We explore the consistency strength of Σ 3 1 and Σ 4 1 absoluteness, for a variety of forcing notions.

We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to $\mathsf {DC}$ -preserving symmetric submodels of forcing extensions. Hence, $\mathsf {ZF}+\mathsf {DC}$ not only provides the right framework for developing classical analysis, but is also the right base theory over which to safeguard truth in analysis from the independence phenomenon in the (...) presence of large cardinals. We also investigate some basic consequences of the Proper Forcing Axiom in $\mathsf {ZF}$, and formulate a natural question about the generic absoluteness of the Proper Forcing Axiom in $\mathsf {ZF}+\mathsf {DC}$ and $\mathsf {ZFC}$. Our results confirm $\mathsf {ZF} + \mathsf {DC}$ as a natural foundation for a significant portion of “classical mathematics” and provide support to the idea of this theory being also a natural foundation for a large part of set theory. (shrink)

We show that Bounded Forcing Axioms (for instance, Martin's Axiom, the Bounded Proper Forcing Axiom, or the Bounded Martin's Maximum) are equivalent to principles of generic absoluteness, that is, they assert that if a $\Sigma_1$ sentence of the language of set theory with parameters of small transitive size is forceable, then it is true. We also show that Bounded Forcing Axioms imply a strong form of generic absoluteness for projective sentences, namely, if a $\Sigma^1_3$ sentence with (...) parameters is forceable, then it is true. Further, if for every real x, $x^{\sharp}$ exists, and the second uniform indiscernible is less than $\omega_2$ , then the same holds for $\Sigma^1_4$ sentences. (shrink)

Ontological pluralism is the view that there are different fundamental ways of being. Trenton Merricks has recently raised three objections to combining pluralism with a generic way of being enjoyed by absolutely everything there is: first, that the resulting view contradicts the pluralist’s core intuition; second, that it is especially vulnerable to the charge—due to Peter van Inwagen—that it posits a difference in being where there is simply a difference in kind; and, third, that it is in tension with (...) various historically influential motivations for pluralism. I reply to each of these objections in turn. My replies will help to bring out the true nature of the pluralist’s basic commitments. (shrink)

The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veličković. We introduce a stronger form of resurrection axioms for a class of forcings Γ and a given ordinal α), and show that RAω implies generic absoluteness for the first-order theory of Hγ+ with respect to forcings in Γ preserving the axiom, where γ = γΓ is a cardinal which depends on Γ. We also prove that the consistency strength of (...) these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. Moreover, we outline that simultaneous generic absoluteness for Hγ0+ with respect to Γ0 and for Hγ1+ with respect to Γ1 with γ0 = γΓ0≠γΓ1 = γ1 is in principle possible, and we present several natural models o... (shrink)

In this paper we study generic complexity of undecidable problems. It turns out that some classical undecidable problems are, in fact, strongly undecidable, i.e., they are undecidable on every strongly generic subset of inputs. For instance, the classical Halting Problem is strongly undecidable. Moreover, we prove and analog of the Rice theorem for strongly undecidable problems, which provides plenty of examples of strongly undecidable problems. Then we show that there are natural super-undecidable problems. i.e., problem which are undecidable (...) on every generic (not only strongly generic) subset of inputs. In particular, there are finitely presented semigroups with super-undecidable word problem. To construct strongly- and super-undecidable problems we introducea method of generic amplification (an analog of the amplification in complexity theory). Finally, we construct absolutely undecidable problems, which stay undecidable on every non-negligible set of inputs. Their construction rests on generic immune sets. (shrink)

In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.

Hospital chaplaincy, in its exposure to clients, colleagues, and care-takers from different faith backgrounds, can be understood in either generic or catholic terms. The first understanding, often merely implicit in denominationalist approaches, assumes that some “Absolute” can be prayerfully invoked through the medium of diverse rituals, confessions, and symbols. This position combines the advantage of unprejudiced acceptance of other creeds and traditions with the disadvantage of lacking resources for discriminating among the spiritualities that may be operative within those other (...) creeds and traditions. Catholicism, in linking true spirituality with the one true church as the mystical body of the Tri-une God, secures such a criterion but fails to satisfy the tolerance-of-acknowledgement in the secular sense, which is canonical in contemporary ecumenism. The Orthodox understanding of Catholicism is portrayed as imposing a non-judgemental humility and repentance which provides a solution to that spiritual-human dilemma of inter-faith cooperation in the hospital. (shrink)

Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type , are equal at any given instance A[T], then they are equal at all instances. They proved that this rule is admissible in a certain extension of System F, but finding (...) a semantically motivated model satisfying this principle remained an open problem.In the present paper, we construct a categorical model of polymorphism, based on game semantics, which contains a large collection of generic types. This model builds on two novel constructions:•A direct interpretation of variable types as games, with a natural notion of substitution of games. This allows moves in games A[T] to be decomposed into the generic part from A, and the part pertaining to the instance T. This leads to a simple and natural notion of generic strategy.•A “relative polymorphic product” which expresses quantification over the type variable Xi in the variable type A with respect to a “universe” which is explicitly given as an additional parameter B. We then solve a recursive equation involving this relative product to obtain a universe in a suitably “absolute” sense.Full Completeness for ML types is proved for this model. (shrink)

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite subsets (...) of $\omega $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

Marie Stenlund’s careful reading of values-based practice and her demonstration of its links with Martha Nussbaum’s Capabilities Framework are innovative theoretically and have potentially important implications for policy and practice in mental health. As she indicates the two approaches converge in a number of key respects. Notably, both recognise the diversity of individual human values. This diversity crucially underpins contemporary person-centred conceptions of recovery in mental health based on quality of life as defined by reference to the values of the (...) person concerned rather than that of a generic professional ‘needs assessment’.1 2 Where the two theories diverge, too, Stenlund finds practically important consequences. Thus Nussbaum’s Capabilities Framework, as Stenlund indicates, is outcomes-oriented, while values-based practice focuses on process. The two approaches are not however thereby necessarily inconsistent. Drawing on early accounts of values-based practice, Stenlund suggests a degree of implicit blurring between it and Nussbaum’s capabilities. Here we need to be careful: values-based practice does not regard recovery as an outcome; it …. (shrink)

In addition to the familiar cardinal and proportional readings of many and few, there is yet another interpretation, the relative proportional reading. This reading, unlike the ordinary absolute proportional reading, is not conservative. Under the relative reading, 'Many ψs are φs' is true just in case the proportion of φs among ψs is greater than the proportion of φs among members of contextually given alternatives to ψ. I provide a definition of proportional readings that reduces the differences between absolute and (...) relative interpretations to the value of a single parameter.I argue that relative readings are not restricted to many and few, but are also exhibited by the adverbs often and seldom, and by generics. Interpretations of determiners that have been treated as "focus-affected readings," interpretations of adverbs of quantification that have been treated as "pure frequency readings," and interpretations of generics which have been claimed to be cases of "reverse interpretation" or "direct kind predication" are, in fact, instances of relative readings.A: Army reserve service is especially hard on people who own a small business.Q: Do many small-business owners serve in your regiment?A: I don't know what it's like in other regiments –Q: I am not asking you about other regiments.A: I know, but relatively speaking . . .(Interview on Israel Army Radio, June 8th, 2001). (shrink)

This article rejects the claim that human beings are religious by nature. This rejection is controversial. It is always said by catholic and protestant philosophers and theologians that human beings are religious by nature. Schleiermacher holds that the feeling of absolute dependence does not define religion, but it is the defining characteristic that makes a certain phenomenon a religiousone. This defining characteristic is borrowed from christian faith in the one God the creator. I raise two questions: 1. how does Schleiermacher (...) judge non-monotheistic religions in which the feeling of absolute dependence is vague 2. how does he judge non-believers who reject religion? As far as the first question is concerned Schleiermacher broadens his conception of religion in such a way that non-monotheistic religions are included. In fact he says that such people should become religious in the sense of having a pure feeling of absolute dependence. Factually, they have not. That is why in my opinion the feeling of absolute dependence is too limited to serve as a general denominator for religions. With regard to the second question Schleiermacher calls the relatedness of the sensible consciousness to the higher self-consciousness, the feeling of absolute dependence, the consummating point of the self-consciousness. In other words: unbelief is a disturbance in the development of the person. If one holds that view, those who are indifferent to religion cannot be equal partners in public discussion. The generic view of religion does not do justice to the unbeliever. He or she is considered as a prodigal son or daughter. Can these two objections of the generic conception of religion be met? Wilfred Cantwell Smith and Paul Tillich can meet the first one. They enlarge the defining characteristic of religion and consider it as faith or ultimate concern. My second objection can hardly be met. Tillich and John Smith tried by means of the conception of ‘quasi-religion’. I have my reservations and agree, that in Tillich and in John Smith secular worldviews are reduced to a form of wrong religiosity or are labelled as nihilism. A generic view of religion is of little or no use for public debate in the contemporary secular culture. With Schleiermacher I hold that religion is an irreducible given and not merely a coincidence. In the interest of a peaceful coexistence in a pluralistic society one needs to seek a generic element to which all people can agree. That generic element is worldview. I mean worldview as an anthropological category. It expresses the integrating and unifying character of our experience. All people have such a worldview as human beings. What worldview – marxism, humanism or a fragmented general worldview – they actually have is a contingent matter. When I substitute the claim that worldview is generic for the generic conception of religion, I do not mean that it is a matter of indifference as to whether one has a religious or a secular worldview. That is why, finally, something needs to be said about further justification of religion. Following Schleiermacher this does not consist of proofs of God or of historical arguments. It concerns the explication of the rationality of faith experience. For a peaceful coexistence between people with different worldviews, mutual dialogue is indispensable. (shrink)

