Do analogical models ever play an essential role in scientific explanation and confirmation, or is their role (at most) heuristic? For many years scientists and philosophers have debated this question. I argue that such models may sometimes play an essential role. My argument is based on a proposal to augment Goodman''s theory of projection in order to make it easier for novel predicates (extensions) to acquire entrenchment. The heart of this proposal is the claim that analogical models may, under certain (...) conditions, be the medium whereby entrenchment is passed from well established predicates to new and unfamiliar ones. (shrink)

In this paper, we show that a restricted form of time travel both accords with special relativity kinematics and avoids several prima facie objections. We argue that such time travel provides a reasonable way to interpret certain phenomena which can readily be described, and the analogues of which have already been observed at the level of elementary particle reactions. We then describe how a time-traveling object could measure itself, and demonstrate how, in the appropriate circumstances, such an experiment could convince (...) a theorist who insisted on a single criterion for length measurements that his standard had itself changed in length. The same experiment can shed light on the possibility of detecting a universal expansion; and we show that, given certain experimental results, one must conclude that every member of a class of time travelers has changed in length simultaneously, though perhaps only while going backwards in time. (shrink)

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)

It is shown that if ZF is consistent, then so is ZFC + GCH + "There is a graph with cardinality ℵ 2 and chromatic number ℵ 2 such that every subgraph of cardinality ≤ ℵ 1 has chromatic number ≤ ℵ 0 ". This partially answers a question of Erdos and Hajnal.

The conventional interpretation of Adam Smith is that he is a prophet of commercialism. The liberal capitalist reading of Smith is consistent with the view that history culminates in commercial society. The first part of the article develops this optimistic interpretation of Smith's view of history. Smith implies that commercial society is the end of history because (1) it supplies the ends of nature that he identifies; (2) it is inevitable; and (3) it is permanent. The second part of the (...) article shows that Smith has some dark moments in his writings where he seems to reject completely such teleological notions. In this more civic humanist mood he confesses that commercial society does not supply the ends of nature, nor is it inevitable, nor is it permanent. Both views exist in Smith and the commentator is forced to choose between passages in Smith's work in order to support a particular interpretation of the former's view of history. (shrink)