A diagnostic judgment of a teacher can be seen as an inference from manifest observable evidence on a student’s behavior to his or her latent traits. This can be described by a Bayesian model of in-ference: The teacher starts from a set of assumptions on the student (hypotheses), with subjective probabilities for each hypothesis (priors). Subsequently, he or she uses observed evidence (stu-dents’ responses to tasks) and knowledge on conditional probabilities of this evidence (likelihoods) to revise these assumptions. Many systematic (...) deviations from this model (biases, e.g. base-rate neglect, inverse fallacy) are reported in literature on Bayesian reasoning. In a teacher’s situation the information (hypotheses, priors, likelihoods) is usually not explicitly represented numerically (as in most research on Bayesian reasoning), but only by qualitative esti-mations in the mind of the teacher. In our study, we ask to which extent individuals (approximately) apply a rational Bayesian strategy or resort on other biased strategies of processing information for their diagnostic judgments. We explicitly pose this question with respect to non-numerical settings. To investigate this question, we developed a scenario that visually displays all relevant information (hypotheses, priors, likelihoods) in a graphically displayed hypothesis space (called “hypothegon”) – without recurring to numerical representations or mathematical procedures. 42 pre-service teach-ers were asked to judge the plausibility of different misconceptions of six students based on their responses to decimal comparison tasks (e.g. 3.39 > 3.4). Applying a Bayesian classification proce-dure, we identified three updating strategies: A Bayesian update strategy (BUS, processing all probabilities), a combined evidence strategy (CES, ignoring the prior probabilities but including all likelihoods), and a single evidence strategy (SES, only using the likelihood of the most probable hypothesis). In study 1, an instruction on the relevance of using all probabilities (priors and likelihoods) only weakly increased the processing of more information. In study 2, we found strong evidence that a visual explication of the prior-likelihood interaction led to an increase of processing the interaction of all relevant information. These results show that the phenomena found in general research on Bayesian reasoning in numerical settings extend to diagnostic judgments in non-numerical settings. (shrink)

Most of the on-going debate is about “how” to protect archaeological ruins, whilst at the same time allowing the general public to enjoy them. Today it is clear how important it is, from the actual planning stages of excavations, to interact with experts from other disciplines, who are working on their own findings and offering them up for collective enjoyment. Whatever might be feasible for an indoor museum is not always feasible with an architectonic ruin, as regards both presenting objects (...) with explicative apparatus that determines their significance, and exploring them in a new way when interpretations change or new ideologies are introduced. First of all, conserving excavations is the not the same as conserving a transportable object. In the past many countries in Europe preferred to “present” Roman remains simply as “gardens of ruins”, often endeavouring to stand them in sharp contrast with a more recurrent evocation of the original contexts of local life. Recently, with regard to the Roman tradition, there has been a noticeable inversion of trend in musealization operations, according to which the mere “contemplation of ruins” should be replaced by emotional contact with history. The main consequence of these new tendencies is the replacement of an informatics-based and didactic approach to musealization, in favour of a more authentically interpretative approach. Back-up resulting from experimentation in the fields of restoration and conservation becomes indispensible in implementing these new strategies for the musealization of archaeology. Continuous research and the progressive advance of conservation techniques have meant that the need to transfer archaeological remains has been avoided and an improved in situ “presentation” of these remains, both movable and immovable, can now be guaranteed. (shrink)

This paper reports the experience of using the PAELLA algorithm as a helper tool in robust regression instead of as originally intended for outlier identification and removal. This novel usage of the algorithm takes advantage of the occurrence vector calculated by the algorithm in order to strengthen the effect of the more reliable samples and lessen the impact of those that otherwise would be considered outliers. Following that aim, a series of experiments is conducted in order to learn how to (...) better use the information contained in the occurrence vector. Using a contrively difficult artificial data set, a reference predictive model is fit using the whole raw dataset. The second experiment reports the results of fitting a similar predictive model but discarding the samples marked as outliers by PAELLA. The third experiment uses the occurrence vector provided by PAELLA in order to classify the observations in multiple bins and fit every possible model changing which bins are considered for fitting and which are discarded in that particular model. The fourth experiment introduces a sampling process before fitting in which the occurrence vector represents the likelihood of being considered in the training data set. The fifth experiment considers the sampling process as an internal step to be performed interleaved between the training epochs. The last experiment compares our approach using weighted neural networks to a state of the art method. (shrink)