We study the preservation under projective ccc forcing extensions of the property of L(ℝ) being a Solovay model. We prove that this property is preserved by every strongly-̰Σ₃¹ absolutely-ccc forcing extension, and that this is essentially the optimal preservation result, i.e., it does not hold for Σ₃¹ absolutely-ccc forcing notions. We extend these results to the higher projective classes of ccc posets, and to the class of all projective ccc posets, using definably-Mahlo cardinals. As a consequence we obtain an exact (...) equiconsistency result for generic absoluteness under projective absolutely-ccc forcing notions. (shrink)

We study the preservation of the property of being a Solovay model under proper projective forcing extensions. We show that every strongly-proper forcing notion preserves this property. This yields that the consistency strength of the absoluteness of under strongly-proper forcing notions is that of the existence of an inaccessible cardinal. Further, the absoluteness of under projective strongly-proper forcing notions is consistent relative to the existence of a -Mahlo cardinal. We also show that the consistency strength of the (...) class='Hi'>absoluteness of under forcing extensions with σ-linked forcing notions is exactly that of the existence of a Mahlo cardinal, in contrast with the general ccc case, which requires a weakly-compact cardinal. (shrink)

This article attempts a subjectively based approach, in fact one phenomenologically motivated, toward some key concepts of forcing theory, primarily the concepts of a generic set and its global properties and the absoluteness of certain fundamental relations in the extension to a forcing model M[G]. By virtue of this motivation and referring both to the original and current formulation of forcing I revisit certain set-theoretical notions serving as underpinnings of the theory and try to establish their deeper subjectively (...) founded content and also their influence in reaching relative consistency results by the forcing method. In this perspective, the present approach may be seen as offering an alternative view of the consistency results of K. Gödel and P. Cohen in mathematical foundations reaching a subjective level that may be taken as ultimately conditioning the non-decidability of key infinity statements on the level of formal theory. (shrink)

We present several results relating the general theory of the stationary tower forcing developed by Woodin with forcing axioms. In particular we show that, in combination with class many Woodin cardinals, the forcing axiom MM++ makes the Π2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_2}$$\end{document}-fragment of the theory of Hℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\aleph_2}}$$\end{document} invariant with respect to stationary set preserving forcings that preserve BMM. We argue that this is a promising generalization to (...) Hℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\aleph_2}}$$\end{document} of Woodin’s absoluteness results for L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document}. In due course of proving this, we shall give a new proof of some of these results of Woodin. Finally we relate our generic absoluteness results with the resurrection axioms introduced by Hamkins and Johnstone and with their unbounded versions introduced by Tsaprounis. (shrink)

We prove that various classical tree forcings—for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing—preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic absoluteness holds and no new equivalence classes are added to thin projective transitive relations by these forcings.

