In his “Bridging mainstream and formal ontology”, Augusto (2021) gives an excellent analysis of Dietrich von Freiberg’s idea of using causality as a partitioning principle for upper ontologies. For this Dietrich’s notion of extrinsic principles is crucial. The question whether causation can and indeed should be used as a partitioning principle for ontologies is discussed using mathematics and physics as examples.

Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the form of equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.

The _Principle of Indifference_ was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called _problem of multiple of partitions_. In ‘Evidential symmetry and mushy credence’ Roger White suggests that we have been too quick to jettison this principle and argues that the problem of multiple partitions rests on a mistake. In this paper I will criticise White’s attempt to revive POI. In so doing, I will argue that what underlies (...) the problem of multiple partitions is a fundamental tension between POI and the very idea of _evidential incomparability_. (shrink)

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean logic (...) of subsets is the normalized counting measure of the subsets (events). Thus logical entropy is a measure on the set of ordered pairs, and all the compound notions of entropy (join entropy, conditional entropy, and mutual information) arise in the usual way from the measure (e.g., the inclusion-exclusion principle)--just like the corresponding notions of probability. The usual Shannon entropy of a partition is developed by replacing the normalized count of distinctions (dits) by the average number of binary partitions (bits) necessary to make all the distinctions of the partition. (shrink)

Some authors have argued that, in order to give an account of weakness of the will, we must assume that the mind is divisible into parts. This claim is often referred to as the partitioning claim. There appear to be two main arguments for this claim. While the first is conceptual and claims that the notion of divisibility is entailed by the notion of non-rational mental causation (which is held to be a necessary condition of weakness of the will), (...) the second is explanatory and claims that the notion of divisibility is required for the causal explanation of weak-willed action. In this paper I want to argue that the partitioning claim remains unsupported, no matter how it is interpreted, and that weakness of the will can be made perfectly good sense of without the idea that the mind is divisible into parts. In fact, there are available various explanatory models each of which characterizes different psychological mechanisms that may be involved in weakness of will, none of which depends on any claims about mental division. I describe three familiar mechanisms and argue that weakness of will may occur as the result of any one of them. (shrink)

One of the criteria to a strong principle in natural sciences is simplicity. This paper claims that the Free Energy Principle (FEP), by virtue of unifying particles with mind, is the simplest. Motivated by Hilbert’s 24th problem of simplicity, the argument is made that the FEP takes a seemingly mathematical complex domain and reduces it to something simple. More specifically, it is attempted to show that every ‘thing’, from particles to mind, can be partitioned into systemic states by virtue of (...) self-organising symmetry break, i.e. self-entropy in terms of the balance between risk and ambiguity to achieve epistemic gain. By virtue of its explanatory reach, the FEP becomes the simplest principle under quantum, statistical and classical mechanics conditions. (shrink)

Medical terminology collects and organizes the many different kinds of terms employed in the biomedical domain both by practitioners and also in the course of biomedical research. In addition to serving as labels for biomedical classes, these names reflect the organizational principles of biomedical vocabularies and ontologies. Some names represent invariant features (classes, universals) of biomedical reality (i.e., they are a matter for ontology). Other names, however, convey also how this reality is perceived, measured, and understood by health professionals (...) (i.e., they belong to the domain of epistemology). We analyze terms from several biomedical vocabularies in order to throw light on the interactions between ontological and epistemological components of these terminologies. We identify four cases: 1) terms containing classification criteria, 2) terms reflecting detectability, modality, uncertainty, and vagueness, 3) terms created in order to obtain a complete partition of a given domain, and 4) terms reflecting mere fiat boundaries. We show that epistemology-loaded terms are pervasive in biomedical vocabularies, that the “classes” they name often do not comply with sound classification principles, and that they are therefore likely to cause problems in the evolution and alignment of terminologies and associated ontologies. (shrink)

