We strengthen a theorem of Gitik and Shelah [6] by showing that if κ is either weakly inaccessible or the successor of a singular cardinal and S is a stationary subset of κ such that $NS_{\kappa} \upharpoonright S$ is saturated then $\kappa \S$ is fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [2], showing in particular that if I is a $\lambda^{+++}-saturated$ (...) normal ideal on $P_{\kappa} \lambda$ then the conditions of being $\lambda^{+}-preserving$ , weakly presaturated, and presaturated are equivalent for I. (shrink)

We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no ideal on Pκ is weakly λ+-saturated. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ to the set of all a with equation image is not λ++-saturated . We actually prove the stronger result that there is equation image with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ for any two distinct members A, B of Q, where NGκ, λ denotes the game (...) class='Hi'>ideal on Pκ. We also remark that for κ > ω1, adding λ+3 Cohen subsets of ω1 to equation image makes NGκ, λ λ+3-saturated. (shrink)

Given a regular cardinal κ > ω1 and a cardinal λ with κ ≤ cf (λ) < λ, we show that NSκ,λ | T is not λ+-saturated, where T is the set of all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a\in P_\kappa (\lambda)}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${| a | = | a \cap \kappa|}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm cf} \big( {\rm sup} (...) (a\cap\kappa)\big) = {\rm cf} \big({\rm sup} (a)\big) = \omega}$$\end{document}. (shrink)

We prove that it is consistent that there exists a saturated tail club guessing ideal on ω1 which is not a restriction of the non-stationary ideal. Two proofs are presented. The first one uses a new forcing axiom whose consistency can be proved from a supercompact cardinal. The resulting model can satisfy either CH or 20=2. The second one is a direct proof from a Woodin cardinal, which gives a witnessing model with CH.

Starting with a λ-supercompact cardinal κ, where λ is a regular cardinal greater than or equal to κ, we produce a model with a stationary subset S of such that , the ideal generated by the non-stationary ideal over together with , is λ+-saturated. Using this model we prove the consistency of the existence of such a stationary set together with the Generalized Continuum Hypothesis . We also show that in our model we can make -saturated, (...) where S is the set of all such that , the order type of x, is a regular cardinal and x is stationary in sup. Furthermore we construct a model where is κ+-saturated but GCH fails. We show that if SS is stationary in , then S can be split into λ many disjoint stationary subsets. (shrink)

We prove that WRP and saturation of the ideal NSω1together imply$\left\{ {a \in [\lambda ]^{\omega _1 } :{\text{cof}}\left( {{\text{sup}}\left( a \right)} \right) = \omega _1 } \right\}$, for every cardinalλwith cof(λ)≥ω2.

We outline the proof of the consistency that there exists a saturated tail club guessing ideal on ω₁ which is not a restriction of the nonstationary ideal. A new class of forcing notions and the forcing axiom for the class are introduced for this purpose.

Let λ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square _{\lambda}^{\ast}$ together with 2 λ = λ⁺ implies $\lozenge _{S}$ for every S ⊆ λ⁺ that reflects stationarily often. In this paper, for a set S ⊆ λ⁺, a normal subideal of the weak approachability ideal is introduced, and denoted by I[S; λ]. We say that the ideal is fat if it contains a stationary set. It is proved: 1. if I[S; λ] (...) is fat, then $\text{NS}_{\lambda ^{+}}$ ↾ S is non-saturated; 2. if I[S; λ] is fat and 2 λ = λ⁺, then $\lozenge _{S}$ holds; 3. $\square _{\lambda}^{\ast}$ implies that I[S; λ] is fat for every S ⊆ λ⁺ that reflects stationarily often; 4. it is relatively consistent with the existence of a supercompact cardinal that $\square _{\lambda}^{\ast}$ fails, while I[S; λ] is fat for every stationary S ⊆ λ⁺ that reflects stationarily often. The stronger principle $\lozenge _{\lambda ^{+}}^{\ast}$ is studied as well. (shrink)

We construct a model with a saturated ideal _I_ over \({\mathcal {P}}_{\kappa }\lambda \) and study the extent of saturation of _I_.

