List,
Jerry, you partly miss my point, partly not.
My ongoing work deals with the interrelations between culture, society, groups and individuals. Triadic, diagammatical thinking is the tool I use.
Well, an individual cell, mutatis mutandis, may be taken as something very similar to a human individual. As an individual, that is. Neither are nothing, not even possible without continuity. CSP takes up the Aristotelian distinction between *atomos* and *singular*, which ist to be noted and - in my view (I'n not certain about CSP) - taken as two perspectives on the individual in question.
Life presupposes continuity. We are used to think that there is a beginning and an end, which can be unequivocally marked on an abstract time-line. Be it a cell or a human (or animal) individual. - Actually that is not the case. There is nothing clear about these, except human markings, with a date and time.
These, as you said in your post I commented, are not very accurate. The time scale is what it is in each particular case. And dependent on (human) observation rate. (Cf. time-series in longitudinal studies.)
CSP writes on continuity (at the time he was, to my mind, on the verge of
rejecting both Aristotelicity and Kanticity as the basis for a sound philosophy
of continuity): We may break sand into smaller and smaller pieces, but it does
not bring back the continuity of the rock (or stone). This is cited on memory,
thus not exact. But I suppose anyone can make a seach and find the exact
quote. I think it appears in CP. Probably not elsewhere in published writings.
To note: I am not, nor do I intend to write on CSP, I take his core ideas and
use them, experiment with them and thus develop them onwards. - Just as I
think you are doing, Jerry, with your own work.
It is a problem publishind CSP's Writings is so slow.
As we all know, CSP was into ordinal arithmetics, not cardinal. - And therein
lies the basic difference between Cantor (etc) and CSP. CSP used playing cards
to demonstrate his ideas on ordinality. (For several decades I have started
every single working day with taking up a pack of cards, using them for
experimentation.)
In ordinal arithmetics, the crucial idea is that of a place (not number in the cardinal sense).
Well, then. In the beginning of Kaina Stoicheia CSP makes a triad (not a
tripartite fork, mind you) for mathematical thinking AS a methodical order
(ordinality! as a methodical principle, and, simultaneously a principle of
logic (in his broad sense). - It is about how you, or anyone, should develop
one's ideas in order to get somewhere. Whatever the aim and topic. (Still,
mutatis mutandis.)
I wrote extensively on this a couple of years back, with my slow read of Kaina Stoicheia.
What, according to CSP, must come first, what second and what third. He writes on the PROPER order in mathematics. - Then he just leaves math, and goes on to propositions etc. - In other words, there is a jump, a break of continuity in the (published) writing.
This gap needs to be bridged. But how?
I have bridged the gap. - Well, anyone may disagree or agree just according to
his or her likings. The crucial thing is to test the bridge, to experiment in
one's own field and thus to find out.
The gap is about the relations between math and logic (philosophy, if you like). (Note that I am not using the word 'relationship'. That is for a reason.)
Topical geometry is to be developed first, write CSP. - Historically, it is not what he did. But logically, it is.
After that, comes perspectival geometry. And only after that comes measuring et alia. Be it measuring time, or idividuals, or their parts or properties etc.. Also: numbering them.
All counting in the cardinal sense presupposes that one marks individuals. In geometry, it may mean marking a point on a line (or a surface etc.)
But in so doing, one breaks the continuity of the line (or surface etc.). This is the core of the conundrum of continuity.
CSP writes a couple of sentences on this. (After Kaina Stoicheia in 1904, I
assume. But it makes no essential difference, whether such an idea was
presented by him earlier. - It sometimes happens that, with ongoing work, one
gets a clear idea, and then gets all confused again. And later understands the
clear idea again, and one's work proceeds with rapid steps.)
To me, to all my knowledge and understanding, CSP never changed his view on
continuity about this: with marking a point, you loose continuity.
Marking (or delineating, whatever) any individual, by any means, you loose
(sight of) continuity. CSP writes, that it is OK to do so, IF it is done
deliberately, with a conscious decision. - Why so? - CSP does not tell. (as far
as I know).
I am not very much interested in the 'WHY' question. I have been interested in
WHAT to DO question.
Here is what I think should be done to overcome the conundrum: Continuity must then be restored.
This has to do with perspectives. What you have lost with marking the point (standing for whatever is at stake in whatever issue and case), is a perspective for continuity.
