This study analyzes the ideals of responsibility and accountability, asking such questions as when it is legitimate to blame top officials of an organization for mistakes made by personnel below them in the bureaucratic hierarchy; when things go wrong in a large and complex organization like the Canadian Forces, who is responsible and accountable; and whether a plea of ignorance is a good excuse. The study also analyzes the doctrine of ministerial responsibility in both the British and Canadian parliamentary traditions, (...) asking whether it is realistic to expect that a government minister should be held responsible for everything that goes wrong in his/her department. Finally, traditional military values are examined, considering the kinds of attitudes and values expected from Canada's armed forces and the differences between the military and civilian sectors. (shrink)

With every σ-ideal I on a Polish space we associate the σ-ideal I* generated by the closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals I and I* and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of (...) the ideal. We also study the 1—1 or constant property of σ-ideals, i.e., the property that every Borel function defined on a Borel positive set can be restricted to a positive Borel set on which it either 1—1 or constant. We prove the following dichotomy: if I is a σ-ideal generated by closed sets, then either the forcing P I adds a Cohen real, or else I has the 1—1 or constant property. (shrink)

Our main result states that a finite iteration of Universal Meager forcing notions adds generic filters for many forcing notions determined by universality parameters. We also give some results concerning cardinal characteristics of the σ-ideals determined by those universality parameters.

We prove that the covering number of the Marczewski ideal is equal to ℵ1 in the extension with the iteration of Hechler forcing.

It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated. This provides (...) a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory. (shrink)

We show that under $\mathsf {BMM}$ and “there exists a Woodin cardinal, $"$ the nonstationary ideal on $\omega _1$ cannot be defined by a $\Pi _1$ formula with parameter $A \subset \omega _1$. We show that the same conclusion holds under the assumption of Woodin’s $(\ast )$ -axiom. We further show that there are universes where $\mathsf {BPFA}$ holds and $\text {NS}_{\omega _1}$ is $\Pi _1(\{\omega _1\})$ -definable. Lastly we show that if the canonical inner model with one Woodin (...) cardinal $M_1$ exists, there is a generic extension of $M_1$ in which $\text {NS}_{\omega _1}$ is saturated and $\Pi _1(\{ \omega _1\} )$ -definable, and $\mathsf {MA_{\omega _1}}$ holds. (shrink)

Given an ideal $I$ , let $\mathbb{P}_{I}$ denote the forcing with $I$ -positive sets. We consider models of forcing axioms $MA(\Gamma)$ which also have a normal ideal $I$ with completeness $\omega_{2}$ such that $\mathbb{P}_{I}\in \Gamma$ . Using a bit more than a superhuge cardinal, we produce a model of PFA (proper forcing axiom) which has many ideals on $\omega_{2}$ whose associated forcings are proper; a similar phenomenon is also observed in the standard model of $MA^{+\omega_{1}}(\sigma\mbox{-closed})$ (...) obtained from a supercompact cardinal. Our model of PFA also exhibits weaker versions of ideal properties, which were shown by Foreman and Magidor to be inconsistent with PFA. Along the way, we also show (1) the diagonal reflection principle for internally club sets ( $\mathit{DRP}(IC_{\omega_{1}})$ ) introduced by the author in earlier work is equivalent to a natural weakening of “there is an ideal $I$ such that $\mathbb{P}_{I}$ is proper”; and (2) for many natural classes $\Gamma$ of posets, $MA^{+\omega_{1}}(\Gamma)$ is equivalent to an apparently stronger version which we call $MA^{+\operatorname{Diag}}(\Gamma)$. (shrink)

Classes of forcings which add a real by forcing with branching conditions are examined, and conditions are found which guarantee that the generic real is of minimal degree over the ground model. An application is made to almost-disjoint coding via a real of minimal degree.

