Tuesday, September 20, 2011
Continuing from the last post, I posted the following in our ongoing IPS discussion “the observer in the observed”:
Nunez's article is a shortened version of Chapter 8 of WMCF. From the latter:
“The uniqueness of the final state of a complete process is the product of human cognition, not a fact about the external world.... The basic metaphor of infinity maps this uniqueness property...onto actual infinity.... What results from the BMI is a metaphorical creation that does not occur literally: a process that goes on and on indefinitely and yet has a final resultant state” (160).
The discussion that follows that quote in interesting in that outside math, applied to philosophy, the BMI was responsible for a categorization hierarchy up to an end state category, the highest state of Being. And that these categories were mistaken as ontological realities, things-in-themselves. Within religion the highest category is God, an actual being, not just a metaphor.
Nunez concluded from his referenced paper:
“The nature of potential and actual infinity can be understood not in terms of transcendental (or platonic) truths, or in terms of formal logic, but in terms of the manipulation of meaningless symbols
in human ideas, and human cognitive mechanisms.”
Of course one issue is what is “just” a metaphor? Terry noted earlier in this discussion that because the observer is in the observed our metaphors are part and parcel of the observed object so therefore this relationship entails an ontological status as well as an epistemological one to actual infinity. It would appear though that Nunez might disagree, and both he and Lakoff are in the general pragmatic school on intersobjectivity that sees the relationship of subject/object as interactive (i.e. intersobject).
Also an infinite regressive (or progressive) series such as in fractals, what is termed potential infinity by Nunez, is “resolved” in an actual infinity by our metaphorical processes. And yet metaphors arise from our embodied interactivity in the world via a continuous process (the very process interpreted as a potential infinity) so therefore metaphors are a part of that intersobjective “field” and thus the resolution seems to come from a “nondual” way of interpreting the relational field so that there is no separation between subject/object. And yet as we can see above Nunez makes the distinction that actual infinity is “not a fact about the external world, it does “not occur literally.”
So it seems there is a con-fusion then with inside/outside and with analogies such as if it occurs in the whole it must also occur in the part. And that there is a final, resultant “whole,” a holon of the uni-verse, the highest category in the hierarchy. Such confusions are examples of synecdoche, one such metaphor. Useful and highly practical, of course. A statement on the true nature of reality, not in Nunez's (or L&J's) view. On the nature of nested hierarchy and its con-fusions, see the real and false reason thread based on L&J's work, particularly some conclusions on p. 7 with reference to one our embodied image-schematic basic categories, the part-whole gestalt. This is why I'm also interested in Joel's work, since he uses nested hierarchies while yet undermining their very premise (and referenced in the link above).