We prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal J (coded in the ground model) a cofinal subset of (J, ⊆*) is order isomorphic to (Q, ≤).

Minami–Sakai :883–898, 2016) investigated the cofinal types of the Katětov and the Katětov–Blass orders on the family of all \ ideals. In this paper we discuss these orders on analytic P-ideals and Borel ideals. We prove the following:The family of all analytic P-ideals has the largest element with respect to the Katětov and the Katětov–Blass orders.The family of all Borel ideals is countably upward directed with respect to the Katětov and the Katětov–Blass orders. In the course of the (...) proof of the latter result, we also prove that for any analytic ideal \ there is a Borel ideal \ with \. (shrink)

In this paper, we study some new examples of ideals on $$\omega $$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order—known as the weak Rudin–Keisler order—and its structure when restricted to these ideals of maximal Tukey type. Mirroring a result of Fremlin (Note Mat 11:177–214, 1991) on the Tukey order, we also show that there is an analytic P-ideal above all (...) other analytic P-ideals in the weak Rudin–Keisler order. (shrink)

Analytical commentary -- Fruits upon one tree -- The continuation of the early draft into philosophy of mathematics -- Hidden isomorphism -- A common methodology -- The flatness of philosophical grammar -- Following a rule 185-242 -- Introduction to the exegesis -- Rules and grammar -- The tractatus and rules of logical syntax -- From logical syntax to philosophical grammar -- Rules and rule-formulations -- Philosophy and grammar -- The scope of grammar -- Some morals -- Exegesis 185-8 -- Accord (...) with a rule -- Initial compass bearings -- Accord and the harmony between language and reality -- Rules of inference and logical machinery -- Formulations and explanations of rules by examples -- Interpretations, fitting and grammar -- Further misunderstandings -- Exegesis 189-202 -- Following rules, mastery of techniques and practices -- Following a rule -- Practices and techniques -- Doing the right thing and doing the same thing -- Privacy and the community view -- On not digging below bedrock -- Private linguists and private linguists : Robinson Crusoe sails again -- Is a language necessarily shared with a community of speakers? -- Innate knowledge of a language -- Robinson Crusoe sails again -- Solitary cavemen and monolinguists -- Private languages and private languages -- Exegesis 203-37 -- Agreement in definitions, judgements, and form of life -- The scaffolding of facts -- The role of our nature -- Forms of life -- Agreement : consensus of human beings and their actions -- Exegesis 238-42 -- Grammar and necessity -- Setting the stage -- Leitmotifs -- External guidelines -- Necessary propositions and norms of representation -- Concerning the truth and falsehood of necessary propositions -- What necessary truths are about illusions of correspondence : ideal objects, kinds of reality, and ultra-physics -- The psychology of the A priori -- Knowledge -- Belief -- Certainty -- Surprise -- Discoveries and conjectures -- Compulsion -- Propositions of logic and laws of thought -- Alternative forms of representation -- The arbitrariness of grammar -- A kinship to the non-arbitrary -- Proof in mathematics -- Conventionalism. (shrink)

By way of countering Tolstoj's reputation as an alogical and inept philosophical thinker, this paper explores the tension between maximalism and reasonableness in his defense of the ethics of nonviolence. Tolstoj's writings of the last decade of his life show that he was perfectly capable of making appropriate conceptual distinctions, recognizing legitimate objections to his position, and responding rationally to them; in so doing, he made valuable points about the unpredictability of human actions, the futility of using violence to combat (...) violence, the equal worth of all humans lives, and the immorality of revenge. Yet his conception of the moral ideal, together with his missionary zeal, led him to exaggerate the absoluteness of his moral message, causing him to predict the unpredictable and demand the impossible of human beings. (shrink)

