We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a theory to have singular compactness.

It is shown in ZF that if $\delta are such that δ and δ + are either both weakly compact or singular cardinals and Ω is large enough for putting the core model apparatus into action then there is an inner model with a Woodin cardinal.

It is shown in ZF that if $\delta < \delta^+ < \Omega$ are such that $\delta$ and $\delta^+$ are either both weakly compact or singular cardinals and $\Omega$ is large enough for putting the core model apparatus into action then there is an inner model with a Woodin cardinal.

We extend the core model induction technique to a choiceless context, and we exploit it to show that each one of the following two hypotheses individually implies that , the Axiom of Determinacy, holds in the of a generic extension of : every uncountable cardinal is singular, and every infinite successor cardinal is weakly compact and every uncountable limit cardinal is singular.

We show that the tree property, stationary reflection and the failure of approachability at \ are consistent with \= \kappa ^+ < 2^\kappa \), where \ is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if \ is a regular cardinal, then stationary reflection at \ is indestructible under all \-cc forcings.

The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the two. (...) We prove from large cardinals that the tree property at κ+ is consistent with failure of the singular cardinal hypothesis at κ. (shrink)

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtained in suitable large cardinals properties.The first example I will treat is the proof that the proper forcing (...) axiom PFA implies the singular cardinal hypothesis SCH, this will easily lead to a new proof of Solovay's theorem that SCH holds above a strongly compact cardinal. I will also outline how some of the ideas involved in these proofs can be used as means to evaluate the “saturation” properties of models of strong forcing axioms like MM or PFA.The second example aims to show that the transfer principle ↠ fails assuming Martin's Maximum MM. Also in this case the result can be translated in a large cardinal property, however this requires a familiarity with a rather large fragment of Shelah's pcf-theory.Only sketchy arguments will be given, the reader is referred to the forthcoming [25] and [38] for a thorough analysis of these problems and for detailed proofs. (shrink)

I use generic embeddings induced by generic normal measures on that can be forced to exist if κ is an indestructibly weakly compact cardinal. These embeddings can be applied in order to obtain the forcing axioms in forcing extensions. This has consequences in : The Singular Cardinal Hypothesis holds above κ, and κ has a useful Jónsson-like property. This in turn implies that the countable tower works much like it does when κ is a Woodin limit of Woodin cardinals. (...) One consequence is that every set of reals in the Chang model is Lebesgue measurable and has the Baire Property, the Perfect Set Property and the Ramsey Property. So indestructible weak compactness has effects on cardinal arithmetic high up and also on the structure of sets of real numbers, down low, similar to supercompactness. (shrink)

Assuming some large cardinals, a model of ZFC is obtained in which $\aleph_{\omega+1}$ carries no Aronszajn trees. It is also shown that if $\lambda$ is a singular limit of strongly compact cardinals, then $\lambda^+$ carries no Aronszajn trees.

The strong tree property and ITP (also called the super tree property) are generalizations of the tree property that characterize strong compactness and supercompactness up to inaccessibility. That is, an inaccessible cardinal $\kappa $ is strongly compact if and only if the strong tree property holds at $\kappa $, and supercompact if and only if ITP holds at $\kappa $. We present several results motivated by the problem of obtaining the strong tree property and ITP at many successive cardinals (...) simultaneously; these results focus on the successors of singular cardinals. We describe a general class of forcings that will obtain the strong tree property and ITP at the successor of a singular cardinal of any cofinality. Generalizing a result of Neeman about the tree property, we show that it is consistent for ITP to hold at $\aleph _n$ for all $2 \leq n < \omega $ simultaneously with the strong tree property at $\aleph _{\omega +1}$ ; we also show that it is consistent for ITP to hold at $\aleph _n$ for all $3 < n < \omega $ and at $\aleph _{\omega +1}$ simultaneously. Finally, turning our attention to singular cardinals of uncountable cofinality, we show that it is consistent for the strong and super tree properties to hold at successors of singulars of multiple cofinalities simultaneously. (shrink)

Let L(Q) be first order logic with Keisler's quantifier, in the λ + interpretation (= the satisfaction is defined as follows: $M \models (\mathbf{Q}x)\varphi(x)$ means there are λ + many elements in M satisfying the formula φ(x)). Theorem 1. Let λ be a singular cardinal; assume □ λ and GCH. If T is a complete theory in L(Q) of cardinality at most λ, and p is an L(Q) 1-type so that T strongly omits $p (= p$ has no support, (...) to be defined in $\S1$ ), then T has a model of cardinality λ + in the λ + interpretation which omits p. Theorem 2. Let λ be a singular cardinal, and let T be a complete first order theory of cardinality λ at most. Assume □ λ and GCH. If Γ is a smallness notion then T has a model of cardinality λ + such that a formula φ(x) is realized by λ + elements of M iff φ(x) is not Γ-small. The theorem is proved also when λ is regular assuming $\lambda = \lambda^{ . It is new when λ is singular or when |T| = λ is regular. Theorem 3. Let λ be singular. If $\operatorname{Con}(ZFC + GCH + (\exists\kappa)$ [κ is a strongly compact cardinal]), then the following in consistent: ZFC + GCH + the conclusions of all above theorems are false. (shrink)

We address some questions raised in the paper by Magidor and Sinapova. An application to weak form of normality for strongly compact is given.

Compact but singularly well thought out material of a theological, logical, poetic as well as philosophical nature.

We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle $\square _{\lambda ,D}^{\mathit{fin}}$ introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ / D is not λ⁺⁺-universal and elementarily equivalent models M and N of size λ for which Mλ / D and Nλ / D are non-isomorphic. The question of the existence of such ultrafilters and models (...) was raised in [1]. (shrink)

We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero [4] calculates correctly the successors of Jónsson cardinals, assuming $O^{Sword}$ does not exist. Namely, if $\kappa$ is a Jónsson cardinal then $\kappa^+ = \kappa^{+K}$ , provided that there is no non-trivial elementary embedding $j:K \longrightarrow K$ . There are a number of related results in ZFC concerning $\cal{P}(\kappa)$ in V and inner models, for $\kappa$ a Jónsson or singular cardinal.

