This book investigates the phenomenon of semantic under-determinacy by seeking an answer to the questions of how it can be explained, and how communication is possible despite it.

In this paper I will tackle three issues. First, I aim to briefly outline the backbone of semantic minimalism, while focusing on the idea of ‘liberal truth conditions’ developed by Emma Borg in her book ‘Minimal Semantics’. Secondly, I will provide an account of the three principal views in legal interpretation: intentionalism, textualism and purposivism. All of them are based on a common denominator labelled by lawyers ‘literal meaning’. In the paper I suggest a novel way of viewing this (...) common denominator as almost identical to the Borgian ‘liberal truth conditions’, at least at a conceptual level. In the third section I will focus on the conceptual similarities between the two ideas. I intend to depict that, although legal theorists do not admit it explicitly, they treat literal legal meaning as minimal propositional content that can be ascribed liberal truth conditions. There are two main objections to liberal truth conditions: their under-determinacy and unintuitive character. Both objections can be applied to ‘literal meaning’. However, the idea of liberal truth conditions gives an adequate account of what lawyers call literal meaning and is helpful in explaining the mechanism of understanding of provisions and reasons leading to the necessity of statutory interpretation. (shrink)

Possibility semantics offers an elegant framework for a semantic analysis of modal logic that does not recruit fully determinate entities such as possible worlds. The present papers considers the application of possibility semantics to the modeling of the indeterminacy of the future. Interesting theoretical problems arise in connection to the addition of object-language determinacy operator. We argue that adding a two-dimensional layer to possibility semantics can help solve these problems. The resulting system assigns to the two-dimensional determinacy (...) operator a well-known logic (coinciding with the logic of universal modalities under global consequence). The paper concludes with some preliminary inroads into the question of how to distinguish two-dimensional possibility semantics from the more established branching framework. (shrink)

All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (i.e. all its non-empty clopen subspaces are homeomorphic), with the trivial exception of locally compact spaces. In fact, we obtain a more general result on the uniqueness of zero-dimensional homogeneous spaces which generate a given Wadge class. This extends work of van Engelen (who obtained the corresponding results for Borel spaces), complements a result of van (...) Douwen, and gives partial answers to questions of Terada and Medvedev. (shrink)

The thesis of Ineffability has it that no proposition can be fully expressed by a sentence, this meaning that no sentence-type, or even sentence-token whose indexicality and ambiguities have been resolved, can fully encode a proposition. The thesis of the propositionality of thoughts has it that thoughts are propositional. An implication of the joint endorsement of these two theses is that thoughts are ineffable. The aim of this paper is to argue that this is not the case: there are effable (...) thoughts, and we can even safely say that, generally, thoughts are effable. In order to defend this insight, I first counter the thesis of the propositionality of thought by bringing some counterexamples to it, which amount to cases of non-fully propositional thought. I then argue that, if thoughts can be and often are non-fully propositional, they can be expressed by sentences that fail to fully express a proposition. I also show that the propositional thoughts that we can entertain are after all effable (in a suitable, relevant sense) and resist some alleged examples of insurmountable ineffability. (shrink)

The notion of individuation has both a semantic and an ontological face. More exactly, the claim can be defended that individuation has a proprietary linguistic or conceptual aspect as distinct from an ontological one. Ontologists such as W. V. Quine would credit neither the possibility of such a divergence nor the intelligibility of its proposal. The ontology of a language, for Quine, is inseparable from its individuative resources, mechanisms such as identity, pluralization, pronouns, and so forth. I aim here (...) to pick apart the ontological from the semantic aspect of individuation at one place where they interact, thereby to show that the distinction, far from being a mere abstraction lacking explanatory leverage, is vital for achieving an adequate characterization of the representational powers of language. I begin by attempting to put the issue into some kind of perspective, a didactic move prudent in virtue of the brassiness of the subsequent tacks. (shrink)

The ‘question under discussion’ (or ‘QUD’) framework is a pragmatic framework that draws on work in the semantics of questions to provide an appealing account of a range of pragmatic phenomena, including the use of prosodic focus in English and restrictions on acceptable discourse moves (Roberts 1996). More recently, however, a number of proposals have attempted to use the framework to help to settle issues at the semantics/pragmatics boundary, fixing the truth-conditions of what is said by a speaker (which (...) many theorists take to be a semantic matter). In this discussion piece, we suggest that this kind of putative extension of the work to be done by the QUD framework is illegitimate, as the framework ultimately seems to depend on a prior grip on semantic content. To see this, we first outline the QUD framework and then raise our concern. (shrink)