This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework linking Woodin’s generic absoluteness results for second order number theory and the theory of universally Baire sets to model companionship and show that (with the required care in details) a $$\Pi _2$$ -property formalized in an appropriate language for second order (...) number theory is forcible from some $$T\supseteq \mathsf {ZFC}+$$ large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T. In particular we show that the first order theory of $$H_{\omega _1}$$ is the model companion of the first order theory of the universe of sets assuming the existence of class many Woodin cardinals, and working in a signature with predicates for $$\Delta _0$$ -properties and for all universally Baire sets of reals. We will extend these results also to the theory of $$H_{\aleph _2}$$ in a follow up of this paper. (shrink)

We consider several kinds of partition relations on the set ${\mathbb{R}}$ of real numbers and its powers, as well as their parameterizations with the set ${[\mathbb{N}]^{\mathbb{N}}}$ of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness, that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing extensions, which yields, for instance, that in these models for every (...) well ordered partition of ${\mathbb{R}^\mathbb{N}}$ there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition of ${[\mathbb{N}]^{\mathbb{N}} \times \mathbb{R}^{\mathbb{N}}}$ there is ${X \in [\mathbb{N}]^{\mathbb{N}}}$ and a sequence ${\{P_{k} : k \in \mathbb{N}\}}$ of perfect sets such that the product ${[X]^{\mathbb{N}} \times \prod_{k}^{\infty}P_{k}}$ lies in one piece of the partition, where ${[X]^{\mathbb{N}}}$ is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness. (shrink)

Let κ be a cardinal, and let H κ be the class of sets of hereditary cardinality less than κ ; let τ (κ) > κ be the height of the smallest transitive admissible set containing every element of {κ}∪H κ . We show that a ZFC-definable notion of long unfoldability, a generalisation of weak compactness, implies in the core model K, that the mouse order restricted to H κ is as long as τ. (It is known that some weak (...) large cardinal property is necessary for the latter to hold.) In other terms we delimit its strength as follows: Theorem Con(ZFC+ω2-Π 1 1-Determinacy) ⇒ ⇒Con(ZFC+V=K+∃ a long unfoldable cardinal ⇒ ⇒Con(ZFC+∀X(X # exists) + ‘‘ $\forall D \subseteq \omega_1 D$ is universally Baire ⇔ ∃r∈R(D∈L(r)))’’, and this is set-generically absolute). We isolate a notion of ω-closed cardinal which is weaker than an ω1-Erd\ os cardinal, and show that this bounds the first long unfoldable: Theorem Let κ be ω -closed. Then there is a long unfoldable ł<κ. (shrink)

A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. ${\sf Sealing}$ is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by set forcings. The ${\sf Largest\ Suslin\ Axiom}$ is a determinacy axiom isolated by Woodin. It asserts that the largest Suslin cardinal is inaccessible for ordinal definable surjections. Let ${\sf LSA}$ (...) - ${\sf over}$ - ${\sf uB}$ be the statement that in all generic extensions there is a model of $\sf {LSA}$ whose Suslin, co-Suslin sets are the universally Baire sets. We outline the proof that over some mild large cardinal theory, $\sf {Sealing}$ is equiconsistent with $\sf {LSA}$ - $\sf {over}$ - $\sf {uB}$. In fact, we isolate an exact theory that is equiconsistent with both. As a consequence, we obtain that $\sf {Sealing}$ is weaker than the theory “ $\sf {ZFC}$ + there is a Woodin cardinal which is a limit of Woodin cardinals.” This significantly improves upon the earlier consistency proof of $\sf {Sealing}$ by Woodin. A variation of $\sf {Sealing}$, called $\sf {Tower \ Sealing}$, is also shown to be equiconsistent with $\sf {Sealing}$ over the same large cardinal theory. We also outline the proof that if V has a proper class of Woodin cardinals, a strong cardinal, and a generically universally Baire iteration strategy, then $\sf {Sealing}$ holds after collapsing the successor of the least strong cardinal to be countable. This result is complementary to the aforementioned equiconsistency result, where it is shown that $\sf {Sealing}$ holds in a generic extension of a certain minimal universe. This theorem is more general in that no minimal assumption is needed. A corollary of this is that $\sf {LSA}$ - $\sf {over}$ - $\sf {uB}$ is not equivalent to $\sf {Sealing}$. (shrink)

