This is the first complete, one-volume English translation of the ancient Chinese text Xunzi, one of the most extensive, sophisticated, and elegant works in the tradition of Confucian thought. Through essays, poetry, dialogues, and anecdotes, the Xunzi articulates a Confucian perspective on ethics, politics, warfare, language, psychology, human nature, ritual, and music, among other topics. Aimed at general readers and students of Chinese thought, Eric Hutton’s translation makes the full text of this important work more accessible in English than ever (...) before. Named for its purported author, the Xunzi has long been neglected compared to works such as the Analects of Confucius and the Mencius. Yet interest in the Xunzi has grown in recent decades, and the text presents a much more systematic vision of the Confucian ideal than the fragmented sayings of Confucius and Mencius. In one famous, explicit contrast to them, the Xunzi argues that human nature is bad. However, it also allows that people can become good through rituals and institutions established by earlier sages. Indeed, the main purpose of the Xunzi is to urge people to become as good as possible, both for their own sakes and for the sake of peace and order in the world. In this edition, key terms are consistently translated to aid understanding and line numbers are provided for easy reference. Other features include a concise introduction, a timeline of early Chinese history, a list of important names and terms, cross-references, brief explanatory notes, a bibliography, and an index. (shrink)

Amodal completion is usually characterized as the representation of those parts of the perceived object that we get no sensory stimulation from. In the case of the visual sense modality, for example, amodal completion is the representation of occluded parts of objects we see. I argue that relationalism about perception, the view that perceptual experience is constituted by the relation to the perceived object, cannot give a coherent account of amodal completion. The relationalist has two options: construe (...) the perceptual relation as the relation to the entire perceived object or as the relation to the unoccluded parts of the perceived object. I argue that neither of these options are viable. (shrink)

This paper attempts an historical analysis of a dream of the physicist George Gamow recorded shortly before his death in 1968. The dream is contextualized through Gamow's extended scientific work and popular scientific efforts, and in light of enduring preoccupations with the notion of a complete science. The analysis extends to an examination of the relationship of the dream to dreaming practices and deliberations apart from Gamow’s, as evident in the relationship and collaboration between the physicist Wolfgang Pauli and C. (...) G. Jung. (shrink)

Amodal completion is the representation of occluded parts of perceived objects. We argue for the following three claims: First, at least some amodal completion-involved experiences can ground knowledge about the occluded portions of perceived objects. Second, at least some instances of amodal completion-grounded knowledge are not sensitive, that is, it is not the case that in the nearest worlds in which the relevant claim is false, that claim is not believed true. Third, at least some instances of (...) amodal completion-grounded knowledge are not safe, that is, it is not the case that in all or nearly all near worlds where the relevant claim is believed true, that claim is in fact true. Thus, certain instances of amodal completion-grounded knowledge refute both the view that knowledge is necessarily sensitive and the view that knowledge is necessarily safe. (shrink)

This is Daoist philosophy’s central tenet, espoused by the person—or group of people—known as Zhuangzi (369?-286? B.C.E.) in a text by the same name.

This is one of the most justly celebrated texts of the Chinese tradition - impressive for both its bold philosophical imagination and its striking literary style. Accepting the challenge of translating this captivating classic in its entirety, Burton Watson has expertly rendered into English both the profound thought and the literary brilliance of the text.

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

v. 1. The birth of tragedy; or, Hellenism and pessimism.--v. 2. Early Greek philosophy & other essays.--v. 3. On the future of our educational institutions. Homer and classical philology.--v. 4-5. Thoughts out of season.--v. 6-7. Human, all-too-human.--v. 8. The case of Wagner. Nietzsche contra Wagner. Selected aphorisms.--v. 9. The dawn of day.--v. 10. The joyful wisdom.--v. 11. Thus spake Zarathustra.--v. 12. Beyond good and evil.--v. 13. The genealogy of morals. Peoples and countries.--v. 14.-15. The will to power.--v. 16.--The twilight of (...) the idols; or, How to philosophise with the hammer. The antichrist.--v. 17. Ecce homo, Nietzsche's autobiography.--v. 18. Guppy, R. Index to Nietzsche. (shrink)

Classic, influential study of Greek tragedy.

