We investigate the following weak Ramsey property of a cardinal κ: If χ is coloring of nodes of the tree κ <ω by countably many colors, call a tree ${T \subseteq \kappa^{ < \omega}}$ χ-homogeneous if the number of colors on each level of T is finite. Write ${\kappa \rightsquigarrow (\lambda)^{ < \omega}_{\omega}}$ to denote that for any such coloring there is a χ-homogeneous λ-branching tree of height ω. We prove, e.g., that if ${\kappa < \mathfrak{p}}$ or ${\kappa > \mathfrak{d}}$ (...) is regular, then ${{\kappa \rightsquigarrow (\kappa)^{ < \omega}_{\omega}}}$ and that ${\mathfrak{b}}$ ${(\mathfrak{b})^{ < \omega}_{\omega}}$ and ${\mathfrak{d}}$ ${(\mathfrak{d})^{ < \omega}_{\omega}}$ . The arrow is applied to prove a generalization of a theorem of Hurewicz: A Čech-analytic space is σ-locally compact iff it does not contain a closed homeomorphic copy of irrationals. (shrink)

The paper highlights analytic aesthetics’ unacknowledged assumption that art is timeless, a view it inherited from Enlightenment thinkers such as Hume and Kant, who in turn inherited it from the Renaissance. This view, I contend, is no longer tenable because it is at odds with our experience of the art of the past. Analytic aesthetics bypasses this dilemma because it confines its attention to topics such as the nature of aesthetic pleasure, whether the appreciation of art should be (...) disinterested and so on, which it partitions off from historical change and encases in a world where time stands still and where, by consequence, the temporal nature of art, including art’s capacity to transcend time, can be ignored. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

Individuals, groups, or nations — if rational and self-interested — will be balancing on the margin between two alternative ways of generating income: peaceful production and exchange, versus appropriative efforts designed to seize resources previously controlled by others. Both production and appropriation, on the assumption here, are entirely normal lines of activity engaged in to the extent that doing so seems profitable.The general-equilibrium steady-state model involves a resource partition function, a social production function, a combat power function, and an (...) income distribution equation. Solutions were obtained under thesymmetrical Cournot protocol and two alternativeasymmetrical assumptions: the familiar Stackelberg condition and a more novel hierarchical protocol called Threat-and-Promise. The analysis demonstrates that, in contrast with the harmonistic bias of orthodox economic theory, a general-equilibrium model can also encompass the hostile and destructive interactions that characterize real-world social relations. (shrink)

We give a simple game-theoretic proof of Silver's theorem that every analytic set is Ramsey. A set P of subsets of ω is called Ramsey if there exists an infinite set H such that either all infinite subsets of H are in P or all out of P. Our proof clarifies a strong connection between the Ramsey property of partitions and the determinacy of infinite games.

In the following we will investigate whether von Mises’ frequency interpretation of probability can be modified to make it philosophically acceptable. We will reject certain elements of von Mises’ theory, but retain others. In the interpretation we propose we do not use von Mises’ often criticized ‘infinite collectives’ but we retain two essential claims of his interpretation, stating that probability can only be defined for events that can be repeated in similar conditions, and that exhibit frequency stabilization. The central idea (...) of the present article is that the mentioned ‘conditions’ should be well-defined and ‘partitioned’. More precisely, we will divide probabilistic systems into object, initializing, and probing subsystem, and show that such partitioning allows to solve problems. Moreover we will argue that a key idea of the Copenhagen interpretation of quantum mechanics (the determinant role of the observing system) can be seen as deriving from an analytic definition of probability as frequency. Thus a secondary aim of the article is to illustrate the virtues of analytic definition of concepts, consisting of making explicit what is implicit. (shrink)

Let ${{\mathcal J}\,(\mathbb M^2)}$ denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is bigger than the covering number of the ideal of the meager subsets of ω ω. We also show that Martin’s Axiom implies that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is 2 ω .Finally we prove that there are no analytic infinite maximal antichains in any finite product of ${\mathfrak{P}{(\omega)}/{\rm fin}}$.

