Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. A recently developed “heteromorphic” (...) theory about adjoints suggests a conceptual structure, albeit abstract and atemporal, for how new relatively autonomous behavior can emerge within a system obeying certain laws. The focus here is on applications in the life sciences (e.g., selectionist mechanisms) and human sciences (e.g., the generative grammar view of language). (shrink)

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. (...) Semiadjunctions (essentially a formulation of universal mapping properties using hets) can then be combined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior). (shrink)

Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim (...) that four truth values, along with contradiction, are admissible in reasoning. Indra's Net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions which are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of Sunyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of Catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's Net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the claim (...) that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

What is cognition? Equivalently, what is cognition good for? Or, what is it that would not be but for human cognition? But for human cognition, there would not be science. Based on this kinship between individual cognition and collective science, here we put forward Isbell conjugacy---the adjointness between objective geometry and subjective algebra---as a scientific method for developing cognitive science. We begin with the correspondence between categorical perception and category theory. Next, we show how the Gestalt maxim is subsumed by (...) the mathematical construct of colimit, a generalization of summation. The universal mapping property definitions of mathematical constructs, by virtue of being the best with respect to the universe of discourse, can be learned using reinforcement learning algorithms, which raises the possibility of abstracting the architecture of mathematics by artificial intelligence. Subsequently, we present naturality (to be contrasted with miracles), understood as 'Becoming consistent with Being', which governs the transformations of both things and their theories, as the zeroth law of change. Furthermore, the contrast---physical [mechanism] vs. biological [organism]---is smoothed via natural transformation, wherein transformations are respectful of the cohesion of the objects transformed. In closing, upon recognizing the scientific value of learning difficult-to-master differential calculus by physicists, of learning a strange four-letter language by biologists, and of learning the grammar of our respective mother tongues, we make a case for learning the theory of naturality / category theory for developing cognitive science. (shrink)

There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start (...) with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of Sets are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences. (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...) exploring the foundations of multialgebras applied to the study of logic systems. -/- It is well known from universal algebra that, for every signature Sigma, there exist algebras over Sigma which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of Sigma-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms (or propositional formulas, in the context of logic). Equivalently, the forgetful functor, from the category of Sigma-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor U, from the category of Sigma-multialgebras to Set, does not have a left adjoint. -/- In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices (which selects how a homomorphism approaches indeterminacies), there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that U does not have a left adjoint. (shrink)

Saunders Mac Lane famously remarked that "Bourbaki just missed" formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre--which then had to wait until Daniel Kan's 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms within a category, i.e., homomorphisms. When Samuel's treatment is reconsidered in view of the treatment of adjoints using heteromorphisms or hets (object-to-object morphisms between objects in (...) different categories), then he, in effect, isolated the concept of a left representation solving a universal mapping problem. When dualized to obtain the concept of a right representation, the two halves only need to be united to obtain an adjunction. Thus Samuel was only a now-simple dualization away for formulating adjoints in 1948. Apparently, Bodo Pareigis' 1970 text was the first and perhaps only text to give the heterodox "new characterization" (i.e., heteromorphic treatment) of adjoints. Orthodox category theory uses various relatively artificial devices to avoid formally recognizing hets--even though hets are routinely used by the working mathematician. Finally we consider a "philosophical" question as to whether the most important concept in category theory is the notion of an adjunction or the notion of a representation giving a universal mapping property (where adjunctions arise as the special case of a bi-representation of dual universal mapping problems). (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory (...) of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

Sensibility, in any of its myriad realms – moral, physical, aesthetic, medical and so on – seems to be a paramount case of a higher-level, intentional property, not a basic property. Diderot famously made the bold and attributive move of postulating that matter itself senses, or that sensibility (perhaps better translated ‘sensitivity’ here) is a general or universal property of matter, even if he at times took a step back from this claim and called it a (...) “supposition.” Crucially, sensibility is here playing the role of a ‘booster’: it enables materialism to provide a full and rich account of the phenomena of conscious, sentient life, contrary to what its opponents hold: for if matter can sense, and sensibility is not a merely mechanical process, then the loftiest cognitive plateaus are accessible to materialist analysis, or at least belong to one and the same world as the rest of matter. This was noted by the astute anti-materialist critic, the Abbé Lelarge de Lignac, who, in his 1751 Lettres à un Amériquain, criticized Buffon for “granting to the body [la machine, a common term for the body at the time] a quality which is essential to minds, namely sensibility.” This view, here attributed to Buffon and definitely held by Diderot, was comparatively rare. If we look for the sources of this concept, the most notable ones are physiological and medical treatises by prominent figures such as Robert Whytt, Albrecht von Haller and the Montpellier vitalist Théophile de Bordeu. We then have, or so I shall try to sketch out, an intellectual landscape in which new – or newly articulated – properties such as irritability and sensibility are presented either as an experimental property of muscle fibers, that can be understood mechanistically (Hallerian irritability, as studied recently by Hubert Steinke and Dominique Boury) or a property of matter itself (whether specifically living matter as in Bordeu and his fellow montpelliérains Ménuret and Fouquet, or matter in general, as in Diderot). I am by no means convinced that it is one and the same ‘sensibility’ that is at issue in debates between these figures (as when Bordeu attacks Haller’s distinction between irritability and sensibility and claims that ‘his own’ property of sensibility is both more correct and more fundamental in organic beings), but I am interested in mapping out a topography of the problem of sensibility as property of matter or as vital force in mid-eighteenth-century debates – not an exhaustive cartography of all possible positions or theories, but an attempt to understand the ‘triangulation’ of three views: a vitalist view in which sensibility is fundamental, matching up with a conception of the organism as the sum of parts conceived as little lives (Bordeu et al.); a mechanist, or ‘enhanced mechanist’ view in which one can work upwards, step by step from the basic property of irritability to the higher-level property of sensibility (Haller); and, more eclectic, a materialist view which seeks to combine the mechanistic, componential rigour and explanatory power of the Hallerian approach, with the monistic and metaphysically explosive potential of the vitalist approach (Diderot). It is my hope that examining Diderot in the context of this triangulated topography of sensibility as property sheds light on his famous proclamation regarding sensibility as a universal property of matter. (shrink)