The Unified Medical Language System and the Gene Ontology are among the most widely used terminology resources in the biomedical domain. However, when we evaluate them in the light of simple principles for wellconstructed ontologies we find a number of characteristic inadequacies. Employing the theory of granular partitions, a new approach to the understanding of ontologies and of the relationships ontologies bear to instances in reality, we provide an application of this theory in relation to an example drawn from (...) the context of the pathophysiology of hypertension. This exercise is designed to demonstrate how, by taking ontological principles into account we can create more realistic biomedical ontologies which will also bring advantages in terms of efficiency and robustness of associated software applications. (shrink)

Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...) FDE worlds (Berto and Jago, 2019) with a Lewisian (1988) understanding of subject matters as partitions. By doing so, I show how subject matters impose some order in the anarchic space of FDE worlds, while the worlds allow for distinctions between contents which would not otherwise be available. Combining the two approaches, then, brings us closer to the desired closure principles for knowledge of minimally rational agents. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...) FDE worlds (Berto and Jago, 2019) with a Lewisian (1988) understanding of subject matters as partitions. By doing so, I show how subject matters impose some order in the anarchic space of FDE worlds, while the worlds allow for distinctions between contents which would not otherwise be available. Combining the two approaches, then, brings us closer to the desired closure principles for knowledge of minimally rational agents. (shrink)

This article builds on C. S. Peirce’s suggestive blueprint for an inclusive outlook that grants reality to his three categories. Moving away from the usual focus on (contentious) cosmological forces, I use a modal principle to partition various ontological layers: regular sign-action (like coded language) subsumes actual sign-action (like here-and-now events) which in turn subsumes possible sign-action (like qualities related to whatever would be similar to them). Once we realize that the triadic sign’s components are each answerable to this asymmetric (...) subsumption, we obtain the means to track at which level of complexity semiosis finds itself, in a given case. Since the bulk of such a “trinitarian” metaphysics would be devoted to countenancing uninterpreted phenomena, I argue that current misgivings about sign-based ontologies are largely misplaced. (shrink)

I argue that Republic presents thumos as a limited, or flawed, principle of psychic unity. My central claim is that Plato both makes this assertion about the necessary limitations of thumos, and can defend it, because he understands thumos as the pursuit of to oikeion, or one’s own. So understood, the thumoetic part divides the world into self and other and pursues the defense of the former from the latter. As a result, when confronted with a conflicting desire, the thumoetic (...) part makes sense of that desire as an irredeemable opponent. That, in turn, precludes the persuasion of desires that Plato sees as necessary for psychic harmony. (shrink)

Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized (...) logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness. (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)

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...) to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics. (shrink)

In the present version of these lecture notes only a number of typos and a few glaring mistakes have been corrected. Thanks to Paul Dekker for his help in this respect. No attempt has been been made to update the original text or to incorporate new insights and approaches. For a more recent overview, see our ‘Questions’ in the Handbook of Logic and Language (edited by Johan van Benthem and Alice ter Meulen, Elsevier, 1997).

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)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

In this paper we propose a formal theory of partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize partitions at two levels: as systems of cells (theory A), and in terms of their projective relation to reality (theory B). We lay down conditions of well-formedness for partitions and we define what it means for partitions to project truly onto reality. We continue by classifying well-formed (...) partitions along three axes: (a) degree of correspondence between partition cells and objects in reality; (b) degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) degree of completeness and exhaustiveness with which a partition represents reality. This classification is used to characterize three types of partitions that play an important role in spatial information science: cadastral partitions, categorical coverages, and the partitions involved in folk categorizations of the geospatial domain. (shrink)

Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate—a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is some sense (...) in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is definitely true and those of which it is definitely false. Taking as primitive the operator ‘it is definitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is definitely true (or definitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (DΦ(x) ∧ D¬Φ(y)) → ¬R(x, y). Here ‘Φ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate—such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the definitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (shrink)

I show that centered propositions—also called de se propositions, and usually modeled as sets of centered worlds—pose a serious problem for various versions of Lewis's Principal Principle. The problem, put roughly, is that in scenarios like Elga's `Sleeping Beauty' case, those principles imply that rational agents ought to have obviously irrational credences. To solve the problem, I propose a centered version of the Principal Principle. My version allows centered propositions to be objectively chancy.