The paper suggests that Samuel Taylor Coleridge’s arguments against sympathy after the French Revolution, Walter Benjamin’s claims against empathy following the traumatic shock of Modernity and the First World War, and Hannah Arendt’s critical take on compassion. after the Holocaust are similar responses to singular historical crises. Reconsidering Arendt’s On Revolution (1963) and its evocation of Hermann Melville’s novella Billy Budd (1891), I show first that the novella bears the traces of an essay by Samuel Taylor Coleridge, “The Appeal (...) to Law” (1809). Then, drawing on Walter Benjamin’s writings on trauma in Illuminations (1968, edited by Arendt), I discuss the political importance Arendt attaches to the proper way of telling a story, at a time when “the communicability of experience is decreasing” (Benjamin, Illuminations, 86). Through the analysis of Benjamin’s “The Storyteller” and Arendt’s “heartless” report on the Eichmann trial (1963), I equally show that, according to Arendt, testimonies must be narrated, or rather performed, in a dispassionate, dry, and compact manner so that they can be historically and politically relevant. (shrink)

When viewed as the most comprehensive theory of collections, set theory leaves no room for classes. But the vocabulary of classes, it is argued, provides us with compact and, sometimes, irreplaceable formulations of largecardinal hypotheses that are prominent in much very important and very interesting work in set theory. Fortunately, George Boolos has persuasively argued that plural quantification over the universe of all sets need not commit us to classes. This paper suggests that we retain the vocabulary of classes, but (...) explain that what appears to be singular reference to classes is, in fact, covert plural reference to sets. (shrink)

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of "non-existing" objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth (...) non unlike the notion of "truth at world" found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization). (shrink)

We prove that in all Mitchell-Steel core models, □ κ holds for all κ. (See Theorem 2.). From this we obtain new consistency strength lower bounds for the failure of □ κ if κ is either singular and countably closed, weakly compact, or measurable. (Corallaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ κ (...) holds iff κ is not subcompact. (See Theorem 15; the only if direction is essentially due to Jensen.). (shrink)

We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we prove a form of “singular cardinal compactness” for Jensen's square principle. We then study the relationship between internally approachable and tight structures, which parallels to a certain extent the relationship between good and approachable points. In particular we characterise the tight structures in terms of PCF theory and use our characterisation (...) to prove some covering results for tight structures, along with some results on tightness and stationary reflection. Finally, we prove some absoluteness theorems in PCF theory, deduce a covering theorem, and apply that theorem to the study of precipitous ideals. (shrink)

In their paper from 1981, Milner and Sauer conjectured that for any poset P,≤, if , then P must contain an antichain of cardinality κ. The conjecture is consistent and known to follow from GCH-type assumptions. We prove that the conjecture has large cardinals consistency strength in the sense that its negation implies, for example, the existence of a measurable cardinal in an inner model. We also prove that the conjecture follows from Martin’s Maximum and holds for all singular (...) λ above the first strongly compact cardinal. (shrink)

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of “non-existing” objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth (...) non unlike the notion of “truth at world” found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization). (shrink)

The extender based Prikry forcing notion is being generalized to super compact extenders.

Mental representations are based upon categories in which the state of a mental system is stable. Acategorial states, on the other hand, are distinguished by unstable behavior. A refined and compact terminology for the description of categorial and acategorial mental states and their stability properties is introduced within the framework of the theory of dynamical systems. The relevant concepts are illustrated by selected empirical observations in cognitive neuroscience. Alterations of the category of the first person singular and features of (...) creative activity will be discussed as examples for the phenomenology of acategorial states. (shrink)

We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if λ > ωα then the logic with the quantifier “there existα many” is (λ,λ)-compact if and only if either λ is weakly compact or λ is singular of cofinality<ωα. As a corollary, for every infinite cardinals λ and μ, there exists a (...) (λ,λ)-compact non-(μ,μ)-compact logic if and only if either λ<μ orcfλcompactness. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Wonder, Imagination, and the Matter of Theatre in The TempestMary MooreAriel occurs. Recounting his performance of "the tempest" in Act I, scene 1 of The Tempest, he presents himself as being and action, fracturing grammar, spatial and temporal logic in ways that amaze and confound:I boarded the King's ship; now on the beak, Now in the waist, the deck, in every cabin, I flamed amazement. Sometime I'd divide, And (...) burn in many places; on the topmast, The yards, and bowsprit would I flame distinctly, Then meet and join...(1.2.195–201) 1"I flamed" means that Ariel emits or is flames, which in the normal order of things would consume him. His very narration, however, proves his survival, evoking wonder through the utterance itself. Forceful and compacted syntax, a recognized source of wonder in Classical and Renaissance accounts of style (Biester, pp. 14; 35–40), magnifies this effect. 2 Shakespeare's transitive use of the usually intransitive verb flame reflects a not uncommon practice, as E. A. Abbott shows; 3 but this syntactic device also reflects The Tempest's own logic. Ariel crosses boundaries between [End Page 496] deed and being, verb and noun, subject and object, matter and spirit: he both is and does flames. What could be more jarring to syntax and semantics than a singular subject whose utterance claims that he can flame, divide, meet and join? Just as "a" fire consists of many flames yet functions grammatically as a singular substance in English, just as the Christian Trinity is both singular and multiple, Ariel burns in many places at once. Meanwhile, this extraordinary language seems belied by the actor's very embodiment. Ariel cannot have done what he claims; yet the prior scene has represented the very storm in which Ariel flamed. In that sense, the actor's embodiment represents what we imagine to be matter's intractability, while Ariel's claims, coupled with the storm we have just witnessed, reveal matter's fluidity and permeability to imagination. Fluidity and intractability co-exist, another source of wonder. Sound mimics these paradoxes: the assonance and consonance in flame and amazement create a near rhyme that echoes the near identity of fire and human amazement. If, as Gurr and Ichikawa observe, a Renaissance audience expected to hear more than see a play, this echo calls attention to Ariel's marvelous powers. 4 Lest the noises and pleasures of the Renaissance theatre, which recent scholarship deems to be considerable, distract audience members from this bit of language, similar moments reinforce Ariel's play in and with language and matter throughout the play. Marvelous poetic language is of a piece with a "fever" that is of "the mind," with music that "creeps," actors who vanish, new found goddesses who speak the discoverers' own language.Amazement provides our cue: it and its cognates name the appropriate response to Ariel, his language, and to The Tempest itself. Attention to Ariel's poetic language reveals that it, like the plot, conforms to the marvels of the play and to the period's well documented love for marvels in several ways. Wonder, an aesthetic "'object of desire'" in itself, and a response to the inexplicable in classical and early modern views, may be evoked by the unexpected in style (and through other strategies that the era's handbooks taught). 5 The clause "I flamed amazement" epitomizes the unexpected in syntax as well as differing from one of the few sources found for The Tempest, William Strachey's 1610 letter, which describes just such a storm. 6 While St. Elmo's fire itself may elicit wonder, Shakespeare's syntax and diction reinforce that marvel. And no wonder: rhetoric and theatre alike depend upon audience attention, and wonders naturally evoke it. Jarring language also harmonizes with The Tempest's structural marvels—loose ends, disrupted actions, unforeseen futures—issues several critics explore. 7 [End Page 497]The wonders of The Tempest, however, also involve imagination—in early modern psychology, the human faculty that permits perception of the world and invention of images. 8 Wonder responds to how the perceived differs from the expected, how the imagined supplants the usual, how an... (shrink)

Let ℛ be an o-minimal expansion of a real closed field R. We continue here the investigation we began in [11] of differentiability with respect to the algebraically closed field [Formula: see text]. We develop the basic theory of such K-differentiability for definable functions of several variables, proving theorems on removable singularities as well as analogues of the Weierstrass preparation and division theorems for definable functions. We consider also definably meromorphic functions and prove that every definable function which is meromorphic (...) on Kn is necessarily a rational function. We finally discuss definable analogues of complex analytic manifolds, with possible connections to the model theoretic work on compact complex manifolds, and present two examples of "nonstandard manifolds" in our setting. (shrink)

