In Barnett and Block (J Bus Ethics 88(4):711–716, 2009a), the present authors claim that borrowing short and lending long is fraudulent, and thus ought to be prohibited on legal grounds. Bagus and Howden (J Bus Ethics 90(3):399, 2009) take issue with our ethical analysis. The present paper is our response to these authors; it is an attempt to defend Barnett and Block (J Bus Ethics 88(4):711–716, 2009a) against the very interesting and important, although we believe, erroneous, criticisms of Bagus and (...) Howden (J Bus Ethics 90(3):399, 2009). (shrink)

We stipulate, arguendo, that fractional-reserve-demand deposit banking is per se fraudulent. We ask whether or not time deposit banking can also be illicit, and answer in the positive, if there is a mismatch between the time dimensions of deposits and loans. To wit, if an intermediary borrows short and lends long.

This article introduces and defends the “pathological complexity thesis” as a hypothesis about the evolutionary origins of minimal consciousness, or sentience, that connects the study of animal consciousness closely with work in behavioral ecology and evolutionary biology. I argue that consciousness is an adaptive solution to a design problem that led to the extinction of complex multicellular animal life following the Avalon explosion and that was subsequently solved during the Cambrian explosion. This is the economic trade-off problem of having to (...) deal with a complex body with high degrees of freedom, what I call “pathological complexity.” By modeling the explosion of this computational complexity using the resources of state-based behavioral and life history theory we will be able to provide an evolutionary bottom-up framework to make sense of subjective experience and its function in nature by paying close attention to the ecological lifestyles of different animals. (shrink)

This paper constitutes a radical departure from the existing philosophical literature on models, modeling-practices, and model-based science. I argue that the various entities and practices called 'models' and 'modeling-practices' are too diverse, too context-sensitive, and serve too many scientific purposes and roles, as to allow for a general philosophical analysis. From this recognition an alternative view emerges that I shall dub model anarchism.

This is the fullest existing collection of the texts, for the moment only in Italian translation, with an introduction, notes, general presentation of the texts, various indexes (part of this material is to be found in an attached CD).

On a currently popular reading of Locke, an idea represents its cause, or what God intended to be its cause. Against Martha Bolton and my former self (among others), I argue that Locke cannot hold such a view, since it sins against his epistemology and theory of abstraction. I argue that Locke is committed to a resemblance theory of representation, with the result that ideas of secondary qualities are not representations.

Like their contemporary counterparts, early modern philosophers find themselves in a predicament. On one hand, there are strong reasons to deny that sensations are representations. For there seems to be nothing in the world for them to represent. On the other hand, some sensory representations seem to be required for us to experience bodies. How else could one perceive the boundaries of a body, except by means of different shadings of color? I argue that Nicolas Malebranche offers an extreme -- (...) and ultimately unworkable -- attempt to solve this riddle. Most commentators claim that Malebranche defends an adverbial theory of sensation, according to which a sensation is merely a way in which an act of sensing happens. The adverbial reading is wrong, or so I argue. Once we arrive at a more accurate reading, we shall see that his position is much more strange than is currently thought. Nevertheless, Malebranche’s view is similar to the adverbial theory in one respect, albeit it at a very high level of generality. His view thus inherits two of the main problems that afflict adverbial theories. Although Malebranche fails to solve them, his ingenious attempts to do so are instructive. (shrink)

Are demands for equality motivated by envy? Nietzsche, Freud, Hayek, and Nozick all thought so. Call this the Envy Objection. For egalitarians, the Envy Objection is meant to sting. Many egalitarians have tried to evade the Envy Objection.. But should egalitarians be worried about envy? In this paper, I argue that egalitarians should stop worrying and learn to love envy. I argue that the persistent unwillingness to embrace the Envy Objection is rooted in a common misunderstanding of the nature of (...) the charge, what it reveals, and what can be said in response to it. I develop what Bernard Williams might call a vindicatory genealogy of envy, thereby allowing us to see that envy, rather than undermining egalitarian intuitions, can in fact play a distinct justificatory role (when it is fitting), which undermines the Envy Objection. (shrink)