We study the structure of analytic ideals of subsets of the natural numbers. For example, we prove that for an analytic ideal I, either the ideal {X (Ω × Ω: En X ({0, 1,…,n} × Ω } is Rudin-Keisler below I, or I is very simply induced by a lower semicontinuous submeasure. Also, we show that the class of ideals induced in this manner by lsc submeasures coincides with Polishable ideals as well as analytic P-ideals. (...) We study this class of ideals and characterize, for example, when the ideals in it are Fσ or when they carry a locally compact group topology. We apply these results to Borel partial orders to rederive a theorem of Todorcevic and to Borel equivalence relations to answer a question of Kechris and Louveau. As another application we give a characterization of σ-ideals of μ-zero sets for Maharam submeasures μ on the Cantor set which is to a large extent analogous to a characterization of the meager ideal due to Kechris and the author. (shrink)

The field of business ethics has shown little attention to the dynamics of memory in maintaining moral character. Yet memory is a complex process that involves the repression of some experiences in order to protect the moral integrity of the personality. Without the capacity to repress what one's moral conscience would not accept, the mind can be overtaken by neurotic ambivalence and moral confusion. In the context of business competition, where the pressures for potential gains and losses can be immense, (...) long repressed desires can receive renewed strength resulting in a weakening of moral constraint. In this essay, I use the psycho-analytic theory of repression to investigate the complex, psychological vicissitudes of human memory. The theory of repression is a particularly powerful tool to investigate the moral implications of memory because memories which are repressed - i.e., forbidden consciousness - are done so at the behest of the individual's moral ideals. Experiences that offend these ideals or threaten the integrity of the ego can be repressed. Repression, then, is an infallible index of moral judgement. I will apply the theory of repression to the characters in and story line of Arthur Miller's play "Death of a Salesman" to elucidate the relationship between memory and ethics in business. "Death of a Salesman" is well suited for this purpose because the memories of the main characters are central to the play and are inextricably linked to the moral challenge competition in business poses. (shrink)

In this paper I hope to show that a conception of human rights requires a view of the social ideal and the good life, and requires a view of the nature of human community. But what I say in favor of these points hardly amounts to a demonstration. Instead I try to exhibit how we think and talk about rights in general, and what the presuppositions of such thought and talk are. Throughout, I emphasize the pragmatic side of rights-discourse (...) and I try to establish some of the contexts in which such discourse can be significantly employed. Much of what I say is motivated by the consideration that an historically important factor in the generation of various rights, their acknowledgement and implementation, and their extension to increasingly larger segments of the population, has been the claims put forward and the demands made by individuals and groups against individuals and groups. This factor constitutes a suggestive clue for the development of a theory of rights. The treatment here, however, is largely programmatic and fragmentary. The space allotted does not permit more. Moreover, I lead up to—but do not go into—the social ideal and the human community. The title of this essay indicates its limited scope. The above points are, of course, hardly novel; many older writers laid great stress upon them. But of late they have not received the attention that they in my view deserve. What does it mean for someone to maintain a conception of human rights? How is this conception given any concrete content? The answers to these questions, I believe, ultimately lead to a consideration of social ideals and the human community. What follows is meant to stimulate new thinking on these old-fashioned topics. (shrink)

Researchers rely on psychometric principles when trying to gain understanding of unobservable psychological phenomena disconfounded from the methods used. Psychometric models provide us with tools to support this endeavour, but they are agnostic to the meaning researchers intend to attribute to the data. We define method effects as resulting from actions which weaken the psychometric structure of measurement, and argue that solution to this confounding will ultimately rest on testing whether data collected fit a psychometric model based on a substantive (...) theory, rather than a search for a model that best fits the data. We highlight the importance of taking the notions of fundamental measurement seriously by reviewing distinctions between the Rasch measurement model and more generalised 2PL and 3PL IRT models. We then present two lines of research that highlight considerations of making method effects explicit in experimental designs. First, we contrast the use of experimental manipulations to study measurement reactivity during the assessment of metacognitive processes with factor-analytic research of the same. The former suggests differential performance-facilitating and -inhibiting reactivity as a function of other individual differences, whereas factor-analytic research suggests a ubiquitous monotonically predictive confidence factor. Second, we evaluate differential effects of context and source on within-individual variability indices of personality derived from multiple observations, highlighting again the importance of a structured and theoretically grounded observational framework. We conclude by arguing that substantive variables can act as method effects and should be considered at the time of design rather than after the fact, and without compromising measurement ideals. (shrink)

