But shouldn't some talk about *arrows* be interesting? ]]>

Thanks, Lee.

]]>@Lee - I agree with Urs: I’m not sure how constructive to the nLab project your comments are. I encourage your to compare your posts with those of regular users here and see how things generally work in this forum.

]]>Hey Lee,

let me be the one to break the silence, as I suppose I am responsible for starting a discussion that may easily look more intellectually unconstrained than it actually is.

I’d like to ask you to refrain from continuing down the path that you are going here.

]]>carries the information that I am not the thinking

that occurs inside me

(even though it does occur inside me)

nor am I my beliefs

(which are expressed by such thinking)

nor again, am I all those doubts

which are the duals of my beliefs, in the sense that

"I doubt X" means "I believe not X" ]]>

self = (thinking, self)

the symmetrical parenthesis in the equation

self = (thinking, self)

symbolize one thing, actually.

Rather than a point--

where a point has no dimension and therefore nothing inside of itself--

the equation

"self = (thinking, self)"

tells us that "self"

is not a empty point.

Because you can see that there is something inside it:

self = (thinking, self)

And if you have something inside of you, as in

self = (thinking, self)

then you are therefore not a dimensionless point,

having nothing inside you.

Inside you: there is something--

self = (thinking, self)

It's as if there is a seemingly impenetrable wall, inside of which there lies a hidden land.

There must be a gate.

Because

self = (thinking, self)

tells us that, first,

there is something inside the self,

inside a surrounding wall that hides what's inside

from everything on the outside.

Then the right hand side of

self = (thinking, self)

says that somehow, self has gotten inside of this impenetrable wall of doubt.

So there must be a gate, through which the self can travel into itself, through the otherwise impenetrable wall of doubt.

In Parmenides poem On Nature this is the path of a chariot, in which an innocent heart is carried through a gate in the mountains into a hidden land which is otherwise guarded all around by impassable mountains.

The hidden land of knowledge

lies hidden within an impenetrable

mountain range of doubt.

But the self gets through!

Because there is a chariot path through a gate.

Which means:

Penetrating through an impenetrable wall of doubt and belief.

And because of this,

self = (thinking, self)

says that the path to the hidden land within

is knowing self,

not believing (thinking).

So to know the chariot is to know the self.

It is like traveling through a gate into a hidden land

which turns out to be

home. ]]>

By means of his paradoxes Zeno expressed mathematical structure in the world described by Parmenides. It was the structure of the infinite.

In a previous post, fragments from Parmenides have also been modeled using non-wellfounded sets, Hamilton’s equations, and mathematical models of Jon Barwise’s informationalism.

There is yet another mathematical structure in fragments from Parmenides.

In the poem, “On Nature,” Parmenides makes the analogy of the human experience of existence as riding in a chariot with strong horses, in which a young person is pulled along a secret path to a gate, through which only the innocent can pass.

In another fragment (newly translated in the above post) the words are: “’Auto’ is for thinking and being.” “Auto” there being translated into “self.”

So in this fragment there is an arrow from self to thinking.

And– there is, as well, an arrow from self to self.

In an equation it looks like this:

self = (thinking, self)

“The self is for thinking and being (self).”

It’s probably clear to everybody that human beings think a lot.

But what about the arrow from self to self?

The “gate” from self to self– the gate in Parmenides’ poem “On Nature”– is found along a secret path that Parmenides knew about.

Human beings don’t tolerate thoughts existing in themselves which they do not believe.

The arrow from self to thinking must therefore involve believing.

While the arrow from self to self must involve knowing.

For example, say that the night before the big race Achilles and the tortoise get into a bar bet. The tortoise bets that Achilles will not win the race tomorrow, because for every halfway point that Achilles can reach between himself the tortoise (out of fairness the tortoise is given a head start), there is yet another half way point.

No matter how much Achilles might believe this about the halfway point the night before the race, he will nonetheless show up the day of the race because of what he knows.

What Achilles knows is the chariot.

