Racial epithets are derogatory expressions, understood to convey contempt toward their targets. But what do they actually mean, if anything? While the prevailing view is that epithets are to be explained pragmatically, I argue that a careful consideration of the data strongly supports a particular semantic theory. I call this view Combinatorial Externalism. CE holds that epithets express complex properties that are determined by the discriminatory practices and stereotypes of their corresponding racist institutions. Depending on the character of the institution, (...) the complex semantic value can be composed of a variety of components. The account has significant implications on theoretical, as well as, practical dimensions, providing new arguments against radical contextualism, and for the exclusion of certain epithets from First Amendment speech protection. (shrink)

Le lecteur moderne demeure dérouté par les ekphraseis de bâtiments des textes byzantins. Il est en effet difficile de les considérer comme des sources pour l'archéologie ou l'Histoire de l'art, et la recherche tend à leur égard à adopter deux approches : l'une, plutôt liée à l'Histoire et à l'Histoire de l'art, s'emploie à retrouver des éléments réels de bâtiments ou d'œuvres d'art dans ces textes ; l'autre, plutôt philologique, cherche à considérer ces textes en eux-mêmes pour leur valeur littéraire. (...) Serait-il cependant possible de chercher une voie médiane? Une voie qui accepterait qu'une part de l'étrangeté de ces textes, nécessairement due à la langue et à l'époque, le soit également parce que l'expérience de lecture entre Moyen Âge et époque moderne a radicalement changé. Il manquerait au lecteur moderne, non l'imagination, mais les mécanismes et les résultats de l'imagination médiévale. Les échos lexicaux et thématiques qui balisent le texte et qui en dessinent l'architecture en seraient la clef aboutiraient à un texte en 3D, c'est-à-dire une projection mentale de l'objet décrit non pas comme simple image donnée par l'information contenue dans le texte, mais comme image construite par la composition du discours. Ainsi, au fur et à mesure qu'un auteur décrit un bâtiment, le texte le construit en mots et in fine en a épousé la forme. (shrink)

The problem of the unity of the proposition asks what binds together the constituents of a proposition into a fully formed proposition that provides truth conditions for the assertoric sentence that expresses it, rather than merely a set of objects. Hanks’ solution is to reject the traditional distinction between content and force. If his theory is successful, then there is a plausible extension of it that readily solves the Frege–Geach problem for normative propositions. Unfortunately Hanks’ theory isn’t successful, but it (...) does point to significant connections between expressivism, unity, and embedding. (shrink)

In theorizing about racial pejoratives, an initially attractive view is that pejoratives have the same reference as their “neutral counterparts”. Call this the identity thesis. According to this thesis, the terms “kike” and “Jew”, for instance, pick out the same set of people. To be a Jew just is to be a kike, and so to make claims about Jews just is to make claims about kikes. In this way, the two words are synonymous, and so make the same contribution (...) to the truth-conditions of sentences containing them. While the fundamental claim for the identity thesis that Jews are kikes sounds anti-semitic, it need not be actually anti-semitic. The identity thesis is usually bolstered with the further claim that the pejorative aspect of “kike” and other such terms is located elsewhere than in truth-conditional content, so what makes “kike” a bad word is a non-truth-conditional association with anti-semitism that is not shared with the word “Jew”. The exact nature and location of the negative moral content of pejoratives is a matter of some dispute among identity theorists. But whatever the intuitive appeal of the identity theory for those persuaded by such views, it is nevertheless inconsistent. (shrink)

The norms surrounding pejorative language, such as racial slurs and swear words, are deeply prohibitive. Pejoratives are typically a means for speakers to express their derogatory attitudes. As these attitudes vary along many dimensions and magnitudes, they initially appear to be resistant to a truth-conditional, semantic analysis. The goal of the paper is to clarify the essential linguistic phenomena surrounding pejoratives, survey the logical space of explanatory theories, evaluate each with respect to the phenomena and provide a preliminary assessment of (...) the initial resistance to a truth-conditional analysis. (shrink)