In _Aims: A Brief Metaphysics for Today_, James W. Felt turns his attention to combining elements of Thomas Aquinas's metaphysics, especially its deep ontology, with Alfred North Whitehead's process philosophy to arrive at a new possibility for metaphysics. In his distinctive style, Felt conciselypulls together the strands of epistemology, ontology, and teleology, synthesizing these elements into his own “process-enriched Thomism.” _Aims_ does not simply discuss the strengths and weaknesses of each philosopher’s position, but blends the two into a cohesive argument (...) based on principles derived from immediate experience. Felt arrives at what he calls a “Whiteheadian-type solution,” appealing to his original concept of the “essential aim” as necessary for understanding our existence in a coherent yet unique world. This concise, finely crafted discussion provides a thoroughly teleological, value-centered approach to metaphysics. _Aims_, an experiment in constructive metaphysics, is a thorough and insightful project in modern philosophy. It will appeal to philosophers and students of philosophy interested in enriching their knowledge of contemporary conceptions of metaphysics. “James Felt's _Aims: A Brief Metaphysics for Today _is an excellent book. It is engagingly written with exemplary clarity, compactness of expression, and admirable thoughtfulness. It is a work in constructive metaphysics that offers a marvelous introduction to the beginner, as well as being engaging to the advanced student. While _Aims_ shows the main influences of Aquinas and Whitehead, with Bergson and Merleau-Ponty also important, more importantly it gives expression to the singular appropriation of some of the basic metaphysical issues by James Felt himself. It develops a view of relational realism, with lucid expositions of themes such as the nature of primary being, the act of existing, freedom, participation and God, and the nature of self-knowledge. It distills the author's long reflection on these issues and communicates his considered insights with measured lucidity.” —_William Desmond, Katholieke Universiteit Leuven, Belgium _ “There is a welcome freshness and easy-access approach in this creative presentation of the central philosophical discipline, metaphysics. It starts firmly anchored in our human experience, then moves easily into deeper waters of a proposed Aquinas-Whitehead synthesis.” —_W. Norris Clarke, S.J., Fordham University_ “With modifications to both Aquinas and Whitehead and their complementary interplay, and in contrast to the priority usually given to effective or originating causality, the author argues for the interactive pre-eminence of teleology and existence in the promotion and enhancement of cosmic and interpersonal value. In so doing he seeks to restore to the transcendental Good its appropriate place and role.” —_Kenneth Schmitz, University of Toronto_. (shrink)