§1. Introduction. Ideals and filters of subsets of natural numbers have been studied by set theorists and topologists for a long time. There is a vast literature concerning various kinds of ultrafilters. There is also a substantial interest in nicely definable ideals—these by old results of Sierpiński are very far from being maximal— and the structure of such ideals will concern us in this announcement. In addition to being interesting in their own right, Borel and analytic ideals occur naturally (...) in the investigations of compact subsets of the space of all Baire class 1 functions on a Polish space, see [12, 18]. Also, certain objects associated with such ideals are of considerable interest and were quite extensively studied by several authors. Let us list here three examples; in all three of them I stands for an analytic or Borel ideal.1. The partial order induced by I on P: X ≥I Y iff X \ Y ϵ I and the partial order.2. Boolean algebras of the form P/I and their automorphisms.3. The equivalence relation associated with I: XEI Y iff X Δ ϵ I.In Section 4, we will have an opportunity to state some consequences of our results for equivalence relations as in 3. (shrink)

Putnam says that "In one way of conceiving it, realism is an empirical theory." In the present work it is maintained that, in another way of conceiving it, realism is a grammatical thesis. That is, many of the principles taken to be definitive of realism, e.g., "Truth is objective," "Truth is mind-independent," Dummett's "a thought can be true only if there is something in virtue of which it is true," are what Wittgenstein would have called "grammatical remarks." They simply call (...) attention to certain features of the grammar of truth and related concepts. Thus, e.g., it is a feature of the way we use "is true" that statements are not spoken of as true for one person and not true for another. ;The character of grammar and of grammatical remarks in general is spelled out in some detail; it is argued in particular that Wittgenstein is not intending to provide, by means of these notions, a particular account of necessary truth. He is suggesting, rather, that looking upon certain philosophical claims as grammatical is a way of "deflating" them, stripping them of their appearance of profundity. Neither can grammatical remarks imply substantive philosophical theses. This is why realism, conceived as comprising grammatical remarks, does not imply scepticism, as is often supposed, and is not itself a controversial or exciting doctrine. ;There are of course some controversial formulations of realism, versions which are not simply underwritten by grammar. Thus some philosophers have held that, because the truth conditions of a proposition are essentially independent of any evidence we may have for the proposition, truth may not be accessible at all. I believe, however, that Putnam has shown, by means of an argument which is instructively viewed as a grammatical investigation, that truth is accessible, at least to an "ideal" theory. ;Recent expressions of idealism are argued to provide helpful accounts of language use and understanding, but fail to establish that truth is nothing but warranted assertibility, or that it must in some sense "arise within us." Such a conclusion runs afoul of the grammar of truth, of which realism is shown to provide the proper account. (shrink)

Curriculum theorists are, among other things, engaged in attempts at producing models of curriculum design and/or curriculum development. Such attempts, according to Robin Barrow, aim at establishing "a set of ideal steps that will both lead to coherent proposals for curriculum change and, when incorporated in the curriculum proposal, enable it to be successfully adopted." Establishing such "a set of ideal steps" involves a consideration of needs, practical constraints, curriculum content and curriculum planning. Such projects also include a (...) formulation of curriculum objectives, ways of implementing objectives and methods of evaluating the success or failure of achieving these objectives. In this paper I propose to reflect on the nature of objectives by focusing on the following questions: 1. Are objectives part of the curriculum? 2. What constitutes a meaningful objective? (shrink)

We study the Katětov order on Borel ideals. We prove two structural theorems, one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals and study the Katětov order among them. We also present a list of fundamental open problems concerning the Katětov order on Borel ideals.