Fictional terms are terms that have null extensions, and in this regard pejorative terms are a species of fictional terms: although there are Jews, there are no kikes. That pejoratives are fictions is the central consequence of the Moral and Semantic Innocence (MSI) view of Hom et al. (2013). There it is shown that for pejoratives, null extensionality is the semantic realization of the moral fact that no one ought to be the target of negative moral evaluation solely in virtue (...) of their group membership. In having null extensions, pejorative terms are much like mythological terms like ‘unicorn horn’ that express concepts with empty extensions, even though it was thought otherwise: people who falsely believed the mythology were mislead into thinking that ordinary objects (i.e. whale tusks) were magical objects, and pejoratives terms work likewise. For example, the term ‘kike’ is supported by the ideology of anti-Semitism, and speakers who fall prey to its influence (perniciously or not) are mislead into thinking that ordinary people (i.e. Jews) are inherently worthy of contempt. In this paper, we explore the consequences of this parallelism, with an eye to criticisms of MSI. In particular, we will re-visit identity expressivist views - those that hold that there are kikes and that they are Jews, and hence deny null extensionality - arguing that this embeds a mistake of fiction for fact. Among the issues to be discussed are the role of fictional truth in understanding pejorative sentences and the relation of the semantics of pejoratives to offensive use of language. We conclude with meta-semantic reflections on the origins of word meanings. (shrink)

Pejoratives are the class of expressions that are meant to insult or disparage. They include swear words and slurs. These words allow speakers to convey emotional states beyond the truth-conditional contents that they are normally taken to encode. The puzzle arises because, although pejoratives seem to be a semantically unified class, some of their occurrences are best accounted for truth-conditionally, while others are best accounted for non-truth-conditionally. Where current, non-truth-conditional, views in the literature fail to provide a unified solution for (...) the puzzle, this paper motivates a novel, semantic, analysis of pejorative language. The significance of the proposed solution is not only linguistic in nature, but also philosophical, as it both provides a new argument for, and sheds further light on, the nature of semantic externalism. (shrink)

Critical congenital heart disease screening is rapidly becoming the standard of care in the United States after being added to the Recommended Uniform Screening Panel in 2011. Newborn screens typically do not require affirmative parental consent. In fact, most states allow parents to exempt their baby from receiving the required screen on the basis of religious or personally held beliefs. There are many ethical considerations implicated with allowing parents to exempt their child from newborn screening for CCHD. Considerations include the (...) treatment of religious exemptions in our current legal system, as well as medical and ethical principles in relation to the rights of infants. Although there are significant benefits to screening newborns for CCHD, when a parent refuses for religious or personal beliefs, in the case of CCHD screening, the parental decision should stand. (shrink)

Juxtaposing Cherríe Moraga's Loving in the War Years and Luce Irigaray's Speculum of the Other Woman, I explore the ways that sex and race intersect to complicate an Irigarayan account of the relations between mother and daughter. Irigaray's work is an effective tool for understanding the disruptive and potentially healing desire between mothers and daughters, but her insistence on sex as primary difference must be challenged in order to acknowledge the intersectionality of sex and race. Working from recent work on (...) the psychoanalysis of race, I argue that whiteness functions as a master signifier in its own right, and as a means of differentiation between the light-skinned Moraga and her brown-skinned mother. Irigaray's concept of blood deepens Moraga's account of her healing and subversive return to her mother. The juxtaposition of Moraga, Irigaray, and contemporary psychoanalysis of race can allow for a necessary revision of Irigaray's psychoanalysis that acknowledges the ways in which sexual difference is indexed by race and sheds new light on her account of the mother–daughter relation. (shrink)

The Negation Problem states that expressivism has insufficient structure to account for the various ways in which a moral sentence can be negated. We argue that the Negation Problem does not arise for expressivist accounts of all normative language but arises only for the specific examples on which expressivists usually focus. In support of this claim, we argue for the following three theses: 1) a problem that is structurally identical to the Negation Problem arises in non-normative cases, and this problem (...) is solved once the hidden quantificational structure involved in such cases is uncovered; 2) the terms ‘required’, ‘permissible’, and ‘forbidden’ can also be analyzed in terms of hidden quantificational structure, and the Negation Problem disappears once this hidden structure is uncovered; 3) the Negation Problem does not arise for normative language that has no hidden quantificational structure. We conclude that the Negation Problem is not really a problem about expressivism at all but is rather a feature of the quantificational structure of the required, permitted, and forbidden. (shrink)

Rebecca Tuvel’s controversial “In Defense of Transracialism” has been criticized for a lack of engagement with critical race theory. Disengagement with salient material on race is a consistent feature of the philosophical conversation out of which it arises. In this article, I trace the origins of feminist philosophy’s disengaged and distorted view of “transracialism” and racial passing through the work of Janice Raymond, Christine Overall, and Cressida Heyes, and consider some of the relevant work on passing that is omitted in (...) the philosophy of “transracialism.” Finally, I offer methodological suggestions to avoid such distortions and omissions in feminist philosophy. (shrink)