continent. 1.1 (2011): 27-32. “My”—what does this word designate? Not what belongs to me, but what I belong to,what contains my whole being, which is mine insofar as I belong to it. Søren Kierkegaard. The Seducer’s Diary . I can’t sleep till I devour you / And I’ll love you, if you let me… Marilyn Manson “Devour” The role of poetry in the relationalities between people has a long history—from epic poetry recounting tales of yore; to emotive lyric poetry; to (...) rude, irreverent limericks; to Hallmark cards which have ditties that allow one to cringe, and somehow fall in love at the same moment. Without going into a notion of aesthetics, or attempting to choose which form of poetry is superior, we might want to consider why the form of poetry itself has long been a part of relationality. And whilst doing so, we might always keep in mind that poetry—especially poetry that moves, transports us—is the form that Plato has been warning us about, particularly if we want to become good citizens.As Avital Ronell teaches us in Stupidity : the poet, irremediably split between exaltation and vulgarity, between the autonomy that produces the concept within intuition and the foolish earthly being, functions as a contaminant for philosophy—a being who at least since Plato, has been trying to read and master an eviction notice served by philosophy. The poet as genius continues to threaten and fascinate, menacing the philosopher with the beyond of knowledge. Philosophy cringes (287). And considering that the philosopher is the lover of wisdom, we might begin to ask ourselves why one lover is warning against another—if the philosopher is in love with wisdom, then is the poet perhaps his rival, his challenger, for that very love? For, one must also remember that Plato—through Socrates—mentions constantly that Homer is his favourite. Moreover, by adopting both his own voice, whilst mixing it with Socrates’, Plato is adopting the form of poetry that he warns most about—the warning almost serves more as a homage to poetry than anything else. Here, we might open the register that one of the main reasons that he ejects a particular kind of poet is on the grounds of effecting effeminacy on the populace—good poetry moves you, affects you, transports you, shifts you beyond reason, puts you “out of your mind.” However, Plato also teaches us that rhetoric in its highest form requires divine inspiration by way of the daemon, or the muse. This moment of divine intervention is one that seizes—perhaps even ceases—you; putting you “beyond yourself.” In other words, a good rhetorician must always already be open to the possibility of otherness—the same otherness that possibly resides in the feminine. One could also trace this back to the poet that he both loved, and feared, most—Homer. Perhaps the effect of effeminacy that Homer's poetry opened is precisely the source of its power: through listening to Homer, one's body, one’s habitus is opened to the possibility of the feminine. And here, one must remember that the source of all learning—and all teaching—also lies in mimesis, in repetition, in habit. Once the habitus is opened to the possibility of invasion, of intervention, of otherness, there is quite possibly no possibility of distinguishing whether the mimesis is that of reproduction, or if there is always already a productive aspect to it. And by extension, if learning cannot be controlled, the very notion of teaching itself is shifted from a master-student relationality to one where the master is potentially changed as well—the relationality between the master and the student is not only inter-changing, but one cannot even know who is teaching, or learning, at any point. All that can be said is that they are in a relationality; which means that one is ultimately unable to locate the locus of knowledge, of wisdom—the site of which Plato is attempting to convince us is the sole domain of the philosopher. And it is this that philosophy is cringing from. To compound matters, philosophy is striving for wisdom; which can only come from the Gods. In other words, this is a gift that has to be bestowed on them—and more than that, wisdom is always already exterior to one’s control and knowledge. At best, it is the role of one to recognise the gift, to answer the call as it were. Here, if we listen carefully, we can hear the echo of Alexander Graham Bell, and the telephone. And as we are attempting to respond to the call of wisdom—the call that both poetry and philosophy are listening out for—it might be helpful to recall the agreement between Alexander Graham Bell and his brother Melville. In the biography, Alexander Graham Bell and the Conquest of Solitude , Robert V. Bruce notes that Aleck and Melly made a “solemn compact that whichever of us should die first would endeavour to communication with the other if it were possible to do so” (63). Since Melville was the one who passed on first, this pact put the onus on Aleck to receive the call of his brother. If you take into consideration the fact that until Melville’s death, both brothers had been working on an early prototype of the telephone, the instrument of distant sound can be read as an attempt by Aleck to maintain the possibility of keeping in touch with Melly, of hearing the voice from beyond. However, this was a connection that was not premised on any knowing, reason, or rationality; it was rather, one that was based on hope, and born out of love. And here, if we eves-drop on a cross-line with The Telephone Book , we can pick up the voice of Avital Ronell once again and hear, “the connection to the other is a reading—not an interpretation, assimilation, or even a hermeneutic understanding, but a reading” (380). In other words, the telephone can be read as the openness to the possibility of responding to the other; one that might always remain unknown. Even in this day of caller-identification, we can never know for sure who the other person on the line is until we pick up: hence, the only decision we can make—the effects of which we remain blind to until it affects us—is to either pick up or not, to either respond or not. And it is not as if the decision to pick up comes without risks: each time we answer a call, we run the risk of it ruining our day. Even when we don’t know who the caller is, perhaps especially when we don’t know who the person on the other end of the line is—and here one only has to think of prank calls—we are leaving ourselves completely open to being affected by another. Thus, philosophy finds itself in the position of Vladimir and Estragon. Since they have no idea who Godot is, they can never know if or when he shows up—thus, if he (and we are taking his gender on the word of the boy, some boy—we don’t even know if it is the same boy—who comes round in the evening) has already come, they would not be in the position to know it. And even if someone comes to them and announces that “I am Godot,” the wait would not be over—without referentiality to the name, they would have to take on faith that that person is indeed Godot. Hence, all they can know is that they are waiting for Godot; and Godot is the name of that waiting itself. All philosophy can know is that it is waiting; and wisdom is the name of that waiting itself. Which brings us to Tina Turner’s eternal question, “what’s love got to do, got to do with it?” In order to begin to consider that, we have to first attempt to examine the notion of love itself. Perhaps we might begin to consider what the difficulty of the statement “I love you.” For, if love is a relationality between two persons—both of whom remain singular, and are attempting to respond to each other—this suggests that neither of them subsume the other under themselves. In other words, the other remains wholly other. If this is so, then the “you” in the statement always remains shrouded in mystery. And even if the “you” was replaced with the name of the person, the veiling remains: for, names refer both to the singularity that is the person, and also every other person bearing that name, at exactly the same time. To compound matters, the only time one has to utter a persons name is in their absence—thus, the correspondence of a name to that particular person is at best an affect of memory. And if we consider the notion of memory, we have to also open the register of forgetting—bringing along with it the problem that there is no object to forgetting. For instance, when one utters “I forgot,” all one is uttering is the fact that one has forgotten, and nothing more—the moment there is an object to the statement, one has strictly speaking remembered what one has forgotten. Moreover, we have no control over when forgetting happens to us. And since it is always already exterior to us, affects us, and has no necessary object, there is no reason to believe that every moment of memory might not bring with it a moment of forgetting. Hence, whenever we utter a name—even if we accept the correspondence between the utterance and the person in front of us—all we are doing is uttering the fact that we are naming. Thus, it is not so much that ‘a rose by any other name would smell as sweet’ but more appropriately, ‘a rose is a rose is a rose’—the relationality between its name and the phenomenon of its sweet smell can only be established after that moment of naming, that instance of catachresis. So, whenever one utters “I love you,” not only is it a performative statement, it is the very naming of that love—all you are doing is establishing a relationality between you and the other. And since there is no necessary referent—one is naming that referentiality as one utters it—this suggests that it is always already a symbolic statement; without which the mystery of the other cannot me maintained. In other words, one cannot love the other without maintaining this symbolic distance—through a ritual; in this case the utterance “I love you.” This might be why Valentine’s Day seems to provoke such a massive reaction: the most common one from people (besides florists) being, Valentine’s Day is mere commercialism. Those among the nay-sayers who maintain a soft spot for Karl Marx would proceed to call it the commodification of relationships; those who prefer the Gods would claim that the sanctity of relationships has been profaned; the gender theorists would note how the fact that males buy the gifts only serves to highlight the unequal power-relation between the genders. Whichever side and variation of the arguments they choose boils down to this: the discomfort lies in the fact that they are confronted with the notion of relationships moving into a mediated sphere. The underlying logic is that love is between two persons only; it should not only remain between them, but more pertinently, be