We show that under the assumption of the existence of the canonical inner model with one Woodin cardinal$M_1$, there is a model of$\mathsf {ZFC}$in which$\mbox {NS}_{\omega _{1}}$is$\aleph _2$-saturated and${\Delta }_{1}$-definable with$\omega _1$as a parameter which answers a question of S. D. Friedman and L. Wu. We also show that starting from an arbitrary universe with a Woodin cardinal, there is a model with$\mbox {NS}_{\omega _{1}}$saturated and${\Delta }_{1}$-definable with a ladder system$\vec {C}$and a full Suslin treeTas parameters. Both results (...) rely on a new coding technique whose presentation is the main goal of this article. (shrink)

We prove, assuming the existence of large cardinals, the relative consistency of the existence of strongly saturated ideals on small cardinals. We also give some information about the problem, how many σ-additive, 0-1-valued measures over a small cardinal are necessary, such that every subset of the cardinal is measurable in at least one of them.

Suppose that λ is the successor of a singular cardinal μ whose cofinality is an uncountable cardinal κ. We give a sufficient condition that the club filter of λ concentrating on the points of cofinality κ is not λ+-saturated.1 The condition is phrased in terms of a notion that we call weak reflection. We discuss various properties of weak reflection. We introduce a weak version of the ♣-principle, which we call ♣*−, and show that if it holds on a (...) stationary subset S of λ, then no normal filter on S is λ+-saturated. Under the above assumptions, ♣*− is true for any stationary subset S of λ which does not contain points of cofinality κ. For stationary sets S which concentrate on points of cofinality κ, we show that ♣*− holds modulo an ideal obtained through the weak reflection. (shrink)

It is shown in this paper that it is consistent (relative to almost huge cardinals) for various club guessing ideals to be saturated.

We show, using a variation of Woodin’s partial order ℙ max , that it is possible to destroy the saturation of the nonstationary ideal on ω 1 by forcing with a Suslin tree. On the other hand, Suslin trees typcially preserve saturation in extensions by ℙ max variations where one does not try to arrange it otherwise. In the last section, we show that it is possible to have a nonmeager set of reals of size ℵ1, saturation of the (...) nonstationary ideal, and no weakly Lusin sequences, answering a question of Shelah and Zapletal. (shrink)

If [Formula: see text] is regular and [Formula: see text], then the existence of a weakly presaturated ideal on [Formula: see text] implies [Formula: see text]. This partially answers a question of Foreman and Magidor about the approachability ideal on [Formula: see text]. As a corollary, we show that if there is a presaturated ideal [Formula: see text] on [Formula: see text] such that [Formula: see text] is semiproper, then CH holds. We also show some barriers to (...) getting the tree property and a saturated ideal simultaneously on a successor cardinal from conventional forcing methods. (shrink)

We describe the countably saturated models and prime models of the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal such that the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal such that the supremum of the ideal exists. We prove that there are infinitely many (...) completions of the theory of Boolean algebras with a distinguished ideal that do not have a countably saturated model. Also, we give a sufficient condition for a model of the theory TX of Boolean algebras with distinguished ideals to be elementarily equivalent to a countably saturated model of TX. (shrink)

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, assuming the existence of the canonical inner model with one Woodin cardinal $M_1 $, there is a model of $ZFC$ in which the nonstationary ideal on $\omega _1 $ is $\aleph _2 $-saturated and whose reals admit a ${\rm{\Sigma }}_4^1 $-wellorder.

An ideal I defined on a group G is called idempotent if for every $A \in I, \{g \in G: Ag^{-1} \not\in I\} \in I$ . We show that a countably complete idempotent ideal on an abelian group cannot be prime but may have strong saturation properties.

We develop the theory of layered posets and use the notion of layering to prove a new iteration theorem is κ-cc, as long as direct limits are used sufficiently often. This iteration theorem simplifies and generalizes the various chain condition arguments for universal Kunen iterations in the literature on saturated ideals, especially in situations where finite support iterations are not possible. We also provide two applications:1 For any n≥1, a wide variety of <ωn−1-closed, ωn+1-cc posets of size ωn+1 can (...) consistently be absorbed by quotients of saturated ideals on ωn.2 For any n∈ω, the tree property at ωn+3 is consistent with Chang’s conjecture ↠. (shrink)

The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω₁ is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω₁ in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.

