John Sowa, Jon Awbrey, Edwina, List, I wanted to see if anyone have might suggestions for thinking about the analogy between (1) mathematical models of the differentiation of spaces starting with a vague continuum of undifferentiated dimensions and trending towards spaces having determinate dimensions to (2) models for logic involving similar sorts of dimensions? How might we understand processes of differentiation of dimensions in the case of logic?
John Sowa says: We have to distinguish (1) time as it is in reality (whatever that may be); (2) time in our stories (which include the formalized stories called physics); (3) the mental sequence of thought; and (4) the logical sequence (dialogic) of connected signs. Let's focus on the (3) and (4). Recently, on the List, we've been examining what Peirce's says in the last lecture of Reasoning and the Logic of Things when he runs through a number of examples in mathematics (i.e., drawn largely from projective geometry, number theory and topology), and then attempts to clarify a logical conception of continuity. Shortly thereafter, he indicates that he is trying to understand how the logical principles that govern our patterns of inference might be subject to an evolutionary process. I take him to making a comparison between how we might conceive of the relationship between mathematical systems with a continuum of vague dimensions--and how those might give rise to systems with more specific numbers of dimensions having a more definite character. One illustration that is offered involves the evolution of our experience of spatial dimensions where we find ourselves in a cave of odors. One idea I take him to be exploring is that the evolution of our subjective systems of logic (e.g. the way we sort out different subjects and predicates that are involved in the propositions found in the premisses and conclusions of an argument into a referential system having different dimensions) can be understood by making a comparison with how mathematical systems dimensions are related--ranging from those with a vague continuum of dimensions to those with determinate dimension. Do you have suggestions about how we might understand an analogy between models of the evolution of mathematical dimensions and logical dimensions? In the context of the later work on the EG, for instance, might we develop this analogy by thinking about a model in which books having many sheets (e.g., of interrogation, assertion, etc.) might evolve starting with those in which the dimensions are vague and continuous to those that are more determinate? Turning to point (2) above, John Sowa seems to suggest that relations of relevance in context are quite fundamental for understanding how logical relations might have evolved (i.e., in either a subjective logic or an objective logic) How do such relations of relevance compare to relations of similarity and dissimilarity (e.g., what Peirce calls equiparance and disquiparance)? That is, do you have suggestions for thinking about the manner in which relations of relevance within a context might bear on the connections between vague predicates connected to indeterminate subjects arrayed in a book consisting of a vague continuum of sheets of interrogation and assertion? --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: John F Sowa [s...@bestweb.net] Sent: Wednesday, November 9, 2016 12:25 PM To: Edwina Taborsky; peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Metaphysics and Nothing (was Peirce's Cosmology) Edwina, Kirsti, list, ET > I wish we could get into the analysis of time in more detail. I came across a short passage by Gregory Bateson that clarifies the issues. See the attached Bateson79.jpg, which is an excerpt from p. 2 of a book on biosemiotics (see below). Following is the critical point: GB > thinking in terms of stories must be shared by all mind or minds > whether ours or those of redwood forests and sea anemones... > A story is a little knot or complex of that species of > connectedness which we call relevance. This observation is compatible with Peirce, but CSP used the term 'quasi-mind' to accommodate the species-bias of most humans: CP 4.551 > Admitting that connected Signs must have a Quasi-mind, it may further > be declared that there can be no isolated sign. Moreover, signs > require at least two Quasi-minds; a Quasi-utterer and a Quasi- > interpreter; and although these two are at one (i.e., are one mind) > in the sign itself, they must nevertheless be distinct. In the Sign > they are, so to say, welded. Accordingly, it is not merely a fact > of human Psychology, but a necessity of Logic, that every logical > evolution of thought should be dialogic. Re time: We have to distinguish (1) time as it is in reality (whatever that may be); (2) time in our stories (which include the formalized stories called physics); (3) the mental sequence of thought; and (4) the logical sequence (dialogic) of connected signs. ET > The question is: Are the Platonic worlds BEFORE or AFTER the so-called > Big Bang? I read them as AFTER while Gary R and Jon S [not John S] > read them as BEFORE. In my reading, before the Big Bang, there was > Nothing, not even Platonic worlds. This question is about time sequences in different kinds of stories: the Big Bang story about what reality may be; and Platonic stories about ideal, mathematical forms. The time sequence of a mathematical story is independent of the time sequence of a physical story. We may apply the math (for example, the definitions, axioms, and proofs of a Platonic form) to the construction of a physical story. But that application is a mapping between two stories. The term 'prior to' is meaningful only *within* a story, not between stories. In short, our "commonsense" notion of time is an abstraction from the stories we tell about our experience. The time sequences in two different stories may have some similarities, but we must distinguish three distinct sequences: the time sequences of each story, and the time sequence of the mapping, which is a kind of meta-story. JFS >> Does anyone know if [Peirce] had written anything about embedding >> our universe in a hypothetical space of higher dimension? KM > I am most interested in knowing more on this. David Finkelstein, p. 277 of the reference below: > Peirce seems to have included geometry in his evolutionism, at least > in principle... [He] seems not to have responded to the continuously- > evolving physical geometry of Riemann and Clifford... nor to Einstein's > conceptual unification of space and time. In any case, I think that the notion of time as an abstraction from stories -- imaginary, factual, or theoretical -- provides a way of relating different views. It also allows for metalevel reasoning that can distinguish and relate different kinds of stories that have independent time scales and sequences. John ____________________________________________________________________ From Google books: _A Legacy for Living Systems: Gregory Bateson as Precursor to Biosemiotics_ edited by Jesper Hoffmeyer, Springer, 2008: https://books.google.com/books?id=dcHqVpZ97pUC&pg=PA246&lpg=PA246&dq=Order+is+simply+thought+embodied+in+arrangement&source=bl&ots=DQUnZlvOYu&sig=X8bH0YAG597uwjyedB4dSf2BuC0&hl=en&sa=X&ved=0ahUKEwizyZD88JrQAhVENxQKHeEeBwoQ6AEIHTAA#v=onepage&q=Order%20is%20simply%20thought%20embodied%20in%20arrangement&f=false David R. Finkelstein, _Quantum Relativity: A Synthesis of the Ideas of Heisenberg and Einstein_, Springer, 1996. https://books.google.com/books?id=OvjsCAAAQBAJ&pg=PA277&lpg=PA277&dq=peirce+relativity&source=bl&ots=0rc7kjxqIJ&sig=Hsgtu9_LwZAoDxH7kbVgvWmAfiI&hl=en&sa=X&ved=0ahUKEwihk4SzpZzQAhWF3YMKHR1kA5wQ6AEIHzAA#v=onepage&q=peirce%20relativity&f=false
----------------------------- 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 . To UNSUBSCRIBE, send a message not to PEIRCE-L but to 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 .