It includes his body.

So what he knows supersedes what he believes and guides Achilles’ action:

He shows up the day of the race no matter what he believed the night before. This is because of what he knows: the chariot.

]]>“’Auto’ is for thinking and being.”

I think this quote from Parmenides is only found in Cicero.

If I leave the Greek word “auto” as the only word not translated in the ancient quote, it suggests to me that “auto” could be translated into the word “self.”

Do you know of anybody who has analyzed the fragment this way?

When I do it, I get an arrow from “self” to “self” which produces a stream of “thinking.”

But I have to use nonwellFounded sets–

self = (thinking, self)

The parenthesis seem to stand for “being.”

And…

“self” is constant . “thinking” is constantly changing.

This reminds me of the chariot drawn by horses in Parmenides’ poem.

So while the preceding text modeled fragment A from Parmenides in the language of nonwellfounded sets, the following text models fragment B in the language of Hamilton’s equations, but now interpreted in the language of informationalism.

The chariot is constant while there is a stream of (information and possibilities).

A human being has some quantity of information available, some number of possibilities available, and the chance to move from one state of such numbers to another state of such numbers, as long as alive that is.

Of course this is a model even farther away from reality than the wind-tunnel model of an airplane is from the real thing. But a few aspects do seem to ring true. For example, death of a human being in this model would be the disappearance of all available information and the disappearance of every possibility. Here’s an equation for modeling this:

$\frac{dH}{dt} = \frac{\partial H}{\partial p}\frac{dp}{dt} + \frac{\partial H}{\partial q}\frac{dq}{dt}$

In this equation “p” would be the number of possibilities. “q” would be the number of information elements available. When “H” is a number greater than zero, this means that the human being is alive. “H=0” would mean death. This would be like modeling the existence of a human being as a kind of chariot drawn by some quantity of horses of number “H”. When all the horses disappear “H = 0”, then the chariot (the existence of the human being) stops.

So the equation for the constant existence of a human being in the midst of all the changes in life would mean dH/dt = 0. Which is satisfied when the following two equations hold:

$IF: \frac{\partial H}{\partial p} = \frac{dq}{dt} AND: \frac{\partial H}{\partial q} = - \frac{dp}{dt} THEN: \frac{dH}{dt} = 0$

Scale– that is, how many horses– in this kind of model would simply be a pragmatic issue– whatever scale fits into the wind tunnel. Everything else being constant, say that H changes by one when the number of possibilities changes by one. H likewise changes by one when the number of information elements available changes by one.

$\frac{\partial H}{\partial p} = 1$

$\frac{\partial H}{\partial q} = 1$

So during the life of the individual, what would this mean? Substituting in the above two equations for making dH/dt = 0, to keep the number of horses constant (maintain existence) whenever during the increment of time the number of possibilities changes by one, then the number of information elements must change by minus one, and vice versa, in order to satisfy the above two equations.

$IF \frac{dq}{dt} = 1 THEN \frac{dp}{dt} = -1 And IF \frac{dp}{dt} = 1 THEN \frac{dq}{dt} = -1$

This might be familiar in several ways.

First, these are basic ideas of Hamilton’s equations.

Second, solving them for changes in possibilities and available information over the increment of time is “The Inverse Principle of Informationalism,” which was expressed years ago by the late Jon Barwise. I first heard about the inverse principle at a workshop at Stanford’s Center for the Study of Language and Information called “The Business Applications of Situation Theory.” Here it is:

“The Inverse Relationship Principle: Whenever there is an increase in available information there is a corresponding decrease in possibilities, and vice versa.”

http://projecteuclid.org/euclid.ndjfl/1039540766

Third, modeling (a) the constant existence that can be felt by every human being as (b) a chariot drawn by horses is due to the pre-Socratic poet Parmenides in his poem “On Nature.” According to Plato, Parmenides was the only person Socrates (“Know thyself”) held in awe. It’s said that as a way of trying to help Parmenides, Zeno created his now-famous paradoxes.

