Equal Justice explores the role of the idea of equality in liberal theories of justice. The title indicates the book’s two-part thesis: first, I claim that justice is the central moral category in the socio-political domain; second, I argue for a specific conceptual and normative connection between the ideas of justice and equality. This pertains to the age-old question concerning the normative significance of equality in a theory of justice. The book develops an independent, systematic, and comprehensive theory of equality (...) and egalitarianism. The principal question is about the importance of equality in a theory of justice. More precisely, we should pose questions in four contracting circles: 1. Is justice the supreme value guiding our setup of the basic structure of society, or are there other, equally important values, such as recognition, care, communal belonging? 2. If justice is the highest guiding principle, which competing ideals—especially equality and freedom—ought to have precedence in a policy oriented toward justice? What status does the ideal of equality have in that framework? 3. If equality is a basic ideal of just policy, how should it be practically realized? What sort of equality (equal opportunity, equality of welfare, resource equality) should be demanded? 4. What patterned distribution of which specific goods does the ideal of equality demand? Which principles of distribution can be justified according to our justice ideal? To conclude and summarize: 5. What is the essential core of an egalitarian theory of justice, as opposed to an inegalitarian theory? These five questions structure the work’s order of argumentation. Part A elaborates the conceptual foundations and basic moral principles of justice and equality. Chapter I sets out to install justice as the central moral category in the socio-political domain. At the beginning of the first chapter, the conceptual foundations of justice are clarified. While not eliminating the classical distinctions between different forms of justice, I argue that the distributive paradigm is of primary importance. The primacy of justice in the socio-political domain is developed out of a confrontation with alternative positions, those which maintain either that justice generally, or distributive justice in particular, are subsidiary virtues. At the end of Chapter I, the first of the questions mentioned above is answered in a way that establishes justice as the guiding normative concept for the foundation and evaluation of any social order. To clarify the role of equality in a theory of justice, Chapter II separates the idea of equality into four different principles. They are organized in a way that begins with the most general and uncontroversial principle of equality, and progresses towards increasingly detailed and contested principles. There are two theses that articulate and defend the significance of equality for justice: First there is a conceptual connection between justice and equality, in that principles of formal and proportional equality are necessary in order to explicate the concept of justice. These two principles establish an unbreakable bond between justice and equality. Justice can only be explained—or so I argue—by reference to these and other (normative) principles of equality. The second thesis posits a normative relationship between justice and equality, which is disclosed by three substantive principles of equality: moral equality, the presumption of equality, and the principle of responsibility. I argue that the normative core of an egalitarian theory of justice is expressed by the latter two principles, which are themselves based on the first principle, that of moral equality. When we view one another as persons, what form of equality or equal treatment is normatively demanded? I argue that the answer to this question is given by the procedural principle of the presumption of equality: regardless of their apparent differences, all persons deserve strictly equal treatment, unless certain kinds of differences have whatever particular relevance would justify, on generally acceptable grounds, unequal treatment or unequal distribution. The justification of the presumption of equality is central to this work and has considerable importance. If the presumption principle’s validity can be justified by enlisting the principle of general justification, then the primacy of equality, and the essential argument for an egalitarian theory of justice, is established. This would likewise provide a procedure for the construction of a material theory of justice. The second question is answered thereby at the end of Chapter II: Equality should have primacy over competing ideals within a justice-oriented policy. The presumption of equality establishes this primacy and, at the same time, offers an appropriate metric and guideline for the construction of a material theory of distributive justice. The presumption of equality in Part B offers an elegant procedure for the development of a theory of distributive justice. Chapter III clearly sets out the necessary prerequisites that a theory of distribution must satisfy in order to determine a liberal-egalitarian distributional framework. We need to specify in which situation the distribution takes place; which goods are and are not to be distributed; in which respect the