Posthumous Fragments: Spring–Autumn 1881 [Excerpts].

In order to predict and explain behavior, one cannot specify the mental state of an agent merely by saying what information she possesses. Instead one must specify what information is available to an agent relative to various purposes. Specifying mental states in this way allows us to accommodate cases of imperfect recall, cognitive accomplishments involved in logical deduction, the mental states of confused or fragmented subjects, and the difference between propositional knowledge and know-how .

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's (...) attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

In this paper, we articulate a version of non-standard A-theory—which we call Flow Fragmentalism—in relation to its take on the issue of supervenience of truth on being. According to the Truth Supervenes on Being (TSB) Principle, the truth of past- and future-tensed propositions supervenes, respectively, on past and future facts. Since the standard presentist denies the existence of past and future entities and facts concerning them that do not obtain in the present, she seems to lack the resources to (...) accept both past and future-tensed truths and the TSB Principle. Contrariwise, positions in philosophy of time that accept an eternalist ontology (e.g., B-theory, moving spotlight, and Fine’s and Lipman’s versions of fragmentalism) allow for a “direct” supervenience base for past- and future-tensed truths. We argue that Flow Fragmentalism constitutes a middle ground, which retains most of the advantages of both views, and allows us to articulate a novel account of the passage of time. (shrink)

In this paper, I will argue that there is a version of possibilism—inspired by the modal analogue of Kit Fine’s fragmentalism—that can be combined with a weakening of actualism. The reasons for analysing this view, which I call Modal Fragmentalism, are twofold. Firstly, it can enrich our understanding of the actualism/possibilism divide, by showing that, at least in principle, the adoption of possibilia does not correspond to an outright rejection of the actualist intuitions. Secondly, and more specifically, it (...) can enrich our understanding of concretism, by proving that, at least in principle, the idea that objects have properties in an absolute manner is compatible with transworld identity. (shrink)

This paper develops and defends a new account of B-theoretic endurantism and a new account of the metaphysics of the quantum state, and highlights the parallels between the considerations that motivate them. These new accounts are both fragmentalist, in the sense that they follow Fine (2005) in invoking a symmetric coordination relation between facts, such that facts that are pairwise incompatible (like Hugh's being happy and Hugh's being sad) can both obtain provided that they are not related by this relation. (...) However, while Fine allows that fragments can be logically incoherent— P can obtain in one fragment while not-P obtains in another—the fragmentalist accounts defended here are motivated even if we insist on logical coherence between fragments. (shrink)

The growing interest in fragmentalism is one of the most exciting trends in philosophy of time and is gradually reshaping the contemporary debate. Providing an extensive interpretation of this view, Samuele Iaquinto and Giuliano Torrengo articulate a novel theory of the passage of time and argue that it is the most effective in vindicating the inherent dynamism of reality. Iaquinto and Torrengo offer the first full-range application of fragmentalism to a number of metaphysical topics, including the open future, (...) causation, the A-theoretic interpretation of special relativity and time travel. The resulting picture, they argue, conveys the potential of a radically new understanding of time. (shrink)

The idea of fragmentalism has been proposed by Kit Fine as a non-standard view of tense realism. This paper examines a modal version of the view, called modal fragmentalism, which combines genuine realism and realism of modality. Modal fragmentalism has been recently discussed by Iaquinto. But unlike Iaquinto, who primarily focused on possibilities de re, in this paper, we focus on expressions of possibilities de dicto. We argue that the chief idea of modal realism should be that (...) different worlds are distinguished not just in terms of how things are differently with respect to each world, but also in terms of how things could have been differently with respect to each world. This demands a realism-oriented semantics for suppositional contents, and more specifically, for conditionals. By deploying a multidimensional semantics for conditionals, we show that there are good reasons to consider modal fragmentalism as a serious approach in metaphysics, which shares many similarities with the fragmentalism of tense. (shrink)