We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma _{1}$ -definability at uncountable regular cardinals. In particular we give its exact consistency strength first in terms of the second uniform indiscernible for bounded subsets of $\kappa $ : $u_2$, and secondly to give the consistency strength of a property of Lücke’s.TheoremThe following are equiconsistent:There exists $\kappa $ which is stably measurable;for some cardinal $\kappa $, $u_2=\sigma $ ;The $\boldsymbol {\Sigma }_{1}$ -club property holds (...) at a cardinal $\kappa $.Here $\sigma $ is the height of the smallest $M \prec _{\Sigma _{1}} H $ containing $\kappa +1$ and all of $H $. Let $\Phi $ be the assertion: TheoremAssume $\kappa $ is stably measurable. Then $\Phi $.And a form of converse:TheoremSuppose there is no sharp for an inner model with a strong cardinal. Then in the core model K we have: $\mbox {``}\exists \kappa \Phi \mbox {''}$ is -generically absolute ${\,\longleftrightarrow \,}$ There are arbitrarily large stably measurable cardinals.When $u_2 < \sigma $ we give some results on inner model reflection. (shrink)

In recent work on context­dependency, it has been argued that certain types of sentences give rise to a notion of relative truth. In particular, sentences containing predicates of personal taste and moral or aesthetic evaluation as well as epistemic modals are held to express a proposition (relative to a context of use) which is true or false not only relative to a world of evaluation, but other parameters as well, such as standards of taste or knowledge or an agent. Thus, (...) a sentence like chocolate tastes good would express a proposition p that is true or false not only at a world of evaluation, but relative to the additional parameter as well, such as a parameter of taste or an agent. I will argue that the sentences that apparently give rise to relative truth should be understood by relating them in a certain way to the first person. More precisely, such sentences express what I will call first­person­based genericity, a form of generalization that is based on or directed toward an essential first­person application of the predicate. The account differs from standard relative truth account in crucial respects: it is not the truth of the proposition expressed that is relative to the first person; the proposition expressed by a sentence with a predicate of taste rather has absolute truth conditions. Instead it is the propositional content itself that requires a first­personal cognitive access whenever it is entertained. This account, I will argue, avoids a range of problems that standard relative truth theories of the sentences in question face and explains a number of further peculiarities that such sentences display. (shrink)

This article develops an interpretation of Hegel that aims to show how a proper understanding of the nature of speculative sentences might achieve what Kant set out to do: to vindicate our most fundamental claims to knowledge as actual knowledge, rather than mere acts of believing. To this end, it develops a conception of speculative geographies (or “maps”) as an interpretive tool and introduces an Hegelian-inspired distinction between empirical, generic, and speculative sentences. On this reading, Kant’s employment of the (...) “boundary concept” of a noumenon is bound to fail as it needs to employ a contrast between our human point of view and that of an omniscient God – which turns out to be an aperspectival “view from nowhere” and thus an incoherent notion. The artcile ends by suggesting ways in which Hegel’s logical analysis can help us to better comprehend the reflective ascent necessary to make our conceptual differentiations and typical ways of understanding intelligible to ourselves. (shrink)

In this paper, I will give a new characterisation of the spaces of complete theories of pseudofinite fields and of algebraically closed fields with a generic automorphism (ACFA) in terms of the Vietoris topology on absolute Galois groups of prime fields.

Although they cannot give absolute certification to moral judgment, the virtues provide a foundation for thought and action in real circumstances. Gouinlock begins his discussion by presenting some of the most fateful traits of existence, from which he proceeds to more specific analyses. He presents the problems of fact and value in a new and vivid light while giving moral discourse original and refreshingly constructive attention. In addition, there is penetrating analysis of the origins of moral values in the conditions (...) of the moral life. Drawing from research in the behavioral sciences, Gouinlock points out the multiple uses of knowledge of human nature in moral reflection and action. He then sets forth the nature of the virtues that are most suitable for contending with these generic conditions. Throughout, Gouinlock draws upon many sources of wisdom in the history of philosophy while laying bare the futilities of contemporary theories. (shrink)