If the Bounded Proper Forcing Axiom BPFA holds, then Mouse Reflection holds at N₂ with respect to all mouse operators up to the level of Woodin cardinals in the next ZFC-model. This yields that if Woodin's ℙ max axiom (*) holds, then BPFA implies that V is closed under the "Woodin-in-the-next-ZFC-model" operator. We also discuss stronger Mouse Reflection principles which we show to follow from strengthenings of BPFA, and we discuss the theory BPFA plus "NS ω1 is precipitous" and (...) strengthenings thereof. Along the way, we answer a question of Baumgartner and Taylor. [2, Question 6.11]. (shrink)

It is shown that cardinals below a real-valued measurable cardinal can be split into finitely many intervals so that the powers of cardinals from the same interval are the same. This generalizes a theorem of Prikry [9]. Suppose that the forcing with a κ-complete ideal over κ is isomorphic to the forcing of λ-Cohen or random reals. Then for some τ<κ, λτ2κ and λ2<κ implies that 2κ=2τ= cov. In particular, if 2κ<κ+ω, then λ=2κ. This answers a question (...) from [3]. If A0, A1,..., An,… are sets of reals, then there are disjoint sets B0, B1,..., Bn,… such that BnAn and μ*=μ* for every n<ω, where μ* is the Lebes gue outer measure. For finitely many sets the result is due to N. Lusin. Let be a σ-centered forcing notion and An ¦n<ω subsets of P witnessing this. If P, An's and the relation of compatibility are Borel, then P adds a Cohen real. The forcing with a κ-complete ideal over a set X, ¦X¦κ cannot be isomorphic to a Hechler real forcing. This result was claimed in [3], but the proof given there works only for X of cardinality κ. (shrink)

We present a version for κ-distributive ideals over a regular infinite cardinal κ of some of the combinatorial results of Mathias on happy families. We also study an associated notion of forcing, which is a generalization of Mathias forcing and of Prikry forcing.

Science is the study of our world, as it is in its messy reality. Nonetheless, science requires idealization to function—if we are to attempt to understand the world, we have to find ways to reduce its complexity. Idealization and the Aims of Science shows just how crucial idealization is to science and why it matters. Beginning with the acknowledgment of our status as limited human agents trying to make sense of an exceedingly complex world, Angela Potochnik moves on to explain (...) how science aims to depict and make use of causal patterns—a project that makes essential use of idealization. She offers case studies from a number of branches of science to demonstrate the ubiquity of idealization, shows how causal patterns are used to develop scientific explanations, and describes how the necessarily imperfect connection between science and truth leads to researchers’ values influencing their findings. The resulting book is a tour de force, a synthesis of the study of idealization that also offers countless new insights and avenues for future exploration. (shrink)