Let$\kappa $be a regular uncountable cardinal, anda cardinal greater than or equal to$\kappa $. Revisiting a celebrated result of Shelah, we show that ifis close to$\kappa $and(= the least size of a cofinal subset of) is greater than, thencan be represented (in the sense of pcf theory) as a pseudopower. This can be used to obtain optimal results concerning the splitting problem. For example we show that ifand, then no$\kappa $-complete ideal onis weakly-saturated.

In contrast to the European historical experience, Africa’s urban infrastructural systems are characterised by stagnation long before demand has been saturated. Water infrastructures have been stabilised as systems predominantly providing services for elites, with millions of poor people lacking basic services in the cities. What is puzzling is that so little emphasis has been placed on innovation and the adaptation of the colonial technological paradigm to better suit the local and current socio-economic contexts. Based on historical case studies of (...) Kampala and Nairobi, this paper argues that the lack of innovation in African urban water infrastructure can be understood using Pinch and Bijker’s concept of technological closure, and by looking at water technology from its embedded values and ideology. Large-scale water technology became part of African leaders’ strategies to build prosperous nations and cities after decolonisation and the ideological purpose of infrastructure may have been much more important than previously understood. Water technology had reached a state of closure in Europe and then came to represent modernisation and progress in the colonial context. It has continued to serve such a similar symbolic purpose after independence, with old norms essentially being preserved. Recent sector reforms have defined problems predominantly as of economic and institutional nature while state actors have become ‘unseeing’ vis-á-vis controversies within the technological systems themselves. In order to induce socio-technical innovation towards equality in urban infrastructure services, it will be necessary to understand the broader incentive structure that governs the relevant social groups, such as governments, donors, water suppliers and the consumers, as well as power-structures and political accountability. (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)

We introduce the notion of skinniness for subsets of $\mathcal{P}_\kappa \lambda$ and its variants, namely skinnier and skinniest. We show that under some cardinal arithmetical assumptions, precipitousness or $2^\lambda$-saturation of $\mathrm{NS}_{\kappa\lambda}\mid X$, where $\mathrm{NS}_{\kappa\lambda}$ denotes the non-stationary ideal over $\mathcal{P}_\kappa \lambda$, implies the existence of a skinny stationary subset of $X$. We also show that if $\lambda$ is a singular cardinal, then there is no skinnier stationary subset of $\mathcal{P}_\kappa \lambda$. Furthermore, if $\lambda$ is a strong limit singular cardinal, (...) there is no skinny stationary subset of $\mathcal{P}_\kappa \lambda$. Combining these results, we show that if $\lambda$ is a strong limit singular cardinal, then $\mathrm{NS}_{\kappa\lambda}\mid X$ can satisfy neither precipitousness nor $2^\lambda$-saturation for every stationary $X \subseteq \mathcal{P}_\kappa \lambda$. We also indicate that $\diamondsuit_\lambda(E^{\lambda}_{<\kappa})$, where $E^{\lambda}_{<\kappa} \stackrel{\mathrm{def}}{=} \{\alpha < \lambda \mid \mathrm{cf}(\alpha) < \kappa\}$, is equivalent to the existence of a skinnier (or skinniest) stationary subset of $\mathcal{P}_\kappa \lambda$ under some cardinal arithmetical hypotheses. (shrink)

We investigate higher dimensional chain conditions, where the largeness notion is given by Fubini products of a given ideal. From strong saturation properties of an ideal, we derive abstractly versions of higher dimensional [Formula: see text]-system lemma, which imply many posets, including any finite support iteration of [Formula: see text]-centered posets and measure algebras, satisfy the higher dimensional chain conditions. We then show that if a poset satisfies a strengthening of the [Formula: see text]-finite chain condition by Horn (...) and Tarski, then it satisfies higher dimensional chain conditions. As an application, we derive Ramsey-theoretic consequences, namely various partition hypotheses as studied by Bannister, Bergfalk, Moore and Todorcevic, from the existence of ideals satisfying strong chain conditions. (shrink)