Pompa’s book is a welcome addition to the sparse English literature on Vico, and it will be of interest not only to philosophers but to historians, anthropologists, and other social scientists. Vico is written and developed as a guide to the final version of the New Science which is surely one of the most obscure books ever written. This is the first book in English which takes as its aim the exposition of the New Science. The other English books, ranging (...) from Flint’s Vico in 1891 to Tagliacozzo and White’s Giambattista Vico: An International Symposium contained either a general survey of ideas, as in Flint, or a wide collection of background materials and analytic, historical, or comparative studies, as in Tagliacozzo and White. A. R. Caponigri in Time and Idea expressed perhaps the historically and philosophically most controversial thesis: that Vico had attempted to temporalize and historicize the Platonic forms in his concept of the "ideal eternal history.". (shrink)

We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. An ideal is representable in a Banach space iff it (...) is a nonpathological analytic P-ideal.We focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic. (shrink)

The project we highlight in this article stems from our philosophical work on moral disagreements that appear to be—and sometimes are—intractable. Deliberative democratic theorists tout the merits of dialogue as an effective way to bridge differences of values and opinion, ideally resulting in agreement, or perhaps more often resulting in greater mutual understanding. Could dialogue mitigate disagreements about a controversial education policy such as affirmative action? Could it foster greater understanding? We conceived of a project that would simultaneously fulfill two (...) goals that we had as philosophers, education researchers, and aspiring public intellectuals. First, it would allow us to use philosophy in research, grounding our mixed methods research in a philosophically informed framework. The tools and analytic techniques that are particular to philosophers felt uniquely suited for an empirical study concerning political theory. Second, we aimed to use philosophy in the community. We were able to put our own expertise in philosophy and race-conscious education policy to good use by purposefully creating opportunities for diverse community members in our larger metropolitan area to engage in dialogue and deliberation with each other over the issue of affirmative action. (shrink)

We study the intersection number of families of tall ideals. We show that the intersection number of the class of analytic P-ideals is equal to the bounding number ${\mathfrak{b}}$ , the intersection number of the class of all meager ideals is equal to ${\mathfrak{h}}$ and the intersection number of the class of all F σ ideals is between ${\mathfrak{h}}$ and ${\mathfrak{b}}$ , consistently different from both.

A two-part symposium. Janaway's article offers an analysis and critique of a methodological assumption current in the history of philosophy, which he labels 'the Analytical Ideal'. It discusses the views of P.F. Strawson, Michael Ayres, and Richard Rorty among others.

We examine the question of how many Boolean algebras, distinct up to isomorphism, that are quotients of the powerset of the naturals by Borel ideals, can be proved to exist in ZFC alone. The maximum possible value is easily seen to be the cardinality of the continuum $2^{\aleph_{0}}$ ; earlier work by Ilijas Farah had shown that this was the value in models of Martin's Maximum or some similar forcing axiom, but it was open whether there could be fewer in (...) models of the Continuum Hypothesis. We develop and apply a new technique for constructing many ideals whose quotients must be nonisomorphic in any model of ZFC. The technique depends on isolating a kind of ideal, called shallow, that can be distinguished from the ideal of all finite sets even after any isomorphic embedding, and then piecing together various copies of the ideal of all finite sets using distinct shallow ideals. In this way we are able to demonstrate that there are continuum-many distinct quotients by Borel ideals, indeed by analytic P-ideals, and in fact that there is in an appropriate sense a Borel embedding of the Vitali equivalence relation into the equivalence relation of isomorphism of quotients by analytic P-ideals. We also show that there is an uncountable definable wellordered collection of Borel ideals with distinct quotients. (shrink)

