In this paper, we describe a framework for studying social agents’ individual decision making, that takes account of the environment and social dynamics. We describe a study in which we explored the efficiency of foraging strategies within a group of individuals faced with a resource-limited environment. We investigated to what extent cooperative and non-cooperative behaviors impacted on the survival rates of a population of individuals. In the experiment presented here, we considered two different types of individuals: selfish individuals (...) who gather energy for their own use, and cooperative individuals who share the energy they gather with others, thus reducing their own individual chances of survival. In order to study the trade-off between non-cooperative and cooperative behaviors in a pseudo-realistic two-dimensional environment, we introduced an agent-based modeling and simulation tool called ACACIA-ES, which simulated local interactions and spatial behavior for large numbers of individuals in complex environments. The main result from our simulation was that a group of cooperative individuals displayed better survival strategies than groups of selfish individuals when faced with a variety of environmental pressures; however, it was very unlikely that such cooperative strategies could resist competition from selfish individuals, if the outcome of past social interactions was memorized, even when a very small group of selfish individuals was introduced. (shrink)

Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the two-dimensional (...) semantics for attitude ascriptions developed in Chalmers (2011a) has no trouble accommodating certain forms of the nesting problem that involve factive verbs such as “know” or “establish”. A certain form of the nesting problem involving apriority and necessity operators does raise an interesting puzzle, but we show how a generalized version of the nesting problem arises independently of two-dimensional semantics—it arises, in fact, for anyone who accepts the contingent a priori. We, then, provide a two-dimensional treatment of the apriority operator that fits the two-dimensional treatment of attitude verbs and apply it to the generalized nesting problem. We conclude that two-dimensionalism is not seriously threatened by cases involving the nesting of epistemic and modal operators. (shrink)

In recent years, two-dimensional (2D) semantics has been used to develop a broadly descriptivist approach to meaning that seeks to accommodate externalists’ counterexamples to traditional descriptivism. The 2D possible worlds framework can be used to capture a speaker’s implicit dispositions to identify the reference of her words on the basis of empirical information about her actual environment. Proponents of 2D semantics argue that this aspect of linguistic understanding plays the core theoretical role of meanings: 2D semantics allows us to (...) specify a reference-fixing criterion implicit mastery of which constitutes semantic competence a particular meaning. (shrink)

The starting point for the contemporary debate about theories of health should be the holistic theory of Lennart Nordenfelt, claims George Khushf, not the refuted theory of Christopher Boorse. The present paper is an attempt to challenge Nordenfelt and to present an alternative theory to his and other theories, including Boorse’s. The main problems with Nordenfelt’s theory are that it is relativistic, that it leads to counter-intuitive results as to what goals can count as healthy, that it focuses on the (...) wrong kind of abilities, that it makes measuring health extra difficult, and that it does not give us a sufficient account of health, at most a necessary one. The alternative theory proposed is two-dimensional. First, health is to have developed the abilities and dispositions that members of one’s culture typically develop, and be able to use them, in acceptable circumstances; and second, health is to experience positive moods and sensations, the kinds that have internal causes. The theory solves the problems attached to Nordenfelt’s theory by not being individual relativistic, by eliminating the goals in the definition, by giving an alternative interpretation of “ability,” by making health easier to measure, and by adding the dimension of well-being that, together with health as ability, not only gives us a necessary, but also a sufficient, account of health. (shrink)

The suggestion that three-dimensional space is represented by a mosaic of neural map fragments, each covering a small area of space in the plane of locomotion, receives support from studies in complex two-dimensional environments. How map fragments are linked, which brain circuits are involved, and whether metric is preserved across fragments are questions that remain to be determined.

