LetA be any nonrecursive set. We define a hierarchy of sets (and a corresponding hierarchy of degrees) that are reducible toA based on bounding the number of queries toA that an oracle machine can make. WhenA is the halting problemK our hierarchy of sets interleaves with the difference hierarchy on the r.e. sets in a logarithmic way; this follows from a tradeoff between the number of parallel queries and the number of serial queries needed to compute a (...) function with oracleK. (shrink)

We use finite model theory to prove:Let m ≥ 2. Then: If there exists k such that NP ⊆ σmTIME ∩ ΠmTIME, then for every r there exists kr such that PNP[nr] ⊆ σmTIME ∩ ΠmTIME; If there exists a superpolynomial time-constructible function f such that NTIME ⊆ Σpm ∪ Πpm, then additionally PNP[nr] ⊈ Σpm ∪ Πpm.This strengthens a result by Mocas [M96] that for any r, PNP[nr] ⊈ NEXP.In addition, we use FM-truth definitions to give a simple sufficient (...) condition for the σ11 arity hierarchy to be strict over finite models. (shrink)

Call a set A n-correctable if every set Turing reducible to A via a Turing machine that on any input makes at most n queries is Turing reducible to A via a Turing machine that on any input makes at most n-queries and on any input halts no matter what answers are given to its queries. We show that if a c.e. set A is n-correctable for some n ≥ 2, then it is n-correctable for all n. (...) We show that this is the optimal such result by constructing a c.e. set that is 1-correctable but not 2-correctable. The former result is obtained by examining the logical closure properties of c.e. sets that are 2-correctable. (shrink)

The relativized propositional calculus is a system of Boolean formulas with query symbols. A formula in this system is called a one-query formula if the number of occurrences of query symbols is just one. If a one-query formula is a tautology with respect to a given oracle A then it is called a one-query tautology with respect to A. By extending works of Ambos-Spies (1986) and us (2002), we investigate the measure of the class of all oracles A such that (...) the set of all one-query tautologies with respect to A does not p-btt-reduce to A, where p-btt denotes polynomial-time bounded-truth-table. We show that certain Dowd-type generic oracles all belong to the class, and hence measure of the class is one. (shrink)

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality, purification, strong symmetry, and informationally consistent composition. Sorkin has (...) defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, because fewer queries provide no information about the solution, then the corresponding “no-information” lower bound in theories lying at the kth level of Sorkin’s hierarchy is \. This lower bound leaves open the possibility that quantum oracles are less powerful than general probabilistic oracles, although it is not known whether the lower bound is achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource that might have power beyond that offered by quantum computation. (shrink)

This work concerns itself with characterising the different types of contents that arise from uses of interrogative sentences, describing what meanings get associated with particular interrogative sentences, and explaining how these get put together compositionally on the basis of the meaning of their constituents, with particular attention to the meaning of interrogative phrases. ;Within most recent work in linguistic semantics, questions, the contents of query uses of interrogatives, have been analysed reductively as higher order propositional objects. The current work argues (...) against such an analysis. In its stead a view of questions is offered wherein these constitute the subclass of singular propositional entities, unresolved states-of-affairs , those that contain one or more argument roles of the propositional entity with whom no entity is associated. This view provides for an inherently richer notion of answerhood that is at the same time based on entities that are more plausibly available to cognitive agents engaged in querying. The need for a richer notion of answerhood is prompted by our demonstration that the class of answers to any given question--contents that can be conveyed by acceptable responses--has been considerably under-recognized in past work. An important gain made by the proposed approach is that it reveals and provides a simple account of systematic and cross-linguistically stable contrasts in the ability of a predicate to take an interrogative meaning as an argument. ;Our proposal for characterising the meaning of interrogative expressions argues that there exist three independent classes of uses which interrogative phrases can undergo, which we dub independent, dependent, and reprise uses. We argue extensively against an assumption common to most past work that interrogatives should be viewed as quantifiers on either syntactic or semantic grounds. We propose that dependent and reprise uses of interrogative expressions are each particular instances of use-types applicable to non-interrogative expressions. Dependent uses include bound variable anaphora as an instance. Reprise uses comprehend quotative uses of declarative sentences. We show how combining the general characteristics of each use type with the characterisation of independent interrogative uses we provide enables the defining conditions pertaining to these additional interrogative uses to be derived. This allows for a simple and comprehensive account of the available interrogative meanings. (shrink)

