The primordial chaos of Genesis 1 may be understood as the Pandemonium Tremendum (or PT), the infinite field of variety or abundance within God. The concept of variety is taken from Claude Shannon's theory of communication. Especially significant is Shannon's notion that communication is the limitation of variety through decision processes. In one model of the divine life suggested by the theory, the PT is the boundless source of potential reaped by an agential God in the act of creation as (...) a communication process. Other models for creation include the PT in a biased mode and creatures themselves as decision agents. (shrink)

As the creator, God is the source of the abundance for immense variety manifest in creation. The reservoir for this abundance is the primordial chaos, identified as the Pandemonium Tremendum. God manages this inexhaustible “storehouse of the snow” through decisions or “willings,” giving rise to constraints that result in the ordered array of creation. Without this active and decisive vigilance, the Pandemonium Tremendum would scour and ravage the creation. Also, as an omniscient, unobtrusive, and impartial witness, God manages the primordial (...) chaos without compromising its unfettered variety. What is the role of chaos as the Ungrund? All creatures are the consequence of acts of decision. God alone is self‐decisive and, hence, the uniquely sovereign creator. That is, God arises spontaneously through an aboriginal act of in–speaking. Otherwise, and in utter contradiction to its radically unprincipled character, the primordial chaos would provide the arche or sufficient reason for divine causation. This mythic and metaphysical account falls in the tradition of Meister Eckhart and Nicolas Berdyaev and is expressed in the rubric of communication theory. (shrink)

Systems theory provides a surprisingly fruitful approach to several important ideas held in common by Paul Tillich and Pierre Teilhard de Chardin. These include complexity or organization as the key to understanding the distinction between the inorganic and the organic, and hierarchy or levels in complex systems. Teilhard and systems theorists accept hierarchy as fundamental. Tillich questions the concept and prefers “dimensions,” including the inorganic, organic, psychological, spiritual, and historical dimensions. Tillich's rejection of hierarchy is questioned, but significant correlations are (...) discovered in the systems interpretation of the psychological and spiritual dimensions as well as in the use of “centeredness” by both thinkers. (shrink)

Progress in general systems theory has been slow. Three recent books in the field reflect both the hopes and continuing frustrations of systems advocates. Frustrations include the widespread perception that systems theory is a kind of gnostic redemption, an abstract program to be administered by an elite cadre of experts for the sake of integrating knowledge and reorganizing society. This mechanistic understanding generates a resistance which could be countered by a more open and organic model of human systems. The ambiguity (...) of systems thought lies ironically in its ability to embrace both of these images within its conceptual scheme. (shrink)

I respond herein to reviews of my recent book by Ann Pederson and Stuart Kurtz. With respect to Pederson's concerns, a constructive theology formulated from the ideas of communication theory need not necessarily neglect pressing historical issues of the poor and powerless. The potential for such relevance remains strong. This is true as well for the application of the system to particular myths and rituals. Also, while I speak positively of computers as instruments of disclosure and the theories upon with (...) they are based as resources for theological construction, this should not be construed as an endorsement of just any application of information technology in a world that tends to distort all good things. With respect to Kurtz's concerns, while thermodynamics plays a role in discussions of the primordial chaos, notions from communication theory are far more central. Also, the use of the language of the theory for theology does not necessarily require theological relevance for all of Claude Shannon's technical conclusions. My uses of infinity are taken from traditional theology and analytic geometry rather than from pure mathematics, although fruitful development along those lines is entirely possible. Pederson and Kurtz are generous with both their praise and concerns. The praise will encourage me to further this project along lines provided by the concerns. (shrink)

The essays range from Hegel and Modernism to Marcel Duchamp and the Avant-Garde, postmodern poetics, boredom and Proust, the romance of Arendt and Heidegger, ...

If dominating functions in ω ω are adjoined repeatedly over a model of GCH via a finite-support c.c.c. iteration, then in the resulting generic extension there are no long towers, every well-ordered unbounded family of increasing functions is a scale, and the splitting number s (and hence the distributivity number h) remains at ω 1.

We study the I-ultrafilters on ω, where I is a collection of subsets of a set X, usually R or ω 1 . The I-ultrafilters usually contain the P-points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.

We study the $I$-ultrafilters on $\omega$, where $I$ is a collection of subsets of a set $X$, usually $\mathbb{R}$ or $\omega_1$. The $I$-ultrafilters usually contain the $P$-points, often as a small proper subset. We study relations between $I$-ultrafilters for various $I$, and closure of $I$-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether $I$-ultrafilters always exist.