The irrational exuberance associated with contemporary artificial intelligence (AI) reminds me of Charles Dickens: "it was the age of foolishness, it was the epoch of belief" (cf. Nature Editorial, 2016; to get a feel for the vanity fair that is AI, see Mitchell and Krakauer, 2023; Stilgoe, 2023). It is particularly distressing—feels like yet another rerun of Seinfeld, which is all about nothing (pun intended); we have seen it in the 60s and again in the 90s. AI might have had (...) an inauspicious beginning, which may very well be the original sin, and our current predicament is the attendant divine condemnation. Being unable to stand it, however divine it may be, without further ado, I get to the genesis (instead of getting lost in the here-and-now of this or that so-called breakthrough of AI). Here's my unvarnished critique! (shrink)

The well-known Principle of Plenitude has it that everything that exists in some possible world exists in the actual world. I argue for an amended version of this principle: If there’s a possible world in which something lacks some positive property, then there’s an object in the actual world that lacks that property. That is, all positive universally held properties in the actual world are necessarily universally held. This rules out that for some positive property, everything in (...) the actual world merely happens to have it. After having presented and defended the argument, I show that it has a wide range of corollaries, such as that there are mereologically simple and composite things, physical and non-physical things, caused and uncaused things, and contingent and necessarily existing things. The argument has three premises. The first premise is the thesis that there are no things that do not exist. The second premise is a Fregean theory of linguistic meaning. According to the third premise, two meanings coincide if and only if their reference sets coincide. The notion of a reference set is defined in the paper. (shrink)

The traditional soft set is a mapping from a parameter set to family of all crisp subsets of a universe. Molodtsov introduced the soft set as a generalized tool for modelling complex systems involving uncertain or not clearly defined objects. In this paper, the notion of neutrosophic soft set is reanalysed. The novel theory is a combination of neutrosophic set theory and soft set theory. The complement, “and”, “or”, intersection and union operations are defined on the neutrosophic soft sets. (...) The neutrosophic soft relations accompanied with their compositions are also defined. The basic properties of the neutrosophic soft sets, neutrosophic soft relations and neutrosophic soft compositions are also discussed. (shrink)

This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.

My goal in this paper is, to tentatively sketch and try defend some observations regarding the ontological dignity of object references, as they may be used from within in a formalized language. -/- Hence I try to explore, what properties objects are presupposed to have, in order to enter the universe of discourse of an interpreted formalized language. -/- First I review Frege′s analysis of the logical structure of truth value definite sentences of scientific colloquial language, to draw suggestions from (...) his saturated vs. unsaturated sentence components paradigm. -/- Next try investigate, in how far reference to non pure math objects might allow for a role as argument of a truth value function. Object kinds to be considered are: common sense objects, technical objects, humanities object kinds (social, psychical, ...), objects of art, ... , be they abstract, concrete, or in this respect mixed objects. -/- Then have a comment on the just referenced label abstract objects. -/- Next try to get an idea wrt the ontological significance of the fact, that pure math objects and functions in some important classical cases can be uniquely defined by means of categorical theories. Here, in the course of my argument, I have a little corollary wrt the standard model of first order Peano arithmetic, reducing the epistemological significance of the existence of the non standard models. -/- Next, wrt a special concept of a formalized empirical theory, I care for whether the impure math objects and mixed objects described here, and complying best with truth value function mapping, are also reliable candidates for the ontological commitment of such theories: and discuss an alternative, which reduces the ontological significance of the universe of discourse of the theories intended models. -/- In the end I sum up what is - from my point of view - the status quo, according to my respective findings. (shrink)

