Finally caught up to here. I'm struggling to follow the demonstration as well, so I'm going to type it out and see where it takes me.

It's the use of R1 that's confusing me. I understand that having derived an expression which is equivalent to the unmarked state we can substitute the unmarked state for said expression, but when I do so it seems like there should still be an "a" left over.

Or re-reading the use of R2 I'm not following again. It seems we have to

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

And by R2 that means the initial J1 becomes

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

Then we start with the conclusion in the next step?

So we start with C1:

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

And substitute the unmarked state from (2) into C1 --

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

And then subsitute $\left. {\overline {\, \left. {\overline {\, a \,}}\! \right| \,}}\! \right|$ for $a$ in the next step? (that seems obviously fatal, but I'm not sure how else to do it)

EDIT: I really feel like that can't be it. I mean I get that we're making a logic, but a logic that assumes its own conclusions to demonstrate relationships is usually only done in a reductio or something like that. (though we haven't gotten to negation or truth yet, so...) It just seems kinda squirrely.

This is more than just an analogy, it is the application which he was working on when he developed the system. I think it's worth trying to get hold of, particularly when it comes to the really difficult section that introduces time. If you are at all familiar with such things, it is quite commonplace for an electrical switch to be electrically operated, for example by means of an electromagnet physically pulling a lever. — unenlightened

Cool. I'm more familiar with the Physics 2 stuff than the practical stuff, and it's been more than a minute since I've studied that. I think I'm tracking better now with your explanation, and I had a gander at this website to get a grasp on the concrete side a bit better.

Let's suppose some news article.

This was the article at the top of google news for me this morning: https://www.cnn.com/2023/08/29/weather/tropical-storm-idalia-florida-tuesday/index.html

Here we have some claims that are written. Some of them have already happened. Some of them are predicted to happen, like the peak storm surge forecast. Now if you follow my original suggestion you couldn't really verify any of what's written down unless you're in Florida. Or you could verify it if you believe that the published weather reports tend to report true things that have happened, but are a little less reliable when it comes to what is going to happen.

Notice how what we're reading is an important part of judging whether we should believe it or not. This is from CNN, it is a weather report, they have a history of having accurate weather reports mostly because they rely upon government agencies and trained individuals. Since it's the weather, rather than an election, there's less of a reason to lie or generate an alternative story to what the other news organizations are saying.

It's that latter bit -- when news is political, or propagandized -- which undermines trust. Or, in some cases, reinforces trust if they're selling the truth you want to hear. But that kind of truth you want to hear isn't usually related to the senses, is it?

And that's where I'd say we have a guide to choosing what to believe.

Using my circuit analogy, on the left, p & r are parallel paths, and so are q & r. So if r = — unenlightened

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

then p & q are redundant, and 'light is on'. On the other hand if r is empty, it can disappear, leaving the expression on the right. So we have the parallel circuits on the right, of the p&q expression and a solitary r to cover both possibilities. — unenlightened

OK so "r" is the switch on the outer ring -- and if it is marked, or reduces to the marked state in the arithmetic, then the light is on because the switch is closed. And if it is not marked, then the light is off because the switch is open, but the marking of p and q is still there to be the wires or something like that.


I think I'm getting lost on the map between the arithmetic and the circuit diagram. I can stick with the arithmetic so far, though -- in the abstract.

EDIT: Outer/inner ring diagram, with ASCII -- for fun and profit:


___+/-___
r00000000|
!00000000|
------p------
!00000000|
!00000000|
------q------

?

(you'll have to read "0" as empty space, and "r" is that first little squiggly on the upper left hand side -- it's supposed to be a switch in my hypothetical)

Also -- I can just move on with the text itself. I realize this is an analogy.

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

...which we can think of as two circuits in parallel on one circuit 'a' operates a switch, and on the other it is the circuit. So if 'a' is on, it turns the switch off and connects via the direct route, and if 'a' is off it connects via the switch. — unenlightened

Hrm I'm not following the analogy here for T8 very well. How would the analogy work for the worked example of T8:

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

?

Two circuits in parallel on a single circuit I follow. So "a" is an arrangment of wires between a battery with a switch on the circuit such that the lights which are wired in parallel both turn off in the worked example of T8, as you say.

So just visualizing a simple circuit diagram, 'a' is on when it turns to switch off -- does that mean the switch is not connected to the parallel wiring? Where is the switch in the diagram, in parallel with the lightbulbs or on the outer circuit?

