This article discusses the thesis that a subject can have a concept, think thoughts containing it, that she incompletely understands. The central question concerns how to construe the distinction between having a concept and understanding it. Two important versions of the thesis are distinguished: a metasemantic version and an epistemic version. According to the first, the subject may have concept C without being a fully competent user, in virtue of deference to other speakers or to the world. According to (...) the second, the subject may have a concept without being able to provide a proper explication of it. It is argued that whereas the epistemic version is plausible, the metasemantic version faces some challenges. First, it needs to be explained precisely how deference enables a speaker to have C. Second, metasemantic incomplete understanding is in tension with the idea that concepts serve to capture the subject’s cognitive perspective. (shrink)

Many philosophers have discussed the ability of thinkers to think thoughts that the thinker cannot justify because the thoughts involve concepts that the thinker incompletely understands. A standard example of this phenomenon involves the concept of the derivative in the early days of the calculus: Newton and Leibniz incompletely understood the derivative concept and, hence, as Berkeley noted, they could not justify their thoughts involving it. Later, Weierstrass justified their thoughts by giving a correct explication of the derivative concept. This (...) paper discusses various accounts of how a thinker manages to think with a concept that they incompletely understand and finds them wanting in the case at hand. Part of the overlooked complexity is that there are many derivative concepts, and it is unclear in virtue of what a thinker would be thinking with one of them rather than another. After critical evaluation of standard accounts, this paper suggests a novel account of how one should think about the derivative concepts with which Newton and Leibniz thought and how Weierstrass could have managed to justify their thoughts even if their thoughts did not involve the same derivative concept as Weierstrass’s. (shrink)

Frege seems committed to the thesis that the senses of the fundamental notions of arithmetic remain stable and are stably grasped by thinkers throughout history. Fully competent practitioners grasp those senses clearly and distinctly, while uncertain practitioners see them, the very same senses, “as if through a mist”. There is thus a common object of the understanding apprehended to a greater or lesser degree by thinkers of diverging conceptual competence. Frege takes the thesis to be a condition for the (...) possibility of the rational intelligibility of mathematical practice. I argue however that the idea that senses could be grasped as a matter of degree is in tension with the constitutive theses that Frege held with regard to sense. Given those theses, there can in fact be no such thing as misty grasp of sense, since any uncertainty as to the logical features of a given sense will entail that one is getting hold of a different sense or of no sense at all. I consider various ways of resolving the tension and conclude that Frege’s thesis cannot be defended if we take it to be a thesis about our competence with concepts. This leaves unresolved what I call the problem of normative guidance, that is, the problem of explaining how the fundamental notions of logic and arithmetic can provide inferential guidance to thinkers. (shrink)

Tyler Burge’s influential arguments have convinced most philosophers that a thinker can have a thought involving a particular concept without fully grasping or having mastery of that concept. In Burge’s (1979) famous example, a thinker who lacks mastery of the concept of arthritis nonetheless has thoughts involving that concept. It is generally supposed, however, that this phenomenon – incomplete understanding, for short – does not require us to reconsider in a fundamental way what it is for a thought (...) to involve a particular concept. In this paper, I argue that the real significance of incomplete understanding has not been appreciated. To the extent that theorists of content address the phenomenon of thoughts involving incompletely grasped contents at all, they tend to assume that some hand-waving about deference to other thinkers who fully grasp the relevant concepts will take care of the inconvenient cases of incomplete understanding. The main lesson of Burge’s arguments is often taken to be that the content of language and thought is socially determined. On this picture, we do not need to change our basic view about what it is to have a concept; we just need to recognize that some thinkers can manage to have a concept by piggybacking on others. In contrast, on the view I defend, taking incomplete understanding seriously forces us to rethink some of our most basic assumptions about the nature of mental content. Deference is a red herring. The role of society in determining the content of thought is not the main lesson, but at most a useful clue as to the nature of mental and linguistic content. (shrink)