Due to the impression that Bruno Latour rejects epistemology, his thought is often considered as part of postmodernism and relativism. This essays will show that this impression is misleading. The target of Latour's critique is the modern paradigm that dichotomizes absolutely between ontology and epistemology, as in subject—object and nature—society. Latour succeeded in showing that modern epistemology is not absolute. To do so, he included a two-dimensional variable in one-dimensional insertions, with the example of a generic scheme created by (...) a variant of the SSK school. The consequence is a priori ontological postponement, with various models of possible scales of values on the schema. For this reason, the principle of symmetry and the use of neutral language that can include (suspend) various ontologies so that epistemic knowledge can be obtained in reality (such as the alignment of humans—non-humans, and actors—actants), becomes important in scientific practice. This essay draws a conclusion with some critical notes and provides a kind of offer as a further consequence of the examination of Bruno Latour’s epistemology Abstrak Kesan bahwa Bruno Latour menolak epistemologi telah membuat pemikirannya kerap dimasukkan ke kategori pascamodernisme dan relativisme. Tulisan ini hendak menunjukkan bahwa kesan tersebut keliru. Sebetulnya sasaran kritik Latour adalah paradigma modern yang mendikotomikan secara absolut antara ontologi dan epistemologi, seperti pada subjek–objek dan alam–masyarakat. Latour memperlihatkan bahwa epistemologi modern itu tidaklah absolut. Caranya, ia memasukkan variabel dua dimensi pada pengutuban satu dimensi, dengan contoh skema generik yang dibuat oleh varian dari mazhab SSK. Konsekuensinya adalah penundaan apriori ontologis, dengan beraneka model kemungkinan skala nilai pada skema. Untuk itu, prinsip simetri dan penggunaan bahasa netral yang dapat mencakupi (penangguhan) pelbagai ontologi agar pengetahuan epistemik dapat diperoleh senyata-nyatanya (seperti kesejajaran manusia—non-manusia, dan aktor—aktan) menjadi penting dalam praktik keilmuan. Di akhir tulisan, penulis memberikan beberapa catatan kritis, serta semacam tawaran sebagai konsekuensi lebih jauh atas pemeriksaan epistemologi Bruno Latour. Kata-kata kunci: epistmeologi, paradigma non-modern, epistemologi moluska, prinsip simetri, meta-modern, aktor-aktan. (shrink)

Is the number an absolute intelligible reality? The author investigates the number and its nature in Plotinus. works trying to solve the following question: what number is considered intelligible - the number in general or the number in particular? Three answers are given over this study. Thus, if the number is generally defined as intelligible (as Plotinus sometimes does), than the number in general is an intelligible reality (a general intelligible number, therefore, exists). On the other hand, if we make (...) a distinction between numbers (the plural) and number (the singular), it seems that, for Plotinus, only the particular number could be considered clearly intelligible, while the number as a generic reality is not so. Actually, the final solution comes out from the agreement between these two divergent theses. This agreement is based on the idea of the total number: a number that is in the same time particular and general, a number which is the object of the final part of the present study. (shrink)

Is the number an absolute intelligible reality? The author investigates the number and its nature in Plotinus. works trying to solve the following question: what number is considered intelligible - the number in general or the number in particular? Three answers are given over this study. Thus, if the number is generally defined as intelligible (as Plotinus sometimes does), than the number in general is an intelligible reality (a general intelligible number, therefore, exists). On the other hand, if we make (...) a distinction between numbers (the plural) and number (the singular), it seems that, for Plotinus, only the particular number could be considered clearly intelligible, while the number as a generic reality is not so. Actually, the final solution comes out from the agreement between these two divergent theses. This agreement is based on the idea of the total number: a number that is in the same time particular and general, a number which is the object of the final part of the present study. (shrink)

In this article, the author argues that the question of educational time is absolutely essential in contemporary debates concerning the fate of the university. In order to examine the nature of educational time, this article first outlines Heidegger's distinction between temporality and Temporality. Second, the author makes a clarification between inauthentic and authentic learning as two forms of educational temporality. Here the article turns to the work of Hubert Dreyfus and Stuart Dreyfus on expert skill building versus standardised or (...) class='Hi'>generic forms of learning. When inauthentic and authentic forms of temporality are brought to light through this distinction, new ways of understanding the convergence and divergence of learning modes open up for critical reflection. Third, the article suggests that while differentiations internal to learning are critical in the struggle to define the nature of education, education cannot be reduced to its temporalising forms. At this point, the work of one of Heidegger's late students, Giorgio Agamben, becomes important for grounding the educational experience in Temporality through study. At stake here is carving out a time in education for enpresencing versus self-projection through action. And finally, the article turns back to Hediegger in order to see the ethical limitations of too quickly collapsing education into learning—even if that learning is authentic. (shrink)