an unmediated experience between two persons. Which of course completely misses the point. For, if we reopen the register that relationships are the result of a negotiation between two persons, there must then be a space between them for this very negotiation to occur. Otherwise, all that is happening is, one person is subsuming the other within their own sphere of understanding; effectively effacing the other. If that were the case, there would no longer be any relationality; all negotiation is gone and the other person is a mere extension of the self—one is in a masturbatory relationality with one’s imaginary. Hence, any relationship must always already carry with it the unknown, and possibly always unknowable. The other person is an enigma, remains—must remain—enigmatic to you. This is the only way in which the proclamation “I love you” remains singular, remains a love that is about the person as a singular person—and not merely about the qualities of the person, what the person is. For, if the mystery of the other is unveiled, then the love for the other person is also a completely transparent love: one that you can know thoroughly, calculate; a check-list. And if they are knowable, this suggests that they can also be negated, and hence, the love can also go away. Only when the love for the other person is an enigmatic one, one that cannot be understood, can that love potentially be an event—and if it is an event, then strictly speaking, it cannot be known before it happens; at best, it can be glimpsed as it is happening, or perhaps even only realised retrospectively. At the point in which it happens, it is a love that comes from elsewhere: this strange phenomenon is best captured in the colloquial phrase, I was struck by love;” or even more so by, “I was blinded by love.” This is a blinding to not only the subject of the encounter—the self—but also of the very object of that encounter, the “you”—all that can be said is that there is an encounter. And it is for this reason Cupid is blind: not just because love is random (and can happen to anyone at any time), but more importantly because even after it happens, both the reason you are in love, and the person you are in love with, remain blind to you. Since there is an unknowable relationality with the other person, the only way you can approach it is through a ritual. This is the lesson that religions have taught us: since one is never able to phenomenally experience the God(s), one has no choice but to approach them symbolically. These rituals are strictly speaking meaningless—the actual content is interchangeable—as it is the form that is important. Rituals allow us momentary glimpses at secrets; and secrets are never about their content(s). Rather, secrets entail the recognition that they are secrets; the secret lies in their form as secret. This can be seen when we consider how group secrets work: since the entire group knows the secret, clearly the content of the secret is not as important as the fact that only members within the group are privy to this secret. Occasionally the actual content can be so trivial that even other people outside the group might know the information; they just do not realize its significance. For instance, if I used my date of birth as my bank-account password, merely knowing when I was born would not instantly give you the key to my life savings. In order for that to happen, you would have had to recognise the significance of the knowledge of my birthday. This means that you have to know that you know something. Since the God(s) are, strictly speaking, unknowable, this suggests that rituals put one in a position to potentially experience the God(s). The meaningless gestures on Valentine’s Day play precisely this ritualised role. It is not so much what you give the other person, but the fact that you give it to them. The gift in this sense is very much akin to an offering; the gift opens the possibility of an exchange. Gift-giving does not guarantee that you will like what is returned; there is always a reciprocation of the gift, but what is returned to you is never known in advance, until the moment it is received. This means that the worst thing that one can do is not give the gift: that would be akin to a cutting off of all possibilities, a complete closing of all communication with the other person. This at the same time also means that you cannot wait for the other person to give you something before you get them their gift: if that were the scenario, the reciprocal gift would be nothing more than a calculated return. The only manner in which both persons can give true gifts is to offer them independently of the other person, whilst keeping them in mind. In this way, the two gifts are always already both uncalculated (in the sense of not knowing what the return is) and also a reciprocation for the other (without knowing whether the other person actually has a gift in the first place). Naturally, this would seem like an irrational, even stupid, way of buying gifts. But it is precisely the stupidity involved that saves the relationship from being banal—more importantly, stupidity prevents it from entering the mere profane. This is not to say that an enigmatic love cannot end—of course it can. However, the difference lies in the fact that if the relationality is wholly transparent, it is subsumed under reason—completely predictable, within the self, and thus never open to the possibility of otherness, exteriority, musing. A love that is an event is one that is also open to the possibility of the divine, the sacred—always already closer to the possibility of wisdom. If we establish that both love and wisdom are exterior, to our knowledge, and the finitude to our selves, this suggests that both are names for the possibility of openness to otherness. In other words, and what choice do we have here but to use the words of the other, the philosopher—the lover of wisdom—is a name for one who is waiting, and nothing more. But that still leaves us with the question of this uncomfortable relationality between philosophy and poetry. But before we address that question, we have to take a momentary detour, and consider the whether it is possible to call one a poet. For, if we take the notion of a poet to be one who reaches the highest levels of rhetoric (beyond the lawyer, and the orator, who only aim to either please the crowds, or convince by way of sophistry), then we must also acknowledge that one can only become a poet at the moment of seizing, the point of inspiration, by the muses. Without this divine moment, all (s)he can do is practice her craft. As no one can control when the muses make their appearance, one could always be practising in vain—in some way, one is always already practising to be least in the way when the muse whispers into one’s ear; one is practising so as not to be vain. And since one cannot know when the muse will appear, there is no time frame to the practising—unlike the lawyer who speaks against a clock, poetry knows no time; the only time that matters is the time appropriate to poetry itself. Thus, all the poet (if one can use this term) is practising for the possibility of effacing her/him self—and waiting. Thus, in order for poetry to occur, in order to be seized, the poet—along with all her concerns—must cease. In other words, there is no poet; there is only the possibility of poetry. However, even as there is no time frame to this waiting, even as all we can say is that poetry is a name for waiting, the one who is practising is always already also in time. And since (s)he is in a symbolic relationality with the possibility of poetry, this suggests that the practising is her sacrifice, and time is precisely what she is sacrificing. Here, it might be helpful to turn to a strange source when it comes to poetry—Georges Bataille—and consider his teachings in the first volume of The Accursed Share where he reminds us that, the “essence [of sacrifice] is to consume profitlessly .” This is where each exchange is beyond rationality, beyond calculability, beyond reason itself, “unsubordinated to the ‘real’ order and occupied only with the present.” He continues: Sacrifice destroys that which it consecrates. It does not have to destroy as fire does; only the tie that connected the offering to the world of profitable activity is severed, but this separation has the sense of a definitive consumption; the consecrated offering cannot be restored to the real order.” (58) Since there is no need for a physical change in the object of sacrifice—“it does not have to destroy as fire does”—this suggests that the tie is severed symbolically. Hence, there is an aspect of trans-substantiation in this sacrifice: the form remains the same; in fact there is no perceivable change—this is the point at which all phenomenology fails—but there is always already a difference, an absolute separation from the “real order,” from logic, calculability, reason. The object of sacrifice, the victim [,] is a surplus taken from the mass of useful wealth…Once chosen, he is the accursed share , destined for violent consumption. But the curse tears him away from the order of things…” (59). And it is this tearing away from the order of things—the order of rationality—that “restores to the sacred world that which servile use has degraded, rendered profane” (55). For, only when it is no longer useful, when it is no longer abstracted—subjected, subsumed under—merely a use-value, can the object be an object as such, can a subject be a subject as such; be a singularity. Thus, it is never so much who or what is sacrificed, but the fact that there is a sacrifice. So even as (s)he is sacrificing her time to poetry, it is always already beyond her knowledge whether what (s)he is doing is actually preparing her for poetry or not—all (s)he can know is that she is sacrificing and nothing more. Hence, all (s)he can do is to open her self to the possibility of this relationality—all (s)he can do is be in love with poetry. At the moment the muse whispers into her ear, (s)he ceases to be, and becomes a medium for poetry—and since this possession is always already beyond our cognitive knowledge, this is also a moment of divine wisdom. In other words, there is no difference between poetry and wisdom—the moment of poetry is the moment of wisdom. And this might be the very reason for the philosopher’s aversion to poets. Not so much because they may corrupt the youth (this is after all the aim of all thinking, all philosophy), but precisely because in order to do so, the philosopher must wait for a moment of possession, for divine musing, for poetry. Hence, all thought, all thinking, all philosophy, is nothing but the waiting for the possibility of poetry itself. (shrink)