This article contains an abstract of Dr. Sanjay Patnaik’s dissertation as well as a commentary essay on the research process in the appendix. In his dissertation, Dr. Patnaik examines the importance of the non-market environment for firm strategy and performance within the context of newly introduced regulations for greenhouse gases in Europe. The dissertation abstract contains a description of each dissertation chapter, including research questions, methodologies, and results. The commentary essay describes the author’s perspective on conducting research as an (...) emerging scholar. (shrink)

In the earlier literature the importance of public policies and regulatory changes to firm performance and competitive position has been well established (e.g., Bonardi, 2004). However, little research has been done on the dynamics of this relationship. In this paper, we examine how and why regulatory changes can affect on the evolution of market and nonmarket strategies of a firm. We use a longitudinal case study on Finnish retail industry to illustrate the interactions between regulatory change, strategic responses and firm (...) performance. (shrink)

A promising strategy for better understanding space and time at the Planck scale, is outlined and further pursued. It is explained in detail, how black hole unitarity demands the existence of transformations that can remove firewalls. This must then be combined with a continuity condition on the horizon, with antipodal identification as an inevitable consequence. The antipodal identification comes with a \ inversion. We claim to have arrived at ‘new physics’, but rather than string theory, our ‘new physics’ concerns (...) new constraints on the topology and the boundary conditions of general coordinate transformations. The resulting theory is conceptually quite non trivial, and more analysis is needed. A strong entanglement between Hawking particles at opposite sides of the black hole is suspected, but questions remain. A few misconceptions concerning black holes, originating from older investigations, are discussed. (shrink)

In cooperative Cournot oligopoly games, it is known that the β-core is equal to the α-core, and both are non-empty if every individual profit function is continuous and concave (Zhao, Games Econ Behav 27:153–168, 1999b). Following Chander and Tulkens (Int J Game Theory 26:379–401, 1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non-emptiness of the induced core, the γ-core, by two different approaches. The first establishes (...) that the associated Cournot oligopoly Transferable Utility (TU)-games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao’s core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU-games with linear cost functions, provides a single-valued allocation rule in the γ-core called Nash Pro rata (NP)-value. This result generalizes Funaki and Yamato’s (Int J Game Theory 28:157–171, 1999) core existence result from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity, and non-cooperative fairness. (shrink)

Population policy has taken two divergent trajectories. In the developing part of the world, controlling population growth has been a major tune of the debate more than a half-century ago. In the more developed part of the world, an inverse pattern results in the discussion over the facilitation of population growth. The ethical debates on population policy have primarily focused on the former and ignored the latter. This paper proposes a more comprehensive account that justifies states’ population policy interventions. (...) We first consider the reasons that support pro-natalist policies to enhance fertility rates and argue that these policies are ethically problematic. We then establish an ethics of population policy grounded on account of self-sustaining the body politic, which consists of four criteria: survival, replacement, accountability, and solidarity. We discuss the implications of this account regarding birth-control and pro-natalist policies, as well as non-procreative policies such as immigration, adoption, and unintended baby-saving strategies. (shrink)

One stable marker of face perception appears to be left-side bias, the tendency to rely more on information conveyed by the left side of the face than the right. Previous studies have shown that left-side bias is influenced by familiarity and prior experience with face stimuli. Since other-race facial recognition is characterized by reduced familiarity, in contrast to own-race facial recognition, the phenomenon of left-side bias is expected to be weaker for other-race faces. Among Chinese participants, face inversion has been (...) found to eliminate the left-side bias associated with own-race faces. Therefore, it is of interest to know whether face inversion influences left-side bias for non-Chinese research participants and can be generalized across own- and other-race faces. This study assessed 65 Caucasian participants using upright and inverted chimeric Caucasian and Asian faces in an identity similarity-judgment task. Although a significant left-side bias was observed for upright own-race faces, this bias was eliminated by facial inversion, indicating that such a bias depends on the applicability of configural processing strategies. For other-race faces, there was no left-side bias in the upright condition. Interestingly, the inverted presentation yielded a right-side bias. These results show that while left-side bias is affected by familiarity differences between own- and other-race faces, it is a universal phenomenon for upright faces. Inverted presentation strongly reduces left-side bias and may even cause it to revert to right-side bias, suggesting that left-side bias depends on configural face processing. (shrink)