Grice introduced generalized conversational implicatures with the following example: "Anyone who uses a sentence of the formX is meeting tz woman this evening would normally implicate that the person to be met was someone other than X’s wife, mother, sister, or perhaps even close platonic friend" (1975 : 37). Concerning this example, he suggested the following account: When someone, by using the form of expression an JQ implicates that the X does not belong to or is not otherwise closely connected (...) with some identifiable person, the implicature is present because the speaker has failed to be specific in a way in which he might have been expected to be specific. (Grice 1975: 38.) Grice went on to sketch an explanation as to why such an implicature should arise, involving the different ways in which we behave towards things that are closely related to.. (shrink)

Hanks develops a theory of propositions as speech-act types. Because speech acts play a role in the contents themselves, the view overturns Frege’s force/content distinction, and as such, faces the challenge of explaining how propositions embed under logical operators like negation. The attempt to solve this problem has lead Hanks and his recent commentators to adopt theoretically exotic resources, none of which, we argue, is ultimately successful. The problem is that although there are three different ways of negating the sentence (...) “Mary’s card is an ace”, current speech-act theories of propositions can only accommodate two of them. We distinguish between “It is false that Mary’s card is an ace”, “Mary’s card is a non-ace”, and “Mary’s card is not an ace” and show that Hanks and his commentators cannot explain content negation. We call this Hanks’ Negation Problem. The problem is significant because content negation is the negation required for logic. Fortunately, we think there is a natural way for Hanks to accommodate content negation as successive acts of predication. The view solves Hanks’ Negation Problem with only resources internal to Hanks’ own view. (shrink)

Although race mixing is often treated as a marginal matter or a transgression against dominant racial logic, this article argues that mixed-race bodies and interracial sexuality are central to the invention of whiteness and the origin of the white settler state in several ways. Race mixing is at the foundation of the modern conception of race; at the material and political origin of the white settler state; and serves as the grounding against which cultural and legal categories of race are (...) articulated. The conceptual history of race looks to mixed-race bodies as the means to define race and delimit races. The colonization and economic success of the white settler state in the United States depended on mixed-race individuals who served as emissaries and interpreters, while interracial sexuality was central to the economy of slavery. Dominant conceptions of whiteness, and of the identity of the white settler state, rely on the scrutiny of mixed bodies as a means of racial demarcation. Mixed race histories and subjects are of central interest to studies of the invention of whiteness and processes of racialization. (shrink)

Moral Victories is the first book-length treatment of the ethical dimensions of victory in war.

Does hindsight knowledge make research seem more ethical and predictable? In line with the notion of hindsight bias, students in 3 experiments knowing the outcome of an animal experiment judged the results as more foreseeable and ethical relative to students who did not know the outcome. Via self to other comparisons, students evaluate themselves more favorably compared to a peer but exhibited hindsight bias in doing so. Uniquely, the findings reveal the possibility that students deem themselves to be more skeptical (...) and objective than their peers. Implications for teaching animal ethics and for Institutional Review Boards are discussed. (shrink)

One of the main criteria for an adequate semantic theory is that it solve the problem of substitution into intensional contexts, otherwise known as Frege's Puzzle. Given common-sense assumptions about how natural language functions, a contradiction arises in explaining attitude reports. For example, Lisa might believe that Twain is tall, but not believe that Clemens is tall. Lisa is perhaps unaware that the names "Twain" and "Clemens" corefer. But Twain's being tall is just Clemens' being tall, so one and the (...) same state of affairs is either believed or not. The tasks are to specify what Lisa believes and to accurately and consistently describe the situation given certain foundational semantic principles. ;I argue that of three main semantic frameworks: Davidsonian Semantics, Model-Theoretic Semantics and Propositional Semantics , PS has the best chance to provide a complete, consistent and natural solution. On my view, dynamic propositions are complex states of affairs where things stand in the propositional relation of having expressions of a certain type which pick them out as semantic values and where those expressions stand in appropriate syntactic relations. The propositional relation crucially involves restricted quantification over expression types which are logical features of the language. The sentences "Twain is tall" and "Clemens is tall" express different DP's because even though their constituents are identical, they stand in distinct propositional relations in virtue of the different syntactic expressions. This explains how Lisa could believe one and not the other. These fine-grained propositions successfully serve as both the truth-conditions of sentences and the objects of propositional attitudes. The solution leads to the surprising result that the question of whether singular terms are Fregean or directly referential is actually irrelevant to Frege's Puzzle. ;While DP's are naturalistic and theoretically well-motivated, they face apparent difficulty accounting for translation and being the objects of mental content. The logical form of DP's limits their possible interpretation and thus sheds light on the conceptual framework of its user. I argue that DP's are not beliefs, but cognitive models that serve as interpretations of beliefs in communication. (shrink)

An interdisciplinary and contemporary response to Irigaray’s work.