presumptive equality is to be produced; and by and to whom, and for what period, the relevant goods are to be distributed. The distribution is based on resources understood as general-purpose means. It is necessary to divide goods into different categories, since the justification for unequal treatment in one domain will not carry over into another. This makes presumptive equality necessarily complex. To that end, four spheres of justice are distinguished: (1) the political sphere, which involves allocating rights through the distribution of civil liberties; (2) the democratic sphere, in which political power and the rights of political participation are regulated; (3) the economic sphere, in which income and property are distributed; (4) the social sphere, in which social positions and opportunities are distributed. This framework of distributive justice answers the third of our guiding questions, about the nature of equality, in terms of equality of resources. Chapters IV and V set out the egalitarian distributive criteria for each sphere. I argue that the generally accepted, fundamental rights of classical liberalism are more effectively reconstructed by reference to the equal resource distribution presumptively required in those spheres. Chapter IV shows that when it comes to the first two spheres, those involving basic rights and freedoms and entitlement political participation, there can be no justified exceptions to the equal distribution of the relevant goods. That section argues, contrary to what we commonly find in theories of freedom or popular sovereignty, that the value of freedom and self-determination as the political basis of autonomy is best realized through the presumption of equal distribution. Chapter V deals with the other two spheres, those of economic goods and social positions, and argues for justified exceptions to equal distribution. In the economic sphere we find one principal reason favouring unequal distribution of resources, and three restrictions and compensations limiting that inequality. The basic exception to equal economic distribution arises from the unequal consequences of personal responsibility. From a suitably egalitarian standpoint, the principle of responsibility is the normative principle that determines which reasons justify economic inequality. Here the basic idea is that unequal shares of social goods are fair if they result from the choices and deliberate actions of the relevant parties. That individuals have to bear the costs of their own choices is a condition of autonomy. However, benefits or disadvantages arising from arbitrary and unmerited differences in social circumstances or natural endowments is unfair. The unequal consequences of independent decision-making and action must therefore be limited by compensating first for preferences, secondly for disadvantages, and thirdly by redistributing wealth in aid of the worse-off. I situations of emergency, compensating for disadvantages has priority over all other claims, owing to the urgency of the situation. Social inequalities go beyond the permissible limit if it is possible to improve the long-term social or economic situation of the worse-off by redistributing wealth to them. These exceptions lead to a complex system of free economic action within a framework of compensatory tax and transfer mechanisms. Finally, in the social sphere, the distribution of social positions, offices and opportunities must be structured to ensure that equally talented and motivated citizens have roughly equal chances of obtaining those offices or positions, irrespective of their economic or social class backgrounds. This compromise is permissible for reasons of freedom and prudence, and it makes a certain measure of inequality acceptable. The fourth of our guiding questions is answered accordingly. There are five principles of justice for the basic structure of society, and five legal principles that govern the special distribution of goods in the respective spheres—all are ranked according to their most defensible grounds of priority, ensuring that everyone is accorded equal justice. Chapter VI recapitulates the initial question of equality’s value. The conception of equal justice developed in this work postulates five principles of equality and five principles of law; these constitute an egalitarian framework because they support and promote social justice. Equality has value with respect to them, but is not given any independent, intrinsic value. That is why I call the account developed here a form of constitutive egalitarianism: justice is realized through the realization of equality, itself accomplished by applying the five postulates of equality and five distributive principles of law. This is an egalitarianism on two levels. The first level is involves the claim that morality or justice is conceptually connected with equality. The second level gives equality a substantial weight in what is conceptually validated at the first level, namely the presumption of equality, and constructs an appropriate interpretation and conception of distributive justice through principles of distribution for the individual spheres. The weight and importance of equality is shown by the distributive criteria applied to those spheres. This answers our final guiding question about the nature of an egalitarian theory. (shrink)