I argue that scientific and poetic modes of objectivity are perspectival duals: 'views' from and onto basic natural forces, respectively. I ground this analysis in a general account of objectivity, not in terms of either 'universal' or 'inter-subjective' validity, but as receptivity to basic features of reality. Contra traditionalists, bare truth, factual knowledge, and universally valid representation are not inherently valuable. But modern critics who focus primarily on the self-expressive aspect of science are also wrong to claim that our knowledge (...) is or should be ultimately mediated by ourselves. In objective science, we represent nature as a field of phenomena determined by and within explanatorily-basic physical structures that encode the causal impact of elemental physical forces. These causally-basic forces hence ground the possibility of objective scientific theory, even though (I argue) they are systematically excluded from its representational contents. I show how my notions of force and field emerge partly through my effort to naturalize concepts of 'God' and 'Laws' in 17th-century natural philosophy. In science, we use the structure of basic forces' impact to see corresponding objects. We do not see these forces themselves—and this relates to the 'transcendence' of 'God'. I supplement this historical analysis by critiquing standard accounts of objectivity, and by synthesizing elements from neo-Kantian epistemology and current 'structural' realism into a view that I call 'dynamic structuralism'. Finally, I argue that physics systematically relies on passive characterizations of phenomena like inertia and impressed force. Dynamic alternatives that are just as empirically adequate are possible, but they are non-scientific. Poetic objectivity involves a direct presentation of nature as an order of interacting forces. I elaborate first by developing a novel theory of the relation between beauty and sublimity, mediated by a basic category of 'sensory force' (e.g. a 'singing' tone in a beautiful melody). I then describe the interaction between sensory and affective dimensions of aesthetic experience, in relation to an original historical analysis of passion and 'disinterestedness' in Kant, Schiller and Nietzsche. I synthesize these lines of analysis into a critique of the role of 'expression' in art. I also resist 'spectator'-centric aesthetics, in this connection, by developing an account of artistic objectivity in dialogue with Ruskin's critique of the 'pathetic fallacy'. I contrast artistic objectivity with Romantic ideals of self-expression, while elaborating its positive relation to certain currents within Victorian and Modernist aesthetics, including Imagists' stress on 'exteriority'. My project creatively extends Nietzsche's view that philosophical and scientific theories are 'perspectival' expressions of theorists' drives. It is a virtue of Nietzsche's account that he takes the outlet of strong human drives in creative acts of theorizing to be just one among many higher modes of 'will to power' in nature—many of which are totally impersonal. But Nietzsche is still too focused on self-expression or willing one's own power. Objective science involves external forces' 'expression' in and through us, not just 'expressing' our own powers. And Nietzsche's vitalistic 'will to power' must be replaced by a basic ontology that better accommodates inorganic phenomena, like the 'lawful' order of celestial motions. Thus I aim to de-anthropomorphize and 'de-organicize' post-Kantian notions of willful striving and organic development, while preserving for force the primary ontological and evaluative status that theorists from Schiller and Goethe to Schelling and Schlegel to Emerson and Nietzsche attributed to will or to life. (shrink)

We show under that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is proper. This answers the question of Khomskii [7, Question 2.6.5]. We also show that the same conclusion holds under if we additionally assume that the set of Borel codes for I‐positive sets is. If we do not assume, the notion of properness becomes obscure as pointed out by Asperó and Karagila [1]. Using the notion of strong properness similar (...) to the one introduced by Bagaria and Bosch [2], we show under without using that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is strongly proper assuming every set of reals is ∞‐Borel and there is no ω1‐sequence of distinct reals. In particular, the same conclusion holds in a Solovay model. (shrink)

This paper explores one way in which the meta-problem may shed light on existing debates about the hard problem (though not directly on the hard problem itself). I'll argue that the possibility of a suitable agent without problem intuitions would undercut the dialectical force of arguments against physicalism. Standard antiphysicalist arguments begin from intuitions about what's ideally conceivable, and argue from there to the falsity of physicalism. For these arguments to be dialectically effective, there must be a shared conception of (...) what ideal conceivability consists in. Unfortunately, proposed accounts of ideal conceivability all make reference to an unexplained 'intuitive' notion of idealization. Consideration of the meta-problem reveals that, when it comes to the hard problem, intuitions about idealization are essentially theory-laden. There is no neutral basis for determining whether agents with or without problem intuitions are more rationally ideal. (shrink)

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$. In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$.

Traditional theories construe approximate truth or truthlikeness as a measure of closeness to facts, singular facts, and idealization as an act of either assuming zero of otherwise very small differences from facts or imagining ideal conditions under which scientific laws are either approximately true or will be so when the conditions are relaxed. I first explain the serious but not insurmountable difficulties for the theories of approximation, and then argue that more serious and perhaps insurmountable difficulties for the theory (...) of idealization force us to sever its close tie to approximation. This leads to an appreciation of lawlikeness as a measure of closeness to laws, which I argue is the real measure of idealization whose main purpose is to carve nature at its joints. (shrink)

We study an extensive connection between quotient forcings of Borel subsets of Polish spaces modulo a σ-ideal and quotient forcings of subsets of countable sets modulo an ideal.

In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.

The relationship between killing ideals and adding reals by forcings is analysed.