This article presents a general conception of aesthetic experience built on an analysis of the relationship between the narrative and the ambient dimensions of the aesthetic value of a natural environment, the forest. First of all, the two dimensions are presented with respect to the possibilities and problems raised by distinguishing between them. Next, the possibilities of their relationship are analysed and it is argued that they are strongly complementary. This complementarity becomes the core of the proposed conception of (...) aesthetic experience, which can explain the difference between the aesthetic and the non-aesthetic, and can also provide an answer to the question of the non-reductive differentiation between the aesthetic experience of nature and the experience of a work of art. The conclusion of the article is mainly concerned to eliminate one of the problems localized in presenting the ambient dimension (the ambience paradox), by means of Ricoeur’s conception of the relationship between time and narrative. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Road to RedemptionAnonymous TwoI “am Dr X.* and I am a trained and board certified neonatologist with some years of experience in a high volume NICU with complex pathologies. I have been dismissed from the care of your baby by the fetal surgeon who is not trained in what he’s attempting to do,” that was how I felt when I left the operating room (OR), after performing initial (...) resuscitation on a newborn with congenital diaphragmatic hernia (CDH) with very poor prenatal prognostic indices. CDH is a diaphragm abnormality that allows abdominal organs to move into the chest and restrict lung development. The better part of me knew not to make such a statement and chose not to do so, as this was about the family and a very sick baby, not the professional wrangling of two medical teams or the expression of frustration by a neonatologist who was morally conflicted.I work in a level four Neonatal Intensive Care Unit (NICU) and a very large one by any standard. Staff turnover had been an almost nonexistent issue in previous years because of the very conducive work environment of the NICU. Every team member (physician, nurse, respiratory therapist, pharmacist, etc.) felt like a stakeholder in providing optimal outcomes for the vulnerable neonates in the NICU.As change is the only constant thing in life, the hospital management decided to explore new frontiers and open a center for fetal medicine, with the hope of being a referral center in the region. They brought in a surgeon who came highly recommended for clinical acumen, but not for interpersonal relationship skills (unbeknownst to me). This surgeon, Dr Y., was hired to oversee the fetal center and build it into a center of excellence. Since this had to be a collaborative effort, other specialties (and subspecialties) had to be involved to make this a success. A representative from each of these specialties, including bioethics, was assigned to the fetal center team.The first inkling of a major problem occurred with the very first patient. The team met for the weekly meeting, reviewed the patient’s history and made a tentative plan, which included multidisciplinary counseling. This would require either a joint meeting with the patient or individual consults with the patient at her convenience. The following week at the weekly meeting, Dr Y. informed the group that he had met with the patient and counseled her and she had agreed to an extraordinary procedure for an oral lesion. In my opinion (and that of others), this lesion was not obstructive and could be immediately dealt with at delivery by an Otolaryngologist (ENT) surgeon, without putting the mother at risk for complications arising from the procedure being offered. There was a long discussion about why this was inappropriate [End Page E1] and why further imaging, discussion between the subspecialties and counseling should have been done prior to making this delivery plan. All felt this delivery plan could be remedied prior to delivery. However the surgeon had made plans with the obstetric team (who were at his mercy for financial/ political reasons) to continue with this plan. On the day of delivery, the NICU resuscitation team was called to another operating room instead of the labor and delivery room. I was even more appalled when I realized that the oral lesion was the size of a peanut! I felt like I failed in my obligation of veracity by avoiding the mother’s questions regarding the necessity of the procedure. Every member of my team felt the same and on several occasions I had to reassure concerned nurses that this was an aberrant occurrence that would not repeat itself... so I thought.I informed my departmental chairperson, Dr Z., who had a conversation with the fetal surgeon, Dr. Y., to inform him of my concerns and the effect of Dr. Y.’s actions on my group (physician, nurse practitioner, nurses). This led to being labeled unsupportive of Dr Y.’s goals and caused a less than cordial relationship towards me and the entire NICU group. The next week a picture of Dr Y. and the parents with the baby was on the front page... (shrink)

This paper starts with the study of realistic three-dimensional models, from the two aspects of ink art style simulation model and three-dimensional display technology, explores the three-dimensional display model of three-dimensional model ink style, and conducts experiments through the software development platform and auxiliary software. The feasibility of the model is verified. Aiming at the problem of real-time rendering of large-scale 3D scenes in the model, efficient visibility rejection method and a multiresolution fast rendering method were designed to realize the (...) rapid construction and rendering of ink art 3D virtual reality scenes in a big data environment. A two-dimensional cellular automaton is used to simulate a brushstroke model with ink and wash style, and outlines are drawn along the path of the brushstroke to obtain an effect close to the artistic style of ink and wash painting. Set the surface of the model with ink style brushstroke texture patterns, refer to the depth map, normal map, and curvature map information of the model, and simulate the drawing effect of the method by procedural texture mapping. Example verification shows that the rapid visualization analysis model of ink art big data designed in this paper is in line with the prediction requirements of ink art big data three-dimensional display indicators. The fast visibility removal method is used to deal with large-scale three-dimensional ink art in a big data environment. High efficiency is achieved in virtual reality scenes, and the multiresolution fast rendering method better maintains the appearance of the prediction model without major deformation. (shrink)

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from (...) each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system. (shrink)

Jeffery et al. extensively and thoroughly describe how different species navigate through a three-dimensional environment. Undeniably, the world offers numerous three-dimensional opportunities. However, we argue that for most navigation tasks a two-dimensional representation is nevertheless sufficient, as physical conditions and limitations such as gravity, thermoclines, or layers of earth encountered in a specific situation provide the very elevation data the navigating individual needs.