Users of sociotechnical systems often have no way to independently verify whether the system output which they use to make decisions is correct; they are epistemically dependent on the system. We argue that this leads to problems when the system is wrong, namely to bad decisions and violations of the norm of practical reasoning. To prevent this from occurring we suggest the implementation of defeaters: information that a system is unreliable in a specific case (undercutting defeat) or independent information that (...) the output is wrong (rebutting defeat). Practically, we suggest to design defeaters based on the different ways in which a system might produce erroneous outputs, and analyse this suggestion with a case study of the risk classification algorithm used by the Dutch tax agency. (shrink)

Process reliabilist accounts claim that a belief is justified when it is the result of a reliable belief-forming process. Yet over what range of possible token processes is this reliability calculated? I argue against the idea that _all_ possible token processes (in the actual world, or some other subset of possible worlds) are to be considered using the case of a user acquiring beliefs based on the output of an AI system, which is typically reliable for a substantial local range (...) but unreliable when all possible inputs are considered. I show that existing solutions to the generality problem imply that these cases cannot be solved by a more fine-grained typing of the belief-forming process. Instead, I suggest that reliability is evaluated over a range restricted by the content of the actual belief and by the similarity of the input to the actual input. (shrink)

How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the (...) initial segment of the natural numbers on the basis of the Fregean definitions, but do not learn the natural number structure as a whole on the basis of Hume's principle. Therefore, we need to account for some of the consistency of our number concepts with the Dedekind-Peano axioms in other terms. (shrink)

In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for (...) the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof. (shrink)

By using the notions of exact truth and exact falsity, one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the Strong Kleene schema. Besides familiar logics such as Strong Kleene logic, the Logic of Paradox and First Degree Entailment, the resulting class of all Strong Kleene generalizations of classical logic also contains a host of unfamiliar (...) logics. We first study the members of our class semantically, after which we present a uniform sequent calculus that is sound and complete with respect to all of them. Two further sequent calculi and \ calculus) will be considered, which serve the same purpose and which are obtained by applying general methods to construct sequent calculi for many-valued logics. Rules and proofs in the SK calculus are much simpler and shorter than those of the \ and the \ calculus, which is one of the reasons to prefer the SK calculus over the latter two. Besides favourably comparing the SK calculus to both the \ and the \ calculus, we also hint at its philosophical significance. (shrink)

The rise of causality and the attendant graph-theoretic modeling tools in the study of counterfactual reasoning has had resounding effects in many areas of cognitive science, but it has thus far not permeated the mainstream in linguistic theory to a comparable degree. In this study I show that a version of the predominant framework for the formal semantic analysis of conditionals, Kratzer-style premise semantics, allows for a straightforward implementation of the crucial ideas and insights of Pearl-style causal networks. I spell (...) out the details of such an implementation, focusing especially on the notions of intervention on a network and backtracking interpretations of counterfactuals. (shrink)

We present the first comprehensive theory of fairness that conceives of fairness as having two dimensions: a comparative and an absolute one. The comparative dimension of fairness has traditionally been the main interest of Broomean fairness theories. It has been analysed as satisfying competing individual claims in proportion to their respective strengths. And yet, many key contributors to Broomean fairness agree that ‘absolute’ fairness is important as well. We make this concern precise by introducing the Fairness formula and the absolute (...) priority rule and analyse their implications for comparative fairness. (shrink)

According to an increasingly popular view among philosophers of science, both causal and non-causal explanations can be accounted for by a single theory: the counterfactual theory of explanation. A kind of non-causal explanation that has gained much attention recently but that this theory seems unable to account for are grounding explanations. Reutlinger :239-256, 2017) has argued that, despite these appearances to the contrary, such explanations are covered by his version of the counterfactual theory. His idea is supported by recent work (...) on grounding by Schaffer and Wilson who claim there to be a tight connection between grounding and counterfactual dependence. The present paper evaluates the prospects of the idea. We show that there is only a weak sense in which grounding explanations convey information about counterfactual dependencies, and that this fact cannot plausibly be taken to reveal a distinctive feature that grounding explanations share with other kinds of explanations. (shrink)

The Approximate Number System (ANS) is a system that allows us to distinguish between collections based on the number of items, though only if the ratio between numbers is high enough. One of the questions that has been raised is what the representations involved in this system represent. I point to two important constraints for any account: (a) it doesn’t involve numbers, and (b) it can account for the approximate nature of the ANS. Furthermore, I argue that representations of pure (...) magnitude with vehicles that have an imprecision in the value of the unit of measurement (further clarified through a formal model from measurement theory) fit both these requirements. (shrink)