In this article, the author argues that the question of educational time is absolutely essential in contemporary debates concerning the fate of the university. In order to examine the nature of educational time, this article first outlines Heidegger's distinction between temporality and Temporality. Second, the author makes a clarification between inauthentic and authentic learning as two forms of educational temporality. Here the article turns to the work of Hubert Dreyfus and Stuart Dreyfus on expert skill building versus standardised or (...) class='Hi'>generic forms of learning. When inauthentic and authentic forms of temporality are brought to light through this distinction, new ways of understanding the convergence and divergence of learning modes open up for critical reflection. Third, the article suggests that while differentiations internal to learning are critical in the struggle to define the nature of education, education cannot be reduced to its temporalising forms. At this point, the work of one of Heidegger's late students, Giorgio Agamben, becomes important for grounding the educational experience in Temporality through study. At stake here is carving out a time in education for enpresencing versus self-projection through action. And finally, the article turns back to Hediegger in order to see the ethical limitations of too quickly collapsing education into learning—even if that learning is authentic. (shrink)

I. Vague Properties and the Problem of Vagueness The philosophical problem of vagueness is to say what vagueness is in a way that helps to resolve the sorites paradox. Saying what vagueness is requires saying what kinds of things can be vague and in what the vagueness of each kind consists. Philosophers dispute whether things of this, that, or the other kind can be vague, but no one disputes that there are vague linguistic expressions. Among vague expressions, predicates hold a (...) special place in the problem of vagueness, for it’s their vagueness that is soritesgenerating. That puts the vagueness of predicates at the hub of the problem of vagueness, and there can be little doubt that we’ll be a short step from home if we can account for it. Any account of vagueness will of course require commitment to theses that are themselves foci of philosophical debate, but one can’t expect to get anywhere without taking on some as working hypotheses and then striving to say something that will be plausible if those hypotheses are plausible. One of the working hypotheses of this paper is that propositional attitudes and propositional speech acts are relations to propositions of some stripe or other, in the generic sense in which a proposition is an abstract, mind- and language-independent entity that has a truth condition, and has that truth condition both essentially and absolutely (i.e. without relativization to anything).1 The existence of propositions requires the existence of properties, in the generic sense in which a property is an abstract, mind- and language-independent entity that has an instantiation condition, and has that instantiation condition both essentially and absolutely. For present purposes it will be harmless to pretend that the propositions we believe and assert are Russellian propositions---structured entities whose basic constituents are the objects and properties our beliefs and speech acts are about. When a propositionalist speaks in loosey-goosey mode, she is apt to say that a sentence token is true just in case the proposition expressed in its utterance is true. (shrink)

Moore's moral programme is increasingly unpopular. Judith Jarvis Thomson's attack has been especially influential; she says the Moorean project fails because ‘there is no such thing as goodness’. I argue that her objection does not succeed: while Thomson is correct that the kind of generic goodness she targets is incoherent, it is not, I believe, the kind of goodness central to the Principia. Still, Moore's critics will resist. Some reply that we cannot understand Moorean goodness without generic goodness. (...) Others claim that even if Moore does not need Thomson's concept, he still requires the objectionable notion of absolute goodness. I undermine both these replies. I first show that we may dispense with generic goodness without losing Moorean intrinsic goodness. Then, I argue that though intrinsic goodness is indeed a kind of absolute goodness, the objections marshalled against the concept are unsound. (shrink)

In studies of Indian theories of meaning it has been standard procedure to examine their relevance to the ontological issues between Brahmin realism about universals and Buddhist nominalism. It is true that Kumārila makes efforts to secure the real existence of a generic property denoted by a word by criticizing Dignāga, who declares that the real world consists of absolutely unique individuals. The present paper, however, concentrates on the linguistic approaches Dignāga and Kumārila adopt to deny or to prove (...) the existence of universals. It turns out that in spite of adopting contrasting approaches they equally distinguish between the semantic denotation of a word and its pragmatic reference to a thing in the physical world. From a purely semantic viewpoint, Dignāga considers the exclusion of others by a word as the result of a conceptual accumulation of the sense-components accepted in the totality of worldly discourse. Among the three characteristics Dignāga held must be met by universals, Kumārila attaches special importance to their entire inherence in each individual. This is because he pragmatically pays attention to the use of a word in the discourse given in a particular context by analyzing a sentence into a topic and a comment. (shrink)