Journal of Mathematical Logic, Ahead of Print. We investigate higher dimensional chain conditions, where the largeness notion is given by Fubini products of a given ideal. From strong saturation properties of an ideal, we derive abstractly versions of higher dimensional [math]-system lemma, which imply many posets, including any finite support iteration of [math]-centered posets and measure algebras, satisfy the higher dimensional chain conditions. We then show that if a poset satisfies a strengthening of the [math]-finite chain condition by (...) Horn and Tarski, then it satisfies higher dimensional chain conditions. As an application, we derive Ramsey-theoretic consequences, namely various partition hypotheses as studied by Bannister, Bergfalk, Moore and Todorcevic, from the existence of ideals satisfying strong chain conditions. (shrink)

In [P. Larson, Martin’s Maximum and the axiom , Ann. Pure App. Logic 106 135–149], we modified a coding device from [W.H. Woodin, The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, Walter de Gruyter & Co, Berlin, 1999] and the consistency proof of Martin’s Maximum from [M. Foreman, M. Magidor, S. Shelah, Martin’s Maximum. saturated ideals, and non-regular ultrafilters. Part I, Annal. Math. 127 1–47] to show that from a supercompact limit of supercompact cardinals one could (...) force Martin’s Maximum to hold while the axiom fails. Here we modify that argument to prove a stronger fact, that Martin’s Maximum is consistent with the existence of a wellordering of the reals definable in H without parameters, from the same large cardinal hypothesis. In doing so we give a much simpler proof of the original result. (shrink)

Let κ B be the least cardinal for which the Baire category theorem fails for the real line R. Thus κ B is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κ B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2 ω 1 be ℵ ω . Similar questions are considered for the ideal of measure zero sets, (...) other ω 1 saturated ideals, and the ideal of zero-dimensional subsets of R ω 1. (shrink)

We show that if κ is an inaccessible cardinal then P κ λ splits into $\lambda^{ many disjoint stationary subsets. We also show that if P κ λ carries a strongly saturated ideal then the nonstationary ideal cannot be λ + -saturated.

We present a technique for destroying stationary subsets of Pκκ+ using partial square sequences. We combine this method with Gitik’s poset for changing the cofinality of a cardinal without adding bounded sets to prove a variety of consistency results concerning saturated ideals and the set S.

Let κ denote a regular uncountable cardinal and NS the normal ideal of nonstationary subsets of κ. Our results concern the well-known open question whether NS fails to be κ + -saturated, i.e., are there κ + stationary subsets of κ with pairwise intersections nonstationary? Our first observation is: Theorem. NS is κ + -saturated iff for every normal ideal J on κ there is a stationary set $A \subseteq \kappa$ such that $J = NS \mid (...) A = \{X \subseteq \kappa:X \cap A \in NS\}$ . Turning our attention to large cardinals, we extend the usual (weak) Mahlo hierarchy to define "greatly Mahlo" cardinals and obtain the following: Theorem. If κ is greatly Mahlo then NS is not κ + -saturated. Theorem. If κ is ordinal Π 1 1 -indescribable (e.g., weakly compact), ethereal (e.g., subtle), or carries a κ-saturated ideal, then κ is greatly Mahlo. Moreover, there is a stationary set of greatly Mahlo cardinals below any ordinal Π 1 1 -indescribable cardinal. These methods apply to other normal ideals as well; e.g., the subtle ideal on an ineffable cardinal κ is not κ + -saturated. (shrink)

We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal.