Or am I just breaking the analogy in trying to concretize your rendition here?

EDIT: Mostly thinking through the analogy here. No need to reply. The below post serves better as a question since it has a diagram.

In a society where govenments try to tell you what is true and raise you into believing what you believe, in a world that is ever more dividing, when we're looking at news or whatever is going on around us, how do we know what to believe in? — Hailey

I'd say start with believing your senses.

But this is a beginning, and a guess. The trouble you raise is we do not know what to believe in, but we do know that there's a fair bit of false beliefs which seem true. In fact I'd go further and say that we don't know that it's the governments, or any one culprit, which is the culprit in spreading false beliefs. And I'd go further to note that I couldn't answer the question for you -- how do you know I'm not from the government, spreading false beliefs about believing your senses first? The government could be an empiricist, in this silly universe I'm proposing, which wants its people to believe that knowledge comes from the senses.

But then remember the suggestion -- you don't have to believe me. You can believe your senses, and work from there, even if you're following the empiricist's shadow-government ;)

Fair point.

Though that's interesting that the book is close enough to work to actually feel like work.

Heh. You gotta read along with us!

I'm guessing I'll be skeptical when I get to those passages, but no matter the text it's a good idea to read it with multiple people.

Yup.

I know @SophistiCat added the SEP article, but it's worth noting the formalization of supervenience in this thread I think --

A weakly supervenes on B if and only if necessarily, if anything x has some property F in A, then there is at least one property G in B such that x has G, and everything that has G has F, i.e., iff

□∀x∀F∈A[Fx → ∃G∈B(Gx & ∀y(Gy → Fy))]
A strongly supervenes on B if and only if necessarily, if anything x has some property F in A, then there is at least one property G in B such x has G, and necessarily everything that has G has F, i.e., iff

□∀x∀F∈A[Fx → ∃G∈B(Gx & □∀y(Gy → Fy))]
(Kim 1984)

Which still is hard for me to read through.

Heh, yes. Undoubtedly.

The obscure and the strange is one of those things that just nabs my attention. Also I had some notions back when learning baby logic that this book seems to run parallel to. Notions which after writing them down I threw out because they seemed nonsensical, but hey -- there was something interesting about how the calculus managed to deal with the notion of the philosophy of philosophy as an unmarked state rather than a marked state.

Originally I wanted to actually put the fourth cannon example underneath a bracket of its own, but I found it difficult to stack multiple bracketed maths within a single bracketed math so there's a bit of a limit there. The only difference, though, would have been that there would have been another step of elimination where the deepest space's value for a was the unmarked state rather than the marked state.

Chapter 3 feels like a set up for chapter 4, which is what I said about 1 and 2 so I may just be in that habit. But I felt like it was all a set up for the final paragraph to make sense -- we have the initials of number and order for the calculus of indications, and Chapter 4 begins to actually write out some proofs from what has been written thus far.

There's something similar to this and using nested sets as representatives of numbers, I think. But then the value isn't numerical, but is rather the marked or unmarked state at its simplest. The first theorem of Chapter 4 points out that these initials are a starting point for building more complicated arrangements and the simple arithmetic of the crosses is what's needed to make sense of the calculus of the crosses.



I'm going to try and work out the proof here by arbitrarily using this arrangement as "a" --

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, s(sub(d)) \,}}\! \right| \left. {\overline {\, * \,}}\! \right| \,}}\! \right| \,}}\! \right|$

s is contained in a cross.

All the crosses in which s(sub(d)) is within are empty other than the space in which s(sub(d)) is in. ("*" counting as the unmarked space)

The arrangement chosen uses both cases --

Case 1 -- there are two crosses that are empty underneath a cross next to one another such that s(sub(d)) could have been in either cross. They're equivalently deep.