The schism between analytic and continental philosophy resists repair because it is not confined to philosophers. It is a local manifestation of a far more profound and pervasive division. In 1959 C.P. Snow lamented the partition of intellectual life in to `two cultures': that of the scientist and that of the literary intellectual. If we follow the practice of most universities and bundle historical and literary studies together in the faculty of humanities on the one hand, and count (...) pure mathematics among the sciences on the other, then it is fair to say that the mutual ignorance and occasional hostility between scientists and humanists decried by Snow is still with us. And it runs through the middle of philosophy. Philosophy aspires to say something about everything, so it is unsurprising that philosophers have reproduced in miniature the division between the arts and the sciences. What is worrying is that we have failed to overcome it. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue (...) that it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue (...) that it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated (...) but that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters. (shrink)

The narrativist insight -- From analytic philosophy of history to narrativism -- Three tenets of narrativist philosophy of historiography -- Representationalism and non-representationalism -- Reasoning in historiography -- Colligation -- Underdetermination and epistemic values -- From truth to warranted assertion -- The tri-partite theory of justification in historiography -- Historiography between objectivism and subjectivism -- Postnarrativist philosophy of historiography.

We prove a partition theorem for analytic sets, namely, if X is an analytic set in a Polish space and [X]n = K0 ∪ K1 with K0 open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect K0-homogeneous subset or X is a countable union of K1-homogeneous subsets. We also prove a partition theorem for analytic sets in the three-dimensional case. Finally, we give some applications of (...) the theorems. (shrink)

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)

The present study proposes a valorization of the work of professor and philosopher Ioan Biriş. The statistics of his books and studies, their distribution by areas of interest, and especially the ideas in his work confirm the need for philosophy in the Romanian cultural life. As a whole, his philosophical endeavor is based on the concept of totality. Thus in the Hegelian spirit, Ioan Biriş successfully convinces us that the logical may exceed the limits of formal exercise and become the (...) organon of philosophy. In this capacity, the logical may operate on the real and valorize the multiple relationships between identity and difference. His books Filosofia și logica științelor sociale, Totalitate, sistem, holon, Rolul imaginarului în cunoașterea științifică, Istorie şi cultură, as well as a series of studies among which let me mention: “L’identité symbolique et la logique partitive des valeurs spirituelles”, “On the logic of religious terms”, “Le rapport identite-difference et la conjonction collective. Aspects logiques”, clearly prove the author’s capacity to integrate existential, religious, cognitive and axiological issues into a unitary vision. As Noica would say, he succeeded to enter the spirit’s life thorough the intellect’s gate. (shrink)

This article aims to unravel the doctrine of the “sign from the manifest to the hidden” of Abū Hāšim al-Ğubbāʾī. It shows that Abū Hāšim tended to interpret this sign as an inference, of which he recognized two main types: Type-1 proceeds by analytical deduction of concepts by neutralizing the conditions of their realization, i. e. their ontological basis. This is, typically, the procedure most directly consonant with Abū Hāšim's modal ontology. Type-2 exhibits the same causal relationship at the known (...) and unknown levels and considers causality at the known level to be itself the cause of causality at the unknown level. This partition was completely new in philosophy and kalām at the time of Abū Hāšim, but it is foreshadowed in al-Ḫwārizmī’s Algebra. In this book, al-Ḫwārizmī distinguishes between proof “by cause”, which consists in transferring a certain geometric deduction to algebra, and proof “by expression”, which operates directly on algebraic expressions, which it reduces analytically. A text by Abū Hāšim devoted to human knowledge that seems to refer to the work of al-Ḫwārizmī suggests, finally, that the close parallel between al-Ḫwārizmī’s doctrine of proof and Abū Hāšim's doctrine of the sign may not be a mere coincidence. Two appendices have been added. The first deals with al-Fārābī’s reading of Abū Hāšim's theory of inference. The second, based on all available data, establishes for the first time the correct and precise dates of Abū Hāšim's life. (shrink)

There are two ways evolution by natural selection is conceptualized in the literature. One provides a ‘recipe’ for ENS incorporating three ingredients: variation, differences in fitness, and heritability. The other provides formal equations of evolutionary change and partitions out selection from other causes of evolutionary changes such as transmission biases or drift. When comparing the two approaches there seems to be a tension around the concept of heritability. A recent claim has been made that the recipe approach is flawed and (...) should be abandoned. In this article, I show that the tension is only a superficial one. If one uses a concept of heritability strictly in line with the formal equations of evolutionary change, the recipe approach keeps its validity and generality. To demonstrate that the intuitive concept of heritability is not a general one, I use one formulation of the Price equation formulated by Okasha, show that the concept of heritability in his formulation incorporates both the intuitive notion of heritability as a measure of similarity between parent and offspring characters, and a measure of persistence. I advocate for persistence to be incorporated in the concept of heritability used in recipes for ENS in the same way heredity is, show that this is readily attainable and thereby dissolve any point of tension concerning heritability between the recipe and the analytical approach to ENS. 1 Introduction2 Heritability in the Price Equation2.1 Different approaches to heredity and heritability2.2 Heritability: From recipes to the Price equation3 A Problem for the Recipes?4 Reinterpreting Heritability for Recipes5 Conclusion Appendix. (shrink)