This paper offers an interpretation of Spinoza's theory of ideas as a theory of power. The consideration of ideas in terms of force and vitality figures ideology critique as a struggle within the power of thought to give life support to some ideas, while starving others. Because ideas, considered absolutely on Spinoza's terms, are indifferent to human flourishing, they survive, thrive, or atrophy on the basis of their relationship to ambient ideas. Thus, the effort to think and live well requires (...) attention to the collective dimensions of thinking life, where "collective" refers to a transpersonal accumulation of ideal power that includes human as well as nonhuman beings. Because it is a matter of force and power rather than truth and falsity, the project of thinking otherwise entails an effort to displace and to reorganize ideas that is best undertaken by coordinating and galvanizing many thinking powers. (shrink)

This chapter contains sections titled: Notes.

S. A. Lloyd proposes a radically new interpretation of Hobbes's Leviathan that shows transcendent interests - interests that override the fear of death - to be crucial to both Hobbes's analysis of social disorder and his proposed remedy to it. Most previous commentators in the analytic philosophical tradition have argued that Hobbes thought that credible threats of physical force could be sufficient to deter people from political insurrection. Professor Lloyd convincingly shows that because Hobbes took the transcendence of religious and (...) moral interests seriously, he never believed that mere physical force could ensure social order. Lloyd's interpretation demonstrates the ineliminability of that half of Leviathan devoted to religion, and attributes to Hobbes a much more plausible conception of human nature than the narrow psychological egoism traditionally attributed to Hobbes. (shrink)

Forced to Fail traces the long legal history of first racial segregation, and then racial desegregation in America. The authors explain how rapidly changing demographics and family structure in the United States have greatly complicated the project of top-down government efforts to achieve an "ideal" racial balance in schools. It describes how social capital—a positive outcome of social interaction between and among parents, children, and teachers—creates strong bonds that lead to high academic achievement.

We argue that the robustness analysis of idealized models can have confirmational power. This responds to concerns recently raised in the literature, according to which the robustness analysis of models whose idealizations are not discharged is unable to confirm the causal mechanisms underlying these models, and the robustness analysis of models whose idealizations are discharged is unnecessary. In response, we make clear that, where idealizations sweep out, in a specific way, the space of possibilities— which is sometimes, though not always, (...) the case—they can be holistically discharged. In turn, this can be used to show that the robustness analysis of idealized models can have confirmational force after all. (shrink)

The two ideals referred to are the ideal of the just state and the ideal of responsible agency. The view of Kant was that not every civil state could rightfully take the life of those that commit murder because not every civil state recognises the freedom, equality, and independence of citizens in the idealised civil state envisioned by Kant. The question is whether the death penalty can be justified in a properly constituted state even if most of the (...) civil states in the world that apply the death penalty are guilty of injustice. Kant's argument does not support the death penalty for even the worst crimes if it is unjustly legislated or unjustly administered. These arguments add weight to arguments against the death penalty. The more severe the penalty, the stronger the safeguards ought to be against its wrongful imposition. In addition to the just state, the ideal of responsible agency impinges on the death penalty. People are able to satisfy the ideal of responsible agency only if they rise above the threshold for being minimally responsible or if they rise above the threshold for being able to be held responsible. They must be able to take --by claiming-- responsibility. The ideal of responsible agency governs not only the execution of intention, but also deliberation before and after the action. A willingness to take the consequences is necessary for full-blown responsible agency. The worldly ideal does not rule out the death penalty because even in an imperfect world it does not cancel out the force of the ideal of responsible agency. (shrink)

Moore introduced the Mapping Reflection Principle and proved that the Bounded Proper Forcing Axiom implies that the size of the continuum is ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\aleph _2$$\end{document}. The Mapping Reflection Principle follows from the Proper Forcing Axiom. To show this, Moore utilized forcing notions whose conditions are countable objects. Chodounský–Zapletal introduced the Y-Proper Forcing Axiom that is a weak fragments of the Proper Forcing Axiom but implies some important conclusions (...) from the Proper Forcing Axiom, for example, the P-ideal Dichotomy. In this article, it is proved that the Y-Proper Forcing Axiom implies the Mapping Reflection Principle by introducing forcing notions whose conditions are finite objects. (shrink)

Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set (...) of indices of the required subsequence should be in a fixed ideal ${{\mathcal{J}}}$ on ω. We introduce the notion of the ${{\mathcal{J}}}$ -covering property of a pair ${({\mathcal{A}}, I)}$ where ${{\mathcal{A}}}$ is a σ-algebra on a set X and ${{I \subseteq \mathcal{P}(X)}}$ is an ideal. We present some counterexamples, discuss the category case and the Fubini product of the null ideal ${\mathcal{N}}$ and the meager ideal ${\mathcal{M}}$ . We investigate connections between this property and forcing-indestructibility of ideals. We show that the family of all Borel ideals ${{\mathcal{J}}}$ on ω such that ${\mathcal{M}}$ has the ${{\mathcal{J}}}$ -covering property consists exactly of non weak Q-ideals. We also study the existence of smallest elements, with respect to Katětov–Blass order, in the family of those ideals ${\mathcal{J}}$ on ω such that ${\mathcal{N}}$ or ${\mathcal{M}}$ has the ${\mathcal{J}}$ -covering property. Furthermore, we prove a general result about the cases when the covering property “strongly” fails. (shrink)

In this paper, I explore how the ideal rationality-based account of propositional justification impacts our understanding of the relation between propositional and doxastic justification. The ideal rationality-based account sits uncomfortably with the widely accepted claim that propositional justification is necessary for doxastic justification. In particular, the combination of the necessity claim and the ideal rationality-based account of propositional justification entails that some plausible doxastic attitudes are doxastically unjustified and thereby severs epistemic justification from connections with epistemic responsibility (...) and the competent formation of beliefs. Thus, those who endorse both the necessity claim and the ideal rationality-based account of propositional justification will be forced to give up either their account of propositional justification or the necessity claim. I argue that there is good reason to give up the ideal rationality-based account of propositional justification instead of the necessity claim. This result indicates that an adequate account of propositional justification should be sensitive to the agent’s cognitive capacities. If propositional justification should be understood in this way, then the widely accepted explanation of doxastic justification in terms of propositional justification is not promising either. This is because an agent’s cognitive capacities and limitations play a prominent role in understanding propositional justification. Instead, I argue that, at the explanatory level, propositional justification relies on doxastic justification. (shrink)

Suppose that T^∗ is an ω_1-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA(T^∗) for proper forcings which preserve these properties of T^∗. We prove that PFA(T^∗) implies many of the strong consequences of PFA, such as the failure of very weak club guessing, that all of the cardinal characteristics of the continuum are greater than ω_1, and the P-ideal dichotomy. On the other hand, PFA(T^∗) implies some of the consequences of diamond principles, such as (...) the existence of Knaster forcings which are not stationarily Knaster. (shrink)

Contemporary public reason liberalism holds that coercion must be publicly justified to an idealized constituency. Coercion must be justified to all qualified points of view, not the points of view held by actual persons. Critics, in particular Nicholas Wolterstorff and David Enoch, have complained that idealization, by idealizing away what actual people accept, risks authoritarianism and disrespect by forcing people to comply with laws they in fact reject. I argue that idealization can withstand this criticism if it satisfies two (...) conditions. First, the standards of idealization, such as the norms of rationality and information, must be grounded in the present commitments of the large majority of members of the public. Second, the standards of idealization must be moderate; that is, they cannot be used to attribute reasons to citizens that stray too far from their actual commitments. (shrink)