In the article ‘How to be absolutely fair, Part I: the Fairness formula’, we presented the first theory of comparative and absolute fairness. Here, we relate the implications of our Fairness formula to economic theories of fair division. Our analysis makes contributions to both philosophy and economics: to the philosophical literature, we add an axiomatic discussion of proportionality and fairness. To the economic literature, we add an appealing normative theory of absolute and comparative fairness that can be used to evaluate (...) axioms and division rules. Also, we provide a novel definition and characterization of the absolute priority rule. (shrink)

It is widely recognized that the innate versus acquired distinction is a false dichotomy. Yet many scientists continue to describe certain traits as “innate” and take this to imply that those traits are not acquired, or “unlearned.” This article asks what cognitive role, if any, the concept of innateness should play in the psychological and behavioural sciences. I consider three arguments for eliminating innateness from scientific discourse. First, the classification of a trait as innate is thought to discourage empirical research (...) into its developmental origin. Second, this concept lumps together a number of different biological properties that ought to be treated as distinct. Third, innateness is associated with the outmoded folk biological theory of essentialism. In response to these objections, I consider two attempts to revise the concept of innateness which aim to make it more suitable for scientific explanation and research. One proposal is that innateness can be defined in terms of the biological property of environmental canalization. On this view, a trait is innate to the extent that it is developmentally buffered against a range of different environments. Another proposal is that innateness serves as an explanatory primitive for cognitive science. This view holds that there exist a sharp boundary between psychological and biological explanations and that to identify a trait as innate means that it falls into the latter explanatory domain. This essay ends with some questions for future research. (shrink)

The entropy-reduction hypothesis claims that the cognitive processing difficulty on a word in sentence context is determined by the word's effect on the uncertainty about the sentence. Here, this hypothesis is tested more thoroughly than has been done before, using a recurrent neural network for estimating entropy and self-paced reading for obtaining measures of cognitive processing load. Results show a positive relation between reading time on a word and the reduction in entropy due to processing that word, supporting the entropy-reduction (...) hypothesis. Although this effect is independent from the effect of word surprisal, we find no evidence that these two measures correspond to cognitively distinct processes. (shrink)

A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (as measured) among testimonies implies a higher probability that the witnesses are reliable. Recently, it has been proved that several coherence measures proposed in the literature are reliability conducive in scenarios of equivalent testimonies (Olsson and Schubert 2007; Schubert, to appear). My aim is to investigate which coherence measures turn out to be reliability conducive in the more general scenario where the (...) testimonies do not have to be equivalent. It is shown that four measures are reliability conducive in the present scenario, all of which are ordinally equivalent to the Shogenji measure. I take that to be an argument for the Shogenji measure being a fruitful explication of coherence. (shrink)

ABSTRACT How do non-experts single out numbers for reference? Linnebo has argued that they do so using a criterion of identity based on the ordinal properties of numerals. Neo-logicists, on the other hand, claim that cardinal properties are the basis of individuation, when they invoke Hume’s Principle. I discuss empirical data from cognitive science and linguistics to answer how non-experts individuate numbers better in practice. I use those findings to develop an alternative account that mixes ordinal and cardinal properties to (...) provide a detailed answer to the question: how do we in fact semantically individuate numbers? (shrink)

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

The recent explosion of interest in epigenetics is often portrayed as the dawning of a scientific revolution that promises to transform biomedical science along with developmental and evolutionary biology. Much of this enthusiasm surrounds what we call the epigenetic switch hypothesis, which regards certain examples of epigenetic inheritance as an adaptive organismal response to environmental change. This interpretation overlooks an alternative explanation in terms of coevolutionary dynamics between parasitic transposons and the host genome. This raises a question about whether epigenetics (...) researchers tend to overlook transposon dynamics more generally. To address this question, we surveyed a large sample of scientific publications on the topics of epigenetics and transposons over the past fifty years. We found that enthusiasm for epigenetics is often inversely related to interest in transposon dynamics across the four disciplines we examined. Most surprising was a declining interest in transposons within biomedical science and cellular and molecular biology over the past two decades. Also notable was a delayed and relatively muted enthusiasm for epigenetics within evolutionary biology. An analysis of scientific abstracts from the past twenty-five years further reveals systematic differences among disciplines in their uses of the term epigenetic, especially with respect to heritability commitments and functional interpretations. Taken together, these results paint a nuanced picture of the rise of epigenetics and the possible neglect of transposon dynamics, especially among biomedical scientists. (shrink)

