Fear and Trembling: "Problema II"
I'm still stuck thinking about the individual vs. the universal that Kierkegaard focuses on so much in this and the previous chapter. I think Adam's right in pointing to Badiou's notion of a "universal singularity" as a fruitful approach to thinking about this issue. I was hoping to gain a better understanding of what this means before posting, but I'm already very late in posting this so I'll have to made due.
In Hallward's appendix to his book on Badiou, he gives a brief history of the Axiom of Choice. I don't understand very well (yet!) how this plays out in Badiou's thought, but it's given me a lot to think about, esp. pertaining to this issue of the individual vs. the universal. First, what is interesting about this axiom is that it is an axiom which is independent from the other, less controversial axioms of Zermelo-Fraenkel (ZF) set theory. This essentially means that we can assert the Axiom of Choice, or the negation of the Axiom of Choice, and the implications of either assertions will be consistent with the rest of the ZF axioms. This ties in with the idea in my previous post about the production of truth(s). And I think it explicitly ties in with D&C 93:30, "all truth is independent in that sphere in which God has placed it, to act for itself." Of course it may just be coincidence that "truth" and "independence" are the terms used here, but I think the possibilities suggested by reading this passage from an Axiom of Choice and Badiouian vantage point are intriguing. In particular, this suggests (to me at least) that the possibility of theology is importantly tied to the independence of truth. Or, to take K's words more directly, "the single individual is higher than the universal" seems to imply that if we are to talk about God, we must talk about his relationship to each of us individually(/independently). This touches importantly on some unique LDS ideas, such as the fact that we don't baptize infants because we believe they are not accountable--accountability itself thus seems to be a radically individual concept. (Note also the several unique LDS scriptural passages regarding sinning against greater light and an individualized rather than universal notion of accountability....)
But doesn't this radical individuality of truth, theology, accountability, etc. undermine the possibility of community and lead to extreme relativism and incoherence? This is where I think set theory makes for an interesting analogy: for an axiom (or any logical proposition) to be independent, it must not contradict other axioms (propositions). How might we appropriate this mathematical result for thinking about the possibility of community, or the structure of families? I think it points to a peculiar notion of peaceful coexistence, perhaps as described in D&C 121:34ff ("principles of righteousness" in v. 36?). If each of us are ourselves independent truths (in a particular sphere), then perhaps our eternal sphere of independence is contingent on provenness to cohere with others, according to these principles of righteousness. And inasmuch as we violate these principles of righteousness, we become captive to the devil--or, in set-theoretic language, we become subject to other axioms/truths (but then does this imply the devil is a truth himself, a "law unto himself" per D&C 88:35?).
Next, considering what the Axiom of Choice means, it essentially assumes the existence of (infinite) sets that cannot be constructed by any rule. I think this has interesting parallels to how we might think about agency and becoming gods in LDS theology (issues that Adam has at least hinted at before). If YHWH is the Unnameable One, and taking his name in vain is such an important prohibition, then perhaps it is related to His radical independence as a God--bound perhaps by principles of righteousness, but unbound in terms of possibility. And so when we are given new names which are not to be uttered in this temporal sphere where we have already been given temporal names, we are effectively being given the promise of eternal independence (as Abraham symbolically gives Isaac...). Only in an eternal setting where infinity is appropriately approached (i.e. sacredly), is the new name uttered. And in that sacred utterance, the name connotes infinite possibility and respect (i.e. it is not a confining, rule-based name like a temporal name...).
Also, part of what seems promising in thinking theologically about the Axiom of Choice is in terms of the relationship between what is sayable in a logically rigorous way and what cannot be said. Without the Axiom of Choice, set theory essentially becomes a constructivist enterprise. This, I think, has deep implications for how we think about faith and sign-seeking (esp. in Alma 32), and the extent to which philosophical discourse can talk about faith, transcendence, etc. Badiou makes an interesting distinction between truth/philosophy and knowledge. As Hallward puts it, "Every universal . . . is a consequence of a decision, . . . a matter of being-true rather than of knowing. Philosophy consists of the analysis and articulation of such universalities" (p. 251).
I am, however, still rather puzzled by this use of the term "universal." I wish I'd looked at this earlier--it's a rather interesting address by Badiou where he lays out 8 theses which give an overview of his philosophy. In particular, he lays out this tension between the singular (K's "individual", roughly) and the universal (K's "absolute," though also related to K's "universal," I think...) in a rather interesting way, but I'm still trying to make sense of this. Is Badiou's event more like the coming-into-being of an unpredictable, unnameable infinite set, or is an event more like the Axiom of Choice itself which declares the existence of such unnameable sets/processes and is independent of all other axioms? In what sense is an event/truth universal? Is this more than what I was describing in terms of independence above? Irrespective of Badiou, is there a meaningful way we can talk about K's absolute duty of the individual (to the absolute)? Although JdS in fact talks about this absolute, to what extent is it more than a poetic-pointing-to? If we accept this abolute individual relationship to God, what is an appropriate language to talk about this relationship? What are the implications for a scriptural hermeneutic--can we meaningfully take up scripture as a community, or is it ultimately an individual undertaking that "cannot be mediated"? K talks to us indirectly through JdS who has not experienced genuine faith--is this indirect and somewhat vague, deconstructive, pointing-to type of discourse the best we can hope for in terms of talking about theology, or can we read scripture in a more positive theological or philosophical sense? (I think Badiou's criticism of all those following Heidegger is that they're doing what essentially amounts to poetry....)
Typical, I guess: a very meager attempt to take a step forward which unleashes a whole host of issues causing me to take several steps back!