The main purpose of this dissertation is to apply and develop new forcing techniques to obtain models where several cardinal characteristics are pairwise different as well as force many (even more, continuum many) different values of cardinal characteristics that are parametrized by reals. In particular, we look at cardinal characteristics associated with strong measure zero, Yorioka ideals, and localization and anti-localization cardinals.In this thesis we introduce the property “F-linked” of subsets of posets for a given free filter F on (...) the natural numbers, and define the properties “ $\mu $ -F-linked” and “ $\theta $ -F-Knaster” for posets in a natural way. We show that $\theta $ -F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. These kinds of posets led to the development of a general technique to construct $\theta $ - $\textrm {Fr}$ -Knaster posets (where $\textrm {Fr}$ is the Frechet ideal) via matrix iterations of ${<}\theta $ -ultrafilter-linked posets (restricted to some level of the matrix). The latter technique allows proving consistency results about Cichoń’s diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal characteristics associated with it are pairwise different. Another important application is to show that three strongly compact cardinals are enough to force that Cichoń’s diagram can be separated into 10 different values. Later on, it was shown by Goldstern, Kellner, Mejía, and Shelah that no large cardinals are needed for Cichoń’s maximum (J. Eur. Math. Soc. 24 (2022), no. 11, p. 3951–3967).On the other hand, we deal with certain types of tree forcings including Sacks forcing, and show that these increase the covering of the strong measure zero ideal $\mathcal {SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal characteristics of the continuum. Even more, Sacks forcing can be used to force that $\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$, which is the first consistency result where more than two cardinal characteristics associated with $\mathcal {SN}$ are pairwise different. To obtain another result in this direction, we provide bounds for $\operatorname {\mathrm{cof}}(\mathcal {SN})$, which generalizes Yorioka’s characterization of $\mathcal {SN}$ (J. Symbolic Logic 67.4 (2002), p. 1373–1384). As a consequence, we get the consistency of $\operatorname {\mathrm{add}}(\mathcal {SN})=\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$ with ZFC (via a matrix iteration forcing construction).We conclude this thesis by combining creature forcing approaches by Kellner and Shelah (Arch. Math. Logic 51.1–2 (2012), p. 49–70) and by Fischer, Goldstern, Kellner, and Shelah (Arch. Math. Logic 56.7–8 (2017), p. 1045–1103) to show that, under CH, there is a proper $\omega ^\omega $ -bounding poset with $\aleph _2$ -cc that forces continuum many pairwise different cardinal characteristics, parametrized by reals, for each one of the following six types: uniformity and covering numbers of Yorioka ideals as well as both kinds of localization and anti-localization cardinals, respectively. This answers several open questions from Klausner and Mejía (Arch. Math. Logic 61 (2022), pp. 653–683).Abstract prepared by Miguel Antonio Cardona-MontoyaE-mail: [email protected]: https://repositum.tuwien.at/handle/20.500.12708/19629. (shrink)

In the debate at the end of the Enlightenment over the place of armed forces and war in society, Johannes [von] Müller's Histories of the Swiss attracted attention as a work of historical interpretation and as a political statement. Müller's idealization of the free "people in arms" is contrasted with Clausewitz's argument that ideals and self-interest contrary to the ideals may be expressed simultaneously by individuals and societies, both qualities made historically effective by people's innate willingness to use violence. Müller's (...) and Clausewitz's positions are paradigmatic of views that continue to influence historical interpretations and political expectations to this day. (shrink)

This paper considers prominent forms of discourse in educational research, the nature of their appeal and the force of the idea of freedom within that appeal. For this, two different aspects of research are juxtaposed, aspects in which the value of freedom is articulated in contrasting ways. First, evidence-based education is considered as a prominent manifestation of faith in scientific method in education: in this, it might be said, there is an obsession with freedom – the freedom of the research (...) from bias. Second, and by contrast, in humanistic forms of educational research, freedom assumes a position of central importance, in the idea of autonomy. Here are two contrasting ethical priorities, respectively, the supposed neutrality that is achieved by excising individual judgement, and the vision of the good life that prioritises the rational exercise of that judgement. In this paper, I wish to discuss the kind of aura that is attached to these ideas, embedded as they are in a western metap... (shrink)