In this paper, the following are proved:Theorem A. The quotient algebra ${\cal P} (\kappa )/I$ is complete if and only if the only non-trivial I -closed ideals extending I are of the form $I\lceil A$ for some $A\in I^+$ .Theorem B. If $\kappa$ is a stationary cardinal, then the quotient algebra ${\cal P} (\kappa )/ NS_\kappa$ is not complete.Corollary. (1) If $\kappa$ is a weak compact cardinal, then the quotient algebra ${\cal P} (\kappa )/NS_\kappa$ is not complete.(2) If $\kappa$ bears (...) $\kappa$ -saturated ideal, then the quotient algebra ${\cal P} (\kappa )/NS_\kappa$ is not complete.Theorem C. Assume that $\kappa$ is a strongly compact cardinal, I is a non-trivial normal $\kappa$ -complete ideal on $\kappa$ and B is an I -regular complete Boolean algebra. Then if ${\cal P} (\kappa )/I$ is complete, it is B -valid that for some $A\subseteq\check\kappa$ , ${\cal P} (\kappa )/({\bf J}\lceil A)$ is complete, where J is the ideal generated by $\check I$ in $V^B$ .Corollary. Let M be a transitive model of ZFC and in M , let $\kappa$ be a strongly compact cardinal and $\lambda$ a regular uncountable cardinal less than $\kappa$ . Then there exists a generic extension M [ G ] in which $\kappa =\lambda^+$ and $\kappa$ carries a non-trivial $\kappa$ -complete ideal I which is completive but not $\kappa^+$ -saturated. (shrink)

Let A be a non-empty set. A set $S\subseteq \mathcal{P}(A)$ is said to be stationary in $\mathcal{P}(A)$ if for every f: [A] <ω → A there exists x ∈ S such that x ≠ A and f"[x] <ω ⊆ x. In this paper we prove the following: For an uncountable cardinal λ and a stationary set S in \mathcal{P}(\lambda) , if there is a regular uncountable cardinal κ ≤ λ such that {x ∈ S: x ⋂ κ ∈ κ} is (...) stationary, then S can be split into κ disjoint stationary subsets. (shrink)

RRI is a broad concept that is subject to different interpretations. This chapter focuses on the view of RRI as a transformative ideal for reforming the research and innovation system in the service of public interest. This is the normatively strong view of RRI that has attracted many policy-makers and young researchers but left cold many senior researchers and innovators. The transformative vision of RRI has failed to materialise, and RRI remains a marginal reality, even in Norway, where arguably (...) the conditions were more propitious than elsewhere. I attempt to explain the failed transformation, focusing on two key objectives of RRI: the ambition of aligning R&I with societal values and the aspiration to steer R&I through generating a shared responsibility for the future (a prospective joint responsibility in technical terms). Alignment proved very hard to achieve because valuing is steeped in well-established practices, habits, and cognitive-emotional frameworks. These cannot be changed at will. Besides, the ambition to make researchers and innovators more responsive to a wider constituency and additional social responsibilities stumbled against what I call moral saturation, namely the lack of capacity and resources to take on additional moral tasks. Furthermore, modern societies are characterised by a pluralism of values and conceptions of the good life, compounded by the lack of methods for composing value conflicts. These problems come back when we look at what it takes to create expanded shared responsibilities: joint intentions and joint commitments. A formal analysis of how these can be generated shows that they need pre-conditions that are seldom obtaining in the real world of R&I. So, the transformative ambition went against the inertia and entrenched habits of the R&I ecosystem and yet very often the task of promoting the change was given to junior researchers: the most vulnerable and less powerful actors. I conclude that RRI ambition to transform the R&I system is unrealistic. What can be attempted is to develop small-scale experiments outside the mainstream, where institutional barriers and perverse incentives are partially removed or corrected. (shrink)

Abstract.A type of subtlety for Pκλ called “strongly subtle” is introduced to show almost ineffability is consistencywise stronger than Shelah property. The following are also shown: is strongly subtle” has rather strong consequences. (ii) The ideal is not strongly subtle} is not λ-saturated, and completely ineffable ideal is not precipitous. (iii) In case that λ<κ=2λ, almost λ-ineffability coincides with λ-ineffability. (iv) It is not provable that κ is λ<κ-ineffable whenever κ is λ-ineffable.