Sarah Sawyer has challenged my claim that social externalism depends on the assumption that individuals have an incomplete grasp of their own concepts. Sawyer denies that Burge's later sofa thought-experiment relies on this assumption: the unifying principle behind the thought-experiments supporting social externalism, she argues, is just that referents play a role in the individuation of concepts. I argue that Sawyer fails to show that social externalism need not rely on the assumption of incomplete understanding. To establish (...) the content externalist conclusions, further considerations are required, and these do commit the externalist to the assumption of incomplete understanding. (shrink)

Burge famously argued that one can have thoughts involving a concept C even if one’s understanding of C is incomplete. Even though this view has been extremely influential, it has also been taken by critics as less than clear. The aim of this paper is to show that the cases imagined by Burge as being ones in which incomplete understanding of concepts is involved can be made clearer given an account of direct concept ascriptions—such as “Peter (...) has the concept of arthritis”—according to which these ascriptions are to be analysed in terms of ascriptions of the knowledge of what something is. The upshot is that the cases imagined by Burge can be explained is terms of the idea of subjects knowing in part what something is. (shrink)

In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary (...) and sufficient for possession of mathematical concepts will always face counterexamples of the kind illustrated by Cardano. I close by suggesting that we should rely more heavily on resources of Anti-Individualism as a framework for understanding the acquisition and possession of concepts of abstract subject matters. (shrink)

It is often thought that acquiring a phenomenal concept requires having the relevant sort of experience. In "Extending Phenomenal Concepts", Andreas Elpidorou defends this position from an objection raised by Michael Tye (in "Consciousness Revisited: Materialism without Phenomenal Concepts"). Here, I argue that Elpidorou fails to attend to important supporting materials introduced by Tye.

Cesario argues that experimental studies of bias tell us little about why group disparities exist. We argue that Cesario's alternative approach implicitly frames understanding of group disparities as a false binary between “bias” and “group differences.” This, we suggest, will contribute little to our understanding of the complex dynamics that produce group disparities, and risks inappropriately rationalizing them.

Incomplete penetrance and variable expressivity are non‐Mendelian phenomena resulting in the lack of correlation between genotype and phenotype. Not withstanding the diversity in mechanisms, differential expression of homologous alleles within cells manifests as variations in penetrance and expressivity of mutations between individuals of the same genotype. These phenomena are seen most often in dominantly inherited diseases, implying that they are sensitive to concentration of the gene product. In this framework and the advances in understanding the role of microRNA (...) (miRNA) in fine‐tuning gene expression at translational level, we propose miRNA‐mediated regulation as a mechanism for incomplete penetrance and variable expressivity. The presence of miRNA binding sites at 3′ UTR, co‐expression of target gene–miRNA pairs for genes showing incomplete penetrance and variable expressivity derived from available data lend support to our hypothesis. Single nucleotide polymorphisms in the miRNA target site facilitate the implied differential targeting of the transcripts from homologous alleles. (shrink)

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP ≠ coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to be (...) special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences. -/- We have introduced the most fundamental conjectures in our earlier works. Our aim in this article is to present them in a more systematic way, along with several new conjectures, and prove new connections between them and some other statements studied before. (shrink)

I argue that Bartolomé de las Casas and Juan Ginés de Sepúlveda differed in their conclusions regarding the status of Indigenous persons at least partly because las Casas had significant, yet incomplete, understanding of Indigenous persons, culture and societies and Sepúlveda had mere knowledge of them. To this end, I show that the epistemic state of understanding explains why Las Casas properly concluded that Indigenous persons deserve the same moral status afforded to Europeans. And I show how (...) las Casas’ understanding of Indigenous persons, culture and societies related to what he got wrong about Indigenous persons. (shrink)