Developing social skills is essential to succeed in social relations. Two important social constructs in middle childhood, prosocial behavior and reactive aggression, are often regarded as separate behaviors with opposing developmental outcomes. However, there is increasing evidence for the co-occurrence of prosociality and aggression, as both might indicate responsivity to the social environment. Here, we tested whether a bi-dimensional taxonomy of prosociality and reactive aggression could predict internalizing and externalizing problems over time. We re-analyzed data of two well-validated experimental (...) tasks for prosociality and reactive aggression in a developmental population sample. Results revealed no associations between prosociality and reactive aggression, confirming the independence of those constructs. Interestingly, although prosociality and reactive aggression independently did not predict problem behavior, the interaction of both was negatively predictive of changes in externalizing problems over time. Specifically, only children who scored low on both prosociality and reactive aggression showed an increase in externalizing problems 1 year later, whereas levels of externalizing problems did not change for children who scored high on both types of behavior. Thus, our results suggest that at an individual level, reactive aggression in middle childhood might not always be maladaptive when combined with prosocial behavior, thereby confirming the importance of studying social competence across multiple dimensions. (shrink)

A number of popular arguments for dualism start from a premise about an epistemic gap between physical truths about truths about consciousness, and infer an ontological gap between physical processes and consciousness. Arguments of this sort include the conceivability argument, the knowledge argument, the explanatory-gap argument, and the property dualism argument. Such arguments are often resisted on the grounds that epistemic premises do not entail ontological conclusion. My view is that one can legitimately infer ontological conclusions from epistemic premises, if (...) one is very careful about how one reasons. To do so, the best way is to reason first from epistemic premises to modal conclusions , and from there to ontological conclusions. Here, the crucial issue is the link between the epistemic and modal domains. How can one reason from theses about what is knowable or conceivable to theses about what is necessary or possible? To bridge the epistemic and modal domains, the framework of two-dimensional semantics can play a central role. I have used this framework in earlier work to mount an argument against materialism. Here, I want to revisit the argument, laying it out in a more explicit and careful form, and responding to a number of objections. In what follows I will concentrate mostly on the conceivability argument. I think that very similar considerations apply to the other arguments mentioned above, however. In the final section of the paper, I show how this analysis might yield a unified treatment of a number of anti-materialist arguments. (shrink)

Two-dimensional approaches to semantics, broadly understood, recognize two "dimensions" of the meaning or content of linguistic items. On these approaches, expressions and their utterances are associated with two different sorts of semantic values, which play different explanatory roles. Typically, one semantic value is associated with reference and ordinary truth-conditions, while the other is associated with the way that reference and truth-conditions depend on the external world. The second sort of semantic value is often held to play a distinctive role in (...) analyzing matters of cognitive significance and/or context-dependence. (shrink)

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study (...) illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985. (shrink)

Why is two-dimensional semantics important? One can think of it as the most recent act in a drama involving three of the central concepts of philosophy: meaning, reason, and modality. First, Kant linked reason and modality, by suggesting that what is necessary is knowable a priori, and vice versa. Second, Frege linked reason and meaning, by proposing an aspect of meaning (sense) that is constitutively tied to cognitive signi?cance. Third, Carnap linked meaning and modality, by proposing an aspect of meaning (...) (intension) that is constitutively tied to possibility and necessity. (shrink)

Two-dimensional semantics is a framework that helps us better understand some of the most fundamental issues in philosophy: those having to do with the relationship between the meaning of words, the way the world is, and our knowledge of the meaning of words. This selection of new essays by some of the world's leading authorities in this field sheds fresh light both on foundational issues regarding two-dimensional semantics and on its specific applications. Contributors: Richard Breheny, Alex Byrne, David Chalmers, Martin (...) Davies, Gareth Evans, Manuel Garcia-Carpintero, Josep Maci`, Martine Nida-Rumelin, Christopher Peacocke, James Pryor, Francois Recanati, Scott Soames, Cara Spencer, Robert Stalnaker, Kai-Yee Wong, Stephen Yablo. (shrink)