Narrativism, as represented by Hayden White and Frank Ankersmit, can fruitfully be analyzed as an inversion of two brands of positivism. First, narrativist epistemology can be regarded as an inversion of empiricism. Its thesis that narratives function as metaphors which do not possess a cognitive content is built on an empiricist, "picture view" of knowledge. Moreover, all the non-cognitive aspects attributed to narrative as such are dependent on this picture theory of knowledge and a picture theory of representation. Most of (...) the epistemological characteristics that White and Ankersmit attribute to historical narratives therefore share the problems of this picture theory.The article's second thesis is that the theories of narrative explanation can also fruitfully be analyzed as inversions of positivist covering-law theory. Ankersmit's brand of narrativism is the most radical in this respect because it posits an opposition between narrative and causal modes of comprehension while simultaneously eliminating causality from narrativist historical understanding. White's brand of narrativism is more of a hybrid than is Ankersmit's as far as its theory of explanation is concerned; nevertheless, it can also be fruitfully interpreted as an inversion of covering-law theory, replacing it by an indefinite multitude of explanatory strategies.Most of the striking characteristics of both White's and Ankersmit's narrativism presuppose positivism in these two senses, especially their claim that historical narratives have a metaphorical structure and therefore no truth-value. These claims are hard to reconcile with the factual characteristics of debates by historians; this problem can be tracked down to the absence in "metaphorical" narrativism of a conceptual connection between historical narratives and historical research. (shrink)

In this paper, I highlight three objections to vice-based accounts of moral evil: (1) the worry that vice-based accounts of evil are explanatorily inadequate; (2) the worry that even extreme vice is not sufficient for evil; and (3) the worry that not all vices are inversions of virtue (and so vice-based accounts will struggle to explain the “mirror thesis”). I argue that it is possible to respond to these objections by developing a vice-based account of evil that draws on insights (...) from virtue (and vice) epistemology. In this way, I seek to defend the strategy of understanding evil in terms of vice, and to provide guidance on how best to develop such an account. I also briefly consider what vice-based accounts of moral evil might imply about evil in other normative domains where it is common to talk of virtue and vice, including the possibilities of epistemic evil and aesthetic evil. (shrink)

I argue that an adequate account of non-reductive realization must guarantee satisfaction of a certain condition on the token causal powers associated with (instances of) realized and realizing entities---namely, what I call the 'Subset Condition on Causal Powers' (first introduced in Wilson 1999). In terms of states, the condition requires that the token powers had by a realized state on a given occasion be a proper subset of the token powers had by the state that realizes it on that occasion. (...) Accounts of non-reductive realization conforming to this condition are implementing what I call 'the powers-based subset strategy'. I focus on the crucial case involving mental and brain states; the results may be generalized, as appropriate. I first situate and motivate the strategy by attention to the problem of mental causation; I make the case, in schematic terms, that implementation of the strategy makes room (contra Kim 1989, 1993, 1998, and elsewhere) for mental states to be ontologically and causally autonomous from their realizing physical states, without inducing problematic causal overdetermination, and compatible with both Physicalism and Non-reduction; and I show that several contemporary accounts of non-reductive realization (in terms of functional realization, parthood, and the determinable/determinate relation) are plausibly seen as implementing the strategy. As I also show, implementation of the powers-based strategy does not require endorsement of any particular accounts of either properties or causation---indeed, a categoricalist contingentist Humean can implement the strategy. The schematic location of the strategy in the space of available responses to the problem of mental (more generally, higher-level) causation, as well as the fact that the schema may be metaphysically instantiated, strongly suggests that the strategy is, appropriately generalized and instantiated, sufficient and moreover necessary for non-reductive realization. I go on to defend the sufficiency and necessity claims against a variety of objections, considering, along the way, how the powers-based subset strategy fares against competing accounts of purportedly non-reductive realization in terms of supervenience, token identity, and constitution. (shrink)

Business Ethics: A European Review, EarlyView.

