Jack, List: JRKC: What role does dimensionality have in Peirce's schema?
I can suggest at least a couple of roles that dimensionality plays in Peirce's thought. CSP: The evolution of forms begins or, at any rate, has for an early stage of it, a vague potentiality; and that either is or is followed by a continuum of forms having a multitude of dimensions too great for the individual dimensions to be distinct. It must be by a contraction of the vagueness of that potentiality of everything in general, but of nothing in particular, that the world of forms comes about. (CP 6.196, 1898) CSP: Let the clean blackboard be a sort of diagram of the original vague potentiality, or at any rate of some early stage of its determination. This is something more than a figure of speech; for after all continuity is generality. This blackboard is a continuum of two dimensions, while that which it stands for is a continuum of some indefinite multitude of dimensions. This blackboard is a continuum of possible points; while that is a continuum of possible dimensions of quality, or is a continuum of possible dimensions of a continuum of possible dimensions of quality, or something of that sort. There are no [actual] points on this blackboard. There are no [actual] dimensions in that continuum. (CP 6.203, 1898) CSP: At the same time all this, be it remembered, is not of the order of the existing universe, but is merely a Platonic world, of which we are, therefore, to conceive that there are many, both coordinated and subordinated to one another; until finally out of one of these Platonic worlds is differentiated the particular actual universe of existence in which we happen to be. (CP 6.208, 1898) In cosmology, he thus posits a *continuum *of potential dimensions within which our "actual universe of existence" with its four dimensions is like "a figure of lower dimensionality" (CP 4.642, 1908). CSP: But I ask you to imagine all the true propositions to have been formulated; and since facts blend into one another, it can only be in a continuum that we can conceive this to be done. This continuum must clearly have more dimensions than a surface or even than a solid ... Nevertheless, in order to represent to our minds the relation between the universe of possibilities and the universe of actual existent facts, if we are going to think of the latter as a surface, we must think of the former as three-dimensional space in which any surface would represent all the facts that might exist in one existential universe. (CP 4.512&514, 1903) CSP: [Existential graphs] are diagrams upon a surface, and indeed must be regarded as only a projection upon that surface of a sign extended in three dimensions. Three dimensions are necessary and sufficient for the expression of all assertions ... (R 654:6-7, 1910 Aug 19) In logic, he thus diagrams "the universe of actual existent facts" with two dimensions, as represented in EGs, and situates it within "the universe of possibilities," which has three dimensions. Moreover, the continuum of "all the true propositions ... must clearly have more dimensions" than three, but three "are necessary and sufficient for the expression of all assertions." Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Oct 8, 2021 at 5:39 PM JACK ROBERT KELLY CODY < jack.cody.2...@mumail.ie> wrote: > Quick scan reveals nothing novel a dimensional framework/problematic: > > "Lorentz has already shown us a convenience in considering a time, if not > exactly as a dimension of time-space, at least as that fourth unit that > Hamilton adds to the three dimensions of space to make up a quaternion, and > indeed one may say that, from the point of view of matrices, > three-dimensional space appears as not altogether comprehensible without a > fourth" 1913 (in EP Volume 2: 474). > > (Einstein worked on relativity between 1907-1915, but built on Lorentz > amongst others - this Peirce quote stems from 1913, I think). > > Also, in *Logic of Drawing History from Ancient Documents* (CP 7.164-231) > Pierce states "Although the reasons those numbers are not at all apodictic, > yet I should... be much *surprised to learn that its dimensionality was > three, which is so much more difficult to conceive than four*. No doubt, > it may be said that rationality as nothing to do with the question..." > (this, I think, is from 1901). > > His familiarity (as a mathematican) with Hamilton/quarternion is > interesting because Hamilton is quoted as stating (in 1843): > > "Time is said to have only one dimension, and