To a modern observer of Western culture, Romanticism might appear conflicted about size. On the one hand, the likes of Chopin and Scriabin best expressed themselves through small-scale compositions, while, on the other, there were those who, like Wagner and Mahler, produced colossal works. The aim of the present article is to explore the phenomenon of miniaturization in Western culture and to examine how miniature works (e.g., literary fragments, preludes) competed with their much larger counterparts. My central claims are threefold: (...) (1) that miniaturization, contrary to common belief, is not a contemporary phenomenon; (2) that the attitude of Romanticism to size was not paradoxical but rather an attempt to harmonize the fragment and the colossal; and (3) that in contemporary culture, the fragment and the colossal are no longer in harmony with each other. (shrink)

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)

Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a (...) model of all the axioms of Zermelo-Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to G\"odel's constructible universe of sets, which G\"odel famously used to show the relative consistency of the continuum hypothesis. More specifically, our proofs appeal to Kripke and Platek's idea of the projectum within the constructible universe as well as to a weak version of uniformization (which does not involve knowledge of Jensen's fine structure theory). The axioms of the Grundgesetze are examples of abstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension. As an application, we resolve an analogue of the joint consistency problem in the predicative setting. (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)

Posthumous Fragments: Spring–Autumn 1881 [Excerpts].

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)

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)

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)

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)

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)

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)

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)

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.

From Descartes to Popper, philosophers have criticized and tried to improve the strategies of reasoning invoked in science and in everyday life. In recent years leading cognitive psychologists have painted a detailed, controversial, and highly critical portrait of common sense reasoning. Stephen Stich begins with a spirited defense of this work and a critique of those writers who argue that widespread irrationality is a biological or conceptual impossibility.Stich then explores the nature of rationality and irrationality: What is it that distinguishes (...) good reasoning from bad? He rejects the most widely accepted approaches to this question approaches which unpack rationality by appeal to truth, to reflective equilibrium or conceptual analysis. The alternative he defends grows out of the pragmatic tradition in which reasoning is viewed as a cognitive tool. Stich's version of pragmatism leads to a radical epistemic relativism and he argues that the widespread abhorrence of relativism is ill founded. (shrink)

In PHILOSOPHICAL FRAGMENTS, Søren Kierkegaard (writing under the pseudonym Johannes Climacus), seeks to explain the nature of Christianity in such as way as to bring out its demands on the individual, and to emphasize its incompatibility with the theology based on the work of Hegel that was becoming progressively more influential in Denmark. If one were to read only two or three of Kierkegaard's works, this is unquestionably one of the ones to read. One cannot understand Kierkegaard's thought without reading (...) this book, and along with its sequel represents the heart of what he was trying to achieve in what he called his "Authorship." Through PHILOSOPHICAL FRAGMENTS, Kierkegaard purports to present the logic of Christianity. (shrink)

Kris McDaniel argues that there are different ways in which things exist. For instance, past things don't exist in the same way as present things. Numbers don't exist in the same way as physical objects; nor do holes, which are real, but less real than what they are in. McDaniel's theory of being illuminates a wide range of metaphysical topics.

Recordar: To remember; from the Latin re-cordis, to pass back through the heart.Forgetting is not secondary; it is not an improvised failing of what has first been constituted as memory. Forgetfulness is a practice.In his search for a community that does not rely upon the false unities of subjectivity or identity, Maurice Blanchot looks to literature and writing. To achieve the common in community, Blanchot argues for the development of unworking writing practices aimed at the silence anterior to language—a silence (...) that constitutes authentic communication. Instead of abiding by the rules of grammar, Blanchot encourages writers to produce fragments, which constitutes one method of unworking writing. This... (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)

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)

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)

Belief fragments and mental files are based on the same idea: that information in people’s minds is compartmentalized rather than lumped all together. Philosophers mostly use the two notions differently, though the exact relationship between fragments and files has yet to be examined in detail. This chapter has three main goals. The first is to argue that fragments and files, properly understood, play distinct yet complementary explanatory roles; the second is to defend a model of belief that includes them both; (...) and the third is to raise and address a shared dilemma that confronts them: that they threaten to be either explanatorily lightweight or empirically refuted. This chapter contends that it is better to embrace the horn of this dilemma that opens up files and fragments to empirical refutation or confirmation, by adopting a psychofunctionalist approach. (shrink)

Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...) investigates how much of Frege’s Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension. (shrink)

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)

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.