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study (...) illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985. (shrink)

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study (...) illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985. (shrink)

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions (...) Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (shrink)

In summary, many extant definitions of the niche concept are based on the geometric metaphor which represents the niche as an object embedded in a geometric space. There are several difficulties with this approach; the activities of organisms are not fully described, certain attributes of the functional aspect of the niche are not represented, the life cycles of organisms are not described, and the heuristic value of the concept diminishes with increasing dimensionality.An alternative and complementary approach to the niche is (...) the linguistic metaphor. This approach is based on the explanatory objective to explain the assembly of the ecosystems of successional seres from species pools and abiotic environmental factors. The linguistic metaphor suggests that a theory of ecosystem assembly is a generative grammar that associates particular species with environmental features. The niche of a particular species is defined in terms of the rules of a generative-transformational grammar used to derive an hierarchically organized description of that species. This approach also has conceptual difficulties: (1) empirically testing competence theories and distinguishing possible and impossible objects (e.g. species and ecosystems) are difficult, (2) evolutionary processes are difficult to incorporate, (3) the mathematical tools associated with grammars do not have the range of applicability of the mathematical tools associated with the geometric metaphor, and (4) the productions (hierarchical trees) of a grammar are not easily visualized.The geometric and linguistic metaphors of the niche should be viewed as complementary pictures of the same object. The geometric representation is most adept at describing community dynamics and stability, niche overlap, and organism response to abiotic environments. The linguistic metaphor represents well organism activities, niche dynamics, and ecosystem assembly. (shrink)

We introduce a two‐dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then we prove completeness and a semantic partial cut elimination theorem down to formulas of a certain type.

At this point in time the two-dimensional (2D) argument against physicalism is well known (Chalmers 2009; 2010), as are the many responses to it. However there has been a recent development that has yet to be widely discussed. Some philosophers have argued that we have equally compelling reasons to think that dualism is false based on the conceivability of mere physical duplicates which enjoy conscious experience in just the way we do (Martin 1998; Sturgeon 2000; Piccinini 2006; Frankish 2007; Brown (...) 2010; Balog MS). This argument has not yet been properly understood and in this paper I aim to correct the most common misunderstandings. (shrink)

Two-dimensional (2D) semantics is a formal framework that is used to characterize the meaning of certain linguistic expressions and the entailment relations among sentences containing them. 2D semantics has also been applied to thought contents. In contrast with standard possible worlds semantics, 2D semantics assigns extensions and truth-values to expressions relative to two possible world parameters, rather than just one. So a 2D semantic framework provides finer-grained semantic values than those available within standard possible world semantics, while using the same (...) basic model-theoretic resources. The 2D framework itself is just a formal tool. To develop a semantic theory for someone’s language, a proponent of 2D semantics must do three things: (i) explain what exactly the two possible world parameters represent, (ii) explain the rules for assigning 2D semantic values to a person’s words and sentences, and (iii) explain how 2D semantic values help in understanding the meanings of the person’s words and sentences. (shrink)

The aim of this paper is to show that Priest's modal Meinongianism might benefit from joining forces with two-dimensionalism. For this purpose, I propose a two-dimensional solution to a problem for modal Meinongianism that is posed by Beall, Sauchelli, and Milne, and show that, by taking recourse to two-dimensionalism, divergent intuitions about the question of whether fictional characters might exist can be reconciled. Moreover, two-dimensionalism helps to rebut Kroon's argument to the conclusion that modal Meinongianism cannot rule out the odd (...) claim that some non-existent objects have existence-entailing properties at the actual world. (shrink)

This paper recalls some applications of two-dimensional modal logic from the 1980s, including work on the logic of Actually and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity. There is some discussion of reactions this material has aroused in commentators since. We also survey related work by Leslie Tharp from roughly the same period.