Eliminativism is a position most readily associated with the eliminative materialism of the Churchlands, denying that there are such things as propositional states. This position has created much controversy, despite the fact that intentionality has long been seen as perhaps the core problem for naturalistic philosophy. There is a more radical interpretation of eliminativism, however, denying not only mental states, such as beliefs and desires, but also intentionality (i.e., aboutness) on a global level. This position traces its contemporary origin back (...) to Quine, but has generally been assumed to undermine naturalism or, worse, to be incoherent by the majority of philosophers who maintain that there clearly are things or mental states that are about others. In a recent paper, Hutto and Satne (2015a) offer an update that tries to revive John Haugeland’s baseball analogy from his influential 1990 review paper The Intentionality All-Stars on the state of the game to argue that the failure of Neo-Cartesians, Neo- Behaviorists, and Neo-Pragmatists should urge us to make them work together to naturalize content and “win the game.” But Hutto and Satne misunderstand what the game is ultimately about. The goal of the Intentionality All-Stars is not to naturalize content against eliminativism but to defend a naturalist “thirdperson” view of the problem against first-person phenomenalists. For this goal, a naturalist defense of global content eliminativism would equally enable them to emerge victorious. Revisiting Haugeland, I will offer my own analysis of the current state of play to argue that global content eliminativism has not received sufficient attention and deserves a more prominent place in the debate than it currently occupies. (shrink)

The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of Hypothetical Syllogism. The improved proof (...) relies upon the semantic claim that conditionals with antecedents irrelevant to the obtaining of an already true consequent are themselves true. Moreover, this semantic insight allows us to provide compelling counterexamples to Hypothetical Syllogism that are resistant to the usual contextualist response. (shrink)

I applaud recent improvements upon previous guidelines for the assessment of pain in non-human species and the application of their framework towards decapod crustaceans. Rather than constituting a mere intermediate solution between the scientific difficulty of settling questions of animal consciousness and the need for a framework for the purposes of animal welfare legislation, I will argue that the longer lists of criteria for animal sentience should make us realize that animal sentience is a multi-dimensional phenomenon that must be studied (...) with a plethora of methods in order to assess its diversity across the tree of life. (shrink)

Wherever I Go the Ministry Follows is an answer to a vision given to Matthew Webster at the young age of fifteen. The book took six years to complete and is a testimony of how God can use the most ordinary people to accomplish extraordinary things through Jesus Christ. It is Matt's prayer that you will be inspired, convicted, and prompted by the Holy Spirit to answer the calling from God to be and act as a chosen generation, a royal (...) priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of Him who hath called you out of darkness into His marvelous light 1 Peter 2:9. The goal of Wherever I Go the Ministry Follows is for you the reader to meditate individually on each chapter and how it relates to surrendering yourself totally to God. This book is short because it is intended to be read slowly and read over and over again. It is an ideal book for a ten or eleven week Bible study. As you read each chapter you are faced with the question, am I taking the gospel everywhere I go? You are challenged to move towards a holy and a righteous lifestyle, to effectively reflect the image of Christ. The amazing thing about Wherever I Go the Ministry Follows is that as you read it you can see how each chapter is intricately woven together to give us the whole picture of what God expects from His people and what God is trying to mold each one of us into. Wherever I Go the Ministry Follows does not shy away from answering the tough questions we face in life like; What is God's will for my life? Is healing for everyone and if so then why am I not healed? Instead of dancing around the issues this book tackles the issues head on. This book is a great book for non-believers, new Christians, and mature Christians alike, because it has something unique to offer each person and it has challenges for all walks with the Lord or for those who currently are not in a personal relationship with Jesus Christ. (shrink)

Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ (...) problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof. (shrink)

This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays (1939) and also how it was later adapted by Kreisel (1950) and Wang (1955) in (...) order to obtain formal undecidability results. A generalization of this method will then be presented whereby Russell’s paradox, a variant of Mirimanoff’s paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems. Some additional observations are then framed relating these results to the unification of the set theoretic and semantic paradoxes, the intensionality of arithmetization (in the sense of Feferman, 1960), and axiomatic theories of truth. (shrink)