The Husserlian phenomenological approach to organisational research as a way to understand how collectives experience and mean their work context, is rarely used although, when it is, it often functions as a negative criticism of objectivist methods. The sociological potential of phenomenological concepts to enable understanding of subjective experience of social contexts, and the characterisation of those social contexts through ideal type construction, deserves to be used more extensively in a positive proposal of organisational research methodologies. However, a consistent (...) phenomenological approach—with its inherent qualities that enable the transcendental understanding of subjective phenomena and social objectivity—can be sociologically fruitful only if it benefits from accumulated sociological knowledge, realised by various approaches that discuss macro and micro aspects of organisations. The proposed phenomenological methodology considers both aspects. It takes account of social theories that consider the influences of both the macro environment and institutionalisation on structure and culture through their relationship with collective and individual action. Also, it performs collaboration between two close perspectives which recognise the importance of the subjective meanings of the individuals constituting the collective: Husserl’s transcendental phenomenology and Weber’s ideal type construction. It also discusses context, participant selection, the concepts of saturation and generalisation, and the applicability of the methodology. (shrink)

We construct a model satisfying “κ is quasi measurable”. Here, we call κ quasi measurable if there is an ℵ1‐saturated κ‐additive ideal on κ. We also show that, in this model, forcing with adds one but not κ Cohen reals. We introduce a weak club principle and use it to show that, consistently, for some ℵ1‐saturated κ‐additive ideal on κ, forcing with adds one but not κ random reals.