“Flat pre-semantics” lets each parameter of truth (etc.) be considered sepa-rately and equally, and without worrying about grammatical complications. This allows one to become a little clearer on a variety of philosophical-logical points, such as the use fulness of Carnapian tolerance and the deep relativity of truth. A more definite result of thinking in terms of flat pre-semantics lies in the articulation of some instructive ways of categorizing operations on meanings in purely logical terms in relation to various parame- ters (...) of truth (etc.); namely, closing vs. leaving open, local vs. translocal, and anchored vs. unanchored. Basic relations among these categories are established. (shrink)

Terence Parsons; II*—Underlying States in the Semantical Analysis of English, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 13.

“Flat pre-semantics” lets each parameter of truth be considered separately and equally, and without worrying about grammatical complications. This allows one to become a little clearer on a variety of philosophical-logical points, such as the usefulness of Carnapian tolerance and the deep relativity of truth. A more definite result of thinking in terms of flat pre-semantics lies in the articulation of some instructive ways of categorizing operations on meanings in purely logical terms in relation to various parameters of truth ; (...) namely, closing vs. leaving open, local vs. translocal, and anchored vs. unanchored. Basic relations among these categories are established. (shrink)

Schmidt’s game and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory. These games are real games, that is, games in which the players make moves from a complete separable metric space. The determinacy of these games trivially follows from the axiom of determinacy for real games, $\mathsf {AD}_{\mathbb R}$, which is a much stronger axiom than that asserting all integer games are determined, $\mathsf {AD}$. (...) One of our main results is a general theorem which under the hypothesis $\mathsf {AD}$ implies the determinacy of intersection games which have a property allowing strategies to be simplified. In particular, we show that Schmidt’s $(\alpha,\beta,\rho )$ game on $\mathbb R$ is determined from $\mathsf {AD}$ alone, but on $\mathbb R^n$ for $n \geq 3$ we show that $\mathsf {AD}$ does not imply the determinacy of this game. We then give an application of simple strategies and prove that the winning player in Schmidt’s $(\alpha, \beta, \rho )$ game on $\mathbb {R}$ has a winning positional strategy, without appealing to the axiom of choice. We also prove several other results specifically related to the determinacy of Schmidt’s game. These results highlight the obstacles in obtaining the determinacy of Schmidt’s game from $\mathsf {AD}$. (shrink)

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L_D and L_I, based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We (...) argue that L_D and L_I naturally resolve a range of interpretational problems that arise in D and I.We also obtain sound and complete axiomatizations for L_D and L_I . (shrink)

Cognitive Science, Volume 46, Issue 5, May 2022.

Planning with incomplete knowledge becomes a very active research area since late 1990s. Many logical formalisms introduce sensing actions and conditional plans to address the problem. The action language $\mathcal{A}_{K}$ invented by Son and Baral is a well-known framework for this purpose. In this paper, we propose so-called cautious and weakly cautious semantics for $\mathcal{A}_{K}$ , in order to allow an agent to generate and execute reliable plans in safety-critical environments. Intuitively speaking, cautious and weakly cautious semantics enable the agent (...) to know exactly what happens after the execution of an action. Computational complexity analysis shows that cautious semantics reduces the reasoning complexity of $\mathcal{A}_{K}$ , it is also worth to point out that many useful domains could still be expressed with this setting. Another important contribution of our work is the development of Hoare style proof systems. These proof systems are served as inference mechanisms for the verification of conditional plans, and proved to be sound and complete. In addition, they could also be used for plan generation, in the sense that constructing a derivation is indeed a procedure to finding a plan. We point out that the proof systems posses a nice property for off-line planning, that is, the agent could generate and store short proofs in her spare time, and perform quick plan query by easily constructing a long proof from the stored shorter ones (under the assumption that sufficient proofs are stored). (shrink)