Are workers dominated? A recent suite of neo-republican and relational egalitarian philosophers think they are. Suppose they are right; that is, suppose that some workers are governed by an unjust and arbitrary power existing in labour relations, which persists even in the presence of the actual ability to exit. My question is this: does that give us reason to impose restrictions on firms? According to the so-called Efficiency Objection there are relevant trade-offs that need to be considered between the efficiency (...) of firms and the freedom of workers, and upon considering these trade-offs, we should reject workplace democracy. In this paper, I present a dilemma for the Efficiency Objection. I argue that either the Efficiency Objection is justified on moral grounds or non-moral grounds; if the Efficiency Objection is justified on moral grounds, then it fails because efficiency cannot be valued for its own sake (it is only instrumentally good); if the Efficiency Objection is justified on non-moral grounds, then it fails because of the respect that we owe to persons as persons; therefore, the Efficiency Objection fails. (shrink)

Like many others, I see Crump et al. (2022) as a milestone for improving upon previous guidelines and for extending their framework to decapod crustaceans. Their proposal would benefit from a firm evolutionary foundation by adding the comparative measurement of life-history complexity as a ninth criterion for attributing sentience to nonhuman animals.

This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincar\'e to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak K\"onig's (...) Lemma, and (iv) the large-scale intellectual backdrop to arithmetical transfinite recursion in descriptive set theory and its effectivization by Borel, Lusin, Addison, and others. (shrink)

Dorothy Edgington’s work has been at the centre of a range of ongoing debates in philosophical logic, philosophy of mind and language, metaphysics, and epistemology. This work has focused, although by no means exclusively, on the overlapping areas of conditionals, probability, and paradox. In what follows, I briefly sketch some themes from these three areas relevant to Dorothy’s work, highlighting how some of Dorothy’s work and some of the contributions of this volume fit in to these debates.

It is commonly held that the natural numbers sequence 0, 1, 2,... possesses a unique structure. Yet by a well known model theoretic argument, there exist non-standard models of the formal theory which is generally taken to axiomatize all of our practices and intentions pertaining to use of the term “natural number.” Despite the structural similarity of this argument to the influential set theoretic indeterminacy argument based on the downward L ̈owenheim-Skolem theorem, most theorists agree that the number theoretic version (...) does not have skeptical consequences about the reference of “natural number” analogous to the ‘relativity’ Skolem claimed pertains to notions such as “uncountable” and “cardinal.” In this paper I argue that recent proposals by Shapiro, Lavine, McGee and Field which aim to distinguish the number and set theoretic indeterminacy arguments by locating extra-mathematical constraints on the interpretation of our number theoretic vocabulary are inadequate. I then suggest that if we consider the manner in which the natural numbers figure in our computational practices – e.g. in characterizing how we compute sums and products or determine prime factorizations – it follows that our application of computational terms such as “computable function” and “tractable computational problem” indirectly uniquely determines their structure. (shrink)

Interpretation is an institutional activity and that may be the most significant fact about it; we are, indeed, a profession, and as such we train students to think about literature in certain ways. Membership in the community is determined by how well one masters the rules of the game. These inescapable facts may be the source of our greatest problems—or their hidden solution. Stanley Fish champions the latter alternative, arguing, in his most recent book, that “the interpretive community” is the (...) ultimate principle of authority in criticism and is capable of resolving all the problems of interpretation.1 If we want to know what reading is, how texts achieve determinate meaning, what constitutes validity in interpretation, or how to resolve the “conflict of interpretations,” we must, Fish argues, focus on the community itself, for it is here alone that these matters are determined.Though he has had more than his share of professional attention, having developed this argument makes Fish’s work worthy of further consideration. He quite simply presents the best picture we are likely to get of the “mind” of the profession, and, in treating him at length here, I am primarily concerned with his representative status. His great achievement is to have articulated the assumptions and beliefs underlying the practices that are favored in our profession: the tacit theoretical position composed of ideas and commonplaces that are so deeply held and constantly in use that they “prestructure” both our dealings with literature and our debates over those dealings. While remaining for the most part “unconscious,” these ideas nevertheless function as self-evident and unassailable truths. If we are to move, as I think we must, toward experiencing a crisis in our discipline, we first have to know where we are. And for that, Fish is invaluable because he has set out to become the official spokesman and efender of the profession. Walter A. Davis, associate professor of English at the Ohio State University, is the author of The Act of Interpretation: A Critique of Literary Reason. The present essay is from a recently completed work on contemporary criticism. He is currently writing a book on modern American drama. (shrink)