According to perspectival realism, reality is (at least partially) constituted by “purely perspectival” facts, that is, facts that appear to describe reality only from a given “perspective”. Fragmentalism is a form of perspectival realism that maintains both that no perspective is privileged and that perspectival facts constitute reality absolutely. Assuming that reality is sufficiently variegated, fragmentalism entails that reality is absolutely constituted by incompatible facts. Given that incompatible facts can never obtain together, reality must be divided into a (...) plurality of “fragments” that never compose a coherent, unitary whole. The main aim of this paper is to provide the first rigorous, detailed map of fragmentalism and its rivals. First, we will argue that fragmentalism is best construed as having two “unitist” (that is, non-fragmentalist) boundaries, which we will call ‘coherent’ and ‘incoherent unitism’. Second, we will present what we take to be the six main viable versions of fragmentalism and show how they can be categorized according to whether they take the logical operations of conjunction and negation to be either “local” or “global”. (shrink)

Many philosophical debates take for granted that there is such a thing as ‘the’ common-sense conception of the phenomenon of interest. Debates about the nature of perception tend to take for granted that there is a single, coherent common-sense conception of vision, consistent with Direct Realism. This conception is often accorded an epistemic default status. We draw on philosophical and psychological literature on naïve theories and belief fragmentation to motivate the hypothesis that untutored common sense encompasses conflicting Direct Realist and (...) Indirect Realist conceptions: there is no such thing as ‘the’ common-sense conception of vision that could enjoy epistemic default status. To examine this hypothesis, a survey administered an agreement rating task with verbal and pictorial stimuli to lay participants. We found many laypeople simultaneously hold conflicting Direct Realist and Indirect Realist beliefs about vision. Against common assumptions, Direct Realist beliefs are not clearly dominant, and consistent adherence to Direct Realism is not the norm, but the exception. These findings are consistent with recent accounts of belief fragmentation. They forcefully challenge common methodology in philosophical debates about the nature of perception and beyond. (shrink)

Fragmentalism allows incompatible facts to constitute reality in an absolute manner, provided that they fail to obtain together. In recent years, the view has been extensively discussed, with a focus on its formalisation in model-theoretic terms. This paper focuses on three formalisations: Lipman’s approach, the subvaluationist interpretation, and a novel view that has been so far overlooked. The aim of the paper is to explore the application of these formalisations to the alethic modal case. This logical exploration will allow (...) us to study (i) cases of metaphysical incompatibility between modal facts and (ii) cases of modal dialetheias. In turn, this will enrich our understanding of the role of impossibility in the fragmentalist framework. (shrink)

We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Minc [14]; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems. The results are (...) generalized to relate a hierarchy of subsystems, all contained in the theory of arithmetic properties, to a corresponding hierarchy of fragments of arithmetic. The proof theoretic tools employed there are used to re-establish in a uniform, elementary way relationships between various fragments of arithmetic due to Parsons, Paris and Kirby, and Friedman. (shrink)

The thesis of mental fragmentation has recently attracted increased attention as a way of explaining facts about mind and language. This volume provides an accessible introduction and essays on foundations and applications of fragmentation.

Fragments of Modernity provides a critical introduction to the work of three of the most original German thinkers of the early 20th century. In their different ways, all three illuminated the experience of the modern in urban life, whether in mid-19th-century Paris or in Berlin at the turn of the century or later as the vanguard city of the Weimar Republic. They related the new modes of experiencing the world to the maturation of the money economy (Simmel), the process of (...) rationalization of capital (Kracauer), and the fantasy world of commodity fetishism (Benjamin) - in each case focusing on those fragments of social experience that could best capture the sense of modernity.David Frisby is Reader in Sociology at Glasgow University. Fragments of Modernity is included in the series Studies in Contemporary German Social Thought, edited by Thomas McCarthy. (shrink)

By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only consistent Πn+1-theory which extends the scheme of induction for parameter free Πn+1-formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first-order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain (...) results on the quantifier complexity, finite axiomatizability and relative strength of schemes for Δn+1-formulas. (shrink)

Belief storage is often modeled as having the structure of a single, unified web. This model of belief storage is attractive and widely assumed because it appears to provide an explanation of the flexibility of cognition and the complicated dynamics of belief revision. However, when one scrutinizes human cognition, one finds strong evidence against a unified web of belief and for a fragmented model of belief storage. Using the best available evidence from cognitive science, we develop this fragmented model into (...) a nascent theory of the cognitive architecture of belief storage. (shrink)

This paper discusses the fragmentation of psychology and proposals for unification hitherto proffered. It is argued that unity will not be achieved until competing ideas regarding morality, ontology, epistemology, and so forth are critically examined and evaluated. Ideas that pass theoretical muster and that cohere with human moral interests will provide a theoretical starting point for unification efforts. 2012 APA, all rights reserved).