Le lecteur moderne demeure dérouté par les ekphraseis de bâtiments des textes byzantins. Il est en effet difficile de les considérer comme des sources pour l'archéologie ou l'Histoire de l'art, et la recherche tend à leur égard à adopter deux approches : l'une, plutôt liée à l'Histoire et à l'Histoire de l'art, s'emploie à retrouver des éléments réels de bâtiments ou d'œuvres d'art dans ces textes ; l'autre, plutôt philologique, cherche à considérer ces textes en eux-mêmes pour leur valeur littéraire. (...) Serait-il cependant possible de chercher une voie médiane? Une voie qui accepterait qu'une part de l'étrangeté de ces textes, nécessairement due à la langue et à l'époque, le soit également parce que l'expérience de lecture entre Moyen Âge et époque moderne a radicalement changé. Il manquerait au lecteur moderne, non l'imagination, mais les mécanismes et les résultats de l'imagination médiévale. Les échos lexicaux et thématiques qui balisent le texte et qui en dessinent l'architecture en seraient la clef aboutiraient à un texte en 3D (trois dimensions), c'est-à-dire une projection mentale de l'objet décrit non pas comme simple image donnée par l'information contenue dans le texte, mais comme image construite par la composition du discours. Ainsi, au fur et à mesure qu'un auteur décrit un bâtiment, le texte le (re)construit en mots et in fine en a épousé la forme. (shrink)

This paper argues that existing food security and food sovereignty approaches are inadequate to fully understand contradictory human development, nutrition, and productivity trends in Nepalese small-scale agriculture. In an attempt to bridge this gap, we developed a new food wellbeing approach that combines insights from food security, food sovereignty, and social wellbeing perspectives. We used the approach to frame 65 semi-structured interviews in a cluster of villages in Kaski district in the mid-hills of Nepal on various aspects of food security, (...) agriculture, off-farm livelihood opportunities, and women’s wellbeing. Our results indicate that context-specific subjective and social relational factors highlighted by the food wellbeing approach are key to understanding a paradox of increased food security, yet decreasing sustainability of small-scale agriculture. Increased levels of male out-migration and opportunities for local off-farm work have increased local capacity to purchase food. The positive consequences for food security are indicated by evidence that households with non-farm income sources had better food sufficiency, absorption capacity, nutritional quality, and stability of food supply. These off-farm employment opportunities have also led to the greater involvement of low caste groups and women in small-scale agriculture. This has been empowering for both groups and led to an increase in wellbeing, particularly for those women who have become de facto heads of household. Yet, small landholdings, persistent patterns of unequal and absentee land ownership, sharecropping, women’s overwork, and the aspirations of low caste farmers and women away from agriculture are simultaneously driving the erosion of local small-scale agricultural productivity and ecological sustainability. (shrink)

In the present paper we concentrate on fundamental problems concerning ω-operations over partial enumerated sets. The notion of “HOM-lifts” seems to be an adequate tool for this kind of investigations. MSC: 03D45, 18A30.

ABSTRACTAnxiety and depression diagnoses are associated with suicidal thoughts and behaviours. However, a categorical understanding of these associations limits insight into identifying dimensional mechanisms of suicide risk. This study investigated anxious and depressive features through a lens of suicide risk, independent of diagnosis. Latent class analysis of 97 depression, anxiety, and suicidality-related items among 616 psychiatric outpatients indicated a 3-class solution, specifically: a higher suicide-risk class uniquely differentiated from both other classes by high reported levels of depression and anxious arousal; (...) a lower suicide-risk class that reported levels of anxiety sensitivity and generalised worry comparable to Class 1, but lower levels of depression and anxious arousal; and a low to non-suicidal class that reported relatively low levels across all depression and anxiety measures. Discriminants of the higher suicide-risk class included borderline personality disorder; report... (shrink)

This volume is fourth in the series of annuals created under the auspices of The Association for Feminist Ethics and Social Theory . The topics covered herein_from peacekeeping and terrorism, to sex trafficking and women's paid labor, to poverty and religious fundamentalism_are vital to women and to feminist movements throughout the world.