In this paper we study 12 four-valued logics arisen from Belnap's truth and/or knowledge four-valued lattices, with or without constants, by adding one or both or none of two new non-regular operations—classical negation and natural implication. We prove that the secondary connectives of the bilattice four-valued logic with bilattice constants are exactly the regular four-valued operations. Moreover, we prove that its expansion by any non-regular connective (such as, e.g., classical negation or natural implication) is strictly functionally complete. Further, finding axiomatizations (...) of the quasi varieties generated by the 12 logics involved (that prove to be varieties), we find naturell equational axiomatizations of these logics. Finally, applying Pynko's general theory of algebraizable sequential consequence operations, we also find equivalent natural sequentiell axiomatizations of the logics under consideration that expand either of two Pynko's sequential calculi for the constant-free truth-lattice four-valued logic. (shrink)

The type of completeness Whitehead and Russell aimed for in their Principia Mathematica was what I call descriptive completeness. This is completeness with respect to the propositions that have been proved in traditional mathematics. The notion of completeness addressed by Gödel in his famous work of 1930 and 1931 was completeness with respect to the truths expressible in a given language. What are the relative significances of these different conceptions of completeness for traditional mathematics? What, if any, effects does incompleteness (...) of the type Gödel had in mind have for the evaluation of the Principia Mathematica project and other projects like it? (shrink)

Investigation of a puzzle concerning complete yet authorless artworks.

Outstanding translations by leading contemporary scholars--many commissioned especially for this volume--are presented here in the first single edition to include the entire surviving corpus of works attributed to Plato in antiquity. In his introductory essay, John Cooper explains the presentation of these works, discusses questions concerning the chronology of their composition, comments on the dialogue form in which Plato wrote, and offers guidance on approaching the reading and study of Plato's works. Also included are concise introductions by Cooper and Hutchinson (...) to each translation, meticulous annotation designed to serve both scholar and general reader, and a comprehensive index. This handsome volume offers fine paper and a high-quality Smyth-sewn cloth binding in a sturdy, elegant edition. (shrink)

This paper uses the notion of Galois-connection to examine the relation between valuation-spaces and logics. Every valuation-space gives rise to a logic, and every logic gives rise to a valuation space, where the resulting pair of functions form a Galois-connection, and the composite functions are closure-operators. A valuation-space (resp., logic) is said to be complete precisely if it is Galois-closed. Two theorems are proven. A logic is complete if and only if it is reflexive and transitive. A valuation-space is complete (...) if and only if it is closed under formation of super-valuations. (shrink)

Response to Gover (2015) on Trogdon and Livingston (2015) on artwork completion.

Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.

In the Eudemian Ethics II 1, 1219a34–b8, Aristotle defines happiness as ‘the activity of a complete life in accordance with complete virtue’. Most scholars interpret a complete life as a whole lifetime, which means that happiness involves virtuous activity over an entire life. This article argues against this common reading by using Aristotle’s notion of ‘activity’ (energeia) as a touchstone. It argues that happiness, according to the Eudemian Ethics, must be a complete activity that reaches its end at any and (...) every moment. The upshot of this reading is that life reaches completeness within a lifetime and that death cannot be the requirement for making life complete. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere hyperdoctrine for which we describe a notion of quotient completion. That notion includes the exact completion on a category with weak finite limits as an instance as well as examples from type theory that fall apart from this.

The Oxford Translation of Aristotle was originally published in 12 volumes between 1912 and 1954. It is universally recognized as the standard English version of Aristotle. This revised edition contains the substance of the original Translation, slightly emended in light of recent scholarship three of the original versions have been replaced by new translations and a new and enlarged selection of Fragments has been added. The aim of the translation remains the same: to make the surviving works of Aristotle readily (...) accessible to English speaking readers. (shrink)

This paper investigates different modes of organizing for corporate social responsibility (CSR). Based on insights from organization theory, we theorize two ways to organize for CSR. “Complete” organization for CSR happens within businesses and depends on the availability of certain organizational elements (e.g., membership, hierarchy, rules, monitoring, and sanctioning). By contrast, “partial” organization for CSR happens when organizers do not have direct access to all these organizational elements. We discuss partial organization for CSR by analyzing how standards and cross-sector partnerships (...) make selective use of organizational elements. We maintain that an important feature of the increasing institutionalization of CSR—not only within businesses but also among non-governmental, governmental, and professional actors—is the rise of partial forms of organization. We discuss the contributions to this Special Issue in the context of our theorization of complete/partial organization for CSR and outline avenues for further research. (shrink)