This article discusses the English construction variously known as Locative Inversion or Stylistic Inversion. It shows that the construction displays a unique ensemble of grammatical and usage properties that can be stated but not motivated through purely grammatical means. In search of an explanatory approach, an analysis is presented that draws on concepts of Artificial Intelligence, in particular plans viewed as complex mental attitudes. It is claimed that utterances of Locative Inversion are associated with a particular communicative plan on the (...) speaker's part that motivates the grammatical and usage properties of the construction where grammar alone cannot. The final section of the article presents corpus examples showing that Locative Inversion is indeed used in the contexts predicted by the plan associated with the construction. This result is both theoretically and methodologically significant, insofar as it constitutes a case where the grammatical properties of a syntactic construction are better explained through its typical conditions of use than through grammatical means proper. (shrink)

Robert Trivers has proposed perhaps the only serious adaptationist account of self-deception—that the primary function of self-deception is to better deceive others. But this account covers only a subset of cases and needs further refinement. A better evolutionary account of self-deception and cognitive biases more generally will more rigorously recognize the various ways in which false beliefs affect both the self and others. This article offers formulas for determining the optimal doxastic orientation, giving special consideration to conflicted self-deception as an (...) alternative to outright self-delusion. A novel taxonomy of self-deception, as it relates to the beliefs held by others, is also presented. While Trivers makes a plausible case for the adaptive value of certain cognitive biases, a more fragmented and nuanced account of the social forces impacting the evolution of self-deception is needed. (shrink)

In this article, I focus on the role of computer simulations as exploratory strategies. I begin by establishing the non-theory-driven nature of simulations. This refers to their ability to characterize phenomena without relying on a predefined conceptual framework that is provided by an implemented mathematical model. Drawing on Steinle’s notion of exploratory experimentation and Gelfert’s work on exploratory models, I present three exploratory strategies for computer simulations: (1) starting points and continuation of scientific inquiry, (2) varying the parameters, and (3) (...) scientific prototyping. (shrink)

Suppose $\lambda$ is a singular cardinal of uncountable cofinality $\kappa$. For a model $\mathscr{M}$ of cardinality $\lambda$, let No ($\mathscr{M}$) denote the number of isomorphism types of models $\mathscr{N}$ of cardinality $\lambda$ which are L$_{\infty\lambda}$- equivalent to $\mathscr{M}$. In [7] Shelah considered inverse $\kappa$- systems $\mathscr{A}$ of abelian groups and their certain kind of quotient limits Gr($\mathscr{A}$)/ Fact($\mathscr{A}$). In particular Shelah proved in [7, Fact 3.10] that for every cardinal $\mu$ there exists an inverse $\kappa$-system $\mathscr{A}$ such that (...) $\mathscr{A}$ consists of abelian groups having cardinality at most $\mu^\kappa$ and card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse $\kappa$-systems and possible values of No (under the assumption that $\theta^\kappa < \lambda$ for every $\theta < \lambda$): if $\mathscr{A}$ is an inverse $\kappa$- system of abelian groups having cardinality < $\lambda$, then there is a model $\mathscr{M}$ such that card $(\mathscr{M}) = \lambda$ and No($\mathscr{M}$) = card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)). The following was an immediate consequence (when $\theta^\kappa < \lambda$ for every $\theta < \lambda$): for every nonzero $\mu < \lambda$ or $\mu = \lambda^\kappa$ there is a model $\mathscr{M}_\mu$ of cardinality $\lambda$ with No$(\mathscr{M}_\mu) = \mu$. In this paper we show: for every nonzero $\mu \leq \lambda^\kappa$ there is an inverse $\kappa$-system $\mathscr{A}$ of abelian groups having cardinality < $\lambda$ such that card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$ (under the assumptions $2^\kappa < \lambda$ and $\theta^{<\kappa} < \lambda$ for all $\theta < \lambda$ when $\mu > \lambda$), with the obvious new consequence concerning the possible value of No. Specifically, the case No($\mathscr{M}$) = $\lambda$ is possible when $\theta^\kappa < \lambda$ for every $\theta < \lambda$. (shrink)