Using video recordings of draft meetings conducted as part of an intramural basketball program as data, this conversation analytic study examines the use of an incomplete utterance in a joint evaluative activity. In particular, we focus on how the participants, volunteer coaches, who meet to draft players for their respective teams, produce a syntactically incomplete utterance as a means to critically assess a player, a non-present third party to the interaction. Analysis reveals that the participants use an (...) class='Hi'>incomplete utterance as part of dispreferred design; it allows them to withhold articulating overt criticism of others. By trailing off where the criticism is due, the participants display reluctance to verbalize what is to be said and treat its articulation as delicate. The syntactic structure of the utterance that includes a contrastive conjunction and accompanying embodied actions such as head shakes help them convey a critical stance. We examine the use of incomplete utterances in both agreement and disagreement sequences; the recipients display their unproblematic understanding of the critical assessment and respond by providing their own assessments that either affiliate or disaffiliate with the conveyed critical stance. (shrink)

Incomplete Archaeologies takes a familiar archaeological concept--assemblages--and reconsiders such groupings, collections and sets of things from the perspective of the work required to assemble them. The discussions presented here engage with the practices of collection, construction, performance and creation in the past (and present) which constitute the things and groups of things studied by archaeologists--and examine as well how these things and thing-groups are dismantled, rearranged, and even destroyed, only to be rebuilt and recreated. The ultimate aim is to (...) reassert an awareness of the incompleteness of assemblage, and thus the importance of practices of assembling (whether they seem at first creative or destructive) for understanding social life in the past as well as the present. The individual chapters represent critical engagements with this aim by archaeologists presenting a broad scope of case studies from Eurasia and the Mediterranean. Case studies include discussions of mortuary practice from numerous angles, the sociopolitics of metallurgy, human-animal relationships, landscape and memory, the assembly of political subjectivity and the curation of sovereignty. These studies emphasise the incomplete and ongoing nature of social action in the past, and stress the critical significance of a deeper understanding of formation processes as well as contextual archaeologies to practices of archaeology, museology, art history, and other related disciplines. Contributors challenge archaeologists and others to think past the objects in the assemblage to the practices of assembling, enabling us to consider not only plural modes of interacting with and perceiving things, spaces, human bodies and temporalities in the past, but also to perhaps discover alternate modes of framing these interactions and relationships in our analyses. Ultimately then, Incomplete Archaeologies takes aim at the perceived totality not only of assemblages of artefacts on shelves and desks, but also that of some of archaeology's seeming-seamless epistemological objects"--From publisher's website. (shrink)

Incomplete Archaeologies takes a familiar archaeological concept--assemblages--and reconsiders such groupings, collections and sets of things from the perspective of the work required to assemble them. The discussions presented here engage with the practices of collection, construction, performance and creation in the past (and present) which constitute the things and groups of things studied by archaeologists--and examine as well how these things and thing-groups are dismantled, rearranged, and even destroyed, only to be rebuilt and recreated. The ultimate aim is to (...) reassert an awareness of the incompleteness of assemblage, and thus the importance of practices of assembling (whether they seem at first creative or destructive) for understanding social life in the past as well as the present. The individual chapters represent critical engagements with this aim by archaeologists presenting a broad scope of case studies from Eurasia and the Mediterranean. Case studies include discussions of mortuary practice from numerous angles, the sociopolitics of metallurgy, human-animal relationships, landscape and memory, the assembly of political subjectivity and the curation of sovereignty. These studies emphasise the incomplete and ongoing nature of social action in the past, and stress the critical significance of a deeper understanding of formation processes as well as contextual archaeologies to practices of archaeology, museology, art history, and other related disciplines. Contributors challenge archaeologists and others to think past the objects in the assemblage to the practices of assembling, enabling us to consider not only plural modes of interacting with and perceiving things, spaces, human bodies and temporalities in the past, but also to perhaps discover alternate modes of framing these interactions and relationships in our analyses. Ultimately then, Incomplete Archaeologies takes aim at the perceived totality not only of assemblages of artefacts on shelves and desks, but also that of some of archaeology's seeming-seamless epistemological objects"--From publisher's website. (shrink)