We prove that the set of all recursive functions cannot be inferred using first-order queries in the query language containing extra symbols $\lbrack +, . The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in $\lbrack +, . Additionally, we resolve an open (...) question in [7] about passive versus active learning. (shrink)

We develop a bounded version of the finite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain {0, …, n − 1}d with only equivalence queries. Applying this method, we show three main results:1. The class of unions of rectangles is polynomial time learnable for constant dimension d.2. The class of unions of rectangles whose projections at some unknown dimension are pairwise-disjoint is polynomial time learnable.3. The class (...) of unions of two disjoint rectangles is polynomial time learnable with unions of two rectangles as hypotheses. (shrink)

We prove that the set of all recursive functions cannot be inferred using first-order queries in the query language containing extra symbols $\lbrack +, < \rbrack$. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in $\lbrack +, < \rbrack$. Additionally, we resolve (...) an open question in [7] about passive versus active learning. (shrink)

The object of this paper is to explain a certain type of construction which occurs in priority proofs and illustrate it with two examples due to Lachlan and Harrington. The proofs in the examples are essentially the original proofs; our main contribution is to isolate the common part of these proofs. The key ideas in this common part are due to Lachlan; we include several improvements due to Harrington, Soare, Slaman, and the author.Our notation is fairly standard. If X is (...) an r.e. set, Xs is the finite set of elements enumerated in X before step s. if Ф is a recursive functional, Фs is the approximation to Ф at step s; it only queries the oracle about numbers xi and iless-than-or-equals, slantx; and right-pointing angle bracketx0,...,xk−1right-pointing angle bracket is an increasing function of each of its arguments. Sets are sometimes identified with their characteristic functions. Wj isthe jth r.e. set. Xc is the complement of X. (shrink)

In Opticks, Newton notes that by following the method of analysis and synthesis, ’the bounds of moral philosophy will also be enlarged’. Hume’s Treatise fulfills this vision, albeit with significant caveats. The chapter argues: 1) Hume’s affinity with Newton is primarily methodological, and Hume’s project is closer to the Queries of Opticks than to the Principia. 2) For Hume, moral philosophy is an experimental study of moral beings qua moral beings which results in ‘an anatomy of the mind’ embodying (...) an epistemic ideal closer to Scottish philosophical chemistry than to any kind of mechanical philosophy. 3) Hume primarily inquires into qualitatively different active principles of human nature that explain why humans function as they do. 4) The knowledge that Hume’s project offers can be used normatively. 5) Thus, in Hume’s hands the boundaries of moral philosophy are enlarged. Yet, being entirely secular, it was not what Newton had envisioned. (shrink)

In our former works, for a given concept of reduction, we study the following hypothesis: “For a random oracle A, with probability one, the degree of the one-query tautologies with respect to A is strictly higher than the degree of A.” In our former works (Suzuki in Kobe J. Math. 15, 91–102, 1998; in Inf. Comput. 176, 66–87, 2002; in Arch. Math. Logic 44, 751–762), the following three results are shown: The hypothesis for p-T (polynomial-time Turing) reduction is equivalent to (...) the assertion that the probabilistic complexity class R is not equal to NP; The hypothesis for p-tt (polynomial-time truth-table) reduction implies that P is not NP; The hypothesis holds for each of the following: disjunctive reduction, conjunctive reduction, and p-btt (polynomial-time bounded-truth-table) reduction. In this paper, we show the following three results: (1) Let c be a positive real number. We consider a concept of truth-table reduction whose norm is at most c times size of input, where for a relativized propositional formula F, the size of F denotes the total number of occurrences of propositional variables, constants and propositional connectives. Then, our main result is that the hypothesis holds for such tt-reduction, provided that c is small enough. How small c can we take so that the above holds? It depends on our syntactic convention on one-query tautologies. In our setting, the statement holds for all c < 1. (2) The hypothesis holds for monotone truth-table reduction (also called positive reduction). (3) Dowd (in Inf. Comput. 96, 65–76, 1992) shows a polynomial upper bound for the minimum sizes of forcing conditions associated with a random oracle. We apply the above result (1), and get a linear lower bound for the sizes. (shrink)

