- I finally managed to get a copy of a translation of this work, which

I thought was some sort of Pythagorean (i.e., Neo-, I assumed) work,

though only in a non-scholarly edition of a version by Thomas Taylor,

published by the Shrine of Wisdom in Britain in 1974. Unfortunately

there is no help in the edition for any information on what original

Taylor is translating here, assuming in fact it is some original and

not his own making. I rather think it's not his. The edition has a

rather floridly written biography of Taylor, and then his translation

followed by what I assume are Taylor's own notes. No mention of the

original text, what edition he was working from - again I assume he

was not accessing some original manuscript, but who knows? The work

itself however is quite odd indeed.

It is a not that lengthy schema of mathematical formulae, which are

annotated in the text (again, are they original or Taylor's

additions? I think original, otherwise the work wouldn't make much

sense at all) with glosses of the philosophical meaning, of what is

being represented mathematically in each formula. But the glosses are

not Neopythagorean at all, rather they reflect the full-blown

procession of the theological philosophy of Proclus or at any rate

the later Neoplatonists.

It starts off with:

A representation in symbols and numbers of the procession of things,

from the One.

x bound

y the infinite

--

yx being

yx

--

y squared

x squared [both with exponents which I can't type here]

yx bound and infinite multiplied

--

y cubed x cubed

--

y cubed x cubed life Intelligible Triad

and it goes one for several pages, with the exponents getting

progessively much, much (!) larger as we proceed farther from the

One, including mention of the various gods in their appropriate

Proclan positions in the scheme of things.

I really don't know what to make of this thing. I haven't spent a lot

of time with Taylor's explanation; he notes there first off that

multiplication should be equated with progession, hence the basic

notion of the schema with multipliers and exponentiation. Also there

is something relating back to the Decad and its relation to One, and

how the exponents are defined, and so there is I suppose a

Pythagorean element after all. I would have much more into Taylor's

notes to get the gist here, and some of it is to be honest rather

abstruse to me.

I just wanted to share this with all, since it seems most curious. I

like the idea of trying to come up with a nice mathematical formula

to represent progression, though frankly it's a little hard

personally at first sight to get that excited about multiplication. I

just wonder what the background is here. The subtitle of the work,

again whether it's Taylor's or not I cannot say, is "A Specimen of

Theological Arithmetic".

Is it possible this thing somehow goes back to one of the lost works

of Iamblichus in his Pythagorean series?

Dennis Clark - As far as I know, the Medicina Mentis is by Ehrenfried Walther von

Tschirnhaus (1651-1708). Sorry, no Iambichus here, I'm afraid.

Best, Mike>

Michael Chase

CNRS UPR 76

Paris-Villejuif

France - --- In neoplatonism@yahoogroups.com, "Goya" <goya@...> wrote:
>

Hi, Mike. I hope this posting isn't doubled. I posted it earlier and

>

>

>

>

> As far as I know, the Medicina Mentis is by Ehrenfried Walther von

> Tschirnhaus (1651-1708). Sorry, no Iambichus here, I'm afraid.

>

>

>

>

> Best, Mike

> >

>

>

>

Yahoo died in the middle.

I am aware, though only from Web research, of Tschirnhaus and his

work with the same name, but I really thought I had read mention of

this as an actual ancient, Pythagorean work. Unfortunately I can't

recall where I read that, though I do recall it was in some reputable

scholarly source.

Or was Tschirnhaus interested in Neoplatonism and produced this?

Dennis Clark >>

M.C. I confess I don't know enough about T. to say (also my curiosity has

>

> Hi, Mike. I hope this posting isn't doubled. I posted it earlier and

> Yahoo died in the middle.

>

> I am aware, though only from Web research, of Tschirnhaus and his

> work with the same name, but I really thought I had read mention of

> this as an actual ancient, Pythagorean work. Unfortunately I can't

> recall where I read that, though I do recall it was in some reputable

> scholarly source.

>

> Or was Tschirnhaus interested in Neoplatonism and produced this?

now been piqued: friend of Leibniz and Spinoza, inventor of porcelain,

wood-burniong kilns and techniques for glass-casting, eniment

mathematician...

The mathematics you describe seem reminiscent of the Tschirnhausen cubic.

But it is true that most describe his philosophical approach as empiricist

(Cf. M. Schonfeld, "Dogmatic metaphysics and Tschirnaus' methodology",

Journal of the history of Philosophy 36.1 1998; C.A. Von Peursen, "E. M.

von Tschirnhaus and the ars inveniendi", Journal of the history of ideas

54.3 (1993), 395-410).

Could the work you have be an application by Taylor himself of

Tschirnhausian mathematics to Neoplatonic metaphysics? I note that the

same Prometheus volume that contains the Medicina mentis also contains

other esays by Taylor such as The Elements of a new arithmetical notation

and the Elements of the true arithmetic of infinites.

Best, Mike.

>

Michael Chase

> Dennis Clark

>

>

CNRS UPR 76

Paris-Villejuif

France- --- In neoplatonism@yahoogroups.com, "Goya" <goya@...> wrote:
>

and

>

> >>

> >

> > Hi, Mike. I hope this posting isn't doubled. I posted it earlier

> > Yahoo died in the middle.

of

> >

> > I am aware, though only from Web research, of Tschirnhaus and his

> > work with the same name, but I really thought I had read mention

> > this as an actual ancient, Pythagorean work. Unfortunately I can't

reputable

> > recall where I read that, though I do recall it was in some

> > scholarly source.

curiosity has

> >

> > Or was Tschirnhaus interested in Neoplatonism and produced this?

>

> M.C. I confess I don't know enough about T. to say (also my

> now been piqued: friend of Leibniz and Spinoza, inventor of

porcelain,

> wood-burniong kilns and techniques for glass-casting, eniment

cubic.

> mathematician...

>

> The mathematics you describe seem reminiscent of the Tschirnhausen

> But it is true that most describe his philosophical approach as

empiricist

> (Cf. M. Schonfeld, "Dogmatic metaphysics and Tschirnaus'

methodology",

> Journal of the history of Philosophy 36.1 1998; C.A. Von

Peursen, "E. M.

> von Tschirnhaus and the ars inveniendi", Journal of the history of

ideas

> 54.3 (1993), 395-410).

the

>

> Could the work you have be an application by Taylor himself of

> Tschirnhausian mathematics to Neoplatonic metaphysics? I note that

> same Prometheus volume that contains the Medicina mentis also

contains

> other esays by Taylor such as The Elements of a new arithmetical

notation

> and the Elements of the true arithmetic of infinites.

I have been wondering the same thing, if this is after all a work by

>

> Best, Mike.

>

>

>

> >

Taylor himself, who started out studying mathematics, by the way. The

other main work on "theological arithmetic" in that Prometheus volume

is indeed his own, and he certainly could have known Tschirnhaus'

work.

Yes, Herr Tschirnhaus does sound interesting, though apparently

somewhat ignored.

I just wish I could remember where it was I first saw mention of

this, but of course it's slipped my mind. It was definitely the title

I read about first, and that set me off looking for more information,

of which only this piece by Taylor was all I could find anywhere, but

I haven't been to the library and any standard work of reference such

as Pauly.

Though to be honest, "medicina mentis" hardly sounds ancient, does

it? Much more like something from a much later period, such as the

Renaissance or 17th century.

Dennis Clark