Although G¨odel proved the first incompleteness theorem by intuitionistically respectable means, G¨odel’s formula, true although undecidable,seems to offer a counter-example to the general constructivist or anti-realistclaim that truth may not transcend recognizability in principle. It is arguedhere that our understanding of the formula consists in a knowledge of itstruth-conditions, that it is true in a minimal sense and, finally, that it is recognized as such given the consistencyand ω-consistency of P. The philosophical lesson to be drawn from G¨odel’sproof is (...) that our capacities for justification in favour of minimal truth exceedwhat is strictly speaking formally provable in P by means of an algorithm. (shrink)

A teaching document I've used in my courses on truth and on incompleteness. Aimed at students who have a good grasp of basic logic, and decent math skills, it attempts to give them the background they need to understand a proper statement of the classic results due to Gödel and Tarski, and sketches their proofs. Topics covered include the notions of language and theory, the basics of formal syntax and arithmetization, formal arithmetic (Q and PA), representability, diagonalization, and the incompleteness (...) and undefinability theorems. (shrink)

Russell urged that some phrases having no meaning in isolation could nonetheless, Contribute to the meaning of sentences in which they occur. In the case of definite descriptive phrases, A proof is offered. It is argued that russell's proof is valid, Contrary to some commentators. Proper understanding of the notion of "incomplete symbol" plays a key role in the assessment of the argument, As well as in full appreciation of the radical departure of russell's analysis from "surface" grammar.

Early in Principia Mathematica Russell presents an argument that "‘the author of Waverley’ means nothing", an argument that he calls a "definite proof". He generalizes it to claim that definite descriptions are incomplete symbols having meaning only in sentential context. This Principia "proof" went largely unnoticed until Russell reaffirmed a near-identical "proof" in his philosophical autobiography nearly 50 years later. The "proof" is important, not only because it grounds our understanding of incomplete symbols in the Principia programme, (...) but also because failure to understand it fully has been a source of much unjustified criticism of Russell to the effect that he was wedded to a naive theory of meaning and prone to carelessness and confusion in his philosophy of logic and language generally. In my paper, I (1) defend Russell’s "proof" against attacks from several sources over the last half century, (2) examine the implications of the "proof" for understanding Russell’s treatment of class symbols in Principia, and (3) see how the Principia notion of incomplete symbol was carried forward into Russell’s conception of philosophical analysis as it developed in his logical atomist period after 1910. (shrink)

Robert M. Adams claims that Leibniz’s rehabilitation of the doctrine of incomplete entities is the most sustained effort to integrate a theory of corporeal substances into the theory of simple substances. I discuss alternative interpretations of the theory of incomplete entities suggested by Marleen Rozemond and Pauline Phemister. Against Rozemond, I argue that the scholastic doctrine of incomplete entities is not dependent on a hylomorphic analysis of corporeal substances, and therefore can be adapted by Leibniz. Against Phemister, (...) I claim that Leibniz did not reduce the passivity of corporeal substances to modifications of passive aspects of simple substances. Against Adams, I argue that Leibniz’s theory of the incompleteness of the mind cannot be understood adequately without understanding the reasons for his assertion that matter is incomplete without minds. Composite substances are seen as requisites for the reality of the material world, and therefore cannot be eliminated from Leibniz’s metaphysics. (shrink)