The term “Complex Systems Biology” was introduced a few years ago [Kaneko, 2006] and, although not yet of widespread use, it seems particularly well suited to indicate an approach to biology which is well rooted in complex systems science. Although broad generalizations are always dangerous, it is safe to state that mainstream biology has been largely dominated by a gene-centric view in the last decades, due to the success of molecular biology. So the one gene - one trait approch, which (...) has often proved to be effective, has been extended to cover even complex traits. This simplifying view has been appropriately criticized, and the movement called systems biology has taken off. Systems biology [Noble, 2006] emphasizes the presence of several feedback loops in biological systems, which severely limit the range of validity of explanations based upon linear causal chains (e.g. gene → behaviour). Mathematical modelling is one the favourite tools of systems biologists to analyze the possible effects of competing negative and positive feedback loops which can be observed at several levels (from molecules to organelles, cells, tissues, organs, organisms, ecosystems). Systems biology is by now a well-established field, as it can be inferred by the rapid growth in number of conferences and journals devoted to it, as well as by the existence of several grants and funded projects.Systems biology is mainly focused upon the description of specific biological items, like for example specific organisms, or specific organs in a class of animals, or specific genetic-metabolic circuits. It therefore leaves open the issue of the search for general principles of biological organization, which apply to all living beings or to at least to broad classes. We know indeed that there are some principles of this kind, biological evolution being the most famous one. The theory of cellular organization also qualifies as a general principle. But the main focus of biological research has been that of studying specific cases, with some reluctance to accept (and perhaps a limited interest for) broad generalizations. This may however change, and this is indeed the challenge of complex systems biology: looking for general principles in biological systems, in the spirit of complex systems science which searches for similar features and behaviours in various kinds of systems. The hope to find such general principles appears well founded, and I will show in Section 2 that there are indeed data which provide support to this claim. Besides data, there are also general ideas and models concerning the way in which biological systems work. The strategy, in this case, is that of introducing simplified models of biological organisms or processes, and to look for their generic properties: this term, borrowed from statistical physics, is used for those properties which are shared by a wide class of systems. In order to model these properties, the most effective approach has been so far that of using ensembles of systems, where each member can be different from another one, and to look for those properties which are widespread. This approach was introduced many years ago [Kauffman, 1971] in modelling gene regulatory networks. At that time one had very few information about the way in which the expression of a given gene affects that of other genes, apart from the fact that this influence is real and can be studied in few selected cases (like e.g. the lactose metabolism in E. coli). Today, after many years of triumphs of molecular biology, much more has been discovered, however the possibility of describing a complete map of gene-gene interactions in a moderately complex organism is still out of reach. Therefore the goal of fully describing a network of interacting genes in a real organism could not be (and still cannot be) achieved. But a different approach has proven very fruitful, that of asking what are the typical properties of such a set of interacting genes. Making some plausible hypotheses and introducing some simplifying assumptions, Kauffman was able to address some important problems. In particular, he drew attention to the fact that a dynamical system of interacting genes displays selforganizing properties which explain some key aspects of life, most notably the existence of a limited number of cellular types in every multicellular organism (these numbers are of the order of a few hundreds, while the number of theoretically possible types, absent interactions, would be much much larger than the number of protons in the universe). In section 3 I will describe the ensemble based approach in the context of gene regulatory networks, and I will show that it can describe some important experimental data. Finally, in section 4 I will discuss some methodological aspects. (shrink)

I reassess the famous arguments of Frank Plumpton Ramsey (1925) against the tenability of the distinction between particulars and universals and discuss their recent elaboration by Fraser MacBride. I argue that Ramsey’s argument is ambiguous between kinds and properties and that his sceptical worries can be resolved once this distinction is taken into account. A crucial role in this dissolution is a notion of what is essential to a property. I close by some epistemological considerations.

The metaphysics of representation poses questions such as: in virtue of what does a sentence, picture, or mental state represent that the world is a certain way? In the first instance, I have focused on the semantic properties of language: for example, what is it for a name such as ‘London’ to refer to something? Interpretationism concerning what it is for linguistic expressions to have meaning, says that constitutively, semantic facts are fixed by best semantic theory. As here developed, it (...) promises to give a reductive, universal and non-revisionary account of the nature of linguistic representation. -/- Interpretationism in general, however, is threatened by severe internal tension, due to arguments for radical inscrutability. These contend that, given the interpretationist setting, there can be no fact of the matter what object an individual word refers to: for example, that there is no fact of the matter as to whether “London” refers to London or to Sydney. -/- A series of challenges emerge, forming the basis for this thesis. 1. What sort of properties is the interpretationist trying to reduce, and what kind of reductive story is she offering? 2. How are inscrutability theses best formulated? Are arguments for inscrutability effective in their own terms? What kinds of inscrutability arise? 3. Is endorsing radical inscrutability a stable position? 4. Are there theoretical virtues—such as simplicity—that can be appealed to in discrediting the rival (empirically equivalent) theories that underpin inscrutability arguments? -/- In addressing these questions, I concentrate on diagnosing the source of inscrutability, mapping the space of ways of resisting the arguments for radical inscrutability, and examining the challenges faced in developing a principled account of linguistic content that avoids radical inscrutability. -/- The effect is not to close down the original puzzles, but rather to sharpen them into a set of new and deeper challenges. (shrink)

Higher-order realists about properties express their view that there are properties with the help of higher-order rather than first-order quantifiers. They claim two types of advantages for this way of formulating property realism. First, certain gridlocked debates about the nature of properties, such as the immanentism versus transcendentalism dispute, are taken to be dissolved. Second, a further such debate, the tropes versus universals dispute, is taken to be resolved. In this paper I first argue that higher-order realism does not (...) in fact resolve the tropes versus universals dispute. In a constructive spirit, I then develop higher-order realism in a way that leads to a dissolution, rather than a resolution, of this dispute too. (shrink)