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can be (...) abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions. (shrink)

The notion of ‘rhetorical bodies’ argues the cause of the rhetorical elements in the material and the material elements in the rhetorical in ways that can be seen as analogous to the bi-partite modes of Deleuzian film philosophy, ‘movement-image’ and ‘time-image’. Tamil films of the 1940s and 1950s bear the strong imprints of the rhetorical elements of the Self-Respect Movement and Dravidian Movement, which took root in different versions during the 1920s–60s. The narrative locations of the bodies in the Tamil (...) films of the 1940s and 1950s provide interesting theoretical and analytical challenges if one seeks to combine the Deleuzian notions of ‘movement-image’ with the notions of material rhetorics. The coming together of these notions provides new pointers to the understanding of an important phase in the history of Tamil cinema for its implications on the long-running nexus between politics and films in the state of Tamil Nadu. The Deleuzian trajectory in film philosophy provides more than enough pointers to examine early Tamil cinema's attempts to construct ‘movement-images’ through rhetorical bodies. This paper seeks to examine the contexts of ‘movement-images’ and the role of ‘rhetorical bodies’ in constructing the same in Velaikari, scripted by C. N. Annadurai. Popularly known as Aringnar Anna, C. N. Annadurai was the former Chief Minister of Tamil Nadu and the Founder of DMK, the party which unseated Congress from power in Tamil Nadu in 1967, and the state remains out of reach of the national parties ever since. (shrink)

This paper discusses two related questions about Plato’s account of the tripartite soul in the Republic and Phaedrus. One is whether we should accept the recently prominent ‘analytical’ reading of the theory, according to which the three parts of the soul are animal-like sub-agents, each with its own distinctive and autonomous package of cognitive and desiderative capacities. The other question is how far Plato’s account so interpreted resembles the findings of contemporary neuroscience, given that this also depicts the mind as (...) complex, partitioned, subject to conflict, and only very incompletely rational. The paper sketches the analytical reading, outlines the similarities and disanologies of the theory so understood to contemporary neuropsychology, and then steps back to consider three problems with such an interpretation. None is decisive; but they raise doubts as to whether the question of the title can really be answered in the way both the analytical reading and the modern parallel presume. (shrink)

The contribution of Big Data to social science is not limited to data availability but includes the introduction of analytical approaches that have been developed in computer science, and in particular in machine learning. This brings about a new ‘culture’ of statistical modelling that bears considerable potential for the social scientist. This argument is illustrated with a brief discussion of model-based recursive partitioning which can bridge the theory and data-driven approach. Such a method is an example of how this new (...) approach can help revise models that work for the full dataset: it can be used for evaluating different models, a traditional weakness of the ‘traditional’ statistical approach used in social science. (shrink)