We present a minimum message length (MML) framework for trajectory partitioning by point selection, and use it to automatically select the tolerance parameter ε for Douglas-Peucker partitioning, adapting to local trajectory complexity. By examining a range of ε for synthetic and real trajectories, it is easy to see that the best ε does vary by trajectory, and that the MML encoding makes sensible choices and is robust against Gaussian noise. We use it to explore the identification of micro-activities (...) within a longer trajectory. This MML metric is comparable to the TRACLUS metric – and shares the constraint of abstracting only by omission of points – but is a true lossless encoding. Such encoding has several theoretical advantages – particularly with very small segments (high frame rates) – but actual performance interacts strongly with the search algorithm. Both differ from unconstrained piecewise linear approximations, including other MML formulations. (shrink)

Theories of phenomenal intentionality have been claimed to resolve certain worries about the indeterminacy of mental content that rival, externalist theories face. Thus far, however, such claims have been largely programmatic. This paper aims to improve on prior arguments in favor of phenomenal intentionality by using attention and Gestalt principles as specific examples of factors that influence the phenomenal character of perceptual experience in ways that thereby help determine perceptual content. Some reasons are then offered for rejecting an alternative (...) interpretation of these examples, according to which the phenomenal effects of attention and Gestalt principles play no role in the determination of perceptual content. (shrink)

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...) a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic. (shrink)

The free-energy principle states that all systems that minimize their free energy resist a tendency to physical disintegration. Originally proposed to account for perception, learning, and action, the free-energy principle has been applied to the evolution, development, morphology, anatomy and function of the brain, and has been called a postulate, an unfalsifiable principle, a natural law, and an imperative. While it might afford a theoretical foundation for understanding the relationship between environment, life, and mind, its epistemic status is unclear. Also (...) unclear is how the free-energy principle relates to prominent theoretical approaches to life science phenomena, such as organicism and mechanism. This paper clarifies both issues, and identifies limits and prospects for the free-energy principle as a first principle in the life sciences. (shrink)

THE PRINCIPLE OF SUPERPOSITION. The need for a quantum theory Classical mechanics has been developed continuously from the time of Newton and applied to an ...

Following the inferences of my previous work "Monadic Conditionality", this work further investigates the nature of being-for-itself's transformations and what happens with any being-for-itself in between eternal returns, completing a quasi-principled view on immortality (suggested and started in my previous work). Through mathematical reasoning, this model infers that infinitesimal differences between successive event lines grow gradually across subspaces, until reaching the state of eternal return; the cycle repeats, resulting in each event line having its own eternal return, preserving monadic homeostasis. (...) Thus, "amor fati" is enriched by extending fixed eternal recurrences with all "inter-idem" variations, ultimately reaching a fertile ground for ataraxia. (shrink)

According to the Principle of Sufficient Reason (henceforth ‘PSR’), everything has an explanation or sufficient reason. This paper addresses three questions. First, how continuous is the contemporary notion of grounding with the notion of sufficient reason endorsed by Spinoza, Leibniz, and other rationalists? In particular, does a PSR formulated in terms of ground retain the intuitive pull and power of the PSR endorsed by the rationalists? Second, to what extent can the PSR avoid the formidable traditional objections levelled against it (...) if it is formulated in terms of ground? And finally, how might historical discussion of the PSR shed light on the contemporary notion of grounding? (shrink)

In this paper, I defend what may seem a surprising view: that John Stuart Mill’s famous harm principle would, if taken to be what justifies government action, disallow the existence of corporations. My claim is not that harmful activities of currently existing corporations warrants their losing corporate status according to the harm principle. The claim, rather, is that taken strictly, the harm principle and the legal possibility of incorporation are mutually exclusive. This view may be surprising—and I do not at (...) all mean to attribute it to Mill—but if I am right, it should be obvious. It should also encourage us to think more about the nature of the markets within which business occurs. (shrink)