This paper contends that some of the recent critical appraisals of universals theories of natural laws, namely, van Fraassen's analysis of Armstrong's probabilistic laws, are largely ineffective since they fail to disclose the incompatibility of universals and any realistic natural law setting. Rather, a more profitable line of criticism is developed that contests the universalists' claim to have resolved the induction problem (i.e., the separation of natural laws from mere accidental regularities), and thereby reveals the universals' philosophically inadequate concept of (...) a physical property. (shrink)

A relatively unknown woman named Maria Theresa Short opened a popular observatory in 1835 in Ed inburgh - a time and place where men of science and property had long failed to make a viable space for astronomy. She exhibited scientific instruments to a general public, along with a great telescope and a walk-in camera obscura that projected live views of the city and continues to delight audiences to this day. To better understand Short's accomplishments, achieved as scientific and (...) public life became increasingly closed to women, this study explores her largely untold story, and maps some of the places of science around it. Finding local contingencies, multiple sites and practices by diverse groups, it proposes that tensions within the connections between science and spectacle and the use of popularization to promote its professionalization produced gaps that even a marginal figure like Maria Short could inhabit and exploit. (shrink)

Gonzalo Rodriguez-Pereyra offers a fresh philosophical account of properties. How is it that two different things (such as two red roses) can share the same property (redness)? According to resemblance nominalism, things have their properties in virtue of resembling other things. This unfashionable view is championed with clarity and rigor.

Palawan is a land of promise, and of paradox. On maps, it appears on the edge of the Philippines, isolated. Indeed, it is a kind of last frontier. Its population remained tiny for centuries, the government offering homestead land in the 1950s practically for free to attract migrants from outside. The Palawan State University was established by law in 1965, but did not become operational until 1972. A commercial airport did not exist until the 1980s, and for many years, flights (...) were limited. Yet Palawan is one of the oldest sites of human habitation in the Philippines with the famous Tabon Cave human fossils. The oldest bone fragment here has been dated to be about 47,000 years. We know, too, that trade with China goes back several centuries. Today, Palawan seems to be making up for lost time with new commercial investments pouring in at breakneck speed. In particular, outsiders have rediscovered its potentials around logging, mining, fisheries, and tourism. This has caused concern among individuals and civil society organizations who want sustainable development, and see the commercial developments mainly as extractive, not just of natural resources but of the human. There’s very cheap labor available. And when potential investors marvel about cheap land, they’re actually talking about displacing earlier settlers, including indigenous people, from their lands. A subtle but still insidious aspect of the exploitation of human resources is a transformation of the very concept of human development. Using the rhetoric of modernity, residents in Palawan are reorienting the way they view themselves as well as their families and friends. The value of a human being now hinges on how they look, and the desired appearance is defined from the outside, as we see in this anthology of research reports coming from the Chemical Youth project of the University of Amsterdam and the University of the Philippines Diliman. We read about the importance of fair skin as a projection of cleanliness, of high social status (meaning someone not engaged in manual labor and therefore not exposed to the sun). We read of how “femininity” is defined around body contours, and cosmetics, and how hormones are used by male-to-female transgenders. We go beyond the visual, reading about the importance of controlling or enhancing body odors among tour guides, who interestingly are especially concerned about the bad odor management of their foreign customers, using car perfumes to keep their work manageable and we learn how difficult it is for security guards to stay alert during their long shifts. Energy drinks and cigarettes help them perform their duties. All these transformations through what the French philosopher and historian Michel Foucault has called “technologies of the self” are as paradoxical as Palawan. On the surface, the products—which are technologies—seem to be mainly in the realm of the self but are, in reality, pushed, through marketing, from the outside, in contexts of inequality and exploitative labour relations. Personal aspirations are not personal but are for predefined standards of modernity, related to work-related demands and expectations. The self must be made presentable to the tourist, to the customers in malls, and to those who may threaten the properties that young people protect. It is not surprising that these transformations become problematic for the “self.” The skin whiteners, the hormones, the body deodorants, and the energy drinks are expensive and can distort budgetary priorities. The money for tonic drinks, for example, could well go into more nutritious food. The tragedy, too, many of the products used are of doubtful safety and efficacy. Even the energy drinks have much too high levels of caffeine that can cause cardiac palpitations. Cosmetics and the skin whiteners imported from China and unregistered with the Food and Drug Administration may contain toxic chemicals like mercury. But even registered skin whiteners can be problematic, their so-called “skin-whitening effect” coming about because they take away the upper layers of the skin, leaving behind a red glow (seen as “whitening”) which is actually inflammation. The whitened skin fails to protect against the sun, leading to adverse effects such as black spots. Ultimately though, the problems come with the very definition of the self. As the reports show, young people use the chemicals with some ambivalence, knowing how expensive they are and experiencing some of the undesirable side effects. There is, too, doubt about whether what they’re doing is indeed “good,” captured by how IP women will put on cosmetics only when they’re away from home and about to go to work. The cosmetics have to be removed before they return home because they are not socially acceptable. The research reports are not for Palawan alone. It must make us more critical and discerning as we revisit concepts of development and exploitation, modernity and tradition, self and community. The chemicals, in many ways, are like the products used in precolonial barter trade. For the Chinese, the beeswax and the sea cucumbers, for the inhabitants of Palawan the ceramics, represented faraway lands. To have those products gave prestige. Today, the skin whiteners and tonic drinks and other chemicals described in this anthology represent modernity with promises of not just of a more attractive self, but of better jobs, a better life. We are proud to have worked with the Palawan State University, and the people of Palawan, to gather powerful narratives that will now challenge the outside, the purveyors of modernity, to be more critical and discerning, the chemicals now to be seen not just as stuff applied to the biological body, but as powerful shapers of social bodies. (shrink)