Formal approaches that aim at representing human reasoning should be evaluated based on how humans actually reason. One way of doing so is to investigate whether psychological findings of human reasoning patterns are represented in the theoretical model. The computational logic approach discussed here is the so-called weak completion semantics which is based on the three-valued ᴌukasiewicz logic. We explain how this approach adequately models Byrne’s suppression task, a psychological study where the experimental results show that participants’ conclusions systematically deviate (...) from the classical logically correct answers. As weak completion semantics is a novel technique in the field of computational logic, it is important to examine how it corresponds to other already established non-monotonic approaches. For this purpose we investigate the relation of weak completion with respect to completion and three-valued stable model semantics. In particular, we show that well-founded semantics, a widely accepted approach in the field of non-monotonic reasoning, corresponds to weak completion semantics for a specific class of modified programs. (shrink)

A skeptical worry known as ‘the indeterminacy of computation’ animates much recent philosophical reflection on the computational identity of physical systems. On the one hand, computational explanation seems to require that physical computing systems fall under a single, unique computational description at a time. On the other, if a physical system falls under any computational description, it seems to fall under many simultaneously. Absent some principled reason to take just one of these descriptions in particular as relevant (...) for computational explanation, widespread failure of computational explanation would appear to follow. This paper advances a new solution to the indeterminacy of computation. Very roughly, I argue that the computational identity of a physical system is determinate relative to a contextually specified way of regarding that system computationally—known as a labelling scheme. When a system simultaneously implements multiple computations, it does so relative to different labelling schemes. But relative to a fixed labelling scheme, a physical system has a unique computational identity. I argue that this relativistic conception of computational identity vindicates computational explanation in the face of simultaneous implementation. (shrink)

We show, assuming weak large cardinals, that in the context of games of length \ with moves coming from a proper class, clopen determinacy is strictly weaker than open determinacy. The proof amounts to an analysis of a certain level of L that exists under large cardinal assumptions weaker than an inaccessible. Our argument is sufficiently general to give a family of determinacy separation results applying in any setting where the universal class is sufficiently closed; e.g., (...) in third, seventh, or \\)th order arithmetic. We also prove bounds on the strength of Borel determinacy for proper class games. These results answer questions of Gitman and Hamkins. (shrink)

After I had delivered the paper (Stechow, 2003), a colleague wrote to me that the system outlined was virtually identical with (Kratzer, 1998), and that this article had not been cited. The longer version (Stechow, 2002 (to appear)) quotes (Kratzer, 1998), and the reference has been deleted by my automatic bibliography program when I rewrote and shortened the paper. I am sorry for that.

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural (...) logic that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)

We study the notion of [Formula: see text]-MAD families where [Formula: see text] is a Borel ideal on [Formula: see text]. We show that if [Formula: see text] is any finite or countably iterated Fubini product of the ideal of finite sets [Formula: see text], then there are no analytic infinite [Formula: see text]-MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective [Formula: see text]-MAD families; and under the full Axiom of Determinacy (...) [Formula: see text][Formula: see text] or under [Formula: see text] there are no infinite [Formula: see text]-mad families. Similar results are obtained in Solovay’s model. These results apply in particular to the ideal [Formula: see text], which corresponds to the classical notion of MAD families, as well as to the ideal [Formula: see text]. The proofs combine ideas from invariant descriptive set theory and forcing. (shrink)

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

Vague expressions are omnipresent in natural language. As such, their use in legal texts is virtually inevitable. If a law contains vague terms, the question whether it applies to a particular case often lacks a clear answer. One of the fundamental pillars of the rule of law is legal certainty. The determinacy of the law enables people to use it as a guide and places judges in the position to decide impartially. Vagueness poses a threat to these ideals. In (...) borderline cases, the law seems to be indeterminate and thus incapable of serving its core rule of law value. -/- In the philosophy of language, vagueness has become one of the hottest topics of the last two decades. Linguists and philosophers have investigated what distinguishes "soritical " vagueness from other kinds of linguistic indeterminacy, such as ambiguity, generality, open texture, and family resemblance concepts. There is a vast literature that discusses the logical, semantic, pragmatic, and epistemic aspects of these phenomena. Legal theory has hitherto paid little attention to the differences between the various kinds of linguistic indeterminacy that are grouped under the heading of "vagueness ", let alone to the various theories that try to account for these phenomena. -/- The paper is an introduction to a book of the same title. Bringing together leading scholars working on the topic of vagueness in philosophy and in law, the book fosters a dialogue between philosophers and legal scholars by examining how philosophers conceive legal ambiguity from their theoretical perspective and how legal theorists make use of philosophical theories of vagueness. (shrink)

We investigate a simple game paradigm for intuitionistic logic, inspired by Wajsberg’s implicit inhabitation algorithm and Beth tableaux. The principal idea is that one player, ∃ros, is trying to construct a proof in normal form while his opponent, ∀phrodite, attempts to build a counter-model. The determinacy of the game implies therefore both completeness and semantic cut-elimination.