The normative mechanics of promising seem complex. The strength and content of promissory obligations, and the residual duties they entail upon being violated, have various prima facie surprising features. We give an account to explain these features. Promises have a point. The point of a promise to φ is a promise-independent reason to φ for the promisee’s sake. A promise turns this reason into a duty. This explains the mechanics of promises. And it grounds a nuanced picture of immoral promises, (...) an argument against promissory bare wrongings, and a constraint on theories of why we have promissory obligations at all. (shrink)

Landgrebe and Smith provide an argument for the impossibility of Artificial General Intelligence based on the limits of simulating complex systems. However, their argument presupposes a very contemporary vision of artificial intelligence as a model trained on data to produce an algorithm executable in a modern digital computing system. The present contribution explores what it means to be artificial. Current artificial intelligence approaches on modern computing systems are not the only conceivable way in which artificial intelligence technology might be created. (...) If there are conceivable routes by which an artificial intelligence might be developed that are not constrained in the same way as the current generation of artificial neural networks, then these might be plausible routes towards the engineered generation of artificial general intelligence that are not precluded by the Landgrebe and Smith argument against the possibility of artificial general intelligence. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. We generically construct a model in which the [math]-separation property is true, i.e. every pair of disjoint [math]-sets can be separated by a [math]-definable set. This answers an old question from the problem list “Surrealist landscape with figures” by A. Mathias from 1968. We also construct a model in which the (lightface) [math]-separation property is true.

Recent examples of rapid evolution under natural selection seem to require that the disciplines of ecology and evolution become better integrated. This inference makes sense only if one’s understanding of these disciplines is based on Hutchinson’s two-speed model of the ecological theater and the evolutionary play. Instead, these disciplines are more accurately viewed as occupying distinct “epistemic niches.” When so understood, we see that rapid evolution under selection, even if it is generally true, does not imply that evolutionary explanations are (...) improved by the inclusion of ecological details. Nor are ecological explanations necessarily improved by the inclusion of information about trait variation, heritability, effective population size, or other standard evolutionary factors. To illustrate, I develop a version of Kitcher’s “gory details” argument to show that, even for some trait that is under strong directional selection, a dynamically sufficient explanation of its ecological relationships should ignore most of the information explaining why that trait is evolving. The wholesale integration of ecology and evolution looks even less appealing when empirical sufficiency, a purely practical requirement, is taken into account. As a way forward, I propose an eco-evo partitioning framework. This strategy enables researchers to estimate the empirical sufficiency of a purely ecological, a purely evolutionary, or a combined eco-evo approach. (shrink)

We investigate the issue of aggregativity in fair division problems from the perspective of cooperative game theory and Broomean theories of fairness. Paseau and Saunders proved that no non-trivial theory of fairness can be aggregative and conclude that theories of fairness are therefore problematic, or at least incomplete. We observe that there are theories of fairness, particularly those that are based on cooperative game theory, that do not face the problem of non-aggregativity. We use this observation to argue that the (...) universal claim that no non-trivial theory of fairness can guarantee aggregativity is false. Paseau and Saunders’s mistaken assertion can be understood as arising from a neglect of the games approach to fair division. Our treatment has two further pay-offs: for one, we give an accessible introduction to the games approach to fair division, whose significance has hitherto not been appreciated by philosophers working on fairness. For another, our discussion explores the issue of aggregativity in fair division problems in a comprehensive fashion. (shrink)