The complete surviving works of Epictetus, the most influential Stoic philosopher from antiquity. “Some things are up to us and some are not.” Epictetus was born into slavery around the year 50 CE, and, upon being granted his freedom, he set himself up as a philosophy teacher. After being expelled from Rome, he spent the rest of his life living and teaching in Greece. He is now considered the most important exponent of Stoicism, and his surviving work comprises a series (...) of impassioned discourses, delivered live and recorded by his student Arrian, and the Handbook, Arrian’s own take on the heart of Epictetus’s teaching. In Discourses, Epictetus argues that happiness depends on knowing what is in our power to affect and what is not. Our internal states and our responses to events are up to us, but the events themselves are assigned to us by the benevolent deity, and we should treat them—along with our bodies, possessions, and families—as matters of indifference, simply making the best use of them we can. Together, the Discourses and Handbook constitute a practical guide to moral self-improvement, as Epictetus explains the work and exercises aspirants need to do to enrich and deepen their lives. Edited and translated by renowned scholar Robin Waterfield, this book collects the complete works of Epictetus, bringing to modern readers his insights on how to cope with death, exile, the people around us, the whims of the emperor, fear, illness, and much more. (shrink)

This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

Standard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of (...) conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID or even CN are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries. (shrink)

Defense of a psychological account of what it is for an artwork to be complete.

Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.

We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal rôle in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems, non-deterministically computable problems, Las Vegas computable problems and effectively Borel measurable functions. The closure operator of completion generates the concept (...) of total Weihrauch reducibility, which is a variant of Weihrauch reducibility with total realizers. Logically speaking, the completion of a problem is a version of the problem that is independent of its premise. Hence, studying the completion of choice problems allows us to study simultaneously choice problems in the total Weihrauch lattice, as well as the question which choice problems can be made independent of their premises in the usual Weihrauch lattice. The outcome shows that many important choice problems that are related to compact spaces are complete, whereas choice problems for unbounded spaces or closed sets of positive measure are typically not complete. (shrink)

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.

The claim defended in the paper is that the mechanistic account of explanation can easily embrace idealization in big-scale brain simulations, and that only causally relevant detail should be present in explanatory models. The claim is illustrated with two methodologically different models: Blue Brain, used for particular simulations of the cortical column in hybrid models, and Eliasmith’s SPAUN model that is both biologically realistic and able to explain eight different tasks. By drawing on the mechanistic theory of computational explanation, I (...) argue that large-scale simulations require that the explanandum phenomenon is identified; otherwise, the explanatory value of such explanations is difficult to establish, and testing the model empirically by comparing its behavior with the explanandum remains practically impossible. The completeness of the explanation, and hence of the explanatory value of the explanatory model, is to be assessed vis-à-vis the explanandum phenomenon, which is not to be conflated with raw observational data and may be idealized. I argue that idealizations, which include building models of a single phenomenon displayed by multi-functional mechanisms, lumping together multiple factors in a single causal variable, simplifying the causal structure of the mechanisms, and multi-model integration, are indispensable for complex systems such as brains; otherwise, the model may be as complex as the explanandum phenomenon, which would make it prone to so-called Bonini paradox. I conclude by enumerating dimensions of empirical validation of explanatory models according to new mechanism, which are given in a form of a “checklist” for a modeler. (shrink)