In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second (...) order that are generically invariant and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing. (shrink)

l investigate versions of the Maximality Principles for the classes of forcings which are <κ-closed. <κ-directed-closed, or of the form Col (κ. <Λ). These principles come in many variants, depending on the parameters which are allowed. I shall write MPΓ(A) for the maximality principle for forcings in Γ, with parameters from A. The main results of this paper are: • The principles have many consequences, such as <κ-closed-generic $\Sigma _{2}^{1}(H_{\kappa})$ absoluteness, and imply. e.g., that ◇κ holds. I give (...) an application to the automorphism tower problem, showing that there are Souslin trees which are able to realize any equivalence relation, and hence that there are groups whose automorphism tower is highly sensitive to forcing. • The principles can be separated into a hierarchy which is strict, for many κ. • Some of the principles can be combined, in the sense that they can hold at many different κ simultaneously. The possibilities of combining the principles are limited, though: While it is consistent that MP<κ-closed(HκT) holds at all regular κ below any fixed α. the "global" maximality principle, stating that MP<κ-closed(Hκ ∪ {κ}) holds at every regular κ. is inconsistent. In contrast to this, it is equiconsistent with ZFC that the maximality principle for directed-closed forcings without any parameters holds at every regular cardinal. It is also consistent that every local statement with parameters from HκT that's provably <κ-closed-forceably necessary is true, for all regular κ. (shrink)

There are many different kinds of model and scientists do all kind of things with them. This diversity of model type and model use is a good thing for science. Indeed, it is crucial especially for the biological and cognitive sciences, which have to solve many different problems at many different scales, ranging from the most concrete of the structural details of a DNA molecule to the most abstract and generic principles of self-organization in networks. Getting a grip (or (...) more likely many separate grips) on this range of topics calls for a teeming forest of techniques, including many different modeling techniques. Barbara Webb’s target article strikes us as a proposal for clear-cutting the forest. We think clear-cutting here would be as good for science as it is for non-metaphorical forests. Our argument for this is primarily a recitation of a few of the ways that diversity has been useful. Recently, looking at the actual practice of artificial life modelers, one of us distinguished four uses of simulation models classified in terms of the position the models take up between theory and data (see Figure 1). The classification is not exhaustive, and the barriers between kinds are not absolute. Rather, the purpose of the taxonomy is to open up the view for an epistemic ecology of modeling practices. First, and closest to the empirical domain, there are mechanistic models, in which there is an almost one-to-one correspondence between variables in the model and observables in the target system and its environment. Webb’s.. (shrink)

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert spaces expanded by a group of generic unitary operators and Hilbert spaces expanded by a generic subspace. We also show how Herbrand's theorem can be used to characterize definable functions in absolutely ubiquitous structures from classical logic.

The author proposes a key of interpretation of the post — modern age not as a mere cultural attitude but as an effective philosophical horizon of our time. Two considerations are needed in order to define it: the proclaimed impossibility of a one-way description of reality, and the conviction of the existence of a plurality of conceptual schemes which can not be absolutely reduced one to the other. Therefore postmodernism severely limits the possibility of analysing notions such as liberty, justice (...) and good, which are laden with universalism. After indicating the different possible solutions, the author presents his personal thesis of reflective authenticity: from the kantian notion of reflective judgement, the author traces in authenticity the quality of "being measure for one-selves" or self-congruence typical of arts’ masterpieces. By disengaging this notion from its original aesthetic ambit it is possible, in Ferrara’s opinion, to refer to a pluralistic or exemplar universalism, applicable to ethics as to law, to the political judgement as to the theoretical one, completely different from that generic universalism which is on the contrary based on trans-contextual principles, typical of the modern age. (shrink)

The essay discusses two different conceptions of human dignity. According to the first conception, ›respecting the dignity of a human being‹ means to respect something specific that is given by her being human. According to the second conception, however, ›respecting the dignity of a human being‹ means to respect her as a human being. With regard to the first understanding, one is bound to respect human dignity, whereas on the basis of the second conception, we owe respect to the human (...) being herself. The duty to respect human dignity serves as a foundation for duties we have with regard to human beings as such. The duty to respect someone as the human being she is, however, is a duty towards her. This duty therefore justifies a right she may claim, namely the right to be respected as a human being. The core of human dignity, then, is this rights-conferring status of being human. This article reacts to the German debate on human embryonic research. Participants in this debate argue that human dignity depends on being human in a generic sense. According to them, the early embryo participates in this sense of being human, which allows them to apply the concept of human dignity, including the absolute protection it entails, to human embryos. The author criticizes this view, claiming that it undermines the very idea of human dignity by neglecting the rights-conferring status of being a particular human being which is at its core. Rather, a »decent society« is characterized by the fact that its members are treated and respected as rights-holders. (shrink)