We give a new characterization of the cardinal invariant $\mathfrak {d}$ as the minimal cardinality of a family $\mathcal {D}$ of tall summable ideals such that an ultrafilter is rapid if and only if it has non-empty intersection with all the ideals in the family $\mathcal {D}$. On the other hand, we prove that in the Miller model, given any family $\mathcal {D}$ of analytic tall p-ideals such that $\vert \mathcal {D}\vert <\mathfrak {d}$, there is an ultrafilter $\mathcal {U}$ (...) which is an $\mathscr {I}$ -ultrafilter for all ideals $\mathscr {I}\in \mathcal {D}$ at the same time, yet $\mathcal {U}$ is not a rapid ultrafilter. As a corollary, we obtain that in the Miller model, given any analytic tall p-ideal $\mathscr {I}$, $\mathscr {I}$ -ultrafilters are dense in the Rudin–Blass ordering, generalizing a theorem of Bartoszyński and S. Shelah, who proved that in such model, Hausdorff ultrafilters are dense in the Rudin–Blass ordering. This theorem also shows some limitations about possible generalizations of a theorem of C. Laflamme and J. Zhu. (shrink)

When is an ideal of a ring radical or prime? By examining its generators, one may in many cases definably and uniformly test the ideal’s properties. We seek to establish such definable formulas in rings of p-adic power series, such as $\mathbb Q_{p}\langle X\rangle $, $\mathbb Z_{p}\langle X\rangle $, and related rings of power series over more general valuation rings and their fraction fields. We obtain a definable, uniform test for radicality, and, in the one-dimensional case, for primality. (...) This builds upon the techniques stemming from the proof of the quantifier elimination results for the analytic theory of the p-adic integers by Denef and van den Dries, and the linear algebra methods of Hermann and Seidenberg.prepared by Madeline G. Barnicle.E-mail: [email protected]: https://escholarship.org/uc/item/6t02q9s4. (shrink)

We examine the question of how many Boolean algebras, distinct up to isomorphism, that are quotients of the powerset of the naturals by Borel ideals, can be proved to exist in ZFC alone. The maximum possible value is easily seen to be the cardinality of the continuum $2^{\aleph_{0}}$ ; earlier work by Ilijas Farah had shown that this was the value in models of Martin's Maximum or some similar forcing axiom, but it was open whether there could be fewer in (...) models of the Continuum Hypothesis. We develop and apply a new technique for constructing many ideals whose quotients must be nonisomorphic in any model of ZFC. The technique depends on isolating a kind of ideal, called shallow, that can be distinguished from the ideal of all finite sets even after any isomorphic embedding, and then piecing together various copies of the ideal of all finite sets using distinct shallow ideals. In this way we are able to demonstrate that there are continuum-many distinct quotients by Borel ideals, indeed by analytic P-ideals, and in fact that there is in an appropriate sense a Borel embedding of the Vitali equivalence relation into the equivalence relation of isomorphism of quotients by analytic P-ideals. We also show that there is an uncountable definable wellordered collection of Borel ideals with distinct quotients. (shrink)

Let ${{\mathcal J}\,(\mathbb M^2)}$ denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is bigger than the covering number of the ideal of the meager subsets of ω ω. We also show that Martin’s Axiom implies that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is 2 ω .Finally we prove that there are no analytic infinite maximal antichains in any finite product of ${\mathfrak{P}{(\omega)}/{\rm (...) fin}}$. (shrink)

Internalism restricts justifiers to what is "within" the subject. two main forms of internalism are (1) perspectival internalism (pi), which restricts justifiers to what the subject knows or justifiably believes, and (2) access internalism (ai), which restricts justifiers to what is directly accessible to the subject. the two forms are analyzed and interrelated, and the grounds for each are examined. it is concluded that although pi is both unacceptable and without adequate support, a modest form of ai might be defended.