Why these notes? After all, I’ve written An Introduction to Gödel’s Theorems. Surely that’s more than enough to be going on with? Ah, but there’s the snag. It is more than enough. In the writing, as is the way with these things, the book grew far beyond the scope of the lecture notes from which it started. And while I hope the result is still pretty accessible to someone prepared to put in the time and effort, there’s a lot more (...) in the book than is really needed by philosophers meeting the incompleteness theorems for the first time. After all, you might want to get your heads around only those technical basics which are actually needed for understanding philosophical discussions about incompleteness. So you need a cut-down version of the book – an introduction to the Introduction! Well, isn’t that what lectures are for? Indeed. But there’s another snag. I haven’t got many lectures to play with. So either I crack on at quite a fast pace, cover those basics, but perhaps leave too many people puzzled and alarmed. Or I do relaxed talk’n’chalk, highlighting the really Big Ideas, making sure everyone is grasping them as we go along, but inevitably omit important stuff and leave quite a gap between what happens in the lectures and what happens in the book. What to do? I’m going for plan. But then I still need to do something to fill that gap between lectures and book. Hence these notes. The idea, then, is to give relaxed lectures, highlighting Big Ideas, not worrying too much about depth or fine-detail. Then after the lecture, I’ll write up notes that expand things just enough, and then give pointers to relevant chunks of IGT. The idea, however, is for the notes to be more or less stand-alone, and to tell a brief but coherent story read by themselves. So occasionally I’ll copy a paragraph or two from the book, rather than just refer to them. Warning: just occasionally in these notes, I’ll no doubt apply that good maxim ‘Where it doesn’t itch, don’t scratch’. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Thomas G. Pavel INCOMPLETE WORLDS, RITUAL EMOTIONS' IN recent years, the notion of "fictional world" has enjoyed a considerable rise in fortune. The expression, however, is not entirely new. To refer to the world of a literary work, of a novel or of a play, has always been a favorite way of speaking for literary critics and aestheticians. In most cases, these were informal worlds. A discussion of (...) the world of Balzac, Dostoyevsky, HenryJames, or Proust often amounts to a description of each author's preferences in die selection and rearrangement of his material. Such discussion primarily fits authors who purposefully attempt to build comprehensive representational artifacts. One speaks quite naturally about l'univers balzacien, or about the universe of Musil. But is one entitled to refer with equal ease to the world ofBenjamin Constant, meagerly perceptible in his Adolphe, a short novel built in the spirit of economy, displaying just a few characters and a minimum of worldly information? Perhaps density and comprehensiveness are not indispensable characteristics of literary worlds. Aestheticians and narratologists using the "fictional worlds" terminology seem to believe mat any kind of artistic text projects a world, be it rich or poor. Such worlds are imagined in the fashion of modern philosophy of logic as states of affairs, more or less comprehensive. Some writers believe that the states of affairs comprised in fictional worlds must be fairly sizable, since diey should include "not only what the author indicates, but also whatever is required (entailed) by that which he indicates." 1 The laws of nature which are not specifically contradicted by the text would belong to its world. Thus, a few notorious cases aside, there is no reason to doubt that every child born in fiction has been engendered by a human fadier as long as the text does not report an exception. And if it does? Then, assuming that the laws of logic still govern if not fiction itself at least our understanding of it, we may appeal to what "possible world" philosophers have called "small miracles." * Editor's note: This article, as well as the contributions by Gerald Prince, Peter van Inwagen, and Kendall Walton which follow it, grew out ofa symposium on "Styles ofFictionality," organized by Professor Pavel and held at Harvard University in 1981. The Fall, 1983 issue of PHILOSOPHY AND LITERATURE will contain additional papers presented at the symposium. 48 Thomas G. Pavel49 Imagine, for instance, the world in which Notre Dame de Paris would be covered with blue paint. While everything else would preserve the properties it possesses in the actual world, with the laws of nature and the caused chains maintained, a small local change, somewhat miraculous, would modify only the color of the venerable building. Similarly, the world of Balzac may be understood as the world of early and mid-nineteenth-century France, slightly modified by the addition of a few hundred imagined characters. That diese conform surprisingly well to the general laws of French society of the time is so much the goal of Balzac's successful project, that for the sociologically-minded reader die' actual nonexistence of Rastignac, Rubempré, Vautrin, or Birotteau may appear a mere accident. These characters, one may surmise, display every trait that actual counterparts of theirs would possess, except existence. Hence, why would Rastignac's or Vautrin's emergence in a world omerwise identical to nineteenth-century France amount to anydiing more than a "small miracle"? On the other hand, Balzac's world being blessed wim hundreds of such miracles, the very magnitude of the project vindicates the attribute of "visionary," ascribed to Balzac by Béguin, or, if metaphorically undercut, mat of"God the Father" given him by Thibaudet. For, would not such magnitude entail more than just local changes in an otherwise faithful representation of the "actual" nineteenthcentury France? Similarly, would we interpret a fictional world in which a child has been engendered not by a human father, but by a divinity, as identical in all respects to the actual world, except for the limited modification attributed to a small miracle? 2 If we grant for a moment the improbable assumption that nineteenth-century France was a given and that Balzac... (shrink)