I argue that semantics is the study of the proprietary database of a centrally inaccessible and informationally encapsulated input–output system. This system’s role is to encode and decode partial and defeasible evidence of what speakers are saying. Since information about nonlinguistic context is therefore outside the purview of semantic processing, a sentence’s semantic value is not its content but a partial and defeasible constraint on what it can be used to say. I show how to translate this thesis (...) into a detailed compositional-semantic theory based on the influential framework of Heim and Kratzer. This approach situates semantics within an independently motivated account of human cognitive architecture and reveals the semantics–pragmatics interface to be grounded in the underlying interface between modular and central systems. (shrink)

This volume contains the papers read at the conference on 'Semantics from different points of view' that took place at Konstanz University in Septem ber 1978. This interdisciplinary conference Vias organized by the':Sonderfor schungsbereich 99 - Linguistik' and sponsored by the Deutsche Forschungsge meinschaft. Li~guists, philosophers, logicians, and psychologists met to dis cuss recent developments in the study of the semantics of natural language from the point of view of their disciplines. But this is not to say that there was (...) one particular topic shared by all the participants. The conference was organized because the seven research groups that constitute the Sonderforschungsbereich wanted to discuss their results in an international context and to get advice and guidance for the work still to be done. Therefore, quite a number of topics were covered, though at different levels of precision, under the general label 'semantics'. And the selection of topics, as well as the relative importance given to them, is due to the research interests currently represented in the Sonderforschungs bereich. (shrink)

In the major French and German etymological dictionaries of Latin, there is some puzzlement over the semantics of exāmen: how can one word refer to a measurement or examination, but also to a swarm of bees? Walde and Hofmann suggest these two dis-parate meanings stem from the diverse meanings of the verb exigō (<*ex-agō, ‘to drive out’), from which exāmen derives. They claim these two senses of exāmen become two words in the Latin Sprachgefühl. Ernout and Meillet agree: there is (...) more than one exāmen in the Latins’ sentiment linguistique. I, too, agree. But this approach does not tell us why these terms derive from exigō, nor does it give any hint of an underlying concept which measurements and swarms of bees share, which makes a derivation from exigō appropriate to both. The present paper addresses this puzzle by reducing the two meanings of exāmen to one meaning of the parent term *ex-agō: ‘to drive out.’ In sum: a swarm of bees is a ‘driving out’ or outpouring, and a measurement or examination is a ‘driving out’ or setting out for scrutiny. This interpretation is moreover supported by semantically parallel uses of cognate terms in other Indo-European languages, notably Greek and Old Irish, and by semantic parallels in English and in the Slavic language family. Along the way, I touch upon a philosophical puzzle: at what point do evolving linguistic items with a common source become distinct from one another? (shrink)

Philosophers and cognitive scientists have worried that research on animal mind-reading faces a ‘logical problem’: the difficulty of experimentally determining whether animals represent mental states (e.g. seeing) or merely the observable evidence (e.g. line-of-gaze) for those mental states. The most impressive attempt to confront this problem has been mounted recently by Robert Lurz. However, Lurz' approach faces its own logical problem, revealing this challenge to be a special case of the more general problem of distal content. Moreover, participants in this (...) debate do not agree on criteria for representation. As such, future debate should either abandon the representational idiom or confront underlying semantic disagreements. (shrink)