space to have three > dimensions. The mathematical quaternion partakes of both these elements; in > technical language it may be said to be "time plus space", or "space plus > time": and in this sense *it has*, *or at least involves a reference to*, > *four > dimensions*" before moving on to this oddly apt lyrical conclusion: > > "And how *the One of Time, of Space the Three, Might in the Chain of > Symbols girdled be*." (William Rowan Hamilton). > > I'm not sure how/why I've overlooked dimensionality in reading Peirce, or > if it will even prove useful, but found this interesting, nonetheless. > > Best > > Jack > > ------------------------------ > *From:* JACK ROBERT KELLY CODY <jack.cody.2...@mumail.ie> > *Sent:* Friday, October 8, 2021 10:03 PM > *To:* Peirce-L <peirce-l@list.iupui.edu>; Jon Alan Schmidt < > jonalanschm...@gmail.com>; JACK ROBERT KELLY CODY < > jack.cody.2...@mumail.ie> > *Subject:* Re: [PEIRCE-L] [EXTERNAL] Re: Connected Signs Theorem (was > Cognitive Signs) > > Just quick revision - the universe is surely four dimensional, not three > (as time counts as an added dimension). > > If time is admitted as a dimension plus the three spatial, then the symbol > makes more sense (to me anyway). Habit requires time. It would also allow > me to make better sense of the [R(O-S-I)] formula whereby there is a sign > external context insofar as we think of semiosis in itself. > > I'm not the best candidate to be making distinctions about either > dimensions or Peircean parlance, though - I just like the analogy insofar > as it solves something for me personally. > > Best > > Jack > > ------------------------------ > *From:* peirce-l-requ...@list.iupui.edu <peirce-l-requ...@list.iupui.edu> > on behalf of JACK ROBERT KELLY CODY <jack.cody.2...@mumail.ie> > *Sent:* Friday, October 8, 2021 9:16 PM > *To:* Peirce-L <peirce-l@list.iupui.edu>; Jon Alan Schmidt < > jonalanschm...@gmail.com> > *Subject:* Re: [PEIRCE-L] [EXTERNAL] Re: Connected Signs Theorem (was > Cognitive Signs) > > Edwina, Jon, List, > > What role does dimensionality have in Peirce's schema? In his letter to > Lady Welby, he invokes the fact that the universe (as we perceive it, at > least) has three dimensions. > > Is icon one dimensional in pure form (the medium is qualitatively the same > as its object, purely), the index, two dimensional in its pure form > (opposition/action-reaction/force/cause-effect), and the symbol three > dimensional in its pure form (habit/law/convention)? If we could accept > this just speculatively, the question would be why icon and index seem to > suit their dimensional counterpart, but symbol seems not to have the same > "natural" fit. > > As with semiosis, we can only experience first, seconds, and thirds, from > our embodied position as situated within a three-dimensional universe. > > Going way off reservation here, but this leads me to look for corollaries > in other areas: > > > "Because gravity is one of the fundamental forces, superstring theory > includes an explanation of general relativity. The problem is, superstring > theory predicts that there are 10 dimensions – 9 spatial and one temporal. > How does this work with our 3-dimensional universe? > > > Superstring theory has remained little more than a theory for years. > Investigations have been restricted to discussing models and scenarios > since performing the actual calculations have been incredibly difficult. As > such, superstring theory’s validity and usefulness have remained unclear. > > > But a group of three researchers, associate professor at KEK Jun > Nishimura, associate professor at Shizuoka University Asato Tsuchiya, and > project researcher at Osaka University Sang-Woo Kim, has succeeded in > generating a model of the universe’s birth based on superstring theory." > > > Using a supercomputer, they found that *at the moment of the Big Bang, > the universe had 10 dimensions – 9 spatial and 1 temporal – but only 3 of > these spatial dimensions expanded*." > > > https://www.universetoday.com/92131/why-do-we-live-in-three-dimension/ > I'm aware that this now moving into the realm of madness, but does Peirce > not posit three trichotomies and ten classes of signs in that same letter? > More of an interesting overlap than anything else. Would be nice if we > could get a physicist, a chemist, a few philosophers, and some of the more > renowned Peirceans into a room together. > > Now returning to my actual work! > > > Best > > > Jack > >
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