This paper examines John Rawls' renowned theory of justice, which outlines two principles of justice and their respective significance. It explores how Rawls' notion of equality aligns with the philosophical concept of equity, emphasizing that his call for citizen equality inherently incorporates fairness. Additionally, the paper discusses the application of Rawls' "Difference Principle" to India's reservation policy. Rawls' principles, which aim to support the worst-off in society, are reflected in India's system of reservations for marginalized groups, including backward (...) classes and differently-abled individuals, to promote equitable opportunities. However, the paper cautions that excessive reservations could limit opportunities for more privileged groups. Ultimately, it is argued that Rawls' concept of social justice has contributed to the promotion of social justice in India. (shrink)

Berkeley’s likeness principle is the claim that “an idea can be like nothing but an idea”. The likeness principle is intended to undermine representationalism: the view (that Berkeley attributes to thinkers like Descartes and Locke) that all human knowledge is mediated by ideas in the mind which represent material objects. Yet, Berkeley appears to leave the likeness principle unargued for. This has led to several attempts to explain why Berkeley accepts it. In contrast to ‘metaphysical’ and ‘epistemological’ interpretations available in (...) the literature, in this paper I defend a ‘conceptual’ interpretation. I argue that Berkeley accepts the likeness principle on the basis of (i) his commitment to the transparency of ideas, and (ii) his account of resemblance which he sets out in his works on vision. Thus, I provide an explanation for Berkeley’s reasons for accepting the likeness principle which, appropriately, focuses on his views concerning ideas and likeness. (shrink)

Should our factual understanding of the world influence our normative theorising about it? G.A. Cohen has argued that our ultimate normative principles should not be constrained by facts. Many others have defended or are committed to various versions or subsets of that claim. In this paper I dispute those positions by arguing that, in order to resist the conclusion that ultimate normative principles rest on facts about possibility or conceivability, one has to embrace an unsatisfactory account of how (...) principles generate normative political judgments. So political theorists have to choose between principles ostensibly unbiased by our current understanding of human motivation and political reality, or principles capable of reliably generating political judgments. I conclude with wider methodological observations in defence of the latter option, and so of a return to political philosophy’s traditional blend of normative and descriptive elements. (shrink)

Allocation of very scarce medical interventions such as organs and vaccines is a persistent ethical challenge. We evaluate eight simple allocation principles that can be classified into four categories: treating people equally, favouring the worst-off, maximising total benefits, and promoting and rewarding social usefulness. No single principle is sufficient to incorporate all morally relevant considerations and therefore individual principles must be combined into multiprinciple allocation systems. We evaluate three systems: the United Network for Organ Sharing points systems, quality-adjusted (...) life-years, and disability-adjusted life-years. We recommend an alternative system—the complete lives system—which prioritises younger people who have not yet lived a complete life, and also incorporates prognosis, save the most lives, lottery, and instrumental value principles. (shrink)

Bashabi Fraser is a poet in her own right. She is also a creative translator. This is a review of her edited volume on the Partition of Bengal. The review highlights our need to read the partition event as a warning for future and ongoing genocides. The review also shows the superiority of literature over history. And finally it has something to say about translation and separately, on P Lal. For instance, this reviewer in many other reviews too insists on (...) the superiority of Fr Mignon SJ over Prof Lal's understanding of translation. (shrink)

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

Alongside a revival of interest in Thomism in philosophy, scholars have realised its relevance when addressing certain contemporary issues in bioethics. This book offers a rigorous interpretation of Aquinas's metaphysics and ethical thought, and highlights its significance to questions in bioethics. Jason T. Eberl applies Aquinas’s views on the seminal topics of human nature and morality to key questions in bioethics at the margins of human life – questions which are currently contested in the academia, politics and the media such (...) as: When does a human person’s life begin? How should we define and clinically determine a person’s death? Is abortion ever morally permissible? How should we resolve the conflict between the potential benefits of embryonic stem cell research and the lives of human embryos? Does cloning involve a misuse of human ingenuity and technology? What forms of treatment are appropriate for irreversibly comatose patients? How should we care for patients who experience unbearable suffering as they approach the end of life? _Thomistic Principles and Bioethics_ presents a significant philosophical viewpoint which will motivate further dialogue amongst religious and secular arenas of inquiry concerning such complex issues of both individual and public concern. (shrink)