Most accounts of our knowledge of the successor axiom claim that this is based on the procedure of adding one. While they usually don’t claim to provide an account of how children actually acquire this knowledge, one may well think that this is how they get that knowledge. I argue that when we look at children’s responses in interviews, the time when they learn the successor axiom and the intermediate learning stages they find themselves in, that there is an empirically (...) viable alternative. I argue that they could also learn it on the basis of a method that has to do with the structure of the numeral system. Specifically, that they (1) use the syntactic structure of the numeral system and (2) attend to the leftmost digits, the one with the highest place-value. Children can learn that this is a reliable method of forming larger numbers by combining two elements. First, a grasp of the syntactic structure of the numeral system. That way they know that the leftmost digit receives the highest value. Second, an interpretation of numerals as designating cardinal values, so that they also realise that increasing or adding digits on the lefthand side of a numeral produces a larger number. There are thus two, currently equally well-supported, ways in which children might learn that there are infinitely many natural numbers. (shrink)

In a recent article, Emanuel Rutten has presented a novel argument for the existence of God, defined as a personal being that is the first cause of reality. An interesting feature of the argument, which caused quite a stir, is that it does not fall within any of the traditional categories of arguments for God’s existence. Rutten calls his argument a modal-epistemic one, which reflects the fact that the first premise of his argument states that all possible truths are knowable. (...) The main purpose of this article is a simple one: to point out that Rutten’s modal-epistemic argument is flawed. (shrink)

In a recent article, Emanuel Rutten defends his Modal-Epistemic Argument (MEA) for the existence of God against various objections that I raised against it. In this article, I observe that Rutten’s defence fails for various reasons. Most notably though, the defence is self-undermining: the very claims that Rutten argues for in his defence yield novel counterexamples to the first premise of the MEA.

Business Ethics, the Environment &Responsibility, Volume 32, Issue 2, Page 415-418, April 2023.

This volume features a collection of essays on consciousness, which has become one of the hot topics at the crossroads between neuroscience, philosophy, and religious studies. Is consciousness something the brain produces? How can we study it? Is there just one type of consciousness or are there different states that can be discriminated? Are so called "higher states of consciousness" that some people report during meditation pointing towards a new understanding of consciousness? Meditation research is a new discipline that shows (...) new inroads into the study of consciousness. If a meditative practice changes brain structure itself this is direct proof of the causal influence of consciousness onto its substrate. If different states of consciousness can be linked with properties and states of the brain this can be used to study consciousness more directly. If the sense of self is modifiable through meditative techniques and this can be objectively shown through neuro-imaging, this has profound implications for our understanding of who we are. Can consciousness, in deep states of meditative absorption, actually access some aspect of reality which we normally don't? Meditation research can potentially foster us with a new access to the phenomenological method in general. This has even been branded with a new catch-phrase: Contemplative Science. It brings together the most modern neuroscientific approach and the most advanced phenomenological methodology of studying the mind from within, through highly skilled self-observation that has gone through many thousand hours of honing the capacity to look carefully, without distraction. This book addresses these issues by bringing together some of the leading researchers and thinkers in the field. The scope of the volume reaches from first person neuroscience to Indian philosophy, from pedagogic applications to epistemological aspects and from compassion meditation to the study of brain activity. (shrink)

Lawton’s contingency thesis states that there are no useful generalizations at the level of ecological communities because these systems are especially prone to contingent historical events. I argue that this influential thesis has been grounded on the wrong kind of evidence. CT is best understood in Woodward’s terms as a claim about the instability of certain causal dependencies across different background conditions. A recent distinction between evolution and ecology reveals what an adequate test of Lawton’s thesis would look like. To (...) date, CT remains untested. But developments in genome and molecular ecology point in a promising direction. (shrink)

Topic of the paper is Q-logic - a logic of agency in its temporal and modal context. Q-logic may be considered as a basal logic of agency since the most important stitoperators discussed in the literature can be defined or axiomatized easily within its semantical and syntactical framework. Its basic agent dependent operator, the Q-operator (also known as Δ- or cstit-operator), which has been discussed independently by E v. Kutschera and B. E Chellas, is investigated here in respect of its (...) relation to other temporal and modal operators. The main result of the paper, then, is a completeness result for a calculus of Q-logic with respect to a semantics defined on the tree-approach to agency as introduced and developed by, among others, E v. Kutschera and N. D. Belnap. (shrink)

In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is a natural dual (...) of entailment. The calculus, and its tableau variant, not only capture the classical connectives, but also the `information' connectives of four-valued Belnap logics. This answers a question by Avron. (shrink)