Case 2 -- the crosses surrounding the two deepest crosses are alone within another cross

So using the steps of condensation and elimination:

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, s(sub(d)) \,}}\! \right| \left. {\overline {\, * \,}}\! \right| \,}}\! \right| \,}}\! \right|$ --> $\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, s(sub(d)) \,}}\! \right| \,}}\! \right| \,}}\! \right|$ Condensation

$\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, s(sub(d)) \,}}\! \right| \,}}\! \right| \,}}\! \right|$ --> $\left. {\overline {\, s(sub(d)) \,}}\! \right|$ Elimination

And by the definition of Expression from chapter 1: "Call any arrangement intended as an indicator an expression" we can draw the conclusion that any arrangement of a finite number of crosses can be taken as the form of an expression. (since we're indicating the marked or the unmarked state)

The argument could also be read syllogistically, in which case 'anything' makes more sense:

All appearances are known mediately
No first-person actions are known mediately
Therefore, no first-person actions are appearances

Of course this is also valid. — Leontiskos

True! And that'd be more appropriate for the source material.

I read a book a while ago "What is life? : how chemistry becomes biology" by Addy Pross. It's about abiogenesis and Pross writes, somewhat convincingly, that it would make sense to think of everything, including non-living matter, as subject to natural selection. That could be seen as evidence for your position, although I don't think it is. Cross-fertilization between disciplines is useful, necessary. That's different from understanding science, all human understanding, as a system of hierarchical levels. Perhaps you don't see that as a useful way of seeing things, but I do. — T Clark

Yeah, that's a big conceptual difference between us there.

So I suppose that's also part of my skepticism with respect to the problem of consciousness' relation to QM -- not only are they two different problems that are heady and complicated, but even in related fields, like chemistry and biology, it seems that there are limits to coherence when we dig deeply enough.

This is not the place for us to get deeply into it. — T Clark

Fair point. Tangentially related, but that'd be going off the deep end.

This reminds me of the problems of emergentism and notions of "downward causation". How does a higher level influence a lower level, if the higher level doesn't exist yet? Are we going to invoke some sort of quantum level of indeterminacy of time? That seems a stretch. I am not saying it's necessarily wrong, but that approach seems a stretch. — schopenhauer1

Heh. Well, therein is the rub to all interpretations of QM -- they all kind of stretch our notions of credulity. It's hard to pick one interpretation or another because it's difficult to determine an experimental set up in the interpretations which allow us to distinguish them. Furthermore I think a lot of the QM interpretations are asking too much of the science, like it's a foundation of reality or something. But there's no reason to pick QM over classical mechanics if we're positing foundations. In a way you could treat them like a step-wise function -- when you get to such-and-such a scale, whether we are zooming in or out, then you use these equations. Which equations you use has more to do with your question and what we know from past experience. So far we've noticed small stuff is better predicted with some difficult equations, and big stuff is better predicted with what are still difficult, but different equations.

I've been pondering this. It is possible, I suppose, that the mathematics in quantum theory has been reified to some extent. The Mathematical Universe is this idea writ large. — jgill

That's pretty much my charge leveled against interpretations of QM. Insofar that we don't require all physical theories to cohere into one logical system there's nothing really in conflict between classical and quantum mechanics. They're just measuring different systems, sort of like life is a different system than a beaker of salt water, though there are connections to be drawn out. And you can choose to use either set of equations as you see fit.

The reverse is not true. — T Clark

I'm skeptical.

Especially now that these two disciplines are interwoven and so have reciprocal support for one another. I don't think there's a "most basic level" as much as there's a wild web of knowledge loosely interwoven, and which concepts get priority at what times has more to do with the experimental apparatus and question we're exploring than general emergent properties of the respective knowledges, such as a hierarchy conditions.

Further -- the big conflict here, with respect to interpreting the sciences in a philosophical manner, is on different notions of causation. The SEP has a lovely page on Teleological Notions in Biology, which you won't find in chemistry except as metaphor. The intersection between physics and biology is interesting specifically because it's where we might be able to understand the relationship between our traditional notion of causation in science (not quite billiard-ball, anymore, but still), and the frequent use of teleology in understanding living systems. That is -- putting biology first isn't so crazy as it sounds because we're not modeling the world off of natural selection, but instead questioning what sort of causation is truly fundamental.

Or, if we are dedicated Humeans, we'll note that neither is fundamental at all, that there is no most basic kind of causation that everything can be reduced to, that it's a mere habit of the mind.

Darwin didn't write his book in those terms, at least. Later on it was confirmed that biology and chemistry get along, but that's not where he started. And I'd say there's still some questions with respect to natural selection and physical science that aren't answered because we're still mapping the proteome (of humans, of various eucary, archaea, and bacteria) , we're still figuring out how the physical and the biological interact -- even in the most practical applications like medicine, but also with respect to basic research.