This work deals with the expressive power of logics on finite graphs with access to an additional "arbitrary" linear order. The queries that can be expressed this way are the order-invariant queries for the logic. For the standard logics used in computer science, such as first-order logic, it is known that access to an arbitrary linear order increases the expressiveness of the logic. However, when we look at the separating examples, we find that they have satisfying models whose (...) Gaifman Graph is complex -unbounded in valence and in treewidth. We thus explore the expressiveness of order-invariant queries over well-behaved graphs. We prove that first-order order-invariant queries over strings and trees have no additional expressiveness over first-order logic in the original signature. We also prove new upper bounds on order-invariant queries over bounded treewidth and bounded valence graphs. Our results make use of a new technique of independent interest: the application of algebraic characterizations of definability to show collapse results. (shrink)

This paper is concerned with techniques for identifying simple and quantified lattice points in 2SAT polytopes. 2SAT polytopes generalize the polyhedra corresponding to Boolean 2SAT formulas, Vertex-Packing and Network flow problems; they find wide application in the domains of Program verification and State-Space search . Our techniques are based on the symbolic elimination strategy called the Fourier-Motzkin elimination procedure and thus have the advantages of being extremely simple and incremental. We also provide a characterization of a 2SAT polytope in terms (...) of its extreme points and derive some interesting hardness results for associated optimization problems. Finally, we provide a brief discussion on the maximum size of a subdeterminant of the linear system representing a 2SAT polytope; this parameter plays a vital role in deriving analytical bounds on the size of the search space for checking whether the polyhedron includes a lattice point. (shrink)

Abstract The increasing prevalence of armed drones in the conduct of military operations has generated robust debate. Among legal scholars, the crux of the dispute generally pits those who herald the new technology's unparalleled precision against those who view such newfound capabilities as an inducement to employ excessive force. Largely overlooked in the discussion over how drone strikes can be accomplished lawfully is a more fundamental question: Can a model of warfare that eschews any risk of harm to one party (...) be squared with the ethical framework that informs the law of war? This matter has less to do with the technology per se than with a policy orientation that utilizes such technology as a strategy in itself, as opposed to one military tool in a larger arsenal. A corollary to the incongruity of riskless warfare is to query whether the ensuing breakdown of ethical and legal norms unwittingly encourages the very instability that the law of war attempts to control, thereby endangering the civilian populations of all parties to the conflict. While other authors have previously addressed the challenges posed by asymmetry to the law of armed conflict in different formats, this article explores these issues through a hypothetical scenario and seeks to elucidate some of the potential ramifications of the pursuit of physical impunity in war. (shrink)

The task of computing a function F with the help of an oracle X can be viewed as a search problem where the cost measure is the number of queries to X. We ask for the minimal number that can be achieved by a suitable choice of X and call this quantity the query complexity of F. This concept is suggested by earlier work of Beigel, Gasarch, Gill, and Owings on “Bounded query classes”. We introduce a fault tolerant (...) version and relate it with Ulam's game. For many natural classes of functions F we obtain tight upper and lower bounds on the query complexity of F. Previous results like the Nonspeedup Theorem and the Cardinality Theorem appear in a wider perspective. (shrink)

The story of the body. Fay Bound Alberti takes the human body apart in order to put it back anew, telling the cultural history of our key organs and systems from the inside out, from blood to guts, brains to sex organs.

In this paper I draw from Martin Heidegger’s phenomenology of the 1920s to outline some basic features of his theory of intentionality that I believe have not been fully appreciated or utilized, and that allow for both novel and fruitful interventions in questions about meaning, the relationship between mind and the world, and epistemic justification, principally as they appear in John McDowell’s synoptic project in Mind and World. I argue that while elements of McDowell’s picture are ultimately unsatisfying and problematic, (...) much of his conceptual framework can and should be put into dialogue with Heidegger’s, and that in so doing we make available powerful resources for amending the McDowellian account. Moreover, these emendations have attractive implications for his distinctive desiderata. In particular, they provide original conceptions of normativity’s place in nature, of the boundaries of the space of reasons, and of the relationship between the answerability of thought both to the world and to human beings as a rational community. (shrink)

Many contemporary scholars argue that Schelling’s version of intellectual intuition retains certain central features of the Kantian and Fichtean conceptions. One of the common claims is that, as with Kant and Fichte, Schelling’s intellectual intuition is the power of the subject’s productive understanding. However, we show that for the Schelling of the Identitätsphilosophie period, intellectual intuition is the power not of an understanding that intuits, or a productive intellect, but of a receptive and penetrating sensibility that understands.