In a series of five experiments, we demonstrate that moral judgments and folk intuitions are often predictably fragmented. Drawing on the domains of ethics and action theory, we illustrate ways in which judgment tends to be associated with stable individual differences such as personality traits and reflective cognitive styles. We argue that these individual differences pose several unique challenges as well as provide opportunities for further theoretical development in the emerging field of experimental philosophy. Implications are briefly discussed.

Bayesian confirmation theory is our best formal framework for describing inductive reasoning. The problem of old evidence is a particularly difficult one for confirmation theory, because it suggests that this framework fails to account for central and important cases of inductive reasoning and scientific inference. I show that we can appeal to the fragmentation of doxastic states to solve this problem for confirmation theory. This fragmentation solution is independently well-motivated because of the success of fragmentation in solving other problems. I (...) also argue that the fragmentation solution is preferable to other solutions to the problem of old evidence. These other solutions are already committed to something like fragmentation, but suffer from difficulties due to their additional commitments. If these arguments are successful, Bayesian confirmation theory is saved from the problem of old evidence, and the argument for fragmentation is bolstered by its ability to solve yet another problem. (shrink)

By a fragment of a natural language we mean a subset of thatlanguage equipped with semantics which translate its sentences intosome formal system such as first-order logic. The familiar conceptsof satisfiability and entailment can be defined for anysuch fragment in a natural way. The question therefore arises, for anygiven fragment of a natural language, as to the computational complexityof determining satisfiability and entailment within that fragment. Wepresent a series of fragments of English for which the satisfiabilityproblem is polynomial, NP-complete, EXPTIME-complete,NEXPTIME-complete (...) and undecidable. Thus, this paper represents a casestudy in how to approach the problem of determining the logicalcomplexity of various natural language constructions. In addition, wedraw some general conclusions about the relationship between naturallanguage and formal logic. (shrink)

One of the dominating themes in the first part is the negative treatment that Marx’s concept of labor has received by late critical theorists, particularly Habermas. While supportive of the rejection of Marx’s economic functionalism entailed by Habermas’s adoption of communicative action as the basic category of critical theory, Honneth worries about the indifference towards the normative potential of labor that he sees in most twentieth-century social theory. Honneth agrees with critics of reductionism that labor is neither the only form (...) of social reproduction, nor a primary source of emancipatory consciousness, as the fragmentation and depolitization of a working class that has suffered the effects of Taylorism clearly manifests. But Honneth is still convinced that the experience of recognition is to a large extent associated with work, and that Habermas tends to understand interaction in terms of instrumental action, making the concept of interaction inadequate to capture the sort of normative claims expressed by workers who do not see themselves sufficiently recognized in the labor they do. Although Honneth acknowledges that he has not settled how to navigate between these competing interests, the clarity of the call for a more complex concept of labor justifies the inclusion of these papers in the volume. (shrink)

Fragments presents a set of brilliantly intriguing interviews with Jean Baudrillard whose work today occupies center stage in the analysis of consumerism, terrorism, and contemporary culture. In these frank discussions with François L'Yvonnet, Baudrillard reveals for the first time in detail the thinkers who have been the dominant influences on his work during his career. Instead of examining his work as a project of intellectual accumulation, he challenges all the major interpretations of his work by suggesting he has always adopted (...) an anti-system, anti-totality strategy. Even globalization is accompanied in his view by a Western culture which itself is no longer a well-founded confident universalism. Perhaps most interestingly, Baudrillard discusses his life's work in relationship to his contemporaries -- Bataille , Barthes, Lyotard and Deleuze - and explores his position as an outsider in the field of French philosophy. Baudrillard in these interviews is in sparkling form, and in his ownwords he presents not only a lively introduction to this great thinker but also gives readers a window into a brilliant mind. (shrink)