To understand biology you need to study biology. To understand chemistry you need study chemistry, and all the same for the other subjects. The intersection between these fields isn't so clean as you present.

I'd be happy to hear from them if they're willing to speak.

I'm not a biophysicist, but I sometimes annoy my coworkers in my insistence on attempting to reduce our experiments to the physical sciences :D. But, that also provides some motivation to reject the reduction -- the working molecular biologists I'm around, who know way more than me about their subject, are perfectly able and I'm still learning concepts from them. Not all the relationships are mathematical. They're linguistic, even in a fairly plain-language sense while occasionally introducing some technical terms, and yet seem to be true.

Then I think about the plots of climate science and how I believe in global warming. There's a lot of supporting ideas, but if I were to look at the math alone then the uncertainty would dissuade me if I didn't know about the reality of the system being studied.

I guess that leaves room open, in my judgment at least, that biology's messiness is actually a virtue with respect to truth.

Cool. Glad to have you along thinking with.

That's basically what I think. I love the German scientists because they were educated in philosophy and so were willing to explore interesting questions that were just their curious thoughts, and I think it was obvious that these curious thoughts lead to some advances in the sciences.

But I'm skeptical of the implications. The first thing I think of is, why not biology as a first science rather than physics? Maybe the results in physics, at certain times at least, aren't fundamental but specific to the system they're studying, and the aggregates of the physical world don't follow the same rules. Not in a superfluous way, where we're just approximating the quantum level, but rather that The Origen of the Species The Origin Of the Species* sets out a wholly different way to interpret the physical world that can be semi-bridged through the genome, but even as we dig into the mechanics of life there are differences that are only half-way related to QM (like proton pumps) or not related at all (like "uh, the cells just changed based on the measurement, but I'm not sure why").

*The Origen of the species would be the end of the species, since he castrated himself. I done did the mispelling thing and so am correcting myself here.

Or -- the Copenhagen interpretation encouraged shut up and calculate, because that's where the literal truth was thought to be.

How can 'something' be 'literally' two completely different kinds? — Wayfarer

By being both a particle and a wave. "particle" refers to matrix mechanics, and "wave" refers to wave mechanics, and it turns out they were mathematically equivalent. It was an old science fight between Schrodinger and Heisenberg which turned out to not matter because they both predicted the same outcomes. So I interpret that as "particle" and "wave" as being inadequate to the task at hand, where the math is adequate even though we still puzzle over what it means.

When we start measuring small stuff it behaves differently than when we measure big stuff. And you can even apply QM to macroscopic objects, like the moon, and you'll see that how small the difference is basically gets erased at the level of the moon. Neither the moon nor the electron cease to exist if the experimenter is not experimenting. It's being measured by all the other electrons, etc, around it.

Eh. I definitely disagree with that. Just because uncertainty is a physical truth doesn't mean that the electron doesn't exist. It just means that there's a relationship between position and momentum, or time and energy, such that an increase in a measurement of position results in a decrease in a measurement of precision for momentum, and further that this is a result of the physical system rather than the various objections Einstein made to it.

The Copenhagen interpretation's fault is not metaphor, but literality. The form of the math expresses the physical reality, rather than represents it. The electron, whatever it might mean, is literally a point and a wave.

In ways this mimics Hegel's dialectic, because these concepts are not Boolean contradictions of the form "A ^ ~A", but rather were two concepts thought to be contradictory. My thought on the Copenhagen interpretation, with respect to dialectics, is that the assertion of point/wave started a dialectic, and the sublation was in the mathematical equivalence between wave and matrix mechanics.

Not that I am at all an advocate for "consciousness causes collapse," but sometimes exploring theories you don't like tells you important things about the ones you do like. In any event, in comparison to infinite parallel universes and infinite copies of ourselves, it doesn't
seem that wild. If the Fine Tuning Problem is bad enough to make people embrace multiple worlds, maybe consciousness causes collapse is due for a resurgence? — Count Timothy von Icarus

More on topic, though --

I'm pretty skeptical of the fine tuning problem. I'd probably count as a deflationist on the question because I'm not so sure that the "physical constants being just this way" is really that surprising. They're constants. That's what they do, and we throw them into equations all the time just to make it work. (ever notice how Hooke's Law isn't so much a law as an approximation with wiggle room that works for springs? There turns out to be a point where it's no longer applicable)

Basically I'm not sure the notion that physical constants are worth taking seriously as ontological assertions. Sure if by the notion that the physical constants are ontological entities than there's a question to explore. But if they're just constants, like Hooke's law or coefficients of friction, which we use for certain circumstances, then there's no mystery there. It's just us making the balance sheet work out right and throwing a constant in to keep our math working while we describe this physical phenomena with it.