Loneliness is one of the most neglected aspects of emotion history, despite claims that the 21st century is the loneliest ever. This article argues against the widespread belief that modern-day loneliness is inevitable, negative, and universal. Looking at its language and etymology, it suggests that loneliness needs to be understood firstly as an “emotion cluster” composed of a variety of affective states, and secondly as a relatively recent invention, dating from around 1800. Loneliness can be positive, and as much a (...) part of the body as the mind. Using a longue durée approach, I argue that we cannot understand loneliness as a “modern epidemic” without considering its history, its meanings, its practice, and its links with the body. (shrink)

This essay explores small “ordinary” experiences of moral harm as problems of social injustice. Starting with two stories, we first argue against a dominant framework of personal responsibility that assigns responsibility to particular blameworthy agents. Instead we sketch an account of why structural responsibility for social harm must be considered, drawing on the work of Iris Marion Young and Pierre Bourdieu. Finally, drawing on Margaret Walker’s notion of moral repair and Christopher Marshall’s interpretation of the parable of the Good Samaritan, (...) we sketch an account of Christian moral responsibility grounded in restorative justice that seeks to address daily experiences of moral harm through the moral repair work of neighbor-love. (shrink)

Let equation image. We show that for many reducibilities, the requirement that a relation be intrinsically reducible to the α-th jump of a countable mode A has a syntactic equivalent. Furthermore, we show that many reducibilities coincide in such a situation.

We here examine the expressive power of first order logic with generalized quantifiers over finite ordered structures. In particular, we address the following problem: Given a family Q of generalized quantifiers expressing a complexity class C, what is the expressive power of first order logic FO(Q) extended by the quantifiers in Q? From previously studied examples, one would expect that FO(Q) captures L C , i.e., logarithmic space relativized to an oracle in C. We show that this is not always (...) true. However, after studying the problem from a general point of view, we derive sufficient conditions on C such that FO(Q) captures L C . These conditions are fulfilled by a large number of relevant complexity classes, in particular, for example, by NP. As an application of this result, it follows that first order logic extended by Henkin quantifiers captures L NP . This answers a question raised by Blass and Gurevich [Ann. Pure Appl. Logic, vol. 32, 1986]. Furthermore we show that for many families Q of generalized quantifiers (including the family of Henkin quantifiers), each FO(Q)-formula can be replaced by an equivalent FO(Q)-formula with only two occurrences of generalized quantifiers. This generalizes and extends an earlier normal-form result by I. A. Stewart [Fundamenta Inform. vol. 18, 1993]. (shrink)

When analyzing database query languages a roperty, of theories, the pseudo-finite homogeneity property, has been introduced and applied (cf. [3]). We show that a stable theory has the pseudo-finite homogeneity property just in case its expressive power for finite states is bounded. Moreover, we introduce the corresponding pseudo-finite saturation property and show that a theory fails to have the finite cover property if and only if it has the pseudo-finite saturation property.

A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are algorithmically solvable (...) for restricted subsets---or, as we say, fragments---of first-order logic, a fact which is today of considerable interest in Computer Science. This book provides an up-to-date survey of the principal axes of research, charting the limits of decision in first-order logic and exploring the trade-off between expressive power and complexity of reasoning. Divided into three parts, the book considers for which fragments of first-order logic there is an effective method for determining satisfiability or finite satisfiability. Furthermore, if these problems are decidable for some fragment, what is their computational complexity? Part I focusses on fragments defined by restricting the set of available formulas. Topics covered include the Aristotelian syllogistic and its relatives, the two-variable fragment, the guarded fragment, the quantifier-prefix fragments and the fluted fragment. Part II investigates logics with counting quantifiers. Starting with De Morgan's numerical generalization of the Aristotelian syllogistic, we proceed to the two-variable fragment with counting quantifiers and its guarded subfragment, explaining the applications of the latter to the problem of query answering in structured data. Part III concerns logics characterized by semantic constraints, limiting the available interpretations of certain predicates. Taking propositional modal logic and graded modal logic as our cue, we return to the satisfiability problem for two-variable first-order logic and its relatives, but this time with certain distinguished binary predicates constrained to be interpreted as equivalence relations or transitive relations. The work finishes, slightly breaching the bounds of first-order logic proper, with a chapter on logics interpreted over trees. (shrink)

