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?

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