A pure-strategy equilibrium existence theorem is extended to include games with non-expected utility players. It is shown that to guarantee the existence of a Nash equilibrium in pure strategies, the linearity of preferences in the probabilities can be replaced by the weaker requirement of quasiconvexity in the probabilities.

Suppose λ is a singular cardinal of uncountable cofinality κ. For a model M of cardinality λ, let No (M) denote the number of isomorphism types of models N of cardinality λ which are L ∞λ - equivalent to M. In [7] Shelah considered inverse κ- systems A of abelian groups and their certain kind of quotient limits Gr(A)/ Fact(A). In particular Shelah proved in [7, Fact 3.10] that for every cardinal μ there exists an inverse κ-system A (...) such that A consists of abelian groups having cardinality at most μ κ and card(Gr(A)/Fact(A)) = μ. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse κ-systems and possible values of No (under the assumption that $\theta^\kappa for every $\theta ): if A is an inverse κ- system of abelian groups having cardinality $\theta^\kappa for every $\theta ): for every nonzero $\mu or μ = λ κ there is a model M μ of cardinality λ with No(M μ ) = μ. In this paper we show: for every nonzero μ ≤ λ κ there is an inverse κ-system A of abelian groups having cardinality $2^\kappa and $\theta^{ for all $\theta when $\mu > \lambda$ ), with the obvious new consequence concerning the possible value of No. Specifically, the case No(M) = λ is possible when $\theta^\kappa for every $\theta. (shrink)

How can Euler diagrams support non-consequence inferences? Although an inference to non-consequence, in which people are asked to judge whether no valid conclusion can be drawn from the given premises, is one of the two sides of logical inference, it has received remarkably little attention in research on human diagrammatic reasoning; how diagrams are really manipulated for such inferences remains unclear. We hypothesized that people naturally make these inferences by enumerating possible diagrams, based on the logical notion of self-consistency, in (...) which every Euler diagram is true in a set-theoretical interpretation. The work is divided into three parts, each exploring a particular condition or scenario. In condition 1, we asked participants to directly manipulate diagrams with size-fixed circles as they solved syllogistic tasks, with the result that more reasoners used the enumeration strategy. In condition 2, another type of size-fixed diagram was used. The diagram layout change interfered with accurate task performances and with the use of the enumeration strategy; however, the enumeration strategy was still dominant for those who could correctly perform the tasks. In condition 3, we used size-scalable diagrams, which reduced the interfering effect of diagram layout and enhanced participants’ selection of the enumeration strategy. These results provide evidence that non-consequence inferences can be achieved by diagram enumeration, exploiting the self-consistency of Euler diagrams. An alternate strategy based on counter-example construction with Euler diagrams, as well as effects of diagram layout in inferential processes, are also discussed. (shrink)

The imbalance between supply of organs for transplantation and demand for them is widening. Although the current international drive to re-establish procurement via non-heart beating organ donation/donor is founded therefore on necessity, the process may constitute a desirable outcome for patient and family when progression to brain stem death does not occur and conventional organ retrieval from the beating heart donor is thereby prevented. The literature accounts of this practice, however, raise concerns that risk jeopardising professional and public confidence in (...) the broader transplant programme. This article focuses on these clinical, ethical, and legal issues in the context of other approaches aimed at increasing donor numbers. The feasibility of introducing such an initiative will hinge on the ability to reassure patients, families, attendant staff, professional bodies, the wider public, law enforcement agencies, and the media that practitioners are working within explicit guidelines which are both ethically and legally defensible. (shrink)