That being said, I'm not sure that consciousness can be explained through wave-function collapse, as if our actions are always measuring wave-functions and collapsing them and so these constants come out of that interaction. The two subjects seem so incredibly disparate to me that I usually think it's foolish to combine the two. The problem of consciousness requires picking apart the supervenience relationship, and quantum wave collapse requires the Hamiltonian operator which generally operates on partial differential equations.

They're both so heady and conceptual that I usually feel like solutions that propose both are a bit hand wavey in saying "Look, there's two complex things going on and maybe we can get two birds with one stone", but to me it just looks even more confusing.

The problem is that for some reason I thought the Logic was notoriously dense but at least shorter than the Phenomenology. Then the book arrives and it's like 1,000 damn pages. — Count Timothy von Icarus

:D

The Science of Logic is something I need to revisit eventually if I ever hope to be able to offer a formalization of sublation, but it's so hard to get through.

If p, then q
Not q
Therefore, not p

you said that is a non-sequitur...did you mean appears like a non-sequitur? — KantDane21

Heh sorry. That's the second version I offered, put into plainer language, and I agree that it's in the form of a modus tollens. The first one I offered would be a way of rendering the argument into a non-sequitur.

But there's another complaint you could make that "Anything" is too vague. Sure it includes "Action" but it also includes "A is A", or "Unicorns" or "The present King of France" or "A and not A" (Contradictions are surely a part of the vast set "Anything")

Trying to parse into sentential logic:

p = "anything is an appearance"
q = "it is known mediately"
r = "he(or she) acts not-mediately"
K(x) = "A person knows that x", where x is a variable.

p -> q
K(r)
Therefore, action cannot be an appearance.


I think Allison might be rendering the argument like that so that it's basically a non-sequiter. We could, however, read more charitably and attempt to render it in a logical form, something like what you suggest. But the natural language makes it difficult to assign the same variables if we're going to use the words exactly as written. I might render P2 as:

Action is known non-mediately.

Then we could render

p = "anything is an appearance"
q = "it is known mediately"

p -> q
~ q
Therefore, ~ p

as you indicate, a modus tollens. Though there's something funny about counting action as an "anything". "Anything" is a remarkably vague category! That might also be what Allison is getting at -- we started with "Anything", and didn't draw out the deduction that "Action" is an anything.

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

Put the following code in between a bracketed math, then the code, then a bracketed \math

\left. {\overline {\, * \,}}\! \right|

It took me a second to get the syntax but I read this as: Start at the left. Use the function "overline". Within the squiggly brackets the first "\," can be read as "start expression underneath the overline" and the "\," on the right hand side still inside the squiggly bracket can be read as "end expression underneath the overline", then we close what's underneath the overline with a closing squiggly, then we close the function we called "overline" with the second squiggly, and then "\!" can be read as "This is the end of the expression which started from the left", and then \right starts the ability to write on the right hand side, and we place "|", the alternate character on the "\" key, so that there's a long line written on the right hand side.

Reading it from the middle upward through the crosses:

1. \left. {\overline {\, * \,}}\! \right|
2. \left. {\overline {\, * \,}}\! \right|
3. \left. {\overline {\, * \,}}\! \right|
4. \left. {\overline {\, * \,}}\! \right|

And the others, while it's easy to get lost in the syntax as I did in my first attempt, are expansions upon this first function such that we put our single overline function with a right bracket into another version of itself, and on and on. I'll just post the code I used, though, because I think the above probably serves as a good enough users guide for copy-pasting the code.

