Gary R, Jon A, Mike B, List,
Let's distinguish between (1) the experience of space and time, (2) various mathematical systems that represent possible spatial and temporal frameworks, and (3) the metaphysical questions that we seem to be asking about the real character of space and time--and our attempt to theorizing about such things in physics and cosmology. My assumption is that you are asking about (3). In a broad sense, Sir William Rowan Hamilton anticipated Einstein's idea that space and time can be conceived as parts of a four dimensional continuum. In fact, he used the algebra of quaternions to articulate a formal framework for conceiving of such physical relations as part of a four dimensional field. For a bit of the context of the 19th century discussion of time as a fourth dimension of a single space-time framework, see: Bork, Alfred M. "The fourth dimension in nineteenth-century physics." Isis 55, no. 3 (1964): 326-338. Turning for a moment to (2), it is clear that Peirce was keenly aware of the major developments in the mathematical conceptions of space and time by Riemann, Cayley, Klein--and that Einstein was drawing on these same sets of mathematical ideas in his development of the cosmological and physical theories of general and special relativity. What is more, Peirce was keenly aware that Newton's notion of an absolute for time--as he had argued for space--contained a number of difficult logical and metaphysical issues that needed sorting. Einstein was fixing his attention on the same issues--but looking at them mainly from the vantage point of the physicist and not that of the logician. In addition to understanding the metaphysical implications of Hamilton's applications of quaternions, Peirce used the logic of relations to articulate a broader framework in which space and time might be conceived as evolving from a larger number of qualitative dimensions. As such, he anticipated Smolin's idea that the dimensions of space and time have evolved. After all, on Peirce's account, all qualities can be conceived of as part of a larger continuum of possible qualities (Lecture 8, RLT). As such, it is reasonable to suppose that the separation between the dimensions of space and time evolved by a processes of specification and differentiation--as did all of the dimensions of possible qualities. With respect to (1) above, I think that Peirce's remarks about the logical character of our conceptions of space and time contain a number of pregnant ideas that are worth sorting out. On the one hand, the conception of space and the experience of spatiality serve the function of allowing us to represent different objects as having the same properties at the same time--but in different places. The conception of time and the experience of temporality, on the other hand, allow us to represent one and the same object as taking different properties--but at different times. This seemingly simple set of logical ideas involve rather large ideas about the possible metaphysical relations that might hold between space and time. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Gary Richmond <gary.richm...@gmail.com> Sent: Monday, May 15, 2017 9:24 AM To: Peirce-L Subject: Re: [PEIRCE-L] Re: Did Peirce Anticipate the Space-Time Continuum? Mike, Jon, List, I asked Fernando Zalamea--my go-to scholar for questions regarding mathematical continutiy--and, while he noted that physics is not at all his field, he responded by writing (in part): FZ: I imagine that the Proceedings of the Harvard Sesquicentennial dedicated to Peirce’s Physics may have clues. [note: for the Proceedings, see; http://catalogue.wellcomelibrary.org/search~S8?/aCharles+S.+Peirce+Sesquicentennial+International+Congress+%281989+%3A+Harvard+University%29/acharles+s+peirce+sesquicentennial+international+congress+++++1989+harvard+university/-3,-1,0,B/browse for the contents of papers selected by Matthew Moore from the Proceedings see, http://catalogue.wellcomelibrary.org/record=b1023422 One paper in that collection by D. Sfendoni-Mentzou has the intriguing title, The role of potentiality in Peirce's tychism and in contemporary discussions in quantum mechanics and microphysics ; see: http://www.academia.edu/20431455/THE_ROLE_OF_POTENTIALITY_IN_PEIRCES_TYCHISM_AND_IN_CONTEMPORARY_DISCUSSIONS_IN_QUANTUM_MECHANICS_AND_MICROPHYSICS GR] FZ: On the other hand, as far as I know, relational logic is far from quantum logic. This second trend originates with von Neumann's Continuous Geometries and orthomodular lattices, something that, I think, Peirce could not envision. (emphasis added) I have not yet read the paper you pointed to Mike (I intend to), but although I have sometimes thought otherwise (based principally on a readong of the 1898 lecture series, published as Reasoning and the Logic of Things), I would at present temd tp agree with Zalamea here. And I agree with the whole of Jon Awbrey's post leading to his conclusion: JA: I think the full import of [Peirce's] on-theoretic and pragmatic-semiotic approaches to scientific inquiry is a task for the future to work out. Best, Gary R [Gary Richmond] Gary Richmond Philosophy and Critical Thinking Communication Studies LaGuardia College of the City University of New York C 745 718 482-5690<tel:(718)%20482-5690> On Sun, May 14, 2017 at 12:05 PM, Jon Awbrey <jawb...@att.net<mailto:jawb...@att.net>> wrote: Mike, List, The mathematical perspectives and theories that made modern physics possible, perhaps even inevitable, were developed by many mathematicians, both abstract and applied, all throughout the 19th Century. There was a definite sea change in the way scientists began to view the relationship between mathematical models and the physical world, passing from a monolithic concept to variational choices among multiple approaches, models, perspectives, and theories. Peirce was an astute observer and active participant in this transformation but it has always been difficult to trace his true impact on its course — so much of what he contributed operated underground, rhizome like, and without recognition. But I think it's fair to say that Peirce articulated the springs and catches of the workings of science better than any other reflective practitioner in his or subsequent times. And I think the full import of his information-theoretic and pragmatic-semiotic approaches to scientific inquiry is a task for the future to work out. Regards, Jon On 5/14/2017 1:34 AM, Mike Bergman wrote: I just encountered this assertion: "In the present work we have indicated that a form of logic, relational logic developed by C. S. Peirce, may serve as the foundation of both quantum mechanics and string theory." [1] Does the list have any comments, further references or criticisms on this pretty bold statement? Thanks, Mike [1] A. Nicolaidis, 2008. "Categorical Foundation of Quantum Mechanics and String Theory," arXiv:0812.1946, 10 Dec 2008. See https://arxiv.org/pdf/0812.1946.pdf -- inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey isw: http://intersci.ss.uci.edu/wiki/index.php/JLA facebook page: https://www.facebook.com/JonnyCache ----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu<mailto:peirce-L@list.iupui.edu> . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu<mailto:l...@list.iupui.edu> with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
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