Elizabeth Prior claims that dispositional predicates are incomplete in the sense that they have more than one argument place. To back up this claim, she offers a number of arguments that involve such ordinary dispositional predicates as ‘fragile’, ‘soluble’, and so on. In this paper, I will first demonstrate that one of Prior’s arguments that ‘is fragile’ is an incomplete predicate is mistaken. This, however, does not immediately mean that Prior is wrong that ‘fragile’ is an incomplete (...) predicate. On the contrary, I maintain that she has offered another valid argument that does indeed establish the claim that ‘fragile’ is an incomplete predicate. I will argue further that Prior is right that ‘soluble’ is an incomplete predicate. Then does this mean that all dispositional predicates are incomplete? I don’t think so. I will suggest that there are complete dispositional predicates that have no more than one argument place. Finally, by relying on my discussion of the incompleteness of dispositional predicates, I will attempt to provide a better understanding of the context-dependence and intrinsic nature of dispositional ascriptions. (shrink)

ABSTRACT In this paper, we show that Kant’s complex concept of an “intuitive understanding”, which operates in his work as a tool for defining the peculiar character of our understanding, is critically absorbed by Hegel’s concept of “objective thought.” By means of this concept, Hegel first rejects the representational conception of thought that is implied by the Kantian concept of an intuitive understanding and, second, he proposes a way of comprehending thought that allows a new conception of (...) the relationship between the subject and reality. (shrink)

Luck egalitarianism makes a fundamental distinction between inequalities for which agents are responsible and inequalities stemming from luck. I give several reasons to find luck egalitarianism a compelling view of distributive justice. I then argue that it is an incomplete theory of equality. Luck egalitarianism lacks the normative resources to achieve its ends. It is unable to specify the prior conditions under which persons are situated equivalently such that their choices can bear this tremendous weight. This means that luck (...) egalitarians need to become pluralists who understand equality not merely in terms of choice, luck, and responsibility. After developing my critical argument that luck egalitarianism is incomplete, I sketch a strategy for rehabilitating and filling out the theory. (shrink)

Berto’s highly readable and lucid guide introduces students and the interested reader to Gödel’s celebrated _Incompleteness Theorem_, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the _Theorem_ in separate chapters Discusses interpretations of the _Theorem_ made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel’s theories Written in an accessible, (...) non-technical style. (shrink)

Can one give an account of a perfectly just society without invoking principles governing our responses to injustice? My claim is that addressing this question puts us in a position to reveal ambiguities and problems with the way in which Rawls draws the ideal/nonideal theory distinction that have so far gone unnoticed. In the first part of my paper, I demonstrate that Rawls’s original definition of the ideal/nonideal theory distinction is ambiguous as it is composed of two different conceptual distinctions, (...) before clarifying the distinctions involved, paying particular attention to the unfamiliar distinction between primary and secondary principles. I then show that we can best account for what Rawls is actually doing at the level of ideal and nonideal theory by invoking this distinction between primary and secondary principles. This result sets the stage for my argument in the second part. I first explain why Rawls does not have access to an understanding of the strict compliance condition that can account for the irrelevance of secondary principles for a complete account of the principles regulating a perfectly just basic structure. I then point out that there is a tension between what Rawls claims to be doing at the level of ideal theory and what he is actually doing at the level of ideal theory. On this basis, I argue that Rawls’s ideal conceptions of justice are incomplete because they do not encompass secondary principles. The Conclusion unpacks the contributions this article makes to the ideal/nonideal theory debate. (shrink)