Les Cyniques grecs ne nous ont pas l gu de savants trait s. Leur philosophie, plut t pragmatique, s'exprimait par l'observance d'une vie asc tique franchement marginale. Le lecteur d couvrira dans ces fragments qui leur sont attribu s, dans ces t moignages de contemporains, pr sent s ici dans leur version fran aise, l'univers et l'id al des Cyniques. Le texte de cette nouvelle dition a t enti rement revu par l'auteur. Les recherches effectu es depuis la premi re (...) publication (1975) ont permis de compl ter plusieurs sections et d'y inclure des fragments nouveaux et des traductions r centes. Une bibliographie enti rement r vis e et deux nouveaux index viennent compl ter l'ouvrage. (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)

Hermann Diels, professor of classics at Berlin, is chiefly remembered for this collection of quotations from, and reports about, Presocratic philosophers; his system of numbering was later adopted as the scholarly standard. This reissue reproduces the original, single-volume edition of 1903, though the book was revised and expanded three times during Diels' lifetime, and again after his death, and new fragments continue to be discovered. Designed as a reference tool to underpin university classes on the beginnings of Greek philosophy, the (...) book sought to enable students to engage with original evidence. Diels aimed to provide a complete corpus of fragments rather than an arbitrary selection. He intentionally reproduced the texts exactly rather than standardising the language, in order to provide a foundation for future research. While admitting he found the material obscure at times, Diels provided German translations to help make the content more accessible to his readers. (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)

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).

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)

This paper argues that what is currently the most popular version of temporal Fragmentalism—‘unstructured’ temporal Fragmentalism, as I shall call it—faces a problem of Tensed Belief Explosion. Four possible solutions to this problem are reviewed and shown to be wanting; two more promising ones risk fostering scepticism about the existence of tensed facts—hence, about Fragmentalism itself. The tentative moral is that unstructured versions of Fragmentalism are at best unmotivated and at worst seriously flawed.

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)

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.

This is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic |$FL_{ew}$| (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. |$FL_{ew}$|-algebras) that includes both Heyting and Nelson algebras (...) and can be characterized algebraically in several alternative ways. The present paper focuses on the algebraic counterpart (a class we dub quasi-Nelson implication algebras, QNI-algebras) of the implication–negation fragment of QNL, corresponding to the connectives that witness the algebraizability of QNL. We recall the main known results on QNI-algebras and establish a number of new ones. Among these, we show that QNI-algebras form a congruence-distributive variety (Cor. 3.15) that enjoys equationally definable principal congruences and the strong congruence extension property (Prop. 3.16); we also characterize the subdirectly irreducible QNI-algebras in terms of the underlying poset structure (Thm. 4.23). Most of these results are obtained thanks to twist representations for QNI-algebras, which generalize the known ones for Nelson and quasi-Nelson algebras; we further introduce a Hilbert-style calculus that is algebraizable and has the variety of QNI-algebras as its equivalent algebraic semantics. (shrink)

Fragmentary utterances such as short answers and subsentential XPs without linguistic antecedents are proposed to have fully sentential syntactic structures, subject to ellipsis. Ellipsis in these cases is preceded by A-movement of the fragment to a clause-peripheral position; the combination of movement and ellipsis accounts for a wide range of connectivity and anti-connectivity effects in these structures. Fragment answers furthermore shed light on the nature of islands, and contrast with sluicing in triggering island effects; this is shown to follow from (...) an articulated syntax and the PF theory of islands. Fragments without linguistic antecedents are argued to be compatible with an ellipsis analysis, and do not support direct interpretation approaches to these phenomena. (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)

Both communitarianism and casuistry have sought to restore ethics as a practical science—the former by incorporating various traditions into a shared definition of the common good, the latter by considering the circumstances of each situation through critical reasoning. Mark G. Kuczewski analyzes the origins and methods of these two approaches and forges from them a new unified approach. This approach takes the communitarian notion of the person as its starting point but also relies upon the narrative and analogical tools of (...) case-based reasoning. He separates out the rhetoric that is incongruent with the Aristotelian aspirations of each method to show that the two are complementary, and that consensus can emerge from fragmentation. He then applies his resulting method to three major problems in bioethics: the difficulties that the issue of personal identity poses for advance directives, the role of the family in medical decision making, and the refusal of treatment because of religious beliefs. He analyzes the need to assume a communitarian notion of the person as a starting point for the application of casuistic insights. Combining theoretical, practical, and scholarly insights, this book will be of interest to philosophers, political and social scientists, and bioethicists. (shrink)

The maqālāt of Abū Qāsim al-Balḫī contain several passages devoted to legal theory. The most important source found there is some extracts of K. al-futyā, a legal treatise by al-Ǧāḥiẓ of which until now only fragments remained, containing the criticisms addressed by al-Naẓẓām to the companions of the Prophet. This article provides a translation of these new extracts preceded by a study of the text and its place in the history of legal theory during this formative period of Islamic thought.

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.

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)