In the first post, I was attempting to work out what causal closure would mean in my Peircean-Deweyan metaphysics. By the end, I came to the conclusion that it means that the natural forces are limited, although the possibilities are not, and yet this limits natural laws. In Peircean language, secondness qua activity is closed, while firstness qua possibility and thirdness qua meaning and law are not. In set-theoretic language, we may say that an (algebraic) structure may emerge, while in contemporary analytic parlance we could say that the set of possible worlds is partially determined. In sum, this is important for an evolutionary metaphysics, because it cannot be the case that anything goes in cosmogenesis, else we cannot answer the question, why is there something rather than nothing, order rather than chaos. Schelling understood this, but also saw how dangerous it was to positively answer the question without presuming a seminal structure of the cosmos and thereby limiting its development and freedom. Peirce to this to heart and presented us with a generative list of categories, the triad.

Another thought. If nature is not causally closed, and God is nature (pantheism),then all is permitted. Or is it? I am not sure, but theists must wrestle with the cosmogenesis question in ways that non-theists need not. Insomuch as God shares in the perfections, which are analogous to the cardinal virtues of humanity, then "anything goes" cannot be the case. But again, then we appear have a limit on God's nature/freedom correspondent with God's goodness that has the effect of a seminal structure of cosmogenesis.

Leon, of After Nature, was kind enough to comment and solicit this response. I will now respond to him directly. I would like to point out a few minor corrections. [Edit: I am not correcting Leon on closed, as I believe he was expositing the views of others, but I thought that I should be more explicit what "closed" means per abstract algebra.] A set need not be finite to be closed, and closure is a peculiar form of limitation that is *not* analogous to a line drawn in the sand or containment. That is, in some sets, the bound of closure appears to sit across from an infinite chasm in which one might find more elements within closure. This is frequently the case with continuous sets, and I take nature to be continuous (Dewey, principle of continuity; Peirce, synechism).

Nature would not be a container. The boundness of nature is due to the possible transformations it may undergo and not anything that "holds it back." Instead, it is due to its structure. A given determinate, finite structure may only undertake so many geometric permutations. Likewise, even an infinite set or nature may have bounds in its permutations, although mathematically speaking I have in mind infinite bounds, i.e., infinite elements, and thus the significance of the statement is in what is not within the bounds rather than what is. For instance, a set may be an infinity of numbers, but not contain the number 2. Likewise, God may be capable of an infinity of acts, but not evil ones--a bounded infinity. This form of mathematics was not available to the scholastics, but I would not be surprised if an analogue were discussed, especially among the muslim scholars. If what I say is unclear, muse upon the examples. Closure per nature would mean that there is a limit to natural forces, which I also think are finite, and thus the forms of natural transformation are limited. This does limit what may be, e.g., an infinite set of numbers without a 2, but it does not specify what is.

One of my goals with closure is to think nature other than as a totality of elements. "Totality" says very little about structure, whereas boundedness and the how of its bound says much more. I am sympathetic to Leon's claims about objects, for what little I know about object-oriented approachs makes it appear that they are like monads in their solitude, and thus we have a "Newtonian pile of objects as." I hope to be corrected, as I am still a neophyte in the details. Leon, in what way is nature an object?

As for the triad, Leon, you have mis-identified Peircean firstness if that is what you meant to name. Firstness proper is pure possibility, not existential possibility. For Peirce, possibility may be unmoored from actuality, whereas existential possibility is anchored by an actual existence. I talk about the latter because of my work in hetero-phenomenology, the unification of process metaphysics and phenomenology, whereas existential possibility is the starting point. Peirce called it "first of a second." Likewise, actuality is second and not first. However, you might be modifying it, as you note that I do as well. Do let me know if you meant original Peirce or a modification or that I erred. As for the implications, I was saying that the forces are closed, but not possibility or meaning, which does not necessitate that what exists is closed. Existence as a second has some relation for firstness and possibility--what exists is an actual possibility--and if possibility is open but natural forces are not, then we cannot conclude that nature is bounded. We can conclude that existence might be bounded, and it is certainly structured (limited). Hence the points about the godhead.

In closing, Leon has understood the ultimate point. We can neither maintain a flat ontology nor one of all depth. Flatness is reductive, while all depth likely cannot explain order from chaos, cosmogenesis and evolution. I am certain that I will revisit this subject soon, especially since I expect such good conversation.

I am responding to Leon, of After Nature (http://afterxnature.blogspot.com/2011/07/reponse-to-hills-immanent-transcendence.html).

ReplyDeleteLeon recalls righty; I have a B.S. in computational mathematics from Rochester Institute of Technology and exhausted their courses in analysis, algebra, number theory, etc. I later decided to become a professional philosopher, as I now am.

Hence, speaking of sets, "ordinal" has a particular meaning in mathematics. When speaking of sets, it designates the relative "size" of a set (or set of sets). The non-negative natural numbers are designated N1, aleph-1. One of the important features of these sets of sets is the case where some of them cannot be constructed by any finite number of operations (analogously, no finite computation can calculate an irrational number such as pi). See http://mathworld.wolfram.com/OrdinalNumber.html .

As pertains the ongoing discussion, this would mean that some created natures cannot be constructed by any finite immanent transformation. Analogously, there is no possible world, set of possible worlds, or any permutation that would achieve certain special possible worlds. Perhaps this is an argument for Corrington's naturing/natured distinction, whereas the finitely natured cannot be maximally generative. But I am stretching to make that inference. Also, see below about emergence requiring a twoness.

I agree with Leon on possibility. In existential phenomenology, existential possibility is paramount and there is nothing more basic. The point is that the kind of possibility implied depends on the kind of analysis one is doing. I mention this again because I deviate from Peirce at points, since I'm doing existential phenomenology at those points.

As for potential, I agree with Leon, although my full definition spans the triad. With Peirce, possibility is independent. Power as activity implies a twoness, which metaphysically requires firstness. Emergence is a twoness. Actualization of a potential, actuality, is threeness and requires the two others.