Fish has always been adept at revising his position to incorporate what he’s learned from his critics while repaying the favor by assigning them a position they never took. The latter practice naturally helps conceal the borrowings, but as Fish’s position evolves it becomes progressively difficult to determine who is the author of his essays. I am, of course, gratified to see how much Fish has learned from me. It is salutary to find that Fish is finally just a humble (...) historian working with others at “recovering a system of thought and feeling” that will enable us to establish the historical context of Milton’s most probable intentions and realizing, as many historians of literature don’t, that we can only do so by bringing concepts provided by literary theory—form, function, artistic purpose, and so forth—to bear on the mass of historical materials at our disposal.3 It is also gratifying to see that Fish has discovered the law of context and now realizes that there are no local matters. Had he discovered that earlier, we’d have been spared Aunt Tilly and the discussion of Mr. Collins—as well as the general notion extrapolated from those examples that anything a sizable group decides to do will fly since nothing else constraints interpretation. We’d also have been spared the concepts of reading and affective criticism presented in Fish’s early work and the unchecked linguistic hijinks used to sustain those readings. I derive my deepest pleasure, however, from finding that Fish has finally discovered the conflict of interpretations proper and its primacy—“the resistance offered by one interpretively produced shape to the production of another” —though I must sadly abridge this progress report by noting that he finds himself powerless to do anything with this recognition. That is as it must be, for the most interesting thing about Fish’s borrowings is where he stops—and why he has to. Having let me write the first 5 ½ pages of his reply, he suddenly stops taking dictation so that he can simply reassert, in all its abstract glory, his tried-and-true resolution of all interpretive controversy by community interest. Had he read further, he would have discovered that a good deal more emerges if one attempts to preserve and deal with the conflict of interpretations rather than to do away with it. He would even have discovered my epistemology and would have learned the main lesson—that his position is not an alternative to mine but an early moment it contains and sublates in a larger context.Have taught Fish so much, I found myself, instead, poorly repaid by the position he foists upon me. Constantly caught up in an effort to reiterate the dichotomy on which his entire theorizing depends, Fish’s fixed need is to rework all disputes into an opposition between the party of independent fact-disinterested reason and the party of interest so that he might triumphantly resolve all difficulties by once again discovering the simple fact of interests. Lest this strategy hide behind a common misconception, our debate is not a case where distinct frameworks are simply misreading one another, as they must, but one where one framework must deliberately and seriously misread others since it has no other way to sustain itself. If the account Fish gives of my argument is the way things must look from his framework, all that this fact signifies is the paucity of his framework and its inability to achieve even minimal descriptive adequacy. 3. But even here things are a good deal more complex than Fish imagines. For a good statement of the logic and problems of historical interpretation, see Robert Marsh, “Historical Interpretation and the History of Criticism,” in Literary Criticism and Historical Understanding, ed. Philip Damon , pp. 1-24. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Democracy, Spirit, and RevitalizationWalter B. Gulick (bio)The assumptions of democracy as an associational ethos of vulnerable life are, first, that we don't already know how best to order our common life and, second, that we don't know what the abstract ideals of empathy, emancipation, and equity entail in the concrete.—Michael Hogue1In American Immanence: Democracy for an Uncertain World, Michael S. Hogue grounds his proposal for a political theology in (...) a critique of American exceptionalism and its supportive "redeemer symbolic."2 In the Anthropocene era, Hogue states, American exceptionalism "legitimates the extraction of diverse forms of value and justifies the externalization of diverse costs" (29) with unconscionable costs to the natural environment and international justice. As indicated in the passage quoted above, Hogue's reaction to the rigid assumptions supportive of American exceptionalism is to offer a humble acknowledgement of political fallibility coupled with what he terms "a theopolitics of resilient democracy" (184; see also 3–6).My concern in this essay is largely practical. I will focus on discerning what intellectual, emotional, and communal resources might be drawn upon to further develop and actually effect the needed changes that Hogue so ably points out. Relatedly, I will inquire into who the most likely candidates are to devote energy to the reconstruction of social structures and practices so that they express values that Americans at their best uphold. Finally, I will reflect upon the role that spiritual ideals and communal practices might play in energizing effective democratic action. [End Page 5]I. Hogue's Critical and Constructive TasksHogue's overriding interest is to outline an epistemic/axiological/environmental/political stance that does not give rise to the various sorts of injustices and dysfunctions that mark the Anthropocene era, especially our allegiance to policies that eventuate in what he calls "climate wickedness." The alternative vision he embraces develops pragmatic naturalism as a method of inquiry and exposition. His reflections are especially indebted to the thought of Dewey, James, and Whitehead (78–82). During a time when e-words are normally associated with forms of electronic communication, Hogue offers instead two trios of e-words with another sort of significance—one that signifies a stance he wishes to overcome and one that communicates what he hopes to achieve. Our current era is unfortunately in thrall, he says, to extraction, externalization, and exception, whereas what we should strive for is a society marked by empathy, emancipation, and equitability. Well put. He presupposes that democratic governance, deeply embedded in American history, ought to serve as the vehicle for achieving what the positive set of e-words promotes. To this end, Hogue quotes appreciatively from Dewey's article, "Democracy is Radical": Democracy "is radical because it requires great change in existing social institutions, economic, legal and cultural" (170). This understanding of democracy slumbers now; what might it take to reawaken it? And if reawakened, what changes might be made to establish the more nearly equitable political influence that is basic to the promise of democracy?Hogue, recognizing in good pragmatic fashion the importance of consequential change, states, "In contrast to foundationalist commitments to antecedents and precedents, pragmatic naturalism commits to a prospective concern with consequents" (80). Foundational commitments to antecedents may certainly impede needed change, but surely attention to the historical events and practices that gave rise to current problems is needed to avoid repeating previous errors. Hogue refers to Whitehead's vision of social symbolism, suggesting that "social change can be catalyzed by the improvised revision of existing symbolic repertoires or the innovative formation or subversive interjection of new symbols" (99). I'm not fully convinced by Whitehead's claim. I suspect that many of our social problems are rooted below the linguistic level in an array of affective issues that elude symbolic adjustment. New strategies are needed to counter the prevalence of fear and resentment in society as promoted for political and commercial reasons and tied to Hogue's strongly voiced recognition that we live in an uncertain world.Here is my understanding of how Hogue both frames our current social and cultural situation and what he says might begin to remediate these circumstances. [End Page... (shrink)