continent. 1.3 (2011): 208-212. … intervals of destructuring paradoxically carry the momentum for the ongoing process by which thought and perception are brought into relation toward transformative action. —Brian Massumi, Parables for the Virtual: Movement, Affect, Sensation 1 Facing a blank canvas or blank page is a moment of pure potential, one that can be enervating or paralyzing. It causes a pause, a hesitation, in anticipation of the moment of inception—even of one that never comes. The implication is that the (...) blank is yours in that moment, and it calls on you to act on it, to think into it, to create on it. Each blank canvas gives you time, of an undefined length, to transform that canvas’ inherent potential into a work. This two-dimensional plane of potential can be projected into a space, which the body can then occupy. When you “destructure” a space in the same way, prepare it to be a blank, much as you build a canvas, you allow your entire body to enter the space of potential, and you rest in anticipation of work, like the hand poised above the page. Artists have found that the deliberate creation of that space of potential through sealing the space and painting it white, thereby erasing details and distractions, can be such a transformative experience as to help define their whole practice. The cessation of distraction, the absence of indicator that a “blanked” workspace provides allows for a new presence of mind, it gives them the room, literally, to move into their work, and from there to move their work into the world. The workspace for the artist, the studio, is often perceived as a lab-like condensation of the gallery or museum, the traditional and idealized white cube. Similarly, with the blank page, a concrete relation between space and time comes forward as the intentional simplification of the architecture changes behavior and perception within the space. The work of “blanking” the studio space is a meditative reduction, an erasure, and in a way, an attempt at drawing away from the world beyond the studio - the sealed space is meant to recede from reality, to become abstracted by its willed lack of details and distractions. Within that space the time for a new beginning is made more present, more attainable, and the focus it fosters becomes another tool to aid creation. At the formative moment of his artistic practice, Tom Friedman used the blank of his studio, saturated in white, sealed off from the world, to fight velocity. He describes how he projected his vision of the end goal, the museum - a place he believes to be defined by slow contemplation - onto his own studio experience. He then sat and reflected on common objects, one by one, framed by the blank box he had created. The domestic objects he brought into the space to study foreshadow his mature works, where often the quotidian object has a single additional element – his intense labor. Friedman makes discrete objects through absurdly intense and focused labor, epitomized, perhaps by his 1,000 hours of Staring , made from 1992-97: Tom Friedman. 1000 Hours of Staring (1992-1997) His labor, to use his own words, is his way to “bring all of who you are to the experience.” Friedman shares his labor, allows the slow, deliberate pace of his work born in the studio to penetrate the museum. Nothing seems effortless, or a gesture, the labor is apparent, displayed, and tangible. He gives us the labor, the personal investment in the physical that saved art for him, that divorced the work from the language he cites as a factor of alienation. When we see his work we do not see words, we see acts, we see objects. He has forced the studio as workspace into the exhibition space, as he stuffs hundreds of more hours of labor into his shows with each new piece, filling the space with material and labor, material and labor – his involvement, his investment, is his gift to us as the viewers, as he introduces the laborious and contemplative pace he feels belongs to the museum. He saves us also from the alienation of language, which first drove him into the sealed studio and away from the discourse of his school. He presents us with his real, the object which stands in stark contrast to the white slate of the studio, the sealed white box he started from, where his individual, self-contained objects begin and end, completed through the intensity of isolation, first of the individual artist, and then of the material he chooses to slowly, slowly, slowly work: Tom Friedman. Untitled (1992) In his in-depth analysis of galleries as a blank white cube, Brian O’Doherty emphasizes the religious connotations implied in the strict laws of the exhibition space and the valuation, aesthetics and elements of control he feels it imposes upon the work. Like Friedman, he recognizes the power of the restricted space – indicating the “perceptual fields of force” – that act on any object introduced into it. Going beyond Friedman’s assessment of the space as highly utilitarian for focusing his perception, O’Doherty emphasizes the rejection of the physical body of the artist or observer, saying that the cube allows for only observation - eyes and mind. He later parallels the picture frame as a psychological container for the artist with the room as the same for the observer. In both cases, this is an emphasis on the alienating nature of the relationship – just as the artist is kept out of the frame by the picture, in the gallery the art forces the body of the spectator out, calling for a self-referential purity. Patrick Ireland. White Cube (1998) O’Doherty makes a point of saying that the installation shot of the gallery without figures is “one of the icons of our visual culture.” In recent years, however, installation shots have begun to include figures, in some cases they are essential to understanding the scale and even the nature of the work, specifically with work that captures the experience of the space and the way that it varies from a white cube. The work of Olafur Eliasson is a case in point, as the Danish artist uses elements of scientific and natural phenomena to alter perception within the controlled gallery environment, tweaking and redirecting O’Doherty’s “perceptual fields of force” to make points about the act of seeing, or seeing yourself seeing, to quote the artist. This indicates a shift in the role of the artwork, not to exclude the body and stand discretely and self-sufficiently, but to include it, to manipulate it and to make the observer aware of the nature of that manipulation and the work’s ability to manipulate. Olafur Eliasson. 360º room for all colours (2002) So though in O’Doherty’s analysis, the intense blankness of the gallery pushed the observer out in favor of the artwork’s isolation, artists can replicate this inhumane sterility in their own workspace to focus their work on the influence of the gallery right from inception. This can be interpreted as an almost opposite understanding of the purpose of sealing and whitewashing the workspace as stated by Friedman. He sought a refuge from the critical language of the art school, and a space that, like the museum, gave him a protracted sense of time, and, he felt, welcomed him in, “to bring all of who you are,” as opposed to O’Doherty’s feeling that the museum was asking you, at least in body, to leave, and allow the work to take on its own life. Friedman does not seem to imply the tension with the cube and critical stance that O’Doherty prioritizes. Where Friedman finds a refuge, O’Doherty defines an opponent. In a third position, Robert Irwin describes his sealed studio space as “the world.” Though he made the same effort as Friedman to seal out all influences and distractions, he implies that he is in dialogue with the world through his own concentration and perception. This is reminiscent of the nature of the monad, as interpreted by Deleuze, a unity that envelops a multiplicity, a sealed container that contains the universe. He went through the same ritual described by Friedman, sealing up the space, painting it white, and then forcing himself to remain inside, staring at his own work, training his concentration relentlessly. But he found that the room became the distraction: …he became aware that a thin crack along the wall a few yards away from the canvas likewise exerted its presence; that when he plastered that crack over and repainted the wall, the canvas itself presented an entirely new aspect.2 The context was in a relentless dialogue with the work, and trying to neutralize that dialogue, to mute the conversation between space and object, became part of his ritual as he “fixed” his space each day in the hope of total concentration on the work. Ultimately, Irwin shaped the trajectory of his art by relinquishing the studio, establishing a post-studio practice, where the work is conceived and created out in the world, in dialogue with the world and reflective of the conditions it finds surrounding it. The white cube failed to ever achieve neutrality, his heightened concentration prevented him from ever neutralizing the space, so, instead of continuing to try to maintain the charade of a perfect blank, he acknowledged the unstoppable voice of place and turned all his efforts onto the object and the world, as a constant dialogue. Some artists push their studio space far from purity, domesticating it like a lair or a living room, and others destroy it, fill it with chaos or detritus, blacken or clutter it so as never to be starting from a blank, and thereby try to avoid the anxiety of facing that void. Similarly artists may never prepare a white canvas, a clean page, a marble block, or other form that is intentionally lacking, in order to try to escape the dialogue with emptiness. But Irwin, like O’Doherty, found an opponent in the white cube, and he learned not to fight it, rather he ended the conflict by making it an ally, an interlocutor, a collaborator. We can vainly strive to start from nothing, to find the lull, the clearing, and to always consider what we do in balance with the empty set. Somehow that intangible cloud of hazy nothingness, that softness of a lapse continually offers a place to bounce off of, to react to, to wrestle with, to rest with, in tension, or a place to begin. Robert Irwin. Excursus: Homage to the Square3 (1998) NOTES 1 Massumi. Parables for the Virtual: Movement, Affect, Sensation. p271. 2 MOMA, NY. Eliasson, 360 ? Room for All Colours . Installation. 2002. (shrink)

