 and re-arrange the expressions to obtain (though it looks more like 5 times rather than thrice?) (Actually I'm making a mistake here... I'm noticing that there's an added cross in the final conclusion that I'm not accounting for... hrm, hrm, hrm...)

$\left. {\overline {\, ba \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|\,}}\! \right|$$\left. {\overline {\, r \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|$ (C9.2) (but not obtained by the above procedure)

**************

Something I like to demonstrate in my postings here is that I'm constantly changing my mind, or noticing mistakes -- my thought is that the finished product never looks like how you get there, and I think that this forum is at its best when sharing our process of thinking in all of its messiness, in all of its faults. So I'm keeping the mistake up above, while working out the correct demonstration here (and simply adding to the post so as not to clog the front page too much) (Also why I'm fine with repeating myself, or going over old ground again)

And I figured out my mistake. The reason I had extra crosses, and needed to perform C1 more than thrice, is that the solution should be--

Let C8's...

a= $\left. {\overline {\, xy \,}}\! \right|r$

b = $\left. {\overline {\, b \,}}\! \right|$

c = $\left. {\overline {\, a \,}}\! \right|$

r = $\left. {\overline {\, r \,}}\! \right|$

Then plugging into the right hand side of C8 we obtain:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|\left. {\overline {\, \left. {\overline {\, b \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, a \,}}\! \right| \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|\left. {\overline {\, \left. {\overline {\, r \,}}\! \right| \,}}\! \right| \,}}\! \right|$

And then we can remove the double crosses, three times (C1 thrice), to obtain:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|ba \,}}\! \right|\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|r \,}}\! \right|$ (C9.12)

Which easily re-arranges to:

$\left. {\overline {\, ba\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|\left. {\overline {\, r\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right|\,}}\! \right|$ (C9.2)

I said that, but I took a hiatus with the USian labor day weekend, and this morning I got stuck on the first transformation of the demonstration of C9. This afternoon I think I worked out the first step, which I'm going to present here because it took me a second to see it.

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, b \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, x \,}}\! \right|r \,}}\! \right|\left. {\overline {\, \left. {\overline {\, y \,}}\! \right|r \,}}\! \right| \,}}\! \right|$ = $\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, b \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|$

Just looking for patterns I noticed how the only transformation occurs on the final two depth=2 crosses, so I simplified to looking at those final two crosses alone:

$\left. {\overline {\, \left. {\overline {\, x \,}}\! \right|r \,}}\! \right|\left. {\overline {\, \left. {\overline {\, y \,}}\! \right|r \,}}\! \right|$

Which to fit the form of C1, as the text suggests, I set this whole expression = a, and from C1 I add two crosses onto the expression:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, \left. {\overline {\, x \,}}\! \right|r \,}}\! \right|\left. {\overline {\, \left. {\overline {\, y \,}}\! \right|r \,}}\! \right| \,}}\! \right| \,}}\! \right|$

Which gets us to something close to J2. From J2 let p = $\left. {\overline {\, x \,}}\! \right|$ and let q = $\left. {\overline {\, y \,}}\! \right|$, then the expression resembles the left hand side of J2. Converting to the right hand side of J2, but substituting back into the original expression we obtain:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, \left. {\overline {\, x \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, y \,}}\! \right| \,}}\! \right| \,}}\! \right|r \,}}\! \right|$

Which from C1, but this time going from the left hand side to the right hand side to remove two crosses above both X and Y, and plugging this expression back into its place from the original expression we get the first step:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, b \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|\left. {\overline {\, \left. {\overline {\, xy \,}}\! \right|r \,}}\! \right| \,}}\! \right|$ (C9.1)

EDIT:

About an hour later, some random thoughts I'm having while working through these:


One of the things I'm thinking of is how we're showing, from the rules set out so far, how one expression equals another expression. But even though we're using variables I remain uncertain that we have really marked out the domain of expressions such that these are proofs. And further it seems that we could show some other expression could equal one of the other conclusions, like C1. Or, at least, it's not clear to me that these hold as proofs in the same way that numerical expressions with variables have proofs in them, or that other logical systems have proofs in them, like De Morgan's Laws.