Ikigai is a Japanese concept, which, in brief, refers to the “reason or purpose to live”. I-risks have been identified as a category of risks complementing x- risks, i.e., existential risks, and s-risks, i.e., suffering risks, which describes undesirable future scenarios in which humans are deprived of the pursuit of their individual ikigai. While some developments in AI increase i-risks, there are also AI-driven virtual opportunities, which reduce i-risks by increasing the space of potential ikigais, largely due to developments in (...) generative AI, virtual worlds as well as AI-driven hyper-personalization. The purpose of this paper is to present a first attempt to map the potential AI-driven virtual hyper-personalised ikigai universe. Moreover, challenges and further ideas are presented. (shrink)

Several variants of Lewis's Best System Account of Lawhood have been proposed that avoid its commitment to perfectly natural properties. There has been little discussion of the relative merits of these proposals, and little discussion of how one might extend this strategy to provide natural property-free variants of Lewis's other accounts, such as his accounts of duplication, intrinsicality, causation, counterfactuals, and reference. We undertake these projects in this paper. We begin by providing a framework for classifying and assessing the (...) variants of the Best System Account. We then evaluate these proposals, and identify the most promising candidates. We go on to develop a proposal for systematically modifying Lewis's other accounts so that they, too, avoid commitment to perfectly natural properties. We conclude by briefly considering a different route one might take to developing natural property-free versions of Lewis's other accounts, drawing on recent work by Williams. (shrink)

Trope theory is an increasingly prominent contender in contemporary debates about the existence and nature of properties. But it suffers from ambiguity concerning the nature of a trope. Disambiguation reveals two fundamentally different concepts of a trope: modifier tropes and module tropes. These types of tropes are unequally suited for metaphysical work. Modifier tropes have advantages concerning powers, relations, and fundamental determinables, whereas module tropes have advantages concerning perception, causation, character-grounding, and the ontology of substance. Thus, the choice between modifier (...) tropes and module tropes is significant and divides the advantages of trope theory simpliciter. In addition, each resulting trope theory is unstable: modifier trope theory threatens to collapse into realism and module trope theory threatens to collapse into austere nominalism. This invites reflection on the stability of trope theory in general. (shrink)

This paper defines relational properties and argues for their reducibility in a, broadly speaking, Armstrongian framework of state of affairs ontology and truthmaking. While Armstrong’s own characterisation and reduction of them arguably is the best one available in the literature of this framework, it suffers from two main problems. As will be shown, it neither defines relational properties very clearly (if at all), nor provides an adequate conception of their reduction. This paper attempts to remedy this situation in four steps. (...) First, it introduces relational properties and why they matter in metaphysics in general. Second, by briefly comparing and contrasting them with extrinsic properties, and by briefly mapping them onto a tripartite division of relations, the particular kinds of relevant relational properties are identified. Third, it classifies relational properties and thereby makes possible an apt definition of them. Finally, using the notion of truthmaking, it outlines a more satisfactory case for their reduction. (shrink)

A number of philosophers and logicians have argued for the conclusion that maps are logically tractable modes of representation by analyzing them in propositional terms. But in doing so, they have often left what they mean by "propositional" undefined or unjustified. I argue that propositions are characterized by a structure that is digital, universal, asymmetrical, and recursive. There is little positive evidence that maps exhibit these features. Instead, we can better explain their functional structure by taking seriously the observation (...) that maps arrange their constituent elements in a non-hierarchical, holistic structure. This is compatible with the more basic claim advanced by defenders of a propositional analysis: that (many) maps do have formal semantics and logic. (shrink)

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the (...) arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

The notion of information processing has dominated the study of the mind for over six decades. However, before the advent of cognitivism, one of the most prominent theoretical ideas was that of Habit. This is a concept with a rich and complex history, which is again starting to awaken interest, following recent embodied, enactive critiques of computationalist frameworks. We offer here a very brief history of the concept of habit in the form of a genealogical network-map. This serves to provide (...) an overview of the richness of this notion and as a guide for further re-appraisal. We identify 77 thinkers and their influences, and group them into seven schools of thought. Two major trends can be distinguished. One is the associationist trend, starting with the work of Locke and Hume, developed by Hartley, Bain, and Mill to be later absorbed into behaviorism through pioneering animal psychologists (Morgan and Thorndike). This tradition conceived of habits atomistically and as automatisms (a conception later debunked by cognitivism). Another historical trend we have called organicism inherits the legacy of Aristotle and develops along German idealism, French spiritualism, pragmatism, and phenomenology. It feeds into the work of continental psychologists in the early 20th century, influencing important figures such as Merleau-Ponty, Piaget, and Gibson. But it has not yet been taken up by mainstream cognitive neuroscience and psychology. Habits, in this tradition, are seen as ecological, self-organizing structures that relate to a web of predispositions and plastic dependencies both in the agent and in the environment. In addition, they are not conceptualized in opposition to rational, volitional processes, but as transversing a continuum from reflective to embodied intentionality. These are properties that make habit a particularly attractive idea for embodied, enactive perspectives, which can now re-evaluate it in light of dynamical systems theory and complexity research. (shrink)