In marked contrast to Husserlian “unities of sense” that structure consciousness around egoic ideal-meaning intention, contemporary phenomenology orders sense according to an excess of givenness – a surfeit of presence – that surpasses this intentional relation. But Emmanuel Falque argues that there is a resistance that precedes the phenomenological order of givenness and sense. Before the saturated phenomena (Marion), the pathos of the flesh (Henry), and the irruption of the Other (Levinas), there is a resistance of presence that (...) is not sensu stricto given at all. Falque turns to the early writings of Emmanuel Levinas on trauma and insomnia and the hum and buzz of the il y a (the “there is …”) that precedes the order of givenness and sense, including the Levinasian Other, in order to make sense of this a priori resistance. There is a presence of the body, experienced in some sense via trauma, insomnia, and Falque’s own notion of the “spread body” that is not given yet constitutes an integral part of embodied experience. The way Falque engages with these bodily experiences reformulates the phenomenological limit, not in terms of excess and givenness, but in terms of resistance and the “extra-phenomenon.” Phenomenological engagement with resistance thus becomes a wager on meaning and sense, the outcome of which cannot be known in advance, that is, cannot be always and already ordered to phenomenological givenness. (shrink)

Along with Husserl's Ideas and Heidegger's Being and Time, Being Given is one of the classic works of phenomenology in the twentieth century. Through readings of Kant, Husserl, Heidegger, Derrida, and twentieth-century French phenomenology (e.g., Merleau-Ponty, Levinas, and Henry), it ventures a bold and decisive reappraisal of phenomenology and its possibilities. Its author's most original work to date, the book pushes phenomenology to its limits in an attempt to redefine and recover the phenomenological ideal, which the author argues has (...) never been realized in any of the historical phenomenologies. Against Husserl's reduction to consciousness and Heidegger's reduction to Dasein, the author proposes a third reduction to givenness, wherein phenomena appear unconditionally and show themselves from themselves at their own initiative. Being Given is the clearest, most systematic response to questions that have occupied its author for the better part of two decades. The book articulates a powerful set of concepts that should provoke new research in philosophy, religion, and art, as well as at the intersection of these disciplines. Some of the significant issues it treats include the phenomenological definition of the phenomenon, the redefinition of the gift in terms not of economy but of givenness, the nature of saturated phenomena, and the question “Who comes after the subject?” Throughout his consideration of these issues, the author carefully notes their significance for the increasingly popular fields of religious studies and philosophy of religion. Being Given is therefore indispensable reading for anyone interested in the question of the relation between the phenomenological and the theological in Marion and emergent French phenomenology. (shrink)

The article tries to answer the following question: what is the most promising epistemological strategy if my objective is the construction of a theory which gives me the opportunity to decrease the risk of getting to what is actually absolute, that is, to irreversible negative actions (irreversible as a theory might not be, but as an action often is)? The answer proposed is a form of epistemological dualism which means that I metaphysically believe (that is, I programmatically and systematically believe, (...) without certainly knowing it) that the epistemological relationship between any theory and any reality is dualistic. More specifically, I metaphysically believe that the epistemological relationship between any theory and any reality is not saturated: in any theory there is an ideal error, because there is no theory which is totally saturated by reality, and any reality can actualize the ideal error, because there is no reality which is totally saturated by theory. (shrink)