In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these (...) logics is left for further work. In this paper, based on our previous work on a functionally complete extension of Belnap’s logic, we present a sound and complete tableau calculus for these logics. It crucially exploits the Cartesian nature of the four values, which is reflected in the fact that each proof consists of two tableaux. The bi-facial notion of truth of Z&S is thus augmented with a bi-facial notion of proof. We also provide translations between the logics for semi-classical negation and classical logic and show that an argument is valid in a logic for semi-classical negation just in case its translation is valid in classical logic. (shrink)

Mathematical cognition has become an interesting case study for wider theories of cognition. Menary :1–20, 2015) argues that arithmetical cognition not only shows that internalist theories of cognition are wrong, but that it also shows that the Hypothesis of Extended Cognition is right. I examine this argument in more detail, to see if arithmetical cognition can support such conclusions. Specifically, I look at how the use of numerals extends our arithmetical abilities from quantity-related innate systems to systems that can deal (...) with exact numbers of arbitrary size. I then argue that the system underlying our grasp of small numbers is an unhelpful case study for Menary; it doesn’t support an argument for externalism over internalism. The system for large numbers, on the other hand, clearly displays important interactions between public numeral systems and our cognitive processes. I argue that the large number system supports an argument against internalist theories of arithmetical cognition, but that one cannot conclude that the Hypothesis of Extended Cognition is correct. In other words, the large number case doesn’t decide between the Hypothesis of Extended Cognition and the Hypothesis of EMbedded Cognition. (shrink)

The dissertation provides a reconstruction of Bernard Bolzano's theory of grounding (both in early and late works) against the background of a classical conception of science and scientific explanation.

In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...) relations will in general require developing four tableaux, while proving that they are in the ⊧ relation may require six. (shrink)

Volume 19, Issue 10, October 2019, Page 90-92.

Los descubrimientos de las neurociencias permiten intervenir en el cerebro humano para mejorar su estado o sus capacidades sin indicación médica. Este fenómeno es conocido como “Neuroenhancement” y está sujeto a un amplio debate ético. Como “Neuroenhancement” es un fenómeno evolutivo, el debate de aspectos éticos está necesariamente orientado al futuro y depende de la información sobre el posible desarrollo de la tecnología y sus consecuencias para la sociedad. Sin embargo, hay que establecer límites para la formulación de previsiones especulativas (...) en argumentos éticos y justificaciones políticas. Propongo distinguir argumentos con tres propósitos distintos: la formación de intuiciones éticas, el reflejo sobre el futuro de la sociedad y justificación de normativas y políticas. Para cada uno de ellos necesitamos estándares adecuados. Es tarea de la filosofía política desarrollar un estándar para los argumentos justificadores.: Neuroscientific findings allow interventions in the human brain to improve its function or modify mental states even without medical indication. This procedure, termed as neuroenhancement, is subject to a broad ethical debate. As neuroenhancement is an evolving phenomenon, the debate is necessarily future-oriented and highly dependent on information about future developments. It remains an open question to what degree uncertain forecasting or even speculation should be considered in the ethical debate and policy-making. I propose to distinguish between arguments with three different purposes: intuition-forming, self-reflecting and justifying arguments. Adequate standards are required for all kinds of future-oriented arguments. The development of these standards for justifying arguments is a task for political philosophy. (shrink)

The Anthropocene concept allows human history to be imagined within the temporal framework of planetary processes. Accordingly, some environmentalists increasingly favour massively lengthening the temporal horizons of moral concern. Whilst there are defensible reasons for doing so, I wish to take issue with the ‘secular time’ perspective underlying some such approaches. To make my case, I present, in the first section, two recent manifestations of the long view perspective: a) ‘deep future’ narratives in popular climate science and futurism; b) the (...) ideas behind the Long Now Foundation. In the second section, I apply a critical lens to these perspectives via classic analyses of secular time by Charles Taylor, Hannah Arendt and Giorgio Agamben. I conclude by suggesting that these post-secular critiques should be considered alongside recent approaches to the Anthropocene and the ‘geological turn’ from new materialist perspectives. (shrink)