Following Burge, many anti-individualists suppose that a subject can possess a concept even if she incompletely understands it. While agreeing that this is possible, I argue that there is a limit on the extent to which a subject can incompletely understand the set of concepts she thinks with. This limit derives from our conception of our ability to reflectively evaluate our own thoughts or, as Burge puts it, our ability to engage in critical reasoning. The paper extends Burge’s own work (...) on critical reasoning. He argued that critical reasoning imposes a limit on the extent to which we can be mistaken about what thoughts we are having; in general, we can know non-empirically what we are thinking . He does not explicitly consider whether critical reasoning also imposes a limit on incomplete understanding of thoughts. (shrink)

I explain what Aristotle means when, after puzzling about the matter of motion in incomplete animals (those without sight, smell, hearing), he suggests in De Anima III 11.433b31–434a5 that just as incomplete animals are moved indeterminately, desire and phantasia are present in those animals, but present indeterminately. I argue that self-motion and its directing faculties in incomplete animals differ in degree but not in kind from those of complete animals. I examine how an object of desire differs (...) for an incomplete animal. Using a comparison with Aristotle’s account of recollection, especially in unfavorable circumstances, I describe indeterminate self-motion. Finally, I discuss implications for our understanding of Aristotle’s accounts of the faculties of the soul and incomplete animals. (shrink)

In this chapter, I examine the concept of vulnerability as a complex constitutive feature of human agency and argue that it is both a constraint on and a resource for practical reasoning. When discussed as an ontological feature of human agency, vulnerability is primarily understood as an aspect of embodiment, which is problematic in different respects. First, in relation to the situatedness of human agency, vulnerability indicates that human agents are subjected to contextual contingencies. Second, in relation to temporality, vulnerability (...) indicates that agents act in time and under the pressure of time. They are finite and produce finite and perishable actions, even though the longlasting effects of an action may survive the action itself. Third, in relation to corporal feature of agency, vulnerability is associated to suffering and frailty, insofar as bodily needs and desires represent both springs of and hindrances to rational action. Finally, in relation to the social nature of human animals, vulnerability indicates the susceptibility to be harmed, obstructed, undercut or manipulated by other agents These varieties of vulnerability are constituive features of human agency, which cannot be removed without removing what is peculiar and specific to human agency. Theories of practical reason are primarily concerned with constitutive vulnerability as a defect, and presume to offer normative guidance by adopting an idealized account of rational agency, which corrects or merely cancels the defective features of human agency. By contrast, theories of bounded rationality understand practical reasoning instrumentally, and thus are concerned with cognitive limitations of practical rationality, in particular with partial and perspectival information. However, the notion of “partial information” is inadequate to capture the complexities and significance of vulnerability, even in its restricted cognitive sense, which has to do with the agent’s situatedness. On the view I propose, instead, vulnerability is declined as a constitutive constraint on practical reasoning. Susceptibility to time constraints makes sense of the agents’ engagement in action and of their distinctive deliberative perspective. Susceptibility to bodily needs and desires tracks the normative relation between motivations and reasons for action, as well as the corporal roots of the agents’ efficacy in a perceived context. Susceptibility to others makes possible to broaden the scope and the modes of individual agency, by way of inter-action and shared agency. Rather than the source of problems and issues for rational agency, I take vulnerability to name the cluster of constitutive constraints that shape practical reasoning. According to the distinctive variety of Kantian constructivism I defend, practical reason is incomplete, rather than imperfect or defective. The completion of practical reason does not aim to correct or dissolve vulnerability, but deploys vulnerability as a resource to build up autonomy. This view accounts for autonomy as a normative relation among vulnerable agents, which develops in time. (shrink)