O-minimal geometry generalizes both semialgebraic and subanalytic geometries, and has been very successful in solving special cases of some problems in arithmetic geometry, such as André–Oort conjecture. Among the many tools developed in an o-minimal setting are cohomology theories for abstract-definable continuous manifolds such as singular cohomology, sheaf cohomology and Čech cohomology, which have been used for instance to prove Pillay’s conjecture concerning definably compact groups. In the present thesis we elaborate an o-minimal de Rham cohomology theory for abstract-definable (...) $C^{\infty }$ manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function. We can specify the o-minimal cohomology groups and attain some properties such as the existence of Mayer–Vietoris sequence and the invariance under abstract-definable $C^{\infty }$ diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must work in a tame context that defines sufficiently many primitives and assume the validity of a statement related to Bröcker’s question.Abstract prepared by Rodrigo Figueiredo.E-mail: [email protected]: https://doi.org/10.11606/T.45.2019.tde-28042019-181150. (shrink)

The goal of this paper is to contrast the representation of models in photography, as well as certain kinds of inanimate beauty, with the average faces constructed by algorithms serving to identify and reproduce beauty. What are the similarities and differences between inanimate objects, characterized by faces devoid of singularities and comparable to sorts of angelic faces, and the algorithmic parameters through which beauty and attractiveness are calculated and predicted? This paper will apply an enunciative semiotic analysis to photographic corpora, (...) propose philosophical reflections on the categories of beauty, and will show that the conception of beauty changes from corpus to corpus and from one cultural domain to the other. The end of the paper states that beauty has to do with a perfect gradation between stillness and movement in the case of the models seen in fashion photography, between neutrality and expressivity for mannequins, and between singularity and multiplicity for dolls such as Barbie, and that, in the algorithmic fabrication of beautiful faces, it is linked with an enhancement of the compactness of the structure of the face. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Wonder, Imagination, and the Matter of Theatre in The TempestMary MooreAriel occurs. Recounting his performance of "the tempest" in Act I, scene 1 of The Tempest, he presents himself as being and action, fracturing grammar, spatial and temporal logic in ways that amaze and confound:I boarded the King's ship; now on the beak, Now in the waist, the deck, in every cabin, I flamed amazement. Sometime I'd divide, And (...) burn in many places; on the topmast, The yards, and bowsprit would I flame distinctly, Then meet and join...(1.2.195–201) 1"I flamed" means that Ariel emits or is flames, which in the normal order of things would consume him. His very narration, however, proves his survival, evoking wonder through the utterance itself. Forceful and compacted syntax, a recognized source of wonder in Classical and Renaissance accounts of style (Biester, pp. 14; 35–40), magnifies this effect. 2 Shakespeare's transitive use of the usually intransitive verb flame reflects a not uncommon practice, as E. A. Abbott shows; 3 but this syntactic device also reflects The Tempest's own logic. Ariel crosses boundaries between [End Page 496] deed and being, verb and noun, subject and object, matter and spirit: he both is and does flames. What could be more jarring to syntax and semantics than a singular subject whose utterance claims that he can flame, divide, meet and join? Just as "a" fire consists of many flames yet functions grammatically as a singular substance in English, just as the Christian Trinity is both singular and multiple, Ariel burns in many places at once. Meanwhile, this extraordinary language seems belied by the actor's very embodiment. Ariel cannot have done what he claims; yet the prior scene has represented the very storm in which Ariel flamed. In that sense, the actor's embodiment represents what we imagine to be matter's intractability, while Ariel's claims, coupled with the storm we have just witnessed, reveal matter's fluidity and permeability to imagination. Fluidity and intractability co-exist, another source of wonder. Sound mimics these paradoxes: the assonance and consonance in flame and amazement create a near rhyme that echoes the near identity of fire and human amazement. If, as Gurr and Ichikawa observe, a Renaissance audience expected to hear more than see a play, this echo calls attention to Ariel's marvelous powers. 4 Lest the noises and pleasures of the Renaissance theatre, which recent scholarship deems to be considerable, distract audience members from this bit of language, similar moments reinforce Ariel's play in and with language and matter throughout the play. Marvelous poetic language is of a piece with a "fever" that is of "the mind," with music that "creeps," actors who vanish, new found goddesses who speak the discoverers' own language.Amazement provides our cue: it and its cognates name the appropriate response to Ariel, his language, and to The Tempest itself. Attention to Ariel's poetic language reveals that it, like the plot, conforms to the marvels of the play and to the period's well documented love for marvels in several ways. Wonder, an aesthetic "'object of desire'" in itself, and a response to the inexplicable in classical and early modern views, may be evoked by the unexpected in style (and through other strategies that the era's handbooks taught). 5 The clause "I flamed amazement" epitomizes the unexpected in syntax as well as differing from one of the few sources found for The Tempest, William Strachey's 1610 letter, which describes just such a storm. 6 While St. Elmo's fire itself may elicit wonder, Shakespeare's syntax and diction reinforce that marvel. And no wonder: rhetoric and theatre alike depend upon audience attention, and wonders naturally evoke it. Jarring language also harmonizes with The Tempest's structural marvels—loose ends, disrupted actions, unforeseen futures—issues several critics explore. 7 [End Page 497]The wonders of The Tempest, however, also involve imagination—in early modern psychology, the human faculty that permits perception of the world and invention of images. 8 Wonder responds to how the perceived differs from the expected, how the imagined supplants the usual, how an... (shrink)

© The Authors 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected] Propositions, Trenton Merricks defends a certain vision of the metaphysics of propositions: propositions exist necessarily and they primitively and essentially represent the world as being a certain way. The book is compact but rich: it is packed with arguments, moves at a fast pace, yet is written with admirable clarity.While I am sympathetic to many of Merrick’s conclusions, (...) I found some of his arguments towards these conclusions lacking. In Section 1, I discuss his claim that arguments constituted by propositions cannot be logically valid. In Section 2, I discuss his argument against singular propositions as having the entities they are about as constituents, and in particular his commitment to necessarily existing singular propositions... (shrink)

The following pcf results are proved:1. Assume thatκ>ℵ0κ>ℵ0is a weakly compact cardinal. Letμ>2κμ>2κbe a singular cardinal of cofinality κ. Then for every regularView the MathML sourceλ sup{suppcfσ⁎-complete|a⊆Reg∩and|a|<μ}.Turn MathJax onAs an application we show that:if κ is a measurable cardinal andj:V→Mj:V→Mis the elementary embedding by a κ-complete ultrafilter over κ, then for every τ the following holds:1. ifjjis a cardinal thenj=τj=τ;2. |j|=|j)||j|=|j)|;3. for any κ-complete ultrafilter W on κ, |j|=|jW||j|=|jW|.The first two items provide affirmative answers to questions from Gitik and (...) Shelah [2] and the third to a question of D. Fremlin. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Future of Environmental PhilosophyJ. Baird Callicott (bio)The old guy in The Graduate had just one word for Dustin Hoffman's character, Ben: "plastics." This old guy has three words for the future pursuit of environmental philosophers, young and old: global climate change (GCC).GCC is emerging as the central environmental concern of the 21st century. Back in the 20th century, E. O. Wilson's mantra was (I paraphrase) 'abrupt mass anthropogenic (...) species extinction is the crime for which posterity is least likely to forgive us.' In view of the multifaceted catastrophe graphically depicted in the recent acclaimed film, An Inconvenient Truth (AIT), Wilson's dictum seems quaint. Rather, a world whose very geography will be anthropogenically altered by risen sea levels, whose weather will be increasingly violent and erratic, whose seas will be stagnant and acidified by carbonic acid, etc., etc., is the crime for which posterity is least likely to forgive us—if there is any posterity to make a judgment.According to Al Gore in AIT anthropogenic GCC is a "moral" and "ethical" issue. But he doesn't elaborate. And at the end of the film he provides a lame list of things you and you and you and you—all of us individually AND voluntarily—can do to mitigate GCC, such as swap out halogen light bulbs for compact florescent ones and drive a hybrid car. Think "tragedy of the commons" for the efficacy of that approach to an adequate ethical response to the challenge of GCC.Gore's naivete apart, environmental ethics (EE) as we know it is singularly ill-prepared for dealing with GCC. The problem is one of scale, temporal as well as spatial. Spatially, EE concern was focused on the scale of biotic communities, ecosystems, and landscapes. And the relevant science was ecology. Temporally, the scale was also ecological: It might take Prince William Sound half a century, perhaps even a whole century, to fully recover from the Exxon Valdez spill. In temperate climates, after a clearcut a mature forest might spring up in a century and, through ecological succession, if left alone it will return to old growth in 300 years. Back in the 20th century that seemed like a long time, and we lamented that the ecological temporal scale and the economic temporal scale of [End Page 119] industries like the timber business and the oil business were out of phase, the former measured in decades the latter in quarters. But now, elderly environmental philosophers like me will personally witness little more than the initial environmental consequences of GCC—the occasional Katrina, the occasional hottest year on record, the disappearance of glaciers in Glacier National Park. We won't live to see (I hope) the cessation of the Gulf Stream or sea-levels rise more than a few centimeters. And the rectification of these consequences will be completed, if they ever are, only after thousands of years have elapsed.How then do we scale EE up to meet the moral challenge of GCC? Spatially we have a huge leap to make from the landscape scale to the biospheric scale. We have to become conversant with a new set of sciences; the relevant sciences are not ecology and conservation biology, but biogeochemistry and earth-systems science.Is a GCC EE even possible? Maybe ethics has temporal-scale limits? We used to marvel at the long view of the Iroquois who considered the consequences of present policies out seven generations. Wow! At 25 years per generation that is all of 250 years (adding on the 75-year life-span of the 7th generation). Can we have ethical concern for the 37th generation, a thousand years out? Or the 121st generation 3000 years out?J. Baird Callicott J. Baird Callicott is Regents Professor of Philosophy and Religion Studies in the Institute of Applied Sciences at the University of North Texas. From 1997–2000 he served the International Society for Environmental Ethics as president. He is author, editor, or co-editor of a score of books and more than a hundred journal articles and book chapters. Callicott's research proceeds on six major fronts: theoretical environmental ethics, land ethics, the philosophy of... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:diacritics 34.2 (2006) 3-13 [Access article in PDF] Biographical Illusion and Methodological Reality Leland De La Durantaye Pierre Bourdieu. Esquisse Pour Une Auto-Analyse. Paris: Raisons d'Agir, 2004. 1 Like his student and friend Nietzsche, Jacob Burckhardt often stressed the necessity for a scholar to work in solitude. Like Nietzsche, he also possessed a gift for acidic analogy and likened the world of academia to a group of dogs sniffing (...) one another.Few observers of the academic interactions of his time had such sharp senses as Pierre Bourdieu, and few have been as torn between solitary reflection and communal exchange. Trained by France's most elite academic institutions (such as the celebrated Parisian lycée Louis-le-Grand and the even more celebrated École Normale Supérieure), Bourdieu was grateful for the opportunities that this training afforded him. And he felt that this gratitude could best be repaid by submitting those elite academic institutions and their insular world to an unsparing critique, to unveiling the distance that separated their stated ideals from their real effects.Like Bergson and Jaurès, like Sartre and Aron, like Foucault and Derrida, Bourdieu studied that which was most difficult and most prestigious where it was most difficult and prestigious: philosophy at the École Normale Supérieure. Like those famous fellow alumni, he was a brilliant student, and like them, he longed to distinguish his personal vision from those around him. This led him to do something surprising, something that, despite their separate and significant dissatisfactions with the philosophy of their day, neither Bergson nor Sartre, neither Foucault nor Derrida ever did: he abandoned philosophy. He left what he saw as the intellectual royal road for the most pedestrian of paths—that of sociology.As he often reminded his readers, sociology was in a sorry state when he entered it. Both in academic appraisal and the popular imagination, it was considered dry and provincial. It was thought to have no true intellectual adventure in it—nothing of the ethnologist tramping through the rain forests of the Amazon, nothing of the lone philosopher working through the night on an opus to end metaphysics. It was laborious and abstract; it dealt in statistical generalities. Bourdieu repeatedly described sociology as "the pariah of disciplines."1 He had, however, a special mission for it in mind. [End Page 3]In Bourdieu's posthumous memoir Esquisse pour une auto-analyse, published in February 2004—two years after his death—by the small publishing house he helped found, Raisons d'Agir, he notes how, "a bit as a joke," he had often defined himself as "the leader of a liberation movement aiming to free the social sciences from philosophy's imperialism" [94].2 From early on in his career, he had wished to revolt against the "empire of the total philosopher"—an empire reigned over by, more than any other, Jean-Paul Sartre [cf. 25].3 Looking back upon this decisive period of his development, Bourdieu goes so far as to state that the shaping of his identity was done "against everything which the Sartrian enterprise represented for me" [37]. In historical accounts, Sartre is often given as counterfigure his friend and fellow normalien Raymond Aron. In his Esquisse, Bourdieu proposes a different, and less conventional, counterfigure for the imperial philosopher: the brilliant Austrian satirist and cultural critic Karl Kraus. Bourdieu notes the particular affection he had always felt for Kraus and attributes it to the latter's singular capacity for "critical reflectivenesss" [37]. Subtly, and appropriately, Bourdieu follows this remark with something that occurs nowhere else in his memoir: an epigram (the composing of which Kraus excelled in). Bourdieu writes: "there are a great many intellectuals who question the world, but there are very few intellectuals who question the intellectual world" [37]. The remark could not more compactly and precisely reflect what Bourdieu had aspired all his life to do: to excel in the art and science of questioning the intellectual world. 2 Leo Spitzer liked to cite Friedrich Gundolf's dictum "Methode ist Erlebnis" (method is lived experience). Nearing the end of his career... (shrink)