]]>Thanks for the pointer.

By the way, I see now one doesn’t need to rely on secondary sources for the statement that Hegel meant his philosophy to be understood from this angle. In the introductory words to his *Lectures on the Philosophy of Religion* he is fully explicit about this

In der Tat ist dagegen die Behauptung zu machen, daß der Inhalt, das Bedürfnis, das Interesse der Philosophie mit der Theologie ein gemeinschaftliches ist.

Der Gegenstand der Religion, wie der Philosophie, ist die ewige Wahrheit in ihrer Objektivität selbst, Gott und Nichts als Gott und die Explikation Gottes. Die Philosophie expliziert nur sich, indem sie die Religion expliziert, und indem sie sich expliziert, expliziert sie die Religion. Sie ist, wie die Religion, beschäftigung mit diesem Gegenstande, sie ist der denkende Geist, der diesen Gegenstand, die Wahrheit, durchdringt, Lebendigkeit und Genuß, Wahrheit und Reinigung des subjektiven Selbstbewusstseins in und durch diese Beschäftigung.

So fällt Religion und Philosophie in eins zusammen, die Philosophie ist in der Tat selbst Gottesdienst, aber beide sind Gottesdienst auf eigentümliche Weise: in dieser Eigentümlichkeit der Beschäftigung mit Gott unterscheiden sich beide.

…

Neu ist aber die Verknüpfung der Philospophie und der Theologie nicht: sie hat Statt gefunden bei denjenigen Theologen, die man die Kirchenväter nennt, bei den vorzüglichen derselben.

…

]]>Diese Verknüpfung der Theologie und Philosophie sehen wir auch im Mittelalter; scholastische Philosophie ist eins und dasselbe mit der Theologie; Philosophie ist Theologie und Theologie ist Philosophie.

Haven’t got around to reading it yet, but this book is presumably helpful for figuring out what esoteric writing is and how it functions: http://www.press.uchicago.edu/ucp/books/book/chicago/P/bo18692306.html

]]>There is also this:

]]>Ah, excellent. That’s precisely what I mean. Have added a pointer here.

]]>You may be interested in Hegel and the Hermetic Tradition by Glenn Alexander Magee. You can read the introduction here.

]]>*Meister Eckart* is linked to from *Science of Logic* as a precursor author who had the habit of combining a baffling claim with the commentary that the average audience will not understand it and should not try to understand it.

I’ll add relevant quotes to the entry, such as

Denn, solange der Mensch dieser Wahrheit nicht gleicht, solange wird er diese Rede nicht verstehen; denn dies ist eine unverhüllte Wahrheit, die da gekommen ist aus dem Herzen Gottes unmittelbar.

but there are others like this. From memory he says at some points

Dies zu verstehen tut nicht not.

etc. I’ll look it up when I have time. (And I will announce this entry when it is in a form that deserves to be announced…)

This is meant to substantiate the claim at *Science of Logic* that Hegel speaks as a mystic (Eckart being an archetype of a mystic).

Excellent! Extra credit if you now find a good online copy of the actual dialogue and link to it from the entry! :-)

]]>Dot done!!!!

Just a query: Is the Meister Eckart entry going to link in with that philosophical question of many and one?

]]>There still seems to be a spurious dot.

(Just kidding you. )

]]>OOPs again. I must have been heavy fingered when I did that! Fixed! (I hope)

]]>It seems to me you still have a typo there. At least compared to standard spelling.

]]>OOPs! I think I should correct that one! (Note u and i are next to each other on my keyboard, but why the ’me’ went ‘AWOL’ I do not know.)

]]>Just to clarify for bystanders: I had started a stub *Parmenides dialogue* in which, it turns out, I broke a link.

But the typo in the title above seems to be Tim’s, not mine (?)

I will announce this and related entries once they have grown into a minimum that could be called an entry.

]]>I fixed a link that was not working. (The brackets were interfering with the link address.) see here

]]>