We introduce multifunction algebras B i τ where τ is a set of 0 or 1-ary terms used to bound recursion lengths. We show that if for all ℓ ∈ τ we have ℓ ∈ O then B i τ = FP Σ i−1 p , those multifunctions computable in polynomial time with at most O )) queries to a Σ i−1 p witness oracle for ℓ ∈ τ and p a polynomial. We use our algebras to obtain independence (...) results in bounded arithmetic. In particular, we show if S 2 i proves Σ j b = PH for some j⩾i then S 2 i ≼ B S 2 . This implies if P NP ≠ P NP then S 2 1 does not prove the polynomial hierarchy collapses. We then consider a subtheory, Z , of the well-studied bounded arithmetic theory S 2 = ∪ i S 2 i . Using our algebras we establish the following properties of this theory: Z cannot prove the polynomial hierarchy collapses. In fact, even Z+ Π ̂ 0 b -consequences of S 2 cannot prove the hierarchy collapses. If Z ⊆ S 2 i for any i then the polynomial hierarchy collapses. If Z proves the polynomial hierarchy is infinite then for all i , S 2 i ⊢ Σ i p ≠ Π i p. (shrink)

First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a family (...) of generalized quantifiers on finite structures. Using the logics L∞ωω, we can express polynomial-time properties that are not definable in L∞ωω, such as “there is an even number of x” and “there exists at least n/2 x” , without going to second-order logic. We show that equivalence of finite structures relative to L∞ωω can be characterized in terms of certain pebble games that are a variant of the Ehrenfeucht—Fraïssé games. We combine this game-theoretic characterization with sophisticated combinatorial tools from Ramsey theory, such as van der Waerden's Theorem and Folkman's Theorem, in order to investigate the scope and limits of generalized quantifiers in finite model theory. We obtain sharp lower bounds for expressibility in the logics L∞ωω and discover an intrinsic difference between adding finitely many simple unary generalized quantifiers to L∞ωω adding infinitely many. In particular, we show that if Qis a finite sequence of simple unary generalized quantifiers, then the equicardinality, or Härtig, quantifier is not definable in L∞ωω. We also show that the query “does the equivalence relation E have an even number of equivalence classes” is not definable in the extension L∞ωω of L∞ωω by the Härtig quantifier I and any finite sequence Q of simple unary generalized quantifiers. (shrink)

We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament–Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Németi ([2002]) had shown that some relations on natural numbers that are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. (...) The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second-order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime, which is thus a universal constant of that spacetime. Theorem C. Assuming the (modest and standard) requirement that spacetime manifolds be paracompact and Hausdorff, for any spacetime there will be a countable ordinal upper bound, , on the complexity of questions in the Borel hierarchy computable in it. Introduction 1.1 History and preliminaries Hyperarithmetic Computations in MH Spacetimes 2.1 Generalising SADn regions 2.2 The complexity of questions decidable in Kerr spacetimes An Upper Bound on Computational Complexity for Each Spacetime CiteULike Connotea Del.icio.us What's this? (shrink)

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

This article examines whether the gender balance on the High Court of Australia has disrupted the gender regime. In so doing it considers the first lead judgments of the three women judges who sat concurrently on the High Court of Australia between 2009 and early 2015. The High Court has adopted an interesting informal practice of welcoming new judges whereby the newest member authors the lead judgment and their judicial colleagues offer a one-line concurrence. The way in which judicial authority (...) is conferred in these judgments is reminiscent of the space in political spheres where an incumbent has their first opportunity to set out their identity and agenda in a speech free of the noise of dissent or debate; the ‘maiden’ speech. In that space the price an incumbent pays for comity is conformity. This article contends that the first judgment is a useful way of situating a discussion about women judges’ contributions vis-à-vis difference by querying the extent to which the woman judge can ever shake-off her status as the maiden bound to conform for the sake of comity. (shrink)