Using the analysis developed in our earlier paper, we show that every uncountable cardinal in Gitik's model of in which all uncountable cardinals are singular is almost Ramsey and is also a Rowbottom cardinal carrying a Rowbottom filter. We assume that the model of is constructed from a proper class of strongly compact cardinals, each of which is a limit of measurable cardinals. Our work consequently reduces the best previously known upper bound in consistency strength for the theory math (...) formula + “All uncountable cardinals are singular” + “Every uncountable cardinal is both almost Ramsey and a Rowbottom cardinal carrying a Rowbottom filter”. (shrink)

Evidence is presented that the singularities induced in causal Lorentzian spacetimes by changes in 3-space topology give rise to infinite particle and energy production under reasonable laws of quantum field propagation. In the case of the gravitational field, if 3-space is compact the total energy must vanish. A topological transition therefore induces a violent collapse that effectively aborts the transition, since the collapse mode is the only mode carrying the negative energy needed to compensate the associated infinite energy production. The (...) existence of the Hamiltonian constraint of general relativity suggests that topological stability is a local property of the quantum theory that is maintained even when 3-space is noncompact. (shrink)

We use Shelah's theory of possible cofinalities in order to solve some problems about ultrafilters. Theorem: Suppose that $\lambda$ is a singular cardinal, $\lambda ' \lessthan \lambda$, and the ultrafilter $D$ is $\kappa$ -decomposable for all regular cardinals $\kappa$ with $\lambda '\lessthan \kappa \lessthan \lambda$. Then $D$ is either $\lambda$-decomposable or $\lambda ^+$-decomposable. Corollary: If $\lambda$ is a singular cardinal, then an ultrafilter is ($\lambda$,$\lambda$)-regular if and only if it is either $\operator{cf} \lambda$-decomposable or $\lambda^+$-decomposable. We also give (...) applications to topological spaces and to abstract logics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Poetic Justice: The Literary Imagination and Public LifeDavid GormanPoetic Justice: The Literary Imagination and Public Life, by Martha C. Nussbaum; xii & 143 pp. Boston: Beacon Press, 1995, $20.00.This volume, a revision of lectures given in 1991, is a philosophical study comparing aspects of law and literature. The law in question is contemporary American case law (hence the reference to “Public Life” in the book’s subtitle). The literature (...) to which it is juxtaposed consists primarily of “realist social novels” (p. 87), represented chiefly by Dickens’s Hard Times, though with some attention also given to E. M. Forster’s Maurice, Richard Wright’s Native Son, and to passages from Whitman’s poetry (quoted, characteristically, at some length). Nussbaum’s thesis is that both this kind of legal discourse and this kind—or kinds—of literary discourse constitute, involve, or otherwise rely upon an imaginative vision of human life and its possibilities. Thus lawyers have a great deal to learn from literature, insofar as contact with the capacious imaginations of a Dickens or a Whitman can only enlarge the sensibilities of those who read them in a sufficiently open-minded, reflective way.It may be both too kind and overly reductive to ascribe to Poetic Justice such a thing as a thesis. On the contrary, this compact book, like all of Nussbaum’s writings, teems with theories and theses. This is the main reason, I suppose, for the dichotomy of responses to Nussbaum: some find this pullulating quality of her work exhilarating, while others just find it annoying. One advantage that I think both parties will recognize in the compactness of Poetic Justice (due to the constraints of the lecture format) is that it inhibits the author’s native prolixity, which makes her previous books—The Fragility of Goodness (1986), Love’s Knowledge (1990), and The Therapy of Desire (1994)—something of an effort even for Nussbaum’s biggest fans to stay with through every last qualification, tertiary argument, and cross-reference. [End Page 196]The opening pages of these lectures seem, if anything, all too simple. Nussbaum’s initial target is the economistic, deterministic school of social analysis associated with the University of Chicago generally and with Richard Posner in particular, which has lately exercised a disproportionate influence in American jurisprudence and—especially during the Reagan-Bush era—in public policymaking. Against this kind of thinking, which attempts to treat human beings and their actions and decisions as much as possible in terms of quantifiable, statistical measures, Nussbaum emphasizes the autonomy, the irreducible singularity of each human being and the qualitative aspects of each person’s experience, which is the kind of cautionary lesson that she sees literary works as driving home—hence their value as a counterweight, or even a vaccine, against reductive economism. Thus readers will tend to assume from the first lecture (“The Literary Imagination”) that what they are in for, pretty much, is something like Bob Cratchit’s comeback to Ebenezer Scrooge. The Dickensian comparison is not fortuitous, of course, because although the text of reference is Hard Times and not A Christmas Carol, the moral antithesis is familiar enough: a coldly, blindly all-embracing utilitarianism versus a warm, empathetic humanism.Yet, as Nussbaum develops her account, things are not so simple. What emerges is that her aim is not simply to mount an attack on the economic-determinist approach to analyzing (and thus judging) human behavior, but in the first place to understand it, to get inside this worldview. This empathetic response to Chicago-style social analysis, in turn, weaves itself into the texture of Nussbaum’s book in two ways. For one thing, it supports her call to treat literature as making a potentially significant contribution to public life, since what better path can there be to understanding neo-utilitarians like Posner than via imaginative portrayals of such paleo-utilitarians as Mr. Gradgrind? For another thing, moreover, the very gesture of trying to empathize with economic determinism rather than trying to bury it serves the purpose of showing up the latter’s limitations, because this kind of other-directed response is just what the utilitarian approach is least... (shrink)