Participants maneuvered a rat image through a circular region on the computer screen to find a hidden target platform, blending aspects of two well-known spatial tasks. Like the Morris water maze task, participants first experienced a series of learning trials before having to navigate to the hidden target platform from different locations and orientations. Like the dot-location task, they determined the location of a position within a two-dimensional circular region. This procedure provided a way to examine how the number of (...) surrounding cues (1, 2, or 3) affects the memory for spatial location in navigation. Memory performance was better when there were more cues and when targets were close to cues, consistent with the idea that cues bolster fine-grain memory, especially in proximal regions. Early and late measures of bias in memory reflected biases in a direction toward the nearest cue, implicating a cue-based category structure of the navigational space. Collectively, results suggest cue-based spatial memory representations that have been inferred from the dot-location task generalize to a navigation task within a simple, computer-based environment, as demonstrated by the good fits of the spatial model developed for the dot-location task (Fitting, Wedell, & Allen, 2005, 2007). (shrink)

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...) some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

Two-dimensional semantics, which can represent the distinction between a priority and necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger operator of Stalnaker’s “Assertion” in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed to Bayesian and (...) Gricean contexts. Finally, I sketch the prospects for extending this two-dimensional upgrade to other kinds of modal logics for natural language. (shrink)

This paper is divided into three sections. In the first section I briefly outline the background of the problem, i.e. Kripke’s modal argument (Kripke 1980). In the second section I present Chalmers’ account of two- dimensional semantics and two-dimensional argument against physicalism. In the third section I criticize Chalmers’ approach based on two crucial points, one is about necessity of identities and the other is about microphysi- cal descriptions and a priori derivation.

In this paper I put forward a representationalist theory of conscious experience based on Robert Stalnaker's version of two-dimensional modal semantics. According to this theory the phenomenal character of an experience correlates with a content equivalent to what Stalnaker calls the diagonal proposition. I show that the theory is closely related both to functionalist theories of consciousness and to higher-order representational theories. It is also more compatible with an anti-Cartesian view of the mind than standard representationalist theories.

Context: Technology has not only changed the way we teach mathematical concepts but also the nature of knowledge, and thus what is possible to learn. While geometric transformations are recognized to be foundational to the formation of students’ geometric conceptions, little research has focused on how these notions can be introduced in elementary schooling. Problem: This project addressed the need for development of students’ reasoning about and with geometric transformations in elementary school. We investigated the nature of students’ understandings of (...) translations, rotations, scaling, and stretching in two dimensions in the context of use of the software application Graphs ’n Glyphs. More specifically, we explored the question “What is the nature of elementary students’ reasoning of geometric transformations when instruction exploits the technological tool Graphs ’n Glyphs?” Method: Using a design research perspective, we present the conduct of a teaching experiment with one pair of fourth-graders, studying translation and rotation. The project investigated how and to what extent activity using Graphs ’n Glyphs can elicit students’ reasoning about geometric transformations, and explored the constraints and affordances of Graphs ’n Glyphs for thinking-in-change about geometric transformations. Results: The students proved adept using the software with carefully designed tasks to explore the behavior of two-dimensional shapes, distinguish among transformations, and develop predictions. In relation to varied conditions of transformations, they formed generalizations about the way a shape behaves, including the use of referent points in predicting outcomes of translations, and recognizing the role of the center of rotation. Implications: The generalizations that the students developed are foundational for developing an understanding of the properties of transformations in the later years of schooling. Dynamic technological approaches to geometry may prove as valuable to elementary students’ understanding of geometry as it is for older students. Constructivist content: This study contributes to ongoing constructivism/constructionism conversations by concentrating on the transformation of ideas when engaging learners in activity through particular contexts and tools. Key Words: Geometry, transformations, constructionist technologies. (shrink)

We present two-dimensional tableau systems for the actuality, fixedly, and up-arrow operators. All systems are proved sound and complete with respect to a two-dimensional semantics. In addition, a decision procedure for the actuality logics is discussed.

This paper is about two requirements on wish reports whose interaction motivates a novel semantics for these ascriptions. The first requirement concerns the ambiguities that arise when determiner phrases, such as definite descriptions, interact with ‘wish’. More specifically, several theorists have recently argued that attitude ascriptions featuring counterfactual attitude verbs license interpretations on which the determiner phrase is interpreted relative to the subject’s beliefs. The second requirement involves the fact that desire reports in general require decision-theoretic notions for their analysis. (...) The current study is motivated by the fact that no existing account captures both of these aspects of wishing. I develop a semantics for wish reports that makes available belief-relative readings but also allows decision-theoretic notions to play a role in shaping the truth conditions of these ascriptions. The general idea is that we can analyze wishing in terms of a two-dimensional notion of expected utility. (shrink)

. David Chalmerss version of two-dimensional semantics is an attempt at setting up a unified semantic framework that would vindicate both the Fregean and the Kripkean semantic intuitions. I claim that there are three acceptable ways of carrying out such a project, and that Chalmerss theory does not coherently fit any of the three patterns. I suggest that the theory may be seen as pointing to the possibility of a double reading for many linguistic expressions (a double reading which, however, (...) is not easily identified with straightforward semantic ambiguity). (shrink)