Online targeting isolates individual consumers, causing what we call epistemic fragmentation. This phenomenon amplifies the harms of advertising and inflicts structural damage to the public forum. The two natural strategies to tackle the problem of regulating online targeted advertising, increasing consumer awareness and extending proactive monitoring, fail because even sophisticated individual consumers are vulnerable in isolation, and the contextual knowledge needed for effective proactive monitoring remains largely inaccessible to platforms and external regulators. The limitations of both consumer awareness and of (...) proactive monitoring strategies can be attributed to their failure to address epistemic fragmentation. We call attention to a third possibility that we call a civic model of governance for online targeted advertising, which overcomes this problem, and describe four possible pathways to implement this model. (shrink)

This paper explores taste fragmentalism, a novel approach to matters of taste and faultless disagreement. The view is inspired by Kit Fine’s fragmentalism about time, according to which the temporal dimension can be constituted—in an absolute manner—by states that are pairwise incompatible, provided that they do not obtain together. In the present paper, we will apply this metaphysical framework to taste states. In our proposal, two incompatible taste states (such as the state of rhubarb’s being tasty and the (...) state of rhubarb’s being distasteful) can both constitute reality in an absolute manner, although no agent can have joint access to both states. We will then develop a formalised version of our view by means of an exact truthmaker semantics for taste assertions. Within this framework—we argue—our linguistic and inferential practices concerning cases of faultless disagreement are elegantly vindicated, thus suggesting that taste fragmentalism is worth of further consideration. (shrink)

I criticize the idea that theories of ‘fragmented’ or ‘compartmentalized’ belief (as found in, e.g., Lewis 1982, Egan 2008) can help to account for the puzzling phenomena they are often taken to account for. After introducing fragmentationalism and a paradigm case that purportedly motivates it, I criticize the view primarily on the grounds that the models and explanations it offers are at best trivial—as witnessed by examples of over-generation—and should be seen as merely re-describing in figurative terms the phenomena it (...) is designed to account for. I also point out that fragments, as used in these theories, are not likely to be psychologically real in any robust sense and so cannot be appealed to on such grounds. (shrink)

Dealing with and collecting fragments has always been one of the core tasks of scholars of classical antiquity, especially classical philologists. As an examination of the relevant editions and treatises reveals, there is no agreement on what a ‘fragment’ should be. This also has to do with the polysemy of this term, which has gained a new and wider understanding, especially since the Romantic period. In the present contribution it is therefore suggested that the term ‘testimony text’ (‘Zeugnistext’) should be (...) used instead of ‘fragment’. In this way, it is also possible to avoid an editorial pre-determination regarding the authenticity of the testimonies in question. Furthermore, the question of the contextualization of the respective testimony texts will be discussed and suggestions for the practice of their presentation will be made. (shrink)

Background: Genetics research is controversial in Native American communities, and the disposition and ownership of biological specimens are central issues. Within Native communities, there is considerable variety in tribal members’ views. This article reports the results from an ethnographic study conducted with a Native American community in the southwestern United States. The purpose of this study was to examine the relationship (past and present) between the tribe and biomedical/genetics research. Methods: Qualitative interviews were conducted with 53 members of a Native (...) American community. Interviewees were purposively recruited to include an approximately equal number of past research participants and nonparticipants, as well as individuals with and without diabetes. Tribal members were also asked whether they identified as a “traditional person,” an emic category used in the community. Results: Tribal members’ views on specimen disposition were linked with their identification as a traditional or nontraditional person. Individuals identifying as traditional people were more likely to believe that biological specimens should be returned at the end of a study and should not be used after the research participant's death, and that they were the property of the individual who provided them. These perspectives were related to broader concerns about fragmentation of the body-self. Conclusions: Through gaining an understanding of the cultural logic related to specimen disposition, researchers may be able to work more effectively with Native American communities on developing procedures for genetics studies. The process of informed consent and other study procedures can be adapted to be culturally respectful of Native American communities. (shrink)

Fragmentalism is the view that reality is not a metaphysically unified place, but fragmented in a certain sense, and constituted by incompatible facts across such fragments. It was introduced by Kit Fine in a discussion of tense realist theories of time. Here I discuss the conceptual foundations of fragmentalism, identify several open questions in Fine’s characterization of the view, and propose an understanding of fragmentalism that addresses these open questions.