This volume is fourth in the series of annuals created under the auspices of The Association for Feminist Ethics and Social Theory (FEAST). The topics covered herein-from peacekeeping and terrorism, to sex trafficking and women's paid labor, to poverty and religious fundamentalism-are vital to women and to feminist movements throughout the world.

Artificial Intelligence-as-a-Service empowers individuals and organisations to access AI on-demand, in either tailored or ‘off-the-shelf’ forms. However, institutional separation between development, training and deployment can lead to critical opacities, such as obscuring the level of human effort necessary to produce and train AI services. Information about how, where, and for whom AI services have been produced are valuable secrets, which vendors strategically disclose to clients depending on commercial interests. This article provides a critical analysis of how AIaaS vendors manipulate the (...) visibility of human labour in AI production based on whether the vendor relies on paid or unpaid labour to fill interstitial gaps. Where vendors are able to occlude human labour in the organisational ‘backstage,’ such as in data preparation, validation or impersonation, they do so regularly, further contributing to ongoing techno-utopian narratives of AI hype. Yet, when vendors must co-produce the AI service with the client, such as through localised AI training, they must ‘lift the curtain’, resulting in a paradoxical situation of needing to both perpetuate dominant AI hype narratives while emphasising AI’s mundane limitations. (shrink)

We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the transfinite. Let \(\bf Ord\) denote the class of all ordinals. Let \(\langle \mathbf{K}_{\alpha}: \alpha\in \bf Ord\rangle\) be a system of varieties definable by a schema. Given any ordinal \(\alpha\), we define an operator \(\mathsf{Nr}_{\alpha}\) that acts on \(\mathbf{K}_{\beta}\) for any \(\beta>\alpha\) giving an algebra in \(\mathbf{K}_{\alpha}\), (...) as an abstaction of taking \(\alpha\)-neat reducts for cylindric algebras. We show that for any positive \(k\), and any infinite ordinal \(\alpha\) that \(\mathbf{S}\mathsf{Nr}_{\alpha}\mathbf{K}_{\alpha+k+1}\) cannot be axiomatized by a finite schema over \(\mathbf{S}\mathsf{Nr}_{\alpha}\mathbf{K}_{\alpha+k}\) given that the result is valid for all finite dimensions greater than some fixed finite ordinal. We apply our results to cylindric algebras and Halmos quasipolyadic algebras with equality. As an application to our algebraic result we obtain a strong incompleteness theorem (in the sense that validitities are not captured by finitary Hilbert style axiomatizations) for an algebraizable extension of \(L_{\omega,\omega}\). (shrink)

Every day, thousands of polls, surveys, and rating scales are employed to elicit the attitudes of humankind. Given the ubiquitous use of these instruments, it seems we ought to have firm answers to what is measured by them, but unfortunately we do not. To help remedy this situation, we present a novel approach to investigate the nature of attitudes. We created a self-transforming paper survey of moral opinions, covering both foundational principles, and current dilemmas hotly debated in the media. This (...) survey used a magic trick to expose participants to a reversal of their previously stated attitudes, allowing us to record whether they were prepared to endorse and argue for the opposite view of what they had stated only moments ago. The result showed that the majority of the reversals remained undetected, and a full 69% of the participants failed to detect at least one of two changes. In addition, participants often constructed coherent and unequivocal arguments supporting the opposite of their original position. These results suggest a dramatic potential for flexibility in our moral attitudes, and indicates a clear role for self-attribution and post-hoc rationalization in attitude formation and change. (shrink)

This paper treats the political and ethical issues associated with the new caretaking technologies. Given the number of feminists who have raised serious concerns about the future of care work in the United States, and who have been critical of the degree to which society “free rides” on women's caretaking labor, I consider whether technology may provide a solution to this problem. Certainly, if we can create machines and robots to take on particular tasks, we may lighten the care burden (...) that women currently face, much of which is heavy and repetitious, and which results in injury and care “burnout” for many female caretakers. Yet, in some contexts, I argue that high-tech robotic care may undermine social relationships, cutting individuals off from the possibility of social connectedness with others. (shrink)