Computer-Assisted Argument Mapping (CAAM) is a new way of understanding arguments. While still embryonic in its development and application, CAAM is being used increasingly as a training and development tool in the professions and government. Inroads are also being made in its application within education. CAAM claims to be helpful in an educational context, as a tool for students in responding to assessment tasks. However, to date there is little evidence from students that this is the case. This paper (...) outlines the use of CAAM as an educational tool within an Economics and Commerce Faculty in a major Australian research university. Evaluation results are provided from students from a CAAM pilot within an upper-level Economics subject. Results indicate promising support for the use of CAAM and its potential for transferability within the disciplines. If shown to be valuable with further studies, CAAM could be included in capstone subjects, allowing computer technology to be utilised in the service of generic skill development. (shrink)

Universal social institutions, such as marriage, commons management and property, have emerged independently in radically different cultures. This requires explanation. As Boyer and Petersen point out ‘in a purely localist framework would have to constitute massively improbable coincidences’ . According to Boyer and Petersen, those institutions emerged naturally out of genetically wired behavioural dispositions, such as marriage out of mating strategies and borders out of territorial behaviour. While I agree with Boyer and Petersen that ‘unnatural’ institutions cannot thrive, (...) this one-sided explanation of universal social institutions in terms of genetic human nature is unsatisfactory. Drawing on the literature on multi-level selection and gene-culture coevolution, I argue that universal social institutions are first and foremost the products of cultural selection. They occupy fitness peaks in the landscape of cultural possibilities, much in the same way that biological adaptations occupy fitness peaks in the landscape of biological possibilities. To show this, I use game-theory. By modelling the domains of social interaction in which marriage, commons management, and property emerged as Prisoner’s dilemma situations, it becomes clear how an institutional framework allows the group to move to an interactive equilibrium with a larger payoff. Institutions do so by incentivising all parties to adopt a cooperative strategy. They are culturally selected ways of optimising genetically constrained domains of human social interaction. (shrink)

The reason for physics’ failure to find a final theory of the universe is examined. Problems identified are: the lack of unequivocal definitions for its fundamental elements (time, length, mass, electric charge, energy, work, matter-waves); the danger of relying too much on mathematics for solutions; especially as philosophical arguments conclude the universe cannot have a mathematical basis. It does not even need the concept of number to exist. Numbers and mathematics are human inventions arising from the human predilection for measurement. (...) Following Aristotle, a single fundamental cause is proposed to explore the efficacy of using pure non-mathematical philosophy to explain the universe, contrary to current quantum physical views. The cause is taken as Time, which is then defined, surprisingly leading automatically to a definition of a three-dimensional space answering the question into what can a universe be placed (space before space seems non-sensical). This enables the philosophical arguments to derive a universal rule giving clear-cut descriptions (definitions) of force (both gravitational and electromagnetic), motion, energy, and particles. The formation of atomic nuclei and atomic properties together with an unexpected role for neutrinos follow. In particular, a Popper-test can be prepared by introducing the concept of measurement to allow the philosophy arguments to be tested in another discipline - mathematics. The solution agrees with human physical observations to a remarkable degree of accuracy, automatically explaining and predicting values for Planck’s and the fine-structure constants. Although mathematical, it is included as confirming the efficacy of philosophy in attaining a final theory. (shrink)

Is it possible to know anything about life we have not yet encountered? We know of only one example of life: our own. Given this, many scientists are inclined to doubt that any principles of Earth’s biology will generalize to other worlds in which life might exist. Let’s call this the “N = 1 problem.” By comparison, we expect the principles of geometry, mechanics, and chemistry would generalize. Interestingly, each of these has predictable consequences when applied to biology. The surface-to-volume (...) property of geometry, for example, limits the size of unassisted cells in a given medium. This effect is real, precise, universal, and predictive. Furthermore, there are basic problems all life must solve if it is to persist, such as resistance to radiation, faithful inheritance, and energy regulation. If these universal problems have a limited set of possible solutions, some common outcomes must consistently emerge. In this chapter, I discuss the N = 1 problem, its implications, and my response (Mariscal 2014). I hold that our current knowledge of biology can justify believing certain generalizations as holding for life anywhere. Life on Earth may be our only example of life, but this is only a reason to be cautious in our approach to life in the universe, not a reason to give up altogether. In my account, a candidate biological generalization is assessed by the assumptions it makes. A claim is accepted only if its justification includes principles of evolution, but no contingent facts of life on Earth. (shrink)

In this paper I investigate where the boundaries of conscious mental life lie in Cavendish’s theory, and why. Cavendish argues for a wholly material yet wholly thinking universe. She claims that all matter is capable of “self-knowledge” and “perception” (OEP, p. 138), so that every part of nature “must have its own knowledge and perception, according to its own particular nature” (OEP, p. 141). It is unclear, however, whether the universal capacity of matter to know and perceive also implies (...) the presence of consciousness. I show that Cavendish’s use of the notions of “self-knowledge” and “perception” implies the attribution of consciousness to all bodies. I identify one condition under which the ubiquitous presence of consciousness is intuitively required in Cavendish’s system: namely the presence of intentional agency in every part of nature, which Cavendish conceives as necessary, alongside the capacity of self-motion, to account for the orderly behavior of any body. (shrink)