It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the same (...) agents and some agents are better off in the first world than they are in the second and no agents are worse off than they are in the second, then the first world is better than the second. I show that if we accept four axioms – the Pareto principle, transitivity, an axiom stating that populations of worlds can be permuted, and the claim that if the ‘at least as good as’ relation holds between two worlds then it holds between qualitative duplicates of this world pair – then we must conclude that there is ubiquitous incomparability between infinite worlds. I show that this is true even if the populations of infinite worlds are disjoint or overlapping, and that we cannot use any qualitative properties of world pairs to rank these worlds. Finally, I argue that this incomparability result generates puzzles for both consequentialist and non-consequentialist theories of objective and subjective permissibility. (shrink)

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles. In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character (...) of the Principles of Contradiction and Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6). (shrink)

The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.

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)

Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue that the opposite (...) is true: if anything, Huemer’s use of the principle of indifference supports the rationality of inductive scepticism. (shrink)

My argument is that Chalmers' zombie fiction and his rigid-designator-argument going back on Kripke comes down to a petitio principii. Rather, at the core it appears to be more related to the essential 'privacy' of the phenomenal internal perspective. In return for Chalmers I argue that the 'principle self-preservation' of living organisms necessarily implies subjectivity and the emergence of sense. The comparison with a robot proves instructive. The mode of 'mere physical' being is transcended if, in the form of phenomenal (...) perception, sense appears on the stage of higher animals – a transition explained here as an emergence phenomenon based on the systemic co-operation of perception, valuation and action ('perc-val-act system'). Some fundamental considerations are added: Those consequences implied by the principle self-preservation reveal the natural-biological origin of the organism – primarily seeming a more insignificant circumstance – as a momentous fundamental difference (end-in-itself-character, subjectivity, constitution of sense) compared to technical artefacts (robot). And the emergentist approach indicates the – maybe paradoxical – possibility of a dualism of physical and psychical phenomena in an overall physical system, that is not dualistic at the same time. (shrink)

The Principle of Sufficient Reason is very seldom, if ever, referred to in the works of whom we might think of as the eminent Asian metaphysicians. In spite of this, the big picture metaphysical views available in the thought of philosophers such as Nāgārjuna, Fazang and Nishida appear to share certain structural features with views more familiar to us from our own tradition; views that explicitly accept or reject the Principle of Sufficient Reason. Nāgārjuna looks to develop a kind of (...) metaphysical infinitism, Fazang an extreme form of coherentism, and Nishida a species of foundationalism. These three positions - infinitism, coherentism and foundationalism - are typically thought to exhaust the spread of possibilities by those working within the Western tradition. -/- In spite of their similarities to positions advanced within our own tradition, the cosmologies of many of the giants of Asian philosophy are characterised by their rather striking conclusions. Amongst such conclusions for Nāgārjuna is that everything is empty; for Fazang that everything is identical to everything else; and for Nishida that everything depends on absolute nothingness. If the Principle of Sufficient Reason is playing a role in the derivation of such striking conclusions, then it looks that there are more options regarding the metaphysical structure of the world available to us than our own tradition typically courts. If, on the other hand, these striking cosmological conclusions are arrived at without any consideration of sufficient reason, then there may well be ways of reasoning about the overarching structure of reality that are powerful but unfamiliar to Western thinking. In this contribution, I explore what, if any, role the PSR might be playing in the thought of Nāgārjuna , Fazang and Nishida, and what we might be able to learn from it. (shrink)

This short article represents the first attempt to define a new core cultural value that will enable engaging the business sector in humankind’s mission to heal nature. First, I start with defining the problem of the current business culture and the extant thinking on how to solve environmental problems, which I called “the eco-deficit culture.” Then, I present a solution to this problem by formulating the “semiconducting principle” of monetary and environmental values exchange, which I believe can generate “an eco-surplus (...) business culture.” This work adds one new element, the eleventh cultural value, to the ten core values of progressive cultures postulated by Harrison (2000). (shrink)