Sellars is well known for his critique of the “myth of the given” in his “Empiricism and the Philosophy of Mind”. That text does not make it unambiguous just how he understands the “myth”. Here I take it that whatever else may be involved, his critique is incompatible with the view that there is a nonconceptual mode of “presentation” or “givenness” of particulars that is the heart of sense perception and what is most distinctive of perception as a type of (...) cognition. A critical examination of Sellars’ arguments, particularly those directed at the Theory of Appearing, results in the conclusion that he has failed to eliminate the above view of perception. Moreover, though Sellars is clearly opposed to the view that perceptual experience cannot provide justification for beliefs about perceived objects, I argue that Sellars has failed to shake the intuitive plausibility of that view. (shrink)

The question I hope to answer is brief: What does every speaker of a natural language know? My answer is briefer still: Nothing, or at least nothing interesting. Explaining the question, and making the answer plausible, is a longer job.

In response to widespread doubts among professional philosophers (Russell, Horwich, Dietrich, McGinn, Chalmers), Stoljar argues for a ‘reasonable optimism’ about progress in philosophy. He defends the large and surprising claim that ‘there is progress on all or reasonably many of the big questions.’ However, Stoljar’s caveats and admitted avoidance of historical evidence permits overlooking persistent controversies in philosophy of mind and cognitive science that are essentially unchanged since the 17th Century. Stoljar suggests that his claims are commonplace in philosophy departments (...) and, indeed, the evidence I adduce constitutes an indictment of the widely shared view among professional analytic philosophers. (shrink)

In the work of interpreting Parmenides we have witnessed in the ’sixties and ’seventies, in English language scholarship, that rarest of phenomena in the study of ancient philosophy, the emergence of a consensus. Four interpretive theses now seem quite widely shared: Parmenides deliberately suppresses the subject of esti, “is,” or einai, “to be,” in his statement of the two “routes” in B2, his intention being to allow the subject to become gradually specified as the argument unfolds. The negative route, ouk (...) esti, “is not,” or mē einai, “not to be,” is banned because sentences that adhere to it fail to refer to actual entities—the latter to be understood broadly, as will shortly be stated in thesis. The argument does not depend on a confusion between the “is” of predication and the “is” of existence. In the relevant contexts, esti and einai involve a “fused” or “veridical” use of the verb “to be”; in other words, esti or einai have the force of “is actual” or “obtains,” or “is the case,” envisaging a variable subject x that ranges over states-of-affairs. (shrink)

On the critical side it is argued that, contrary to a widespread view, the explanation of particular facts does not play a central role in pure science and hence that philosophers of science are misguided in supposing that the understanding of such explanations is one of the central tasks of the philosophy of science. It is suggested that the view being attacked may stem in part from an impression that the establishing of a general law is tantamount to the explanation (...) of particular facts that "fall under" the law. This suggestion effects a bridge to the more positive part of the paper, which consists of an exploration of the complexities exhibited by the relation between the two activities. More specifically, I point out a number of disabilities, any one of which could prevent us from being able to explain particular facts that fall under a given law even after having established the law. Some of these have to do with the form of the law, and some have to do with our powers of detection vis-a-vis the particular facts in question. The former sort have to do with the ways in which laws may deviate from the strict-necessary-and-sufficient-condition ideal. The latter include the following points. (1) The individual explanatory factors may lie beyond our present powers of detection. (2) The complexity of such factors may be too great for us to be able to interrelate them. (3) We may be unable to apply concepts used in the law to facts in this area (although they are in fact applicable). (shrink)

Skepticism about the external world may very well be correct, so the question is in order: what theory of knowledge flows from skepticism itself? The skeptic can give a relatively simple and intuitive account of knowledge by identifying it with indubitable certainty. Our everyday ‘I know that p’ claims, which typically are part of practical projects, deploy the ideal of knowledge to make assertions closely related to, but weaker than, knowledge claims. The truth of such claims is consistent with (...) skepticism; various other vexing problems don’t arise. In addition, even if no claim about the world outside my mind can be more probable than its negation, the project of pure scientific research remains well motivated. (shrink)