This article proposes reframing the justice discourse in climate negotiations. In so doing, it makes two claims. First, global climate negotiations deserve to be addressed as an issue of justice on their own due to their peculiar characteristics. Second, a multidimensional theory of justice is superior to distributional theories for this task. To support these arguments, I apply the multidimensional theory of justice to global climate negotiations. This analysis reveals that injustice in the negotiations is multidimensional and irreducible to distributional (...) questions. Furthermore, it shows how promoting justice in this broad sense would have significant effect on the negotiation procedures and substantive outcomes. (shrink)

The paper identifies two major strands of truth theories, ontological and epistemological ones, and argues that both are of equal primacy and find their home within two-dimensional semantics. Contrary to received views, it argues further that epistemological truth theories operate on Lewisian possible worlds and ontological truth theories on Wittgensteinian possible worlds and that both are mediated by the so-called epistemic-ontic map the further specification of which is of utmost philosophical importance.

I review and reconsider some of the themes of ‘Two notions of necessity’ (Davies and Humberstone, 1980) and attempt to reach a deeper understanding and appreciation of Gareth Evans’s reflections (in ‘Reference and contingency’, 1979) on both modality and reference. My aim is to plot the relationships between the notions of necessity that Humberstone and I characterised in terms of operators in two-dimensional modal logic, the notions of superficial and deep necessity that Evans himself described, and the epistemic notion of (...) a priority. (shrink)

The theories that form the heterogeneous family of two‐dimensional or 2D semantics are rooted in the tradition of possible‐worlds semantics made popular by Saul Kripke and David Lewis. Advocates of 2D semantics agree that recognizing a dependence of truth on fact is not enough. Advocates of two‐dimensional semantics share a second trademark idea. They agree that the familiar apparatus of worlds‐cum‐intensions can be modified so as to capture both the dependencies they see. The commitments of all 2D theories (...) can basically be captured by one and the same formal framework of worlds‐cum‐intensions. David Kaplan's semantics aims to cover pure indexicals such as 'today' alongside impure indexicals such as 'you' and demonstratives such as 'this'. Kaplan starts off with two 'obvious principles': The referent of an indexical systematically depends on the respective context; and Indexicals are directly referential. (shrink)

Principles of chance deference face two kinds of problems. In the first place, they face difficulties with a priori knowable contingencies. In the second place, they face difficulties in cases where you've lost track of the time. I provide a principle of chance deference which handles these problem cases. This principle has a surprising consequence for Adam Elga's Sleeping Beauty Puzzle.

In contrast to standard possible worlds semantics, possible worlds in a two-dimensional semantic framework play two kinds of roles, rather than just one. This allows the framework to assign two kinds of intensions to expressions, rather than just one. Its fruitful use in explicating modal operators and the meanings of referential expressions like indexicals has led to two-dimensional accounts that seek to revive the Fregean conception of meaning, or more specifically the descriptivist view of reference, which has fallen into disrepute (...) due to intense criticisms, most famously, by Saul Kripk’s seminal work Naming and Necessity (1972). This entry provides a critical overview of the two most prominent of such accounts, proposed by Frank Jackson and David Chalmers. Unfortunately, there is not space to describe either account in detail, so I rely largely on brief descriptions and plenty of references to primary and secondary sources. More importantly, I rely on focusing on how the accounts explain the phenomenon of necessary a posteriori identity that Kripke’s well-known examples (such as ‘Hesperus is Phosphorus’) have brought to light. Focusing on and structuring our discussions around this phenomenon is by no means just an expository convenience. These cases are of central importance in themselves. They epitomize a large part of the contribution of Naming and Necessity to the theory of reference. This is why section 2 outlines Kripke’s critique of the Fregean theory of referential expressions and section 3 explains rigid designation and identity statements. Section 4 discusses rigidification and the notion of a world considered as actual, leading to the introduction of two-dimensional functions in Section 5. I discuss, finally, Frank Jackson’s and David Chalmers’ two-dimensionalism in Sections 6 and 7. Section 8 makes a few critical remarks on Jackson’s handling of the semantic argument. I conclude (Section 8) by discussing the important distinction between semantics and metasemantics. (shrink)

Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based (...) on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko’s Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued. (shrink)

In this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions (...) Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to “lift” a Kripke frame for a one-dimensional modal logic into two dimensions. (shrink)