The first chapters of Michalos’ book give an account of the controversy between Karl Popper and Rudolph Carnap following the former’s critique of Carnap in "Degree of Confirmation". Michalos very compactly summarizes the controversy and argues: 1) that Popper was mistaken when he tried to show that Carnap always identified the quantitative degree of confirmation with the acceptability of scientific theories; 2) that Popper is mistaken in accusing Carnap of confusing classificatory, comparative, and quantitative concepts; 3) that a conflict between (...) Popper and Carnap, apparently over the problem of unrestricted universals, was in fact over the everyday practical use of such universal sentences; 4) that Popper’s critique of Carnap’s theorem for the singular predictive inference is incorrect because Popper construes the theorem with respect to two different kinds of evidential statements. The final chapters of the book deal with some additional issues that have developed out of the central controversy. One chapter consists largely in a reply to Imre Lakatos in further defense of Carnap. A second presents a critique of the Hintikka-Hilpinen acceptance rule. The last chapter is a comparison of cost—benefit versus utility acceptance rules in which Michalos claims to show the superiority of the former. In general, the book is an attempt to defend an inductive logic against the criticisms offered by Popperian deductive methodologists. A great deal of this material already appeared in various forms. The book is useful insofar as it collects material in one place and provides references to the important contributions to the controversy. Unfortunately, the book is cramped, explicitly discussing only some of the narrow issues found in the journal literature, and some sections are so compact as to be incomprehensible without extensive knowledge of the source material. Michalos might have given himself wider scope so that he could develop the implications of these limited problems for the broader issues of the philosophy of science.—K. M. (shrink)

We prove that every weakly square compact cardinal is a strong limit cardinal, and therefore weakly compact. We also study Aronszajn trees with no uncountable finitely splitting subtrees, characterizing them in terms of being Lindelöf with respect to a particular topology. We prove that the class of such trees is consistently non-empty and lies between the classes of Suslin and Aronszajn trees.

The Compactness Theorem The compactness theorem is a fundamental theorem for the model theory of classical propositional and first-order logic. As well as having importance in several areas of mathematics, such as algebra and combinatorics, it also helps to pinpoint the strength of these logics, which are the standard ones used in mathematics and arguably … Continue reading Compactness →.

Perceptual experiences seem to in some sense have singular contents. For example, a perceptual experience of a dog as fluffy seems to represent some particular dog as being fluffy. There are important phenomenological, intuitive, and semantic considerations for thinking that perceptual experiences represent singular contents, but there are also important phenomenological, epistemic, and metaphysical considerations for thinking that they do not. This paper proposes a two-tier picture of the content of singular perceptual experiences that is based on (...) phenomenal intentionality theories of intentionality combined with self-ascriptivism about derived representation, a combination of views that allows mental states to have two types of contents: phenomenal contents and derived contents. On the proposed picture, singular perceptual experiences represent singular phenomenal contents, which do not involve worldly objects, as well as singular derived contents, which do involve worldly objects. This picture accommodates and reconciles the considerations for and against thinking that perceptual experiences have singular contents. (shrink)

We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these characterizations to prove new results in computable analysis and effective topology. We also apply the technique of computable compactness to give new and less combinatorially involved proofs of known results from the literature. Some of these results do not have computable compactness or compact spaces in their statements, and thus (...) these applications are not necessarily direct or expected. (shrink)

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks to (...) me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

Judea Pearl (2000) was the first to propose a definition of actual causation using causal models. A number of authors have suggested that an adequate account of actual causation must appeal not only to causal structure but also to considerations of normality. In Halpern and Hitchcock (2011), we offer a definition of actual causation using extended causal models, which include information about both causal structure and normality. Extended causal models are potentially very complex. In this study, we show how it (...) is possible to achieve a compact representation of extended causal models. (shrink)

SINGULARITY: 12 Precepts for Transcendental Living | © 2022 Cromwell Black Publishing House | Original work by Luis Herrera. -/- Living transcendentally is not the same as ‘having the answers to life.’ The intention with which this book is written is to help you identify the God within yourself. Religion is a guidepost, but not the answer. Philosophy is a guidepost, not the answer. People that over-identify with one group or tribe for ideological reasons invariably meet with disappointment because there (...) will always be some tenets they internally oppose and disagree with. Yet they ignore their inner voice in order to ‘fit in with the rest.’ Man is a social animal and excommunication from the tribe has been tantamount to extinction of our lineage since our days as hunters and gatherers. By living transcendentally I have learned to acknowledge, welcome and accept the space between myself and my tribe. I invite you to do the same. -/- Learning to listen to the God within, I can trust my inner voice more because there is a message spoken there, uniquely for me, that will never be printed on the pages of the Bible, or the Koran, or the Tao Te Ching, or any other book for that matter. There’s only one YOU. Others may have your name, but not your identity. They may share your birth date and hospital, but not your parents. They may share your parents, but not your name. Do you see what I’m getting at here? Therefore how can a ‘one-size fits all’ religion, education or philosophy possibly answer the question to your meaning of life? There is no the meaning of life, because there is no the life. There are infinite lives, for which infinite meanings must be furnished. Hence the importance of learning to trust yourself, your inner voice, conscience – the God within. (shrink)