Kirsti,
Your discussion is intriguing and so, at the point when you paraphrased
Peirce and mentioned anyone could look up the quote in CP, I took on that
role. Looking up "sand" in the Electronic edition of Peirce's CW I found
the following and copied 12 paragraphs. I will attach them to this post
for
anyone else's use. I look forward to any ensuing discussion.
Mary Libertin
On Wed, Nov 12, 2014 at 10:13 AM, Kirsti Määttänen
<[email protected]>
wrote:
> 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 [[email protected]] 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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