A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are algorithmically solvable (...) for restricted subsets---or, as we say, fragments---of first-order logic, a fact which is today of considerable interest in Computer Science. This book provides an up-to-date survey of the principal axes of research, charting the limits of decision in first-order logic and exploring the trade-off between expressive power and complexity of reasoning. Divided into three parts, the book considers for which fragments of first-order logic there is an effective method for determining satisfiability or finite satisfiability. Furthermore, if these problems are decidable for some fragment, what is their computational complexity? Part I focusses on fragments defined by restricting the set of available formulas. Topics covered include the Aristotelian syllogistic and its relatives, the two-variable fragment, the guarded fragment, the quantifier-prefix fragments and the fluted fragment. Part II investigates logics with counting quantifiers. Starting with De Morgan's numerical generalization of the Aristotelian syllogistic, we proceed to the two-variable fragment with counting quantifiers and its guarded subfragment, explaining the applications of the latter to the problem of query answering in structured data. Part III concerns logics characterized by semantic constraints, limiting the available interpretations of certain predicates. Taking propositional modal logic and graded modal logic as our cue, we return to the satisfiability problem for two-variable first-order logic and its relatives, but this time with certain distinguished binary predicates constrained to be interpreted as equivalence relations or transitive relations. The work finishes, slightly breaching the bounds of first-order logic proper, with a chapter on logics interpreted over trees. (shrink)

We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly -game-closed forcings. PFA can be destroyed by a strongly -game-closed forcing but not by an ω2-closed.

In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T (...) prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising. (shrink)

Centers have been out of intellectual and political fashion, because they have been often oppressive. We both celebrate and worry about postmodern fragmentation as we enact it in our technology, while fearing hidden centralization. But centering is important. I would like to mull over some issues concerning centers and criticism.

We study the long-standing open problem of giving$\forall {\rm{\Sigma }}_1^b$separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the$\forall {\rm{\Sigma }}_1^b$Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole (...) principle for FPNPfunctions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of$T_2^1$augmented with the surjective weak pigeonhole principle for polynomial time functions. (shrink)

We strengthen a result of Harrington and Shelah by showing that, unless ω1 is an inaccessible cardinal in L, a relatively weak fragment of Martin's axiom implies that there exists a δ13 set of reals without the property of Baire.

To reconcile the standard possible worlds model of knowledge with the intuition that ordinary agents fall far short of logical omniscience, a Stalnakerian strategy appeals to two components. The first is the idea that mathematical and logical knowledge is at bottom metalinguistic knowledge. The second is the idea that non-ideal minds are often fragmented. In this paper, we investigate this Stalnakerian reconciliation strategy and argue, ultimately, that it fails. We are not the first to complain about the Stalnakerian strategy. But (...) in contrast to existing complaints, we want to cause trouble for the strategy directly on its home turf. That is, we will advance our objection while granting both the plausibility of the fragmentation component—save for an extreme version of it—and that of the metalinguistic component. Once our central objection to the Stalnakerian strategy is in place, we will show how it negatively affects Adam Elga and Augustín Rayo’s recent attempt to apply the Stalnakerian strategy in the context of Bayesian decision theory. (shrink)

Edited with New Translation by Richard McKirahan With a New Preface by Malcolm Schofield This book is a revised and expanded version of A.H. Coxon's full critical edition of the extant remains of Parmenides of Elea—the fifth-century B.C. philosopher by many considered "one of the greatest and most astonishing thinkers of all times." Coxon's presentation of the complete ancient evidence for Parmenides and his comprehensive examination of the fragments, unsurpassed to this day, have proven invaluable to our understanding of the (...) Eleatic since the book's first publication in 1986. This edition, edited by Richard McKirahan and with a new preface by Malcolm Schofield, is released on the 100th anniversary of Coxon's birth. This new edition for the first time includes English translations of the testimonia and of any Ancient Greek throughout the book, as well as an English/Greek glossary by Richard McKirahan, and revisions by the late author himself. The text consists of Coxon's collations of the relevant folios of manuscripts of Sextus Empiricus, Proclus and Simplicius and includes all extant fragments, a commentary, the testimonia, a complete list of sources, linguistic parallels from both earlier and later authors, and the fullest critical apparatus that has appeared since Diels’ _Poetarum Philosophorum Fragmenta _. The collection of testimonia includes the philosophical discussions of Parmenides by Plato, Aristotle and the Neoplatonists, most of which had been omitted by Diels. The introduction discusses the history of the text, the language and form of the poem, Parmenides’ use and understanding of the verb ‘to be’, his place in the history of earlier and later philosophy and the biographical tradition. In the commentary Coxon deals in detail with both the language and the subject matter of the poem and pays full attention to Parmenides’ account of the physical world. The appendix relates later Eleatic arguments to those of Parmenides. (shrink)

Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic as the (...) extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts. (shrink)

Jason Merchant (2004, and Chap. 3, this volume) proposes to account for all speech acts performed with “fragments,” whether in discourse-initial position or otherwise, by appealing to syntactic ellipsis. Though his proposal is insightful, I offer empirical and methodological considerations against it. Empirical problems include: (a) His alleged “elliptical sentences” do not embed the way they should; (b) in some cases where Merchant requires fronting to take place, it is blocked – either by an island (e.g., in English) or because (...) nonsubject fronting is not allowed in the language in question (e.g., in Malagasy); and (c) his “limited ellipsis” strategy, allowing do it and this is __ to be licensed in discourse-initial position, is not general enough. The methodological problem is that, his protests to the contrary, Merchant’s view multiplies hidden structure without necessity. (shrink)

_ Source: _Volume 54, Issue 1, pp 46 - 107 The present paper discusses the question of Marsilio Ficino’s lost translations of Proclus’ _Elements of Physics_ and _Elements of Theology_. It reviews all known evidence for Ficino’s work on the _Elements of Physics_ and _Elements of Theology_, examines new references and fragments of these texts in Ficino’s manuscripts, especially in his personal manuscript of Plotinus’ _Enneads_, and studies how they fit within the Florentine’s philosophical oeuvre. The present case studies of (...) manuscript evidence demonstrate how Proclus accompanied Ficino from his early ‘scholastic background’ through to his mastery of the Platonic tradition late in his career, especially, as is shown, in his study of Pseudo-Dionysius and Plotinus. Despite the fact that scholarship at times pits scholasticism and Renaissance Platonism against each other, in this sense Proclus—largely due to the _Elements_—bridges the two cultures. (shrink)

Keine ausführliche Beschreibung für "Nachgelassene Fragmente 1875-1879" verfügbar.

By a fragment of a natural language, we understand a collection of sentences forming a naturally delineated subset of that language and equipped with a semantics commanding the general assent of its native speakers. By the semantic complexity of such a fragment, we understand the computational complexity of deciding whether any given set of sentences in that fragment represents a logically possible situation. In earlier papers by the first author, the semantic complexity of various fragments of English involving at most (...) transitive verbs was investigated. The present paper considers various fragments of English involving ditransitive verbs and determines their semantic complexity. (shrink)

Publishing a collection of fragments from a classical author is a risky business: the moment the book appears in print, it may already be outdated, as new fragments could have come to light. Or, in the words of Ecclesiasticus 18:7: ‘When a man hath done, then he beginneth; and when he leaveth off, then he shall be doubtful’. The same fate befell me shortly after the publication of my collection of fragments from Rufus of Ephesus' On Melancholy. Manfred Ullmann wrote (...) to me that the late Rainer Degen had discovered a new fragment; in the course of my research, I came across some relevant quotations in the Hippocratic Treatments by the tenth-century author aṭ-Ṭabarī; and recently, Klaus-Dietrich Fischer published two related fragments. The following short note contains these new fragments together with an English translation and commentary. At the end, I also offer some addenda and corrigenda, partly in light of the reviews that have since appeared. (shrink)

Pluralist and eliminativist positions have proliferated within both science and philosophy of science in recent decades. This paper asks the question why this shift of thinking has occurred, and where it is leading us. We provide an explanation which, if correct, entails that we should expect pluralism and eliminativism to transform other debates currently unaffected, and for good reasons. We then consider the question under what circumstances eliminativism will be appropriate, arguing that it depends not only on the term in (...) question, but also on the context of discussion and details of the debate at hand. The resultant selective eliminativism is an appealing compromise for various ‘pluralists’ and ‘eliminativists’ who are currently locking horns. (shrink)

We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...) of set theory that is in one of the following forms: ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns distinct values to all of the variables y1,…,yl, ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns the same value to all of the variables y1,…,yl. (shrink)