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

The code used within the math brackets:
\left. {\overline {\, * \,}}\! \right|

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

The code used within the math brackets:
\left. {\overline {\, \left. {\overline {\, * \,}}\! \right| \,}}\! \right|

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

The code used within the math brackets:
\left. {\overline {\, \left. {\overline {\, \left. {\overline {\, * \,}}\! \right| \,}}\! \right| \,}}\! \right|

And to construct the crosses in the Fourth Canon in chapter 3:

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

Which I did by copying the first code with a single cross, and then in place of the "*" I put the copy of the original code twice right where the original "*" was in the first code with a single cross. Then I just copied the code again in a separate Math bracket to have it sit alongside

EDIT: Or the code --

\left. {\overline {\, \left. {\overline {\, * \,}}\! \right| \left. {\overline {\, * \,}}\! \right| \,}}\! \right|[/math] $\left. {\overline {\, * \,}}\! \right|$

I'd be happy if these considerations induce a small doubt as to the ubiquity of pragmatic epistemology. — Banno

I agree.

With your bolded bits too. But that should not be a surprise.

Mostly using this as an opportunity to say that in spite of my various misgivings I'm not a pragmatist, and not even tempted by it.

...the dialogic nature of philosophy means that one should... remain open to what they might teach us, and to the possibility that there may be questions without answers and problems without solutions. — Fooloso4

Please forgive the requote, but I think this a sound bit of advice worth highlighting. "Remaining open" is key!

but perhaps the way to understand is to read through first, and then go back and worry at the terms when you have a grasp of the 'idea of the game'. and all this 's' and 'c' is just a way of talking about


The idea of the game, at first, anyway, is that the stop light is on when the train is in the tunnel and off when the train is not in the tunnel. Mark, or no mark. And that game is what comes next. — unenlightened

Yeah that makes sense, given how chapter 1 didn't even begin to make sense without chapter 2. I'll keep along. I'm still figuring out the accounting, and how to make the crosses pretty.

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

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



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

*Been messing with it to try and figure out how it works, but updating the quote to reflect the code I'm using -- right now I'm uncertain why there's a gap between the top line and the cross-line in the embedded cross I Think I got it now.I'm going to respond to this post to make it appear more user friendly though. See the post below for better instructions.

I notice that if I do not put anything but a space where the "*" presently is that I get a negative symbol popping up, and also I'm still uncertain where that gap is. My hope, in the long run, is to offer strings which people can simply copy-paste with clear delineations for plug-and-play. If I'm running across a limitation rather than just messing up then perhaps "*" could serve as a blank space? But that kind of ruins the effect too.

Cool! I think I'm actually following so far then from what lookedlooks* like a very intimidating book.

*EDIT: I shouldn't get cocky, I just started.

Some more on chapter 2 --

For 2 I think we could use brackets, thus:

[ ], [[ ]], [[ ] [ ]], [a], [[[a] [[b] [c]] [ ]] Not very clear, and it might be better to alternate square and curly by depth, thus:

[{ } { }], [{[a] [{b} {c}] { }] — unenlightened

So, following along with the axioms in chapter 2...

[][] = []

and axiom 2

[{}] = .

?

I tried messing with 's bit of code and looking for tutorials but got lost in the information web. If there's a easy link to figuring out how to embed multiple crosses, @jgill, I'd be happy if you could pass it along because it does look prettier, and if I can figure out the syntax it's probably not that hard to embed multiple crosses.

Part of me is wondering if we can read Axiom 1 as the line above, and axiom 2 as the crossing of the line above. So when we, while using the form of the meta-language to parse order, draw a segment from left to right that is the law of calling. And when we draw a segment perpendicular to the calling that is a crossing. So if we cross again we negate, but it's easier to see that when we embed the original cross within a series of crosses rather than a series of lines coming off of the original calling.

This makes sense at a purely formal level because they complement one another -- the calling and the crossing are perpendicular but simultaneously need one another in order to be a calling or a crossing. In a sense the perpendicularity of the crossing removes some of the form of space of the meta-language, but not quite because the space of this formal system is defined by the cross rather than by a set of axioms describing space. Perpendicularity can be defined by reference to the cross, rather than the other way about, and from that we can name the space "Cartesian" if we take space to have an infinite series of crosses. (not Euclidean, that would be harder, or at least different, I think) (a bit speculative here.... just trying to think through the ideas towards something familiar) ((Also -- it'd probably have to be two orthogonal and infinite cross-spaces to define the Cartesian plane))

Then Chapter 2 is the use of the axioms to draw a distinction -- a form taken out of the original form of calling-crossing. Which, from chapter 1, is perfect continence.