According to semantic minimalism, context-invariant minimal semantic propositions play an essential role in linguistic communication. This claim is key to minimalists’ argument against semantic contextualism: if there were no such minimal semantic propositions, and semantic content varied widely with shifts in context, then it would be “miraculous” if communication were ever to occur. This paper offers a critical examination of the minimalist account of communication, focusing on a series of examples where communication occurs without a (...) minimal semantic proposition shared between speaker and hearer. The only way for minimalists to respond to these examples is by restricting the scope of their account to intra-lingual communication. It can then be shown that the minimalist’s notion of a language shrinks to a point, such that practically no instances of communication will fall under that account, and that the retreat to intra-lingual communication is in any case self-defeating, since the only way for minimalists to account for the individuation of languages is by resort to precisely the kinds of contextual considerations they abjured in the first place. In short, if, as minimalists allege, contextualism founders because it renders communication contingent on speaker and hearer sharing a context, it can now be seen that minimalism faces a parallel problem because it renders communication contingent on speaker and hearer sharing a language. I end by arguing that the possibility of communication cannot, as minimalists assume, be grounded in shared semantic conventions; rather, successful communication must precede the establishment of any particular set of semantic conventions. (shrink)

Moeser suggested participants default to linear ordering elements but they can be primed to impose either linear or partial ordering. This study seems problematic insofar as ‘greater than’ might be understood to incline participants to favor linear orderings. Recent follow-up studies strongly suggest participants do not default to linear ordering. It seems plausible, moreover, that the observed priming effect is far more pervasive than Moeser countenanced. The present work explores the extent to which priming for linear or partial orders conflicts (...) with the construction of linear or partial ordering lists. Our two experiments suggest friction between priming and task, and also show once the priming tasks are cleared of potentially confounding semantic content, participants perform equally with respect to constructing linear or partial orders under similar priming conditions. (shrink)

Previous studies have shown that children retreat from argument‐structure overgeneralization errors (e.g., *Don’t giggle me) by inferring that frequently encountered verbs are unlikely to be grammatical in unattested constructions, and by making use of syntax‐semantics correspondences (e.g., verbs denoting internally caused actions such as giggling cannot normally be used causatively). The present study tested a new account based on a unitary learning mechanism that combines both of these processes. Seventy‐two participants (ages 5–6, 9–10, and adults) rated overgeneralization errors with higher (...) (*The funny man’s joke giggled Bart) and lower (*The funny man giggled Bart) degrees of direct external causation. The errors with more‐direct causation were rated as less unacceptable than those with less‐direct causation. This finding is consistent with the new account, under which children acquire—in an incremental and probabilistic fashion—the meaning of particular constructions (e.g., transitive causative = direct external causation) and particular verbs, rejecting generalizations where the incompatibility between the two is too great. (shrink)

Two-player, zero-sum, non-cooperative, blindfold games in extensive form with incomplete information are considered in this paper. Any information about past moves which players played is stored in a database, and each player can access the database. A polynomial game is a game in which, at each step, all players withdraw at most a polynomial amount of previous information from the database. We show resource-bounded determinacy of some kinds of finite, zero-sum, polynomial games whose pay-off sets are computable by non-deterministic (...) polynomial-time function-oracle Turing machines. We call a pay-off set -determined if, for any polynomial game G associated with the given pay-off set, either player has a winning strategy which is in for any subgames of G. We show that there exists an FP-strongly-determined pay-off set which is computed by an exponential-time oracle Turing machine, where FP is the set of polynomial-time computable functions. We also discuss several relationships between the determinacy of polynomial games and recursion-theoretic properties for the classes co-NP and co-NEXP. We show that the polynomial version of the axiom of choice holds under some assumption of polynomial determinacy for a pay-off set which is polynomial-time computable with parallel queries. This principle of choice implies that co-NP has the separation property. (shrink)

Semantics for Reasons is a book about what we mean when we talk about reasons. It not only brings together the theory of reasons and natural language semantics in original ways but also sketches out a litany of implications for metaethics and the philosophy of normativity. In their account of how the language of reasons works, Bryan R. Weaver and Kevin Scharp propose and defend a view called Question Under Discussion Reasons Contextualism. They use this view to argue for (...) a series of novel positions on the ontology of reasons, indexical facts, the reasons-to-be-rational debate, moral reasons, and the reasons-first approach. (shrink)

In this paper, we offer a novel analysis of presuppositions, paying particular attention to the interaction between the knowledge resources that are required to The analysis has two main features. First, we capture an analogy between presuppositions, anaphora and scope ambiguity (cf. van der Sandt 1992), by utilizing semantic under-specification (c£ Reyle 1993). Second, resolving this underspecification requires reasoning about how the presupposition is rhetorically connected to the discourse context. This has several consequences. First, since pragmatic information plays (...) a role in computing the rhetorical relation, it also constrains the interpretation of presuppositions. Our account therefore provides a formal framework for analysing problematic data, which require pragmatic reasoning. Second, binding presuppositions to the context via rhetorical links replaces accommodating them, in the sense of adding them to the context (cf. Lewis 1979). The treatment of presupposition is thus generalized and integrated into the discourse update procedure. We formalize this approach in SDRT (Asher 1993; Lascarides & Asher 1993), and demonstrate that it provides a rich framework for interpreting presuppositions, where semantic and pragmatic constraints are integrated. (shrink)