We have synthesized a 582,970-base pair Mycoplasma genitalium genome. This synthetic genome, named M. genitalium JCVI-1.0, contains all the genes of wild-type M. genitalium G37 except MG408, which was disrupted by an antibiotic marker to block pathogenicity and to allow for selection. To identify the genome as synthetic, we inserted "watermarks" at intergenic sites known to tolerate transposon insertions. Overlapping "cassettes" of 5 to 7 kilobases (kb), assembled from chemically synthesized oligonucleotides, were joined by in vitro recombination to produce intermediate (...) assemblies of approximately 24 kb, 72 kb ("1/8 genome"), and 144 kb ("1/4 genome"), which were all cloned as bacterial artificial chromosomes in Escherichia coli. Most of these intermediate clones were sequenced, and clones of all four 1/4 genomes with the correct sequence were identified. The complete synthetic genome was assembled by transformation-associated recombination cloning in the yeast Saccharomyces cerevisiae, then isolated and sequenced. A clone with the correct sequence was identified. The methods described here will be generally useful for constructing large DNA molecules from chemically synthesized pieces and also from combinations of natural and synthetic DNA segments. 10.1126/science.1151721. (shrink)

In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question (...) in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to ${\cal V}$-baos, namely the provability logic $GLB$. We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is ${\cal V}$-complete. After these results, we generalize the Blok Dichotomy to degrees of ${\cal V}$-incompleteness. In the end, we return to van Benthem’s theme of syntactic aspects of modal incompleteness. (shrink)

It is proved that the relevance logic \ has no structurally complete consistent axiomatic extension, except for classical propositional logic. In fact, no other such extension is even passively structurally complete.

This paper expands upon the work by Wang (Proceedings of TARK, pp. 493–512, 2017) who proposes a new framework based on quantifier-free predicate language extended by a new bundled modality \(\exists x\Box \) and axiomatizes the logic over S5 frames. This paper first gives complete axiomatizations of the logics over K, D, T, 4, S4 frames with increasing domains and constant domains, respectively. The systems w.r.t. constant domains feature infinitely many additional rules defined inductively than systems w.r.t. increasing domains. In (...) the second part of the paper, we show that these rules are admissible in the systems without them by providing a general strategy for proving completeness theorems for the logics without these rules over constant domain models (also increasing domain models). (shrink)

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic with (...) implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature. (shrink)

A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P ≥s (with the intended meaning ‘‘the probability is at least s’’). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.

The only complete edition in English of Baruch Spinoza's works, this volume features Samuel Shirley’s preeminent translations, distinguished at once by the lucidity and fluency with which they convey the flavor and meaning of Spinoza’s original texts. Michael L. Morgan provides a general introduction that places Spinoza in Western philosophy and culture and sketches the philosophical, scientific, religious, moral and political dimensions of Spinoza’s thought. Morgan’s brief introductions to each work give a succinct historical, biographical, and philosophical overview. A chronology (...) and index are included. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

We prove completeness of the propositional modal logic S 4 for the measure algebra based on the Lebesgue-measurable subsets of the unit interval, [0, 1]. In recent talks, Dana Scott introduced a new measure-based semantics for the standard propositional modal language with Boolean connectives and necessity and possibility operators, and . Propositional modal formulae are assigned to Lebesgue-measurable subsets of the real interval [0, 1], modulo sets of measure zero. Equivalence classes of Lebesgue-measurable subsets form a measure algebra, , and (...) we add to this a non-trivial interior operator constructed from the frame of ‘open’ elements—elements in with an open representative. We prove completeness of the modal logic S 4 for the algebra . A corollary to the main result is that non-theorems of S 4 can be falsified at each point in a subset of the real interval [0, 1] of measure arbitrarily close to 1. A second corollary is that Intuitionistic propositional logic (IPC) is complete for the frame of open elements in. (shrink)

The taxonomy proposed by Pessoa et al. should be extended to include “pathological” completion phenomena in patients with unilateral brain damage. Patients with visual field defects (hemianopias) may “complete” whole figures, while patients with parietal lobe damage may “complete” partial figures. We argue that the former may be consistent with the brain “filling-in” information, and the latter may be consistent with the brain ignoring the absence of information.

We introduce a general notion of semantic structure for first-order theories, covering a variety of constructions such as Tarski and Kripke semantics, and prove that, over Zermelo–Fraenkel set theory, the completeness of such semantics is equivalent to the Boolean prime ideal theorem. Using a result of McCarty, we conclude that the completeness of Kripke semantics is equivalent, over intuitionistic Zermelo–Fraenkel set theory, to the Law of Excluded Middle plus BPI. Along the way, we also prove the equivalence, over ZF, between (...) BPI and the completeness theorem for Kripke semantics for both first-order and propositional theories. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)