To make a list of what we are able to do so far: substitution, the marked state, the unmarked state, variables, equality, and step-wise transformation from J1/J2 (and all demonstrations from J1/J2). The demonstrations are claiming to be a calculus of the marked or unmarked state, but how to delimit that space such that these demonstrations are proofs, in that they hold for the whole space of all expressions? Are there no other expressions other than the marked/unmarked state, or is there a value in-between marked/unmarked? Or is the law of the excluded middle an assumption of the calculus such that we also can conclude that?

One of the differences I'm seeing between this logic and the other two I listed (algebra, Boolean logic) is the lack of negation. There is no negation in this system. There is marked/unmarked, but no negation of the marked/unmarked, which I wonder if that somehow ties into making a consistent system of symbol manipulation. It makes me think that we can think of the unmarked state as more in analogue with 1/1, like it can perpetuate anywhere within an expression in the same way that (1/1) can always be added to either side of an algebraic expression.

Still meandery. One thing these exercises is providing me is a vantage from which to see how logical systems work in the abstract, or at least a vantage to reach for that perspective. ALSO, back of the mind thought, if negation never shows up then perhaps Godel's Incompleteness Theorem will not apply here. (Back of the mind for so many reasons... but I've noticed that the system may not be powerful enough to represent arithmetic, and that's why I have the thought)

Also interesting to note how the proofs of J1/J2 work by showing all cases: under the assumption that p,q, or r is such and such we show the whole expression is equal in all possible cases. This is important, I think, because it may be the case that at some additional variable point we would be unable to check by the method of all cases (which reminds me of truth-tables' check for validity, actually), and so one wonders if a multitude of variables could lead to undecidable, or multiply decidable expressions such that they could lead to both the marked/unmarked state. I think this is the thing that would have to be secured to count these demonstrations as proofs -- we have the demonstration, but is it possible for the demonstration to turn out the opposite value? Like with C1, is it possible to come up with an expression that reduced a-cross-cross to the unmarked state without a from the transformation rules? It's a niggling thought at the back of my mind, and it would be hard to find such an expression, and I may just be completely off base. But hey, sharing the thoughts in the spirit of the thread.

Good stuff.

I especially like the connection between vulnerability and transparency: forthrightness can be a boast, but if you're really at your limit of certainty then it's a good idea to let go of the desire for certainty -- especialy the certainty that you'll win the argument ;).

Transparency, though, is a way to subject yourself to the criticism of philosophy.

Also true.

:)

I'm pleased to see you thinking through the problem. It's something I tend to think about, once and again.

The reason I say the guide is the senses has to do with my time as an activist. I am no longer an activist, so don't trust this as a forever-truth -- one of the things I learned as an activist is that it's too easy to think you have a forever-truth, at least for the philosophically inclined.

But then the world you live within has a way of interrupting thoughts and forever-truths and even certain truths.

****

A dark note -- "violates human rights" in the universal sense is something the United States does. Not in an "on occasion" basis, but of course this will involve a discussion on what human rights are, and when they are worth violating (like war).

But if "human rights" has any meaning outside of the nation, at least, then the U.S. is really good at killing people -- sometimes in the name of war, but sometimes in the name of selling weapons.

My response was a joke, of course, but a joke with a point -- the question needs refinement, else the little modus ponens I offered is an answer: touch is possible because I'm touching something, and in order for me to be able to touch something it must be possible for me to touch it. (Or, if we want to be sticklers about form, I should have started with the implication)

Note that the original question didn't mention anything of physics, but rather was speaking in terms of spaces. After @T Clark pointed out that touching is not when two objects occupy the same space, and @elucid saying it makes sense I read the problem as being resolved.

Still -- the argument I offered wasn't entirely vacuous. For one, you know I'm touching a keyboard because I'm typing out to you (or, at least, you could infer that it likely, given that I have no reason to lie about it even though it's possible I could be using a talk-to-text program), and so the argument points out a relationship between possibility and true statements -- to demonstrate that something is possible all you need is one true statement of the case.

For your argument you'd need to somehow introduce physics and electrons as worthwhile entities in the domain of discourse about touching.

Thanks for the tip -- that would have been a frustrating discovery to make on my own. I'll still check it with C6 first to see, but C9 looked like quite a doozy already.