Several canonical partition theorems are obtained, including a simultaneous generalization of Neumer's lemma and the Erdos-Rado theorem. The canonical partition relation for infinite cardinals is completely determined, answering a question of Erdos and Rado. Counterexamples are given showing that in several ways these results cannot be improved.

Let κ denote a regular uncountable cardinal and NS the normal ideal of nonstationary subsets of κ. Our results concern the well-known open question whether NS fails to be κ + -saturated, i.e., are there κ + stationary subsets of κ with pairwise intersections nonstationary? Our first observation is: Theorem. NS is κ + -saturated iff for every normal ideal J on κ there is a stationary set $A \subseteq \kappa$ such that $J = NS \mid A = \{X \subseteq (...) \kappa:X \cap A \in NS\}$ . Turning our attention to large cardinals, we extend the usual (weak) Mahlo hierarchy to define "greatly Mahlo" cardinals and obtain the following: Theorem. If κ is greatly Mahlo then NS is not κ + -saturated. Theorem. If κ is ordinal Π 1 1 -indescribable (e.g., weakly compact), ethereal (e.g., subtle), or carries a κ-saturated ideal, then κ is greatly Mahlo. Moreover, there is a stationary set of greatly Mahlo cardinals below any ordinal Π 1 1 -indescribable cardinal. These methods apply to other normal ideals as well; e.g., the subtle ideal on an ineffable cardinal κ is not κ + -saturated. (shrink)

One of the contemporary results of Germany’s memorial conundrum is the rise of its “counter-monuments”: brazen, painfully self-conscious memorial spaces conceived to challenge the very premises of their being. On the former site of Hamburg’s greatest synagogue, at Bornplatz, Margrit Kahl has assembled an intricate mosaic tracing the complex lines of the synagogue’s roof construction: a palimpsest for a building and community that no longer exist. Norbert Radermacher bathes a guilty landscape in Berlin’s Neukölln neighborhood with the inscribed light of (...) its past. Alfred Hrdlicka began a monument in Hamburg to counter—and thereby neutralize—an indestructible Nazi monument nearby. In a suburb of Hamburg, Jochen Gerz and Esther Shalev-Gerz have erected a black pillar against fascism and for peace designed to disappear altogether over time. The very heart of Berlin, former site of the gestapo headquarters, remains a great, gaping wound as politicians, artists, and various committees forever debate the most appropriate memorial for this site.4 4. The long-burning debate surrounding projected memorials, to the Gestapo-Gelände in particular, continues to exemplify both the German memorial conundrum and the state’s painstaking attempts to articulate it. For an excellent documentation of the process, see Topographie des Terrors: Gestapo, SS und Reichssicherheitshauptamt auf dem “Prinz-Albrecht-Gelände,” ed. Reinhard Rürup . For a shorter account, see James E. Young, “The Topography of German Memory,” The Journal of Art 1 : 30. James E. Young is assistant professor of English and Judaic studies at the University of Massachusetts, Amherst. He is the author of Writing and Rewriting the Holocaust: Narrative and the Consequences of Interpretation and The Texture of Memory: Holocaust Memorials and Meaning in Europe, Israel, and America , from which this essay is drawn. He is also the curator of “The Art of Memory,” an exhibition at the Jewish Museum of New York. (shrink)

We study various aspects of the size, including the cardinality, of closed unbounded subsets of [λ]<κ, especially when λ = κ+n for n ε ω. The problem is resolved into the study of the size of certain stationary sets. Relative to the existence of an ω1-Erdös cardinal it is shown consistent that ωω3 < ωω13 and every closed unbounded subsetof [ω3]<ω2 has cardinality ωω13. A weakening of the ω1-Erdös property, ω1-remarkability, is defined and shown to be retained under a large (...) class of Easton-like forcings applied to ω1-Erdös cardinals. A class of reverse-Easton forcings preserving α-Erdösness is also described, with special attention to the establishment of □-principles. Article Outline. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. I argue (...) for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

It is shown that for any cardinal $\kappa, \dbinom{(2^{ , and if κ is weakly compact $\dbinom{\kappa^+}{\kappa} \rightarrow \dbinom{\kappa}{\kappa}_{.

I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ properties like shape, mass, and causal (...) powers. (shrink)