Wittgenstein took the _Tractatus Logico-Philosophicus_ to be eventually invalidated by logical atomism. Our main thesis is that it can be revalidated, provided that we subtract the thesis 2.02 (“The object is simple.”) from it: atoms are not simple objects but, rather, bits of information the objects are made of. Starting from an introductory discussion about what is meant by a ‘logic of colors’, an explanatory framework is then proposed in the form of a partition semantics. The philosophical problem of (...) Wittgenstein’s color-statements is reformulated accordingly, thus overcoming the trouble with logical atomism. A Boolean treatment is advanced to solve the initial difficulty and leads to two final results: Wittgenstein’s logic of colors requires a mereological understanding of the relations between colors in order to make sense; the analysis of psychophysical concepts like colors casts some additional doubt about the analytic–synthetic distinction, to the point of treating relations between colors as analytic a posteriori judgments. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Experiential Avoidance and Superstition: Considering Concepts in ContextRoger Vilardaga (bio) and Steven C. Hayes (bio)Keywordsacceptance, contextualism, influence, therapyThe target article (García-Montes et al. 2008) explores the application of the concept of superstition, examined from a Sartrian perspective, to psychopathology such as obsessive–compulsive disorder and psychosis. They compare their analysis to two different technical terms taken from current research programs in psychology, which are the notions of Thought–Action Fusion and (...) Experiential Avoidance (EA). We have been asked to respond because our work in Acceptance and Commitment Therapy (ACT; Hayes, Strosahl, and Wilson 1999) and Relational Frame Theory (RFT; Hayes, Barnes-Holmes, and Roche 2001) are part of the foundational work in EA, and thus in this short commentary we comment on the article from the point of view of our research program.The article notes several areas of overlap between the ACT/RFT work on EA and their Sartrian perspective on superstition, such as the holistic and contextualistic nature of the analysis, but also several differences which the authors feel advantage their own view.It is difficult to compare the two lines of work without appreciating their context and purpose. Sartre was not a scientific psychologist; ACT/RFT are part of a specific effort at scientific system building, which we term here “contextual behavioral science” (AKA, post-Skinnerian behavior analysis).Contextual behavioral science is a social enterprise that has as its purpose the development of increasingly organized statements of relations among events that allow actions embedded in their historical and situational context to be predicted and influenced with precision, scope, and depth. “Precision” means that a limited set of analytic constructs apply to any one event; “scope” means that a limited set of constructs are needed to analyze a broad range of events; and “depth” means that constructs should cohere across different levels of analysis.Although a real world (or at least the one world) is assumed, the partitioning of the world is thought to be the result of our continuous interactions in and with it. These partitions are not ontological constructions from the perspective of contextual behavioral science because they, too, are actions that are purposive and embedded in their historical and situational contexts. The [End Page 269] deliberate attempt to analyze the world scientifically does not contradict the holistic standpoint of contextualism. When analytic goals are accomplished, constructs are “true,” but multiple truths are possible given multiple goals and historical and situational contexts. Conversely, all forms of contextualism become dogmatic and self-contradictory if their goals are not stated. It is common for contextualists of all varieties to state and defend the ultimate apprehension of reality as a whole, for example, without realizing that any statement about the world including such a defense is a form of breaking down this whole into parts. As we will try to show, the target article seems to fall into this usual contextualistic trap by arguing for what is better, without stating clearly “better for what, assessed how” and without viewing concepts with relevance to their purpose.Prediction and influence with precision, scope, and depth is a purpose, stated naked and in the wind. It is not defended, justified, or given ontological status. To generate powerful ways of speaking as measured against that purpose, contextual behavioral science has embraced a wide variety of methodologies, including laboratory research designed to refine behavioral principles with high levels of precision and scope, and applied research such as randomized controlled trials, analog research, and measure development that test the scope of the principles and theories that result (e.g., Hayes et al. 2006). Whether concepts like EA are helpful is a matter to be considered relevant to the goals of the analysis.As example of the kind of problems the authors create for themselves, consider the following quote from the target article:Although the post-Skinnerians who proposed the EA concept call themselves “contextualists,” they pay no more than lip service to the role of the “social/verbal community” and the cultural context. Their research focuses almost exclusively on laboratory experiments, and does not consider the important role of particular social practices and contexts, such as modernity.(García... (shrink)

The main result of the present article is the following: Let N be an infinite subset of,, and let be a matrix with infinitely many rows of completely Ramsey subsets of such that for every n,. Then there exist, a sequence of nonempty finite subsets of N, and an infinite subset T of such that for every infinite subset I of. We also give an application of this result to partitions of an uncountable analytic subset of a Polish space (...) X into sets belonging to the σ‐algebra generated by the analytic subsets of X. (shrink)

Science today is an international business, of course, and there has hardly ever been a partition wall between the logical work in Poland and Germany. However, apart from long lasting personal scientific contacts there are good reasons to further intensify the relations between the German and the Polish Community of Logic and Logical Philosophy. So it was only natural to think about bringing them together at a scientific event in a friendly environment. This idea was carried out as a (...) common initiative of the Polish Association for Logic and Theory of Science (PTL) and of the German based Society for Analytic Philosophy (GAP). The First German-Polish Workshop on Logic and Logical Philosophy was held in Bachotek/Poland from September 10.–13., 1995. It was organized by Kazimierz Świrydowicz (PTL), Heinrich Wansing (GAP) and Max Urchs (both). This part of the present volume of Logic and Logical Philosophy is not the proceedings of the workshop. On one hand, not all the papers presented at the workshop (see previous page for the programme) are attended to this volume. Due to their more technical character, the contributions of Gregory Restall, Tomasz Skura, Heinrich Wansing, Andrzej Wroński and others will appear in the next number of Reports on Mathematical Logic. Some papers included in this issue were changed considerably for publication. On the other hand, colleagues who intended to join the workshop but had to cancel for some reason were invited to submit their material, too. We would like to thank the editors of both journals very kindly for their suggestion to publish the submitted material. (shrink)