Is it right to read "construction" as what's happening in the rest of the chapter? That's the impression I get -- if distinction is perfect continence then drawing a distinction will accord with what is given -- distinction and indication. (interestingly, comparing 1 and 2, we can interpret the cross as a kind of circle, but with the space-properties of this formal, rather than a geometric, system)

But what we get is the space cloven by the first distinction is* the form, and that all others are following this form. The space is cleaved by a cross indicating/distinguishing, but distinction is the form by which we can indicate an inside or an outside. In a way we could look at the cross as a mere mark rather than an intent. It would have content but it would not be a* used signal.

The notion of "value" is really interesting to me. The value is marked/unmarked, at the most simple. The name indicates the state, and the state is its value insofar that an expression indicates it. And then with equivalence we are able to compare states through the axioms. At this point I think we can only hold equivalence between the basic axioms, which turns out to have an inside and an outside, and gives a rule for "condensation" and "cancellation". So in a way the value is just what is named at this point, but there's still a distinction to be had between marked and unmarked due to the law of crossing canceling rather than reducing to the original name.

Then the end of the chapter is what follows from everything before. "The end" as I'm reading it starts at "Operation" -- this is where we can now draw a distinction, having constructed everything prior, and it entails some properties about the system being built such as depth, shallowness, and a need to define space in relation to the cross.

*added in as an edit, was confusing upon a re-read

Re-reading Depth I think I'm getting it this time. (I'm doing this in bits -- in the morning I like philosophy to wake up my mind, and in the afternoon I like philosophy to take a little mental break to something totally different)

This is talking about the

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

So s(sub"0") is the blank page surrounded by an unwritten cross. So in this example there are 2 crosses which pervade a which is then named c. In this case that would be the pervading space.

'Let' is a command from on High. This how it shall be henceforth. 'Let x be the number of angels that can dance on the head of a pin. 'Let' happens outside the formal system to create it. 'Call' is an action that happens inside the the system. You can call the distinction into being by making the distinction, that is by writing the sign. and If you write it twice in a row you call and recall. — unenlightened

Alright, that helps. So we have our meta-language which we're speaking now, and that differs from the formal system being created with the use of the meta-language.

Reading Chapter 1-2 (for some reason I'm finding them linked as I read this the first time -- like I can't talk about chapter 1 without chapter 2, and vice versa) again I can see the opening of 2 as a re-expression of Chapter 1, like The Form needed to be explicated before talking about forms out of the form, and the form takes as given distinction and indication which it also folds together as complementary to one another.

But then I get stuck right after "Operation" is introduced. "Cross" is a name for an instruction. Instruction, from just a bit before, leads to the form of cancellation. But what is the connection between states and instructions? Reading "Operation" again I'm reminded of the First canon "what is no allowed is forbidden". The name operates already as an instruction.

And then I get stuck on "continence", even though that was part of the opening. "Continence" is the name of the only relation between crosses, and that relationship is such that the cross contains what's inside, and does not contain what is not inside of it.

But this is where I really got lost entirely: What is going on from "Depth" to "Pervasive space", or are these concepts that, like the first chapter, will become elucidated by reading chapter 3? Like a puzzle unfolding?

The anarchist in me is determined :D.

Which I hadn't thought about until now -- but the question "How to learn philosophy at all?" is not innocent specifically because Plato continued the project of Socrates to corrupt the youth by the powers of reason, but more safely than him. So teaching has kind of always been a part of philosophy's practice.

I have to suggest that silence might at least be as good as declarations of not needing to convince, and so on, back and forth, and that this application might go some way to explaining the frustration that is commonly the result of enquiries into the nature and definition of philosophy. — unenlightened

Fair point. You hooked me with your application of the book to this problem ;)

And yup I don't think we're disagreeing. Maybe that's what's hard about distinguishing philosophy, too -- we're so used to the engine being disagreement that continual agreement upon things that look disparate seems to run counter to what we usually call philosophy, and it may just be a case of the snake eating its own tail and becoming incoherent.

I'd say any of the offered lists here, and even the reactions to the lists, could be considered methods of the sort I'm thinking. There are philosophical methods, like the Socratic and the Phenomenological method, but I was thinking more pedagogically -- how to learn philosophy at all?

Interesting use of the first chapters.

Something I'm stuck on, from a first reading of the first two chapters, is the distinction between letting and calling. I think I have to read "Let" as "Call a function" or something like that. It's naming an instruction rather than naming a distinction.

EDIT: Actually, thinking that through -- calling a function, more generally, a relation, would just be a distinction with a map.