Explanatory economic analysis of the common law has long been subject to deep philosophical skepticism for two reasons. First, common law decisions appear to be cast in the language of deontic morality, not the consequentialist language of efficiency. For this reason, philosophers have claimed that explanatory economic analysis cannot satisfy the transparency criterion, which holds that a legal theory's explanation must provide a plausible account of the relationship between the reasoning it claims judges actually use to decide cases and the (...) express reasoning judges provide in their opinions. Philosophers have doubted that the economic analysis has a plausible account of why judges would use deontic moral terms to explain cases they decide using consequentialist economic reasoning, arguing instead that only a deontic moral account of judicial reasoning can be squared with the judicial use of deontic moral language. Second, the common law has a bilateral structure, in which a plaintiff's right to recover and a defendant's duty to compensate are treated as correlative. Philosophers have observed that this structure seems custom tailored to retrospective moral rights adjudication and ill suited to prospective efficient regulation. Recently, two philosophers, Jules L. Coleman and Stephen A. Smith, have developed these ideas into a full-scale assault on the explanatory credentials of the economic analysis. I defend the economic analysis by arguing that the bilateral structure of the common law either constitutes a "second best" approach to providing incentives for efficient behavior, as economic analysts have maintained, or that it is the vestigial remnant of the common law's originally deontic conception. I also claim that the economic analysis satisfies the transparency criterion by arguing that terms with a deontic plain meaning have acquired a consequentialist contextual meaning within the common law. Although this "contextualist convergence" thesis is counterintuitive, I build on Coleman's semantic theory to explain how it is possible. To demonstrate that it is plausible as well, I argue that evolutionary forces would have naturally led to this result over the course of the common law's development. In particular, I claim that the substantial indeterminacy of deontic moral theory, and the superior determinacy of the economic analysis, explains why judges would be intuitively attracted to reasoning that is best reconstructed in economic terms, notwithstanding the superior normative force of deontic moral theory. Thus, the core of my defense of explanatory economic analysis is that its critics overlook the central theoretical and practical role determinacy plays in explanation and justification generally, and in the explanation of judicial reasoning in particular, where determinacy is prized, if not above all else, no less than any other virtue. (shrink)

Using the concept of progress measure, we give a new proof of Rabin's fundamental result that the languages defined by tree automata are closed under complementation. To do this we show that for certain infinite games based on tree automata, an immediate determinacy property holds for the player who is trying to win according to a Rabin acceptance condition. Immediate determinancy is stronger than the forgetful determinacy of Gurevich and Harrington, which depends on more information about the (...) past, but applies to another class of games. Next, we show a graph theoretic duality theorem for winning conditions. Finally, we present an extended version of Safra's determinization construction. Together, these ingredients and the determinacy of Borel games yield a straightforward recipe for complementing tree automata. Our construction is almost optimal, i.e. the state space blow-up is essentially exponential- thus roughly the same as for automata on finite or infinite words. To our knowledge, no prior constructions have been better than double exponential. (shrink)

1. The last 25 years have seen an increasing interest in the area of formal argumentation. The ultimate goal of the field is to come up with computational models of how we make decisions, based on...

The most common form of direct realism is Phenomenological Direct Realism. PDR is the theory that direct realism consists in unmediated awareness of the external object in the form of unmediated awareness of its relevant properties. I contrast this with Semantic Direct Realism, the theory that perceptual experience puts you in direct cognitive contact with external objects but does so without the unmediated awareness of the objects’ intrinsic properties invoked by PDR. PDR is what most understand by direct realism. (...) My argument is that, under pressure from the arguments from illusion and hallucination, defenders of intentionalist theories, and even of relational theories, in fact retreat to SDR. I also argue briefly that the sense-datum theory is compatible with SDR and so nothing is gained by adopting either of the more fashionable theories. (shrink)