One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

We summarize the essential ingredients, which enabled us to derive the path-integral for a system of harmonically interacting spin-polarized identical particles in a parabolic confining potential, including both the statistics (Bose–Einstein or Fermi–Dirac) and the harmonic interaction between the particles. This quadratic model, giving rise to repetitive Gaussian integrals, allows to derive an analytical expression for the generating function of the partition function. The calculation of this generating function circumvents the constraints on the summation over the cycles of the (...) permutation group. Moreover, it allows one to calculate the canonical partition function recursively for the system with harmonic two-body interactions. Also, static one-point and two-point correlation functions can be obtained using the same technique, which make the model a powerful trial system for further variational treatments of realistic interactions. (shrink)

This book argues that conscious experience is sometimes extended outside the brain and body into certain kinds of environmental interaction and tool use. It shows that if one accepts that cognitive states can extend, one must also accept that consciousness can extend. The proponents of Extended Mind defend the former claim, but usually oppose the latter claim. The most important undertaking of this book is to show that this partition is not possible on pain of inconsistency. Pii Telakivi presents (...) three arguments for the hypothesis of Extended Conscious Mind, examines and answers the most common counterarguments, and introduces a novel means to interpret and apply the concept of constitution. She also addresses the tensions between analytic philosophy of mind and enactivism, and builds a bridge between two different traditions: on the one hand, extended mind, and on the other, enactivism and embodied mind—and maintains that a unifying approach is necessary for a theory about extended consciousness. (shrink)

This paper distinguishes four recognisably different geographical processes in principle causing species to die out. One of these processes, the one we dub “range eclipse”, holds that one range expands at the expense of another one, thereby usurping it. Channell and Lomolino (2000a, Journal of Biogeography 27: 169–179; 2000b, Nature 403: 84–87; see also Lomolino and Channell, 1995, Journal of Mammalogy 76: 335–347) measured the course of this process in terms of the proportion of the total range remaining in its (...) original centre, thereby essentially assuming a homogeneous distribution of animals over the range. However, part of their measure seems mistaken. By giving a general, analytical formulation of eclipsing ranges, we estimate the exact course of this process. Also, our formulation does not partition a range into two spatially equal parts, its core and its edge, but it assumes continuity. For applying this model to data on the time evolution of species, individual time series should be available for each of them. For practical purposes we give an alternative way of plotting and interpreting such time series. Our approach, being more sensitive than Channell and Lomolino’s, gives a less optimistic indication of range eclipses than theirs once these have started. (shrink)

Of recent attempts to appropriate pragmatism for communication studies, Robert Craig’s inclusion of a pragmatist “tradition” in his influential “metamodel” of communication theoriesconstitutes one of the most prominent proposals to date. In this model, pragmatism is principally understood by contrast to other alternatives, such as phenomenology, semiotics, and rhetoric. As a communication-theoretical tradition in Craig’s sense, the pragmatist approach is expected to provide distinctive articulations of the nature of communication and communication problems, expressed in a particular vocabulary. Useful as such (...) a partitioning may be for analytical and dialogical purposes, the delimitation of pragmatism that emerges from Craig’s efforts is in many respects problematic. After a summary of the background assumptions and disciplinary aims of Craig’s project, this article identifies three serious weaknesses in his account: its neglect of relevant intra-tradition distinctions and debates, its straightforward association of pragmatism with a strongly constitutive approach to communication, and its tendency to disconnect pragmatism from other communication-theoretical positions in ways that are not conducive to his objectives. This discussion highlights the contrast between Craig’s constructionist instrumentalism and the habit-realism of the classical pragmatisms of Peirce and Dewey. (shrink)

In this article, we give a summary of Leonhard Euler’s work on the pentagonal number theorem. First we discuss related work of earlier authors and Euler himself. We then review Euler’s correspondence, papers and notebook entries about the pentagonal number theorem and its applications to divisor sums and integer partitions. In particular, we work out the details of an unpublished proof of the pentagonal number theorem from Euler’s notebooks. As we follow Euler’s discovery and proofs of the pentagonal number theorem, (...) we pay attention to Euler’s ideas about when we can consider a mathematical statement to be true. Finally, we discuss related results in the theory of analytic functions. (shrink)

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (...) (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable. (shrink)

This is a re-look at the (Indian) Partition event through the lens of Advaita Vedanta.