This paper delves into the nature of intellectual property rights in aesthetic creations, particularly works of visual art and literary works. The discussion focuses on copyrights interests, but there are also implications for trademark and patent rights. The argument assumes a fairly conventional definition of "property," namely, the set of legal relations between the owner and all other persons relating to the use, enjoyment and disposition of a tangible thing. The problem with such a definition as applied to (...) aesthetic creations is that no ordinary tangible thing necessarily embodies a creation which can exist in multiple copies, so the paper takes the transcendent view that the tangible thing subject to legal relations is the entire terra firma or material universe being shaped in the image, sounds or words of the aesthetic creation. Therefore, the paradigm suggested for intellectual property is a monopoly on shaping the entire physical universe, thus the Worldmaking concept. It then follows that intellectual property in an aesthetic creation enables the owner to stop plagiarists from using any part of the material world to recreate in the audience the imaginative experiences first created by the protected work. (shrink)

In order to describe my findings/conclusions systematically, a new semantic system (i.e., a new language) has to be intentionally defined by the present article. Humans are limited in what they know by the technical limitation of their cortical language network. A reality is a situation model (SM). For example, the conventionally-called “physical reality” around my conventionally-called “physical body” is actually a “geometric” SM of my brain. The universe is an autonomous objective parallel computing automaton which evolves by itself automatically/unintentionally – (...) wave-particle duality and Heisenberg’s uncertainty principle can be explained under this “first-order” SM of my brain. Each elementary particle (as a building block of the universe) is an autonomous mathematical entity itself (i.e., a thing in itself). If we are happy to accept randomness, it is obviously possible that all other worlds in the many-worlds interpretation do not exist objectively. The conventionally-called “space” does not exist objectively. “Time” and “matter” are not physical. Consciousness is the subjective-form (aka quale) of the mathematical models (of the objective universe) which are intracorporeally/subjectively used by the control logic of a Turing machine’s program objectively-fatedly. A Turing machine’s consciousness or deliberate decisions/choices should not be able to actually/objectively change/control/drive the (autonomous or objectively-fated) world line of any elementary particle within this world. Besides the Schrodinger equation (or its real-world counterpart) which is a valid/correct/factual causality of the universe, every other causality (of the universe) is either invalid/incorrect/counterfactual or can be proved by deductive inference based on the Schrodinger equation only. If the “loop quantum gravity” theory is correct, time/space does not actually/objectively exist in the objective-evolution of the objective-reality, or in other words, we should not use the subjective/mental concept of “time”, “state” or “space” to describe/imagine the objective-evolution of the universe. (shrink)

The Successive Addition Argument (SAA) is one of the key arguments espoused by William Lane Craig for the thesis that the universe began to exist. Recently, Malpass, Mind, 131(523), 786–804 (2021) has developed a challenge to the SAA by way of constructing a counterexample that originates in the work of Fred Dretske. In this paper, I show that the Malpass-Dretske counterexample is in fact no counterexample to the argument. Utilizing a distinction between properties of members and properties of collections, I (...) argue that Malpass’ counterexample has no bearing on the soundness of the SAA. I also develop a novel parity argument against Malpass’ argument that I demonstrate can only be resolved by way of the aforementioned analysis. (shrink)

Certain realists about properties and relations identify them with universals. Furthermore, some hold that for a wide range of meaningful predicates, the semantic contribution to the propositions expressed by the sentences in which those predicates figure is the universal expressed by the predicate. I here address ontological issues raised by predicates first introduced to us via works of fiction and whether the universal realist should accept that any such predicates express universals. After assessing arguments by Braun, D. and (...) Sawyer, S. for fictional universal anti-realism, I propose a novel, Kripke-inspired argument for the same conclusion. I ultimately defend the claim that while this argument presents the strongest case for fictional universal anti-realism, it is nonetheless unsound. I conclude that nothing stands in the way of accepting that some fictional predicates express fictional universals. (shrink)

Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove (...) some facts about that function and facts about some sound logics for those languages. In doing so, I prove that, given some plausible metaphysical assumptions, a large class of sentences about properties of concrete objects are “safe” on nominalistic grounds. Whenever some true sentences about concrete objects and some sentences belonging to this class that are true according to platonists collectively entail a conclusion about concrete objects, some nominalistically acceptable sentences are true and entail the same conclusion. Because the proof can itself be formulated without abstract objects, it provides a nominalistic explanation of the success of theories that invoke properties of concrete objects. (shrink)

I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: linearization* (...) class='Hi'>property; I then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable. (shrink)

In the creation of maps, scientific knowledge related to mathematics and physics combines with knowledge specific to graphic or artistic disciplines. Since all maps are artifacts whose aesthetic qualities convey information that simultaneously engages the fields of ontology, epistemology, and politics, they are objects of undeniable interest for philosophical inquiry. Following what has been termed “the cartographic turn in social sciences”, The Art of Mapping Between Land and Mind delves into two intertwining issues. On one side, it examines how (...) the aesthetic properties of maps convey cognitive, cultural, and political meanings. On the other, it explores the role of visual arts in reflecting on cartographic thought, shaping both its methods and motivations. The volume is divided into four sections. Embracing the point of view of both the philosopher and the geographer, the first one sheds light on the relationship between epistemology and cartography (Kukla; Costantini; Tanney). The second addresses mapmaking as an art form (Tanca; Haugdal) or, conversely, considers maps from the perspective of their aesthetic properties (Török; Ogundiwin; Elhaik). The third focuses on the digital condition of today’s cartography (Tschochohei; Quaranta; Keller). Finally, the last section includes two contributions that represent attempts to guide cartography toward its future (Bosca; Ianniello). Opening this issue, a special essay by Elizabeth Povinelli offers a generous précis of her upcoming book. (shrink)