The Paradox of the Knower was originally presented by Kaplan and Montague [26] as a puzzle about the everyday notion of knowledge in the face of self-reference. The paradox shows that any theory extending Robinson arithmetic with a predicate K satisfying the factivity axiom K → A as well as a few other epistemically plausible principles is inconsistent. After surveying the background of the paradox, we will focus on a recent debate about the role of epistemic closure principles in the (...) Knower. We will suggest this debate sheds new light on the concept of knowledge which is at issue in the paradox – i.e. is it a “thin” notion divorced from concepts such as evidence or justification, or is it a “thick” notion more closely resembling mathematical provability? We will argue that a number of features of the paradox suggest that the latter option is more plausible. Along the way, we will provide a reconstruction of the paradox using a quantified extension of Artemovʼs [2] Logic of Proofs, as well as a series of results linking the original formulation of the paradox to reflection principles for formal arithmetic. On this basis, we will argue that while the Knower can be understood to motivate a distinction between levels of knowledge, it does not provide a rationale for recognizing a uniform hierarchy of knowledge predicates in the manner suggested by Anderson. (shrink)

Behavior, language, development, identity, and science—all of these phenomena are commonly characterized as 'social' in nature. But what does it mean to be 'social'? Is there any intrinsic 'mark' of the social shared by these phenomena? In the first book to shed light on this foundational question, twelve distinguished philosophers and social scientists from several disciplines debate the mark of the social. Their varied answers will be of interest to sociologists, anthropologists, philosophers, psychologists, and anyone interested in the theoretical foundations (...) of the social sciences. (shrink)