There are some who defend a view of vagueness according to which there are intrinsically vague objects or attributes in reality. Here, in contrast, we defend a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being (...) its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts on the one hand and correlated portions of reality on the other. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. (shrink)

We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it (...) provides an account of how cells and subcells relate to objects in reality. We define a notion of well-formedness for partitions, and we give an account of what it means for a partition to project onto objects in reality. We continue by classifying partitions along three axes: (a) in terms of the degree of correspondence between partition cells and objects in reality; (b) in terms of the degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) in terms of the degree of completeness with which a partition represents this domain. (shrink)

The last section made it clear that an analysis which at first seems to fail is viable after all. It is viable if we let it depend on a partition function to be provided by the context of conversation. This analysis leaves certain traits of the partition function open. I have tried to show that this should be so. Specifying these traits as Pollock does leads to wrong predictions. And leaving them open endows counterfactuals with just the right (...) amount of variability and vagueness. (shrink)

Nineteenth and twentieth century philosophies of science have consistently failed to identify any rational basis for the compelling character of scientific analogies. This failure is particularly worrisome in light of the fact that the development and diffusion of certain scientific analogies, e.g. Darwin’s analogy between domestic breeds and naturally occurring species, constitute paradigm cases of good science. It is argued that the interactivist model, through the notion of a partition epistemology, provides a way to understand the persuasive character of (...) compelling scientific analogies without consigning them to an irrational or arational context of discovery. (shrink)

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$. In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$.

Two partition-theorems are proved for a particular causal decision theory. One is restricted to a certain kind of partition of circumstances, and analyzes the utility of an option in terms of its utilities in conjunction with circumstances in this partition. The other analyzes an option's utility in terms of its utilities conditional on circumstances and is quite unrestricted. While the first form seems more useful for applications, the second form may be of theoretical importance in foundational exercises. (...) Comparisons are made with theorems of Richard Jeffrey, Brad Armendt, and Peter Fishburn. (shrink)

Lewis sender‐receiver games illustrate how a meaningful term language might evolve from initially meaningless random signals (Lewis 1969; Skyrms 2006). Here we consider how a meaningful language with a primitive grammar might evolve in a somewhat more subtle sort of game. The evolution of such a language involves the co‐evolution of partitions of the physical world into what may seem, at least from the perspective of someone using the language, to correspond to canonical natural kinds. While the evolved language may (...) allow for the sort of precise representation that is required for successful coordinated action and prediction, the apparent natural kinds reflected in its structure may be purely conventional. This has both positive and negative implications for the limits of naturalized metaphysics. (shrink)

C W Evers, J C Walker; Knowledge, Partitioned Sets and Extensionality: a refutation of the forms of knowledge thesis, Journal of Philosophy of Education, Volume.

This article examines the problem of mental partitioning and mental conflict in Han 漢 dynasty sources. It begins by outlining two Greek psychological models—the Platonic tripartite model and the Stoic monistic model—and explains the connection between the two psychological models and their differing descriptions of mental conflict. It then analyzes passages from a seldom discussed text, the _Extended Reflections_ (_Shenjian_ 申鑒), written by the Eastern Han thinker X un Yue 荀悅. A combined analysis of the _Extended Reflections_ with fragments from (...) other Han dynasty thinkers uncovers debates on mental partitioning and mental conflict that are in some ways analogous to those found in Greek philosophical literature. One view posits that the human psyche is composed of two parts capable of producing conflicting motivations. The other view sees all actions as stemming from a single psychological center. The conclusions of this article offer new perspectives on early Chinese moral psychology that have important implications for modern research on early Chinese philosophy. (shrink)

We consider finite partitions of the closure F¯ of an ωα-uniform barrier F. For each partition, we get a homogeneous set having both the same combinatorial and topological structure as F¯, seen as a subspace of the Cantor space 2N.