Recent research suggests that individuals with relatively weak global precedence (i.e., a smaller propensity to view visual stimuli in a configural manner) show a reduced face inversion effect (FIE). Coupled with such findings, a number of recent studies have demonstrated links between an advantage for feature‐based processing and the presentation of traits associated with autism among the general population. The present study sought to bridge these findings by investigating whether a relationship exists between the possession of autism‐associated traits (i.e., as (...) indicated by individuals’“autism quotient” [(AQ) and the size of the FIE. Participants completed an on‐line study in which the AQ was measured prior to a standard face recognition task where half of the faces were inverted at test. The results confirmed that higher AQ levels were predictive of smaller FIEs. Implications for a common underlying factor relating to processing orientation are discussed. (shrink)

Recent research suggests that individuals with relatively weak global precedence (i.e., a smaller propensity to view visual stimuli in a configural manner) show a reduced face inversion effect (FIE). Coupled with such findings, a number of recent studies have demonstrated links between an advantage for feature-based processing and the presentation of traits associated with autism among the general population. The present study sought to bridge these findings by investigating whether a relationship exists between the possession of autism-associated traits (i.e., as (...) indicated by individuals’“autism quotient” [(AQ) and the size of the FIE. Participants completed an on-line study in which the AQ was measured prior to a standard face recognition task where half of the faces were inverted at test. The results confirmed that higher AQ levels were predictive of smaller FIEs. Implications for a common underlying factor relating to processing orientation are discussed. (shrink)

Recently a gender-selective harvesting strategy has been proposed for possible control of aquatic invasive species, wherein females of the invasive species are harvested, whilst stocking the males (abbreviated as FHMS strategy) (Lyu et al. in Nat Resour Model 33(2):e12252, 2020). We consider the FHMS strategy with a weak Allee effect, and show that its extinction boundary need not be hyperbolic. To the best of our knowledge, this is the first example of a non-hyperbolic extinction boundary in two-compartment (...) mating models structured by sex. The model possesses a rich dynamical structure, with several local co-dimension one bifurcations occurring. We also show the occurrence of a global homoclinic bifurcation, which has applicability for large scale strategic bio-control. (shrink)

The imbalance between supply of organs for transplantation and demand for them is widening. Although the current international drive to re-establish procurement via non-heart beating organ donation/donor (NHBOD) is founded therefore on necessity, the process may constitute a desirable outcome for patient and family when progression to brain stem death (BSD) does not occur and conventional organ retrieval from the beating heart donor is thereby prevented. The literature accounts of this practice, however, raise concerns that risk jeopardising professional and public (...) confidence in the broader transplant programme. This article focuses on these clinical, ethical, and legal issues in the context of other approaches aimed at increasing donor numbers. The feasibility of introducing such an initiative will hinge on the ability to reassure patients, families, attendant staff, professional bodies, the wider public, law enforcement agencies, and the media that practitioners are working within explicit guidelines which are both ethically and legally defensible. (shrink)

The following is the second part of our Archaeology of the Inverse Square Law. Together these papers examine the transformation of the inverse square ratio from its origins in a metaphysical image of medieval thought in Grosseteste and the perspectivist tradition, through a playful magical practice in the Renaissance with Cusanus and Dee, and into a mathematical tool, applicable to the physical world. This last transformation allowed Newton to condense the geometrical image into a celebrated algebraic equation for (...) universal gravity, but it proved particularly confusing for the people who wrought it, Kepler and Hooke. (shrink)

Non-profit (NP) organizations present complex challenges in managing stakeholder relationships, particularly during times of environmental change. This places a premium on knowing which stakeholders really matter if an effective relationship marketing strategy is to be developed. This article presents the successful application of a model, which combines Mitchell’s theory of stakeholder saliency and Coviello’s framework of contemporary marketing practices in a leading NP organization in the U.K. A cooperative enquiry approach is used to explore stakeholder relationships, dominant marketing practices, (...) and to surface differing perceptions about the organization’s marketing strategy. Resolving these differences sets the scene for developing choices in marketing strategy for the future. (shrink)