They envisioned a brave new world, and what they got was fascism. As vibrant as its counterparts in Paris, Munich, and Milan, the avant-garde of Florence rose on a wave of artistic, political, and social idealism that swept the world with the arrival of the twentieth century. How the movement flourished in its first heady years, only to flounder in the bloody wake of World War I, is a fascinating story, told here for the first time. It is the history (...) of a whole generation's extraordinary promise--and equally extraordinary failure. The "decadentism" of D'Annunzio, the philosophical ideals of Croce and Gentile, the politics of Italian socialism: all these strains flowed together to buoy the emerging avant-garde in Florence. Walter Adamson shows us the young artists and writers caught up in the intellectual ferment of their time, among them the poet Giovanni Papini, the painter Ardengo Soffici, and the cultural critic Giuseppe Prezzolini. He depicts a generation rejecting provincialism, seeking spiritual freedom in Paris, and ultimately blending the modernist style found there with their own sense of toscanità or "being Tuscan." In their journals--Leonardo, La Voce, Lacerba, and l'Italia futurista--and in their cafe life at the Giubbe Rosse, we see the avant-garde of Florence as citizens of an intellectual world peopled by the likes of Picasso, Bergson, Sorel, Unamuno, Pareto, Weininger, and William James. We witness their mounting commitment to the ideals of regenerative violence and watch their existence become increasingly frenzied as war approaches. Finally, Adamson shows us the ultimate betrayal of the movement's aspirations as its cultural politics help catapult Italy into war and prepare the way for Mussolini's rise to power. (shrink)

This dissertation addresses a variety of foundational issues pertaining to the notion of algorithm employed in mathematics and computer science. In these settings, an algorithm is taken to be an effective mathematical procedure for solving a previously stated mathematical problem. Procedures of this sort comprise the notional subject matter of the subfield of computer science known as algorithmic analysis. In this context, algorithms are referred to via proper names of which computational properties are directly predicated )). Moreover, many formal results (...) are traditionally stated by explicitly quantifying over algorithms. These observations motivate the view that algorithms are themselves abstract mathematical objects -- a view I refer to as algorithmic realism. The status of this view is clearly related to that of Church's Thesis -- i.e. the claim that a function is computable by an algorithm just in case it is partial recursive. But whereas Church's Thesis is widely accepted on the basis of several well-known mathematical analyses of algorithmic computability, there is presently no consensus on how we can uniformly identify individual algorithms with mathematical objects. In the first chapter of this work, I attempt to illustrate the theoretical significance of algorithmic realism. I suggest that this view is not only of foundational significance to computer science, but also worth highlighting due to the role algorithms play in the fixation of mathematical knowledge and their relationship to intensional entities such as propositions and properties. Chapter Two presents a formal framework for reducing computational discourse to mathematical discourse modeled on contemporary discussion of mathematical nominalism. Chapter Three is centered on a case study intended to illustrate the technical exigencies involved with defending algorithmic realism. Chapter Four explores various ways in which algorithms might be identified with models of computation. And finally, Chapter Five argues that no such identification can uniformly satisfy all statements of algorithmic identity and non-identity affirmed by computational practice. I suggest that the technical crux of algorithmic realism lies in the necessity of reducing recursive specifications of algorithms to iterative models of computation in a manner which preserves algorithmic identity. (shrink)

This short autobiographical text evokes the atmosphere of the years which marked the beginning of my friendship with Alexandru Dragomir: i.e. our student years in Bucharest, the circle of Romanian students studying in the 40s in Freiburg i. Br. and the intellectual intensity of Martin Heidegger’s seminars and courses, which influenced both of us for the rest of our lives. From the 15 members of Heidegger’s Oberseminar (dedicated in this period to Hegel’s Phenomenology of Spirit), three were from Romania: Alexandru (...) Dragomir, Octavian Vuia and the author of these lines. The relationship between Dragomir and I became closer as we translated “Was ist Metaphysik?” into Romanian. Alexandru Dragomir was highly appreciated by Heidegger and beloved by other students for his penetrating spirit, for his spontaneity, but also for his sense of humor. After more than 30 years in which the history thrown us in parallel worlds, we had the joy to meet again in Bucharest. His texts, now published, present him as a brilliant and original thinker. (shrink)