This is the Introduction to Etienne Balibar's book Identity and Difference: John Locke and the Invention of Consciousness. It begins with a brief reprise of Balibar’s main argument concerning Locke’s role in the ‘invention of consciousness’ and draws out the most important aspects of Balibar’s multi-faceted interpretation of Locke on personal identity. After a condensed overview of the main trends in the mainstream interpretation and criticism of Locke’s argument, focusing in particular on the two major objections that continue to be (...) leveled against Locke’s account, it then relocates Locke’s argument and Balibar’s interpretation of it within the context of recent work on the philosophical history of the concept of the subject. This new context for the interpretation of Locke allows us both to understand the dogged persistence of the main criticisms of Locke – from the earliest to some of his most recent ‘analytical’ critics – in a new way and to form of a connection between this part of the Essay Concerning Human Understanding and Locke’s political philosophy. (shrink)

This book covers completeness of first-order logic, some model theory, Gödel's incompleteness theorems and related results, and a smattering of computability theory. The text is self-contained and provides full proofs of the main facts. Ideally, the reader of this work has already taken at least one introductory logic course; however, everything needed to understand the syntax and semantics of first-order logic is presented herein. Students from philosophy, linguistics, computer science, physics, and other related subjects will find this work useful and (...) enlightening. (shrink)

According to Aristotle, the present is an indivisible instant, or now. Aristotle holds that present-tense movement claims are sometimes true, but he argues that nothing ‘kineitai’ (moves/is moving) in the now. He characterizes movement as something that is ‘incomplete’ while it is occurring. My paper is an attempt to understand this combination of views. I draw a contrast between Aristotle’s position and an alternative view (defended by certain modern philosophers, but also by Plotinus), on which a present-tense movement claim (...) is made true by the existence of something that is wholly present in the now. And I give some reasons for preferring Aristotle’s position. (shrink)

Kurt Gödel’s Incompleteness theorem is well known in Mathematics/Logic/Philosophy circles. Gödel was able to find a way for any given P (UTM), (read as, “P of UTM” for “Program of Universal Truth Machine”), actually to write down a complicated polynomial that has a solution iff (=if and only if), G is true, where G stands for a Gödel-sentence. So, if G’s truth is a necessary condition for the truth of a given polynomial, then P (UTM) has to answer first that (...) G is true in order to secure the truth of the said polynomial. But, interestingly, P (UTM) could never answer that G was true. This necessarily implies that there is at least one truth a P (UTM), however large it may be, cannot speak out. Daya Krishna and Karl Potter’s controversy regarding the construal of India’s Philosophies dates back to the time of Potter’s publication of “Presuppositions of India’s Philosophies” (1963, Englewood Cliffs Prentice-Hall Inc.) In attacking many of India’s philosophies, Daya Krishna appears to have unwittingly touched a crucial point: how can there be the knowledge of a ‘non-cognitive’ mokṣa? [‘mokṣa’ is the final state of existence of an individual away from Social Contract]—See this author’s Indian Social Contract and its Dissolution (2008) mokṣa does not permit the knowledge of one’s own self in the ordinary way with threefold distinction, i.e., subject–knowledge-object or knower–knowledge–known. But what is important is to demonstrate whether such ‘knowledge’ of non-cognitive mokṣa state can be logically shown, in a language, to be possible to attain, and that there is no contradiction involved in such demonstration, because, no one can possibly express the ‘experience-itself’ in language. Hence, if such ‘knowledge’ can be shown to be logically not impossible in language, then, not only Daya Krishna’s arguments against ‘non-cognitive mokṣa’ get refuted but also it would show the possibility of achieving ‘completeness’ in its truest sense, as opposed to Gödel’s ‘Incompleteness’. In such circumstances, man would himself become a Universal Truth Machine. This is because the final state of mokṣa is construed as the state of complete knowledge in Advaita. This possibility of ‘completeness’ is set in this paper in the backdrop of Śrī Śaṅkarācārya’s Advaitic (Non-dualistic) claim involved in the mahāvākyas (extra-ordinary propositions). (Mahāvākyas that Śaṅkara refers