Sometimes it feels like the demonstrations are purposefully harder than need be -- to get you in the habit of switching out variables for one another. After getting this far the substitution rules made more sense upon reading them -- they were formal statements of what we're doing to check Brown's work that were needed to give meaning to "equality".

And I checked out what comes after C9, and can say that I find it confusing. This is the first appearance of "integration" that I could find by checking the names of each transformation from before, and I don't understand what the part with the series of "is changed to" symbols are arranged means. "The unmarked state is changed to the unmarked state is changed to the unmarked state is equal to the unmarked state is changed to the unmarked state" is the literal translation of the first example, and I don't know what he's getting at with it.

I'll probably at least work out C9 by the time you get back, but probably wait from there. Have a good week!

What are your thoughts? — elucid

I'm touching a keyboard.

If I'm touching a keyboard then it is possible to touch something.

Therefore, it is possible to touch something.

Hell yeah. Finally managed to prove a truth.

C8

$\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, br \,}}\! \right|\left. {\overline {\, cr \,}}\! \right| \,}}\! \right|$ (1)

Call C1: $\left. {\overline {\, \left. {\overline {\, a \,}}\! \right| \,}}\! \right| = a$

Let C1's a = $\left. {\overline {\, br \,}}\! \right|\left. {\overline {\, cr \,}}\! \right|$

Reflect from the right hand side to the left hand side to place two crosses:

$\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, br \,}}\! \right|\left. {\overline {\, cr \,}}\! \right| \,}}\! \right| \,}}\! \right| \,}}\! \right|$ (2)

Call J2: $\left. {\overline {\, \left. {\overline {\, pr \,}}\! \right|\left. {\overline {\, qr \,}}\! \right| \,}}\! \right|$ = $\left. {\overline {\, \left. {\overline {\, p \,}}\! \right|\left. {\overline {\, q \,}}\! \right| \,}}\! \right|r$

Let J2's:
p = b, q = c, and r = r and collect r from the left hand side of J2 to the right hand side of J2:

$\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, b \,}}\! \right|\left. {\overline {\, c \,}}\! \right| \,}}\! \right|r \,}}\! \right| \,}}\! \right|$ (3)

Call C7:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, a \,}}\! \right|b \,}}\! \right|c \,}}\! \right|$ = $\left. {\overline {\, ac \,}}\! \right|\left. {\overline {\, \left. {\overline {\, b \,}}\! \right|c \,}}\! \right|$

This one took me several guesses. What helped me was to see that the form of C7 has c on both sides of the two separate crosses on its right hand side, and so C7's c must equal (3)'s $\left. {\overline {\, a \,}}\! \right|$ since the conclusion has $\left. {\overline {\, a \,}}\! \right|$ collected into two separate crosses.

Once I saw that then I Let C7's a = $\left. {\overline {\, b \,}}\! \right|\left. {\overline {\, c \,}}\! \right|$, and I transposed (3)'s $\left. {\overline {\, a \,}}\! \right|$ to the right hand side so that it fit the form of C7 more apparently. Then plugging it in sure enough I got C8:

$\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, b \,}}\! \right|\left. {\overline {\, c \,}}\! \right| \,}}\! \right|$ $\left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, r \,}}\! \right| \,}}\! \right|$

If you use the keyboard shortcut Ctrl+C after highlighting it copies to your clipboard and can be pasted here. (At least, that worked for me when I tested it)

I think I figured out C7 this morning. (and the others prior -- I figured out 5 when it clicked that the unmarked state was taking the place of "b" in using C4)

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, a \,}}\! \right|b \,}}\! \right|c \,}}\! \right|$

By C1 -- $\left. {\overline {\, \left. {\overline {\, a \,}}\! \right| \,}}\! \right| = a$, which we apply to the token $\left. {\overline {\, b \,}}\! \right|$ to obtain

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, a \,}}\! \right|\left. {\overline {\, \left. {\overline {\, b \,}}\! \right| \,}}\! \right| \,}}\! \right|c \,}}\! \right|$

Then by J2:

$\left. {\overline {\, \left. {\overline {\, pr \,}}\! \right|\left. {\overline {\, qr \,}}\! \right| \,}}\! \right|$ = $\left. {\overline {\, \left. {\overline {\, r \,}}\! \right|\left. {\overline {\, q \,}}\! \right| \,}}\! \right|r$

Let p = a, q = $\left. {\overline {\, b \,}}\! \right|$ and r = c then distribute from the Right-hand side to the left hand side.