The lifting of lockdown is a typical case of the tragedy of the commons, and as such should be regulated by public authority, instead of being left to the ethics and responsibility of single individuals. I would therefore argue that we should think about an intermediate phase between the lockdown and the opening of shops (which in the Italian case is the transition from the red zone to the orange zone): diversified access to commercial activities, on an hourly basis, for (...) different population groups. This can be achieved either by creating different opening hours for different commercial activities and offices, or by opening them all at the same time but introducing free entrance hours based on age groups of clients. Both solutions would imply an extension of business and office hours, contrary to what has happened in most countries, where an attempt has been made to shorten the days and in some cases, such as in Italy, a curfew has even been introduced at a certain time of the day (in Italy, at 10 pm). (shrink)

In this short paper, we describe another class of forcing notions which preserve measurability of a large cardinal $\kappa$ from the optimal hypothesis, while adding new unbounded subsets to $\kappa$. In some ways these forcings are closer to the Cohen-type forcings—we show that they are not minimal—but, they share some properties with treelike forcings. We show that they admit fusion-type arguments which allow for a uniform lifting argument.

We survey the meta-ethical tools and institutional processes that traditional Islamic ethicists apply when deliberating on bioethical issues. We present a typology of these methodological elements, giving particular attention to the meta-ethical techniques and devices that traditional Islamic ethicists employ in the absence of decisive or univocal authoritative texts or in the absence of established transmitted cases. In describing how traditional Islamic ethicists work, we demonstrate that these experts possess a variety of discursive tools. We find that the ethical responsa—i.e., (...) the products of the application of the tools that we describe—are generally characterized by internal consistency. We also conclude that Islamic ethical reasoning on bioethical issues, while clearly scripture-based, is also characterized by strong consequentialist elements and possesses clear principles-based characteristics. The paper contributes to the study of bioethics by familiarizing non-specialists in Islamic ethics with the role, scope, and applicability of key Islamic ethical concepts, such as “aims” (maqāṣid), “universals” (kulliyyāt), “interest” (maṣlaḥa), “maxims” (qawā`id), “controls” (ḍawābit), “differentiators” (furūq), “preponderization” (tarjīḥ), and “extension” (tafrī`). (shrink)

The Harvard Graduate School of Education convocation speech, praised as "powerful" by Hillary Rodham Clinton in Teen Vogue and "inspired" by Justin Timberlake, that has offered inspiration to millions around the world In Lift Off, Donovan Livingston offers a groundbreaking rallying call about education, race, and the true nature of equality. In emotionally charged spoken-word poetry, Livingston shares a message of hope and hard truths, declaring that education can become an equalizer only if we first acknowledge the inequality and racial (...) divides holding back America's future. Livingston is dedicated to helping young people reach their celestial potential, and in his galvanizing commencement address, now adapted for the first time to the page, he calls on us to raise our voices on behalf of all children, as their brighter futures can light up our own. Together, we can lift off! Praise for Donovan Livingston "Donovan Livingston gave a powerful speech at the Harvard Graduate School of Education's convocation. In a spoken-word poem, he shared his struggles in life and urged his fellow graduates to fight inequality and inspire students. Donovan's message hit home. [He is] part of a rising generation that's. standing up to some of the biggest challenges in the world today."--Hillary Rodham Clinton, Teen Vogue "These are the words, and Donovan Livingston's voice and spirit are the music, but in any form, this rare graduation speech tells us that learning is full of bias yet can lead us to the stars."--Gloria Steinem "Donovan Livingston's Lift Offis our youth's gift to us. In this joyous young man's voice is the promise of tomorrow."--James McBride. (shrink)

We investigate the problem how to lift the non - $\forall \Sigma^b_1(\alpha)$ - conservativity of $T^2_2(\alpha)$ over $S^2_2(\alpha)$ to the expected non - $\forall \Sigma^b_i(\alpha)$ - conservativity of $T^{i+1}_2(\alpha)$ over $S^{i+1}_2(\alpha)$ , for $i > 1$ . We give a non-trivial refinement of the “lifting method” developed in [4,8], and we prove a sufficient condition on a $\forall \Sigma^b_1(f)$ -consequence of $T_2(f)$ to yield the non-conservation result. Further we prove that Ramsey's theorem, a $\forall \Sigma^b_1(\alpha)$ - formula, is not provable (...) in $T^1_2(\alpha)$ , and that $\forall \Sigma^b_j(\alpha)$ - conservativity of $T^{i+1}_2(\alpha)$ over $T^{i}_2(\alpha)$ implies $\forall \Sigma^b_j(\alpha)$ - conservativity of the whole $T_2(\alpha)$ over $T^{i}_2(\alpha)$ , for any $j \geq 2$. (shrink)