In this paper, I argue that for the purposes of ordinary reasoning, sentences about properties of concrete objects can be replaced with sentences concerning how things in our universe would be related to inscriptions were there a pluriverse. Speaking loosely, pluriverses are composites of universes that collectively realize every way a universe could possibly be. As such, pluriverses exhaust all possible meanings that inscriptions could take. Moreover, because universes necessarily do not influence one another, our universe would not be any (...) different intrinsically if there were a pluriverse. These two facts enable anti-realists about abstract objects to replace, e.g. talk of anatomical features with talk of the inscriptions concerning anatomical structure that would exist were there a pluriverse. The availability of such replacements enables anti-realists to carry out essential ordinary reasoning without referring to properties, thereby making room for a consistent anti-realist worldview. The inscriptions of the would-be pluriverse are so numerous and varied that sentences about them can play the roles in ordinary reasoning served by simple sentences about properties of concrete objects. (shrink)

As individuals we often face complex issues about which we must weigh evidence and come to conclusions. Corporations also have to make decisions on the basis of strong and compelling arguments. Legal practitioners, compelled by arguments for or against a proposition and underpinned by the weight of evidence, are often required to make judgments that affect the lives of others. Medical doctors face similar decisions. Governments make purchasing decisions—for example, for expensive military equipment—or decisions in the areas of public or (...) foreign policy. These issues involve many arguments on all sides of difficult debates. These issues involve understanding the arguments of others and being able to make objections and provide rebuttals to objections. Students in universities deal with arguments all the time. A major purpose of a university education—regardless of subject matter—is to teach students how to read, understand, and respond to complex arguments. The ability to do this makes for highly employable, adaptable, and reflectively critical individuals. We often call the skill of marshaling arguments and assessing them “critical thinking.” All universities claim to instill the skill of critical thinking in their graduates and routinely note this in their advertising and promotional documents. This short paper outlines one way this skill can be taught. (shrink)

An argument map visually represents the structure of an argument, outlining its informal logical connections and informing judgments as to its worthiness. Argument mapping can be augmented with dedicated software that aids the mapping process. Empirical evidence suggests that semester‐length subjects using argument mapping along with dedicated software can produce remarkable increases in students’ critical thinking abilities. Introducing such specialised subjects, however, is often practically and politically difficult. This study ascertains student perceptions of the use of argument (...) mapping in two large, regular, semester‐length classes in a Business and Economics Faculty at the University of Melbourne. Unlike the semester‐length expert‐led trials in prior research, in our study only one expert‐led session was conducted at the beginning of the semester and followed by class practice. Survey results conducted at the end of the semester, show that, with reservations, even this minimalist, ‘one‐shot inoculation’ of argument mapping is effective in terms of students’ perceptions of improvements in their critical thinking skills. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

This paper examines how the concepts of utility, impartiality, and universality worked together to form the foundation of Adam Smith's jurisprudence. It argues that the theory of utility consistent with contemporary rational choice theory is insufficient to account for Smith's use of utility. Smith's jurisprudence relies on the impartial spectator's sympathetic judgment over whether third parties are injured, and not individuals' expected utility associated with individuals' expected gains from rendering judgments over innocence or guilt.

An endomorphism on an algebra \ is said to be strong if it is compatible with every congruence on \; and \ is said to have the strong endomorphism kernel property if every congruence on \, other than the universal congruence, is the kernel of a strong endomorphism on \. Here we characterise the structure of those double MS-algebras that have this property by the way of Priestley duality.

Book synopsis This book is devoted to the condition of the university under the pressures of globalization, with particular reference to Central Europe. It is intended as a companion volume for all those who combine their academic and disciplinary research with wider interests in the functioning of higher education institutions under the new pressures affecting Central Europe. Drawing on its interdisciplinary nature and the wide range of scholars involved, it intends to outline a useful map of new, often challenging, areas, (...) topics and concerns to be taken into account in rethinking the function of the university today. -/- Contents Contents: Philip G. Altbach: Academic Freedom: International Realities and Challenges - Richard Rorty: Does Academic Freedom Have Philosophical Presuppositions? - Stanley N. Katz: Can Liberal Education Cope? - Marek Kwiek: The State, the Market, and Higher Education. Challenges for the New Century - Roger Deacon/Ben Parker: The Schooling of Citizens, or the Civilizing of Society? - Tadeusz Buksinski: The University and Learning in a Situation of Depression - Martin Jay: The Menace of Consilience: Keeping the Disciplines Unreconciled - Voldemar Tomusk: Towards a Model of Higher Education Reform in Central and East Europe - Wolf Lepenies: Im Osten viel Neues. Wissenschafts- und Kulturpolitik für Europa - Zbigniew Drozdowicz: Academic Accreditation: a Polish Case Study - Marek Kwiek: The Nation-State, Globalization and the Modern Institution of the University. (shrink)