Non-Relational Realism is a popular solution to the Bradleyan regress of facts or truths. It denies that there is a relational universal of exemplification; for an object a to exemplify a universal F-ness, on this view, is not for a relation to subsist between a and F-ness. An influential objection to Non-Relational Realism is that it is unacceptably obscure. The author argues that Non-Relational Realism can be understood as a selective application of satisfaction semantics to predicates like ‘exemplify’, and that (...) so understood, it is not obscure. This kind of selective use of satisfaction semantics may be feasible in other contexts as a means of making theories more parsimonious. (shrink)

The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still (...) working in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide. (shrink)

This chapter examines the spectrum inversion hypothesis as an argument against certain kinds of account of what it’s like to be conscious of color. The hypothesis aims to provide a counterexample to accounts of what it’s like to be conscious of color in non-qualitative terms, as well as to accounts of what it’s like to be conscious of color in terms of the representational content of conscious visual states (which, according to some philosophers, is in turn given an account in (...) non-qualitative terms). I explain the hypothesis’s reasoning in sections 1 and 2. I then take up background issues: since the counterexample provided by the hypothesis is typically given as a possibility rather than an actuality, I briefly discuss the kind of possibility involved in section 3, and the methodologies used to evaluate the plausibility of possibilities in section 4. In section 5, I describe some general considerations that are commonly used against the spectrum inversion hypothesis. I take up attempts to support the hypothesis with findings from color science in section 6. I end with comments skeptical of both the motivation for the spectrum inversion hypothesis and the methodology used to support it. (shrink)

We investigate, for several modal logics but concentrating on KT, KD45, S4 and S5, the set of formulas B for which ${\square B}$ is provably equivalent to ${\square A}$ for a selected formula A (such as p, a sentence letter). In the exceptional case in which a modal logic is closed under the (‘cancellation’) rule taking us from ${\square C \leftrightarrow \square D}$ to ${C \leftrightarrow D}$ , there is only one formula B, to within equivalence, in this inverse (...) image, as we shall call it, of ${\square A}$ (relative to the logic concerned); for logics for which the intended reading of “ ${\square}$ ” is epistemic or doxastic, failure to be closed under this rule indicates that from the proposition expressed by a knowledge- or belief-attribution, the propositional object of the attitude in question cannot be recovered: arguably, a somewhat disconcerting situation. More generally, the inverse image of ${\square A}$ may comprise a range of non-equivalent formulas, all those provably implied by one fixed formula and provably implying another—though we shall see that for several choices of logic and of the formula A, there is not even such an ‘interval characterization’ of the inverse image (of ${\square A}$ ) to be found. (shrink)

In the pure powers ontology (PPO), basic physical properties have wholly dispositional essences. PPO has clear advantages over categoricalist ontologies, which suffer from familiar epistemological and metaphysical problems. However, opponents argue that because it contains no qualitative properties, PPO lacks the resources to individuate powers, and generates a regress. The challenge for those who take such arguments seriously is to introduce qualitative properties without reintroducing the problems that PPO was meant to solve. In this paper, I distinguish the core claim (...) of PPO: (i) basic physical properties have dispositional essences, from a hitherto unnoticed assumption: (ii) the dispositional essences of basic physical properties exclusively involve type-causal relations to other basic physical properties. I reject (ii), making room for a structuralist ontology in which all basic physical properties are pure powers, individuated by their places in a causal structure that includes not only other powers, but also physically realized qualitative properties such as shapes, patterns and structures. Such qualities individuate pure powers in the way that non-mental input and output properties individuate realized mental properties in functionalist theories of mind, except that here it is basic physical powers that are individuated by relations to realized non-powers. I distinguish one Platonic and two Aristotelian version of this theory, and argue that the Aristotelian versions require that grounding is not always a relative fundamentality relation, because the powers ground the qualities that individuate them. By considering ontic structural realism, I argue that symmetric grounding is the best way to make sense of relational individuation in structuralist ontologies, and is therefore no additional commitment of the one proposed here. (shrink)