Deliberate change between perspectives is what is needed. But, in order to
actually do what is needed (to proceed), you have to have the ablility to do
so. Which means you have to practice your skills in doing so.
What are mistakenly called visual illusions are a very good objects to train oneself with. The famous duck/rabbit figure Wittgenstein talked about.
My claim that I can see both at once, and chance at will the figure I see, caused quite a stirr here on the list way back. Here in Finland the same has happened. Lots of indignation at such a presumptious claim have arisen. With lots of responses and discussions missing the point at the outset.
Well, just a week ago a taught a friend and colleague to see the stearcase, at will, as going up, going down and both simultaneously. It took less than an hour. - My case of seeing duck, rabbit or both at will, proved to me it is definitely possible. The comments on the list, proved to me that people are not willing to accept the possibility. (According to the logic of possibilities, one case is enough for a possibility. For getting convinced, that takes more...)
Our minds, any human minds are in many, many ways culturally conditioned. The culture we are bourn into, educated to its ways etc, acts in many ways as our bootstrap. - As long as there is only one (basic) bootstrap guiding our mental vision, there is no way to the ability to change, at will, the most basic perspectives. - But that is, alas, what is needed in order to understand both continuity and continuums. Though dealing with them, in an orderly manner, demands that you take up one at a time.
There is no problem with doing eg. all one's published work from one perspective. If the perspective of continuity is also taken into account, in an orderly manner. Taking it seriously means learnig to understand and put up with vagueness. - But the alternative is confusion. Which is a nasty experience and does not lead anywhere.
We all are not just vehicles, but also tools for thinking. We must make
ourselves better tools, in order to do work that matters. CSP devoted
considerable hours, daily, to do just that. - It not only diagrams, just as
well it is a question of learning to look at, of learning to see and understand
what one sees.
And Jerry, mathematical statements (in a broad sense or in a restricted sense?) may be viewed as philosophical statements. But not all do. At least unless they are guided to so so. I have no doubt in that you understand your mathematical statements simultaneously as philosophical statements. I have no problem with that.
I myself, not having practiced my mathematical skills except in simplest
mathematics, when reading your papers and discussing them with you, am able to
follow the philosophical side of your writings. And comment on them also on the
basis of my simple, basic skills in math.
But the basics never loose their relevance. They are most prone to get in a
state of confusion when something truly new and revolutionary is being
accomplished.
Best,
Kirsti
Jerry LR Chandler [jerry_lr_chand...@me.com] kirjoitti:
List, Kirsti, Stephen:
On Nov 11, 2014, at 12:27 PM, Kirsti Määttänen wrote:
> That is the distinction between continuity and continuums. CSP's synechism
is about the principle of continuity. Which is a philosophical statement (having
to do with mathematics, but not a mathematical statement).
>
>
> If anyone writes "continuity" and then changes into talking about continuum, that is something to be duly noticed. That is what I wish to say. There is a difference.
>
> Best,
>
> Kirsti
An important post from the perspective of "Natural Propositions"
Will you clarify your distinction?
I am a bit discomforted by the implication that mathematical statements are not
philosophical statement, although I agree that the relation between philosophy
and mathematics is asymmetric, or, from my perspective, differential usages of
grammars and meanings of symbols.
I suspect that your intent is to distinguish the continuity of an object or
process, inferring a temporal stability of one sort or another, a weak
invariance.
In this sense would you also like to imply the desire for a "what" and a "how"
to place the meaning of continuity in a relative context? Or, am I missing the point?
Stephen Rose's post appeared just as I was about to send this response.
His distinction is an important one. A continuity of a process can be restricted to a finite Cantorian interval of any duration. This is closely related to the principles of biosemiotics.
An interesting example of the sort of conundrums that arise is with a small
metabolite of a cell. In the dynamic processes of life, individual small
molecules are created and consumed at very high rates. Or, they may only
appear as a consequence of induction by exterior inducers and become a part of
the continuity of the cell, but only as long as the external inducer is
present. Remove the external inducer and the biosemiotics of the cell changes,
and the metabolite is no longer part of the cell. (This is just a re-statement
of the narratives constructed to describe the Lac operon in terms of both the
continuity and dis-continuity of bio-semiotics in relation to the generative
chemistry of life.)
Cheers
Jerry
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