In Hallward's appendix to his book on Badiou, he gives a brief history of the Axiom of Choice. I don't understand very well (yet!) how this plays out in Badiou's thought, but it's given me a lot to think about, esp. pertaining to this issue of the individual vs. the universal. First, what is interesting about this axiom is that it is an axiom which is independent from the other, less controversial axioms of Zermelo-Fraenkel (ZF) set theory. This essentially means that we can assert the Axiom of Choice, or the negation of the Axiom of Choice, and the implications of either assertions will be consistent with the rest of the ZF axioms. This ties in with the idea in my previous post about the production of truth(s). And I think it explicitly ties in with D&C 93:30, "all truth is independent in that sphere in which God has placed it, to act for itself." Of course it may just be coincidence that "truth" and "independence" are the terms used here, but I think the possibilities suggested by reading this passage from an Axiom of Choice and Badiouian vantage point are intriguing. In particular, this suggests (to me at least) that the possibility of theology is importantly tied to the independence of truth. Or, to take K's words more directly, "the single individual is higher than the universal" seems to imply that if we are to talk about God, we must talk about his relationship to each of us individually(/independently). This touches importantly on some unique LDS ideas, such as the fact that we don't baptize infants because we believe they are not accountable--accountability itself thus seems to be a radically individual concept. (Note also the several unique LDS scriptural passages regarding sinning against greater light and an individualized rather than universal notion of accountability....)
But doesn't this radical individuality of truth, theology, accountability, etc. undermine the possibility of community and lead to extreme relativism and incoherence? This is where I think set theory makes for an interesting analogy: for an axiom (or any logical proposition) to be independent, it must not contradict other axioms (propositions). How might we appropriate this mathematical result for thinking about the possibility of community, or the structure of families? I think it points to a peculiar notion of peaceful coexistence, perhaps as described in D&C 121:34ff ("principles of righteousness" in v. 36?). If each of us are ourselves independent truths (in a particular sphere), then perhaps our eternal sphere of independence is contingent on provenness to cohere with others, according to these principles of righteousness. And inasmuch as we violate these principles of righteousness, we become captive to the devil--or, in set-theoretic language, we become subject to other axioms/truths (but then does this imply the devil is a truth himself, a "law unto himself" per D&C 88:35?).
Next, considering what the Axiom of Choice means, it essentially assumes the existence of (infinite) sets that cannot be constructed by any rule. I think this has interesting parallels to how we might think about agency and becoming gods in LDS theology (issues that Adam has at least hinted at before). If YHWH is the Unnameable One, and taking his name in vain is such an important prohibition, then perhaps it is related to His radical independence as a God--bound perhaps by principles of righteousness, but unbound in terms of possibility. And so when we are given new names which are not to be uttered in this temporal sphere where we have already been given temporal names, we are effectively being given the promise of eternal independence (as Abraham symbolically gives Isaac...). Only in an eternal setting where infinity is appropriately approached (i.e. sacredly), is the new name uttered. And in that sacred utterance, the name connotes infinite possibility and respect (i.e. it is not a confining, rule-based name like a temporal name...).
Also, part of what seems promising in thinking theologically about the Axiom of Choice is in terms of the relationship between what is sayable in a logically rigorous way and what cannot be said. Without the Axiom of Choice, set theory essentially becomes a constructivist enterprise. This, I think, has deep implications for how we think about faith and sign-seeking (esp. in Alma 32), and the extent to which philosophical discourse can talk about faith, transcendence, etc. Badiou makes an interesting distinction between truth/philosophy and knowledge. As Hallward puts it, "Every universal . . . is a consequence of a decision, . . . a matter of being-true rather than of knowing. Philosophy consists of the analysis and articulation of such universalities" (p. 251).
I am, however, still rather puzzled by this use of the term "universal." I wish I'd looked at this earlier--it's a rather interesting address by Badiou where he lays out 8 theses which give an overview of his philosophy. In particular, he lays out this tension between the singular (K's "individual", roughly) and the universal (K's "absolute," though also related to K's "universal," I think...) in a rather interesting way, but I'm still trying to make sense of this. Is Badiou's event more like the coming-into-being of an unpredictable, unnameable infinite set, or is an event more like the Axiom of Choice itself which declares the existence of such unnameable sets/processes and is independent of all other axioms? In what sense is an event/truth universal? Is this more than what I was describing in terms of independence above? Irrespective of Badiou, is there a meaningful way we can talk about K's absolute duty of the individual (to the absolute)? Although JdS in fact talks about this absolute, to what extent is it more than a poetic-pointing-to? If we accept this abolute individual relationship to God, what is an appropriate language to talk about this relationship? What are the implications for a scriptural hermeneutic--can we meaningfully take up scripture as a community, or is it ultimately an individual undertaking that "cannot be mediated"? K talks to us indirectly through JdS who has not experienced genuine faith--is this indirect and somewhat vague, deconstructive, pointing-to type of discourse the best we can hope for in terms of talking about theology, or can we read scripture in a more positive theological or philosophical sense? (I think Badiou's criticism of all those following Heidegger is that they're doing what essentially amounts to poetry....)
Typical, I guess: a very meager attempt to take a step forward which unleashes a whole host of issues causing me to take several steps back!
posted by Robert C. at 10:10 AM
1 Comments:
Robert,
Your thoughts here about the axiom of choice are, for me, interesting and productive - though the complexity of the issues leaves me generally unsure about how to respond or where to even begin a response. (Though I especially admire the point about the connection between "constructivist" thought, the project of sign-seeking, and an unwillingness to risk one's life in fidelity to the possibility of something radically new.)
Let me chew on this.
My best,
Adam
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