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, ac \,}}\! \right|\left. {\overline {\, \left. {\overline {\, b \,}}\! \right|c \,}}\! \right| \,}}\! \right| \,}}\! \right|$

Then by C1, Let a = $\left. {\overline {\, ac \,}}\! \right|\left. {\overline {\, \left. {\overline {\, b \,}}\! \right|c \,}}\! \right|$ and reflect from the left-hand side to the right hand side to remove the top two crosses to obtain... well, exactly what I just wrote.

End of demonstration for C7.

A modal definition - it's a slab if it has slabbyness in every possible world? Or is it enough for it to have slabbiness in this possible world? Or it's a slab IFF it's width is greater than it's height...

Or it's a slab if the builder places it horizontally, a block if he places it vertically... — Banno

Heh. I thought my response clever but upon inspection, not so much. I think the act of pointing has a place in the definition of "slab!", for the initiate. Or the act of the other builder bringing a slab such that the initiate sees what a slab is without an essence.

How it happens, so I'd maintain @Leontiskos, is not known to the Aristotelian, though the Aristotelian could probably derive a complicated enough description to satisfy the definition of "slab" that fits for all cases thus far seen.

But then I might give you a slab of steak.

Well, that answers that question. Cool. Then I'm tracking!

And actually I had that thought, but then I thought -- well of course we can Let p = whatever we want. It's the form that matters. If I wanted to make sure I was tracking things correctly I could introduce another variable, like s, and let it equal $\left. {\overline {\, \left. {\overline {\, a \,}}\! \right| \,}}\! \right|$ and the form would still work out.

Thanks for working that with me.

OK I've worked my way through to the last step with that help. I think you're right about the presentation being confusing. When I started thinking of the equality symbol as more like the --> symbol that helped, and then when I started looking at the initials like things I could plug into my starting point in a step-wise fashion then that also helped.

The last step I'm struggling with because it seems like I have to Let p = $\left. {\overline {\, \left. {\overline {\, a \,}}\! \right| \,}}\! \right|$ -- is it allowed to switch what p equals in the middle of a demonstration?

That's half way through the proof. With me so far? — unenlightened

That helps. Thanks. I'm with you up to this point now.

"It's the slabby one. The one with the essence of slab"

Fun idea.

What is…

Being — Mikie

Good question.

Awareness

I presume it's the same for most humans in this respect: the focus of our consciousness -- not in a collective sense, but rather I think most humans have an individual focus on their consciousness, whereas you can still feel a pain even if you're not focused on it.

Consciousness

The phenomenal "feeliness" of the world. The taste of pizza isn't just salty-spicy-sweet, but the particular combination of your bodily make-up and its bodily make-up in conjunction -- if you want a cognitive answer -- or what it tastes like, if you don't.

Thinking

I'm not sure.

Time

Not sure.

Sensation

I think this one can't have an answer. The other topics are more general than "sensation".

Perception

Discrimination.

Mind

Body

Good

All uncertain for me.

Happiness

Justice

Interlinked. Happiness is ataraxia, and ataraxia is only achievable by living in a just society.

Truth

...is embedded in language.

Actually hold.... C1 can be derived from axiom 2 as well. So I'm even more lost. :rofl: What is going on with C1? (EDIT: Maybe it's a demonstration of substitution rules?)

EDIT2:

(that seems obviously fatal, but I'm not sure how else to do it) — Moliere

Actually.... then they'd be exactly equal in form too. There is something very confusing about substituting for the unmarked state*. I did it on both sides of the equation, like you'd do for a variable in algebra, but I think maybe Brown did it only on one side of the equation. This relates to another confusion I had put aside, but the notion of the unmarked cross maybe relates?


*Like, if we can do that can we constantly substitute any amount of crosses which equate to the unmarked state into any unmarked part of an expression?