The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been (...) strong enough! However, with his celebrated work on generalised side conditions, I. Neeman introduced us to a novel paradigm to iterate forcings. In particular, he could, among other things, reprove the consistency of the Proper Forcing Axiom using an iterated forcing with finite supports. In 2015, using his technology of virtual models, Veličković built up an iteration of semi-proper forcings with finite supports, hence reproving the consistency of Martin’s Maximum, an achievement leading to the notion of a virtual model.In this thesis, we are interested in constructing forcing notions with finitely many virtual models as side conditions to preserve three uncountable cardinals. The thesis constitutes six chapters and three appendices that amount to 118 pages, where Section 1 is devoted to preliminaries, and Section 2 is a warm-up about the scaffolding poset of a proper forcing. In Section 3, we present the general theory of virtual models in the context of forcing with sets of models of two types, where we, e.g., define the “meet” between two virtual models and prove its properties.The main results are joint with Boban Veličković, and partly appeared in Guessing models and the approachability ideal, J. Math. Log. 21 (2021).Pure Side Conditions. In Section 4, we use two types of virtual models (countable and large non-transitive ones induced by a supercompact cardinal, which we call Magidor models) to construct our forcing with pure side conditions. The forcing covertly uses a third type of models that are transitive. We also add decorations to the conditions to add many clubs in the generic $\omega _2$. In contrast to Neeman’s method, we do not have a single chain, but $\alpha $ -chains, for an ordinal $\alpha $ with $V_\alpha \prec V_\lambda $. Thus, starting from suitable large cardinals $\kappa <\lambda $, we construct a forcing notion whose conditions are finite sets of virtual models described earlier. The forcing is strongly proper, preserves $\kappa $, and has the $\lambda $ -Knaster property. The relevant quotients of the forcing are strongly proper, which helps us prove strong guessing model principles. The construction is generalisable to a ${<}\mu $ -closed forcing, for any given cardinal $\mu $ with $\mu ^{<\mu }=\mu <\kappa $.The Iteration Theorem. In Section 5, we use the forcing with pure side conditions to iterate a subclass of proper and $\aleph _2$ -c.c. forcings and obtain a forcing axiom at the level of $\aleph _2$. The iterable class is closely related to Asperó–Mota’s forcing axiom for finitely proper forcings.Guessing Model Principles. Section 6 encompasses the main parts of the thesis. We prove the consistency of the guessing principle $\mathrm {GMP}^+(\omega _3,\omega _1)$ that states for any cardinal ${\theta \geq \omega _3}$, the set of $\aleph _2$ -sized elementary submodels M of $H(\theta )$, which are the union of an $\omega _1$ -continuous $\in $ -chain of $\omega _1$ -guessing, I.C. models is stationary in $\mathcal P_{\omega _3}(H(\theta ))$. The consistency and consequences of this principle are demonstrated in the following diagram. We also prove that one can obtain the above guessing models in a way that the $\omega _1$ -sized $\omega _1$ -guessing models remain $\omega _1$ -guessing model in any outer transitive model with the same $\omega _1$, and we denote this principle by $\rm{SGMP}^+(\omega_3,\omega_1)$.In the following diagram, $\mathrm{TP}$ stands for the tree property; $w\mathrm{KH}$ stands for the weak Kurepa Hypothesis; $\mathrm{MP}$ stands for Mitchell property, i.e., the approachability ideal is trivial modulo the nonstationary ideal; $\mathrm{AP}$ stands for the approachability property; $\mathrm {AMTP}(\kappa ^+)$ states that if $2^\kappa <\aleph _{\kappa ^+}$, then every forcing which adds a new subset of $\kappa ^+$ whose initial segments are in the ground model, collapses some cardinal $\leq 2^{\kappa }$. The dotted arrow denotes the relative consistency, while others are logical implications.Appendices. Appendix A includes merely the above diagram. Appendix B presents a proof of the Mapping Reflection Principle with finite conditions under $\mathrm {PFA}$. Appendix C contains open problems. Finally, the thesis’s bibliography consists of 42 items.Abstract prepared by Rahman MohammadpourE-mail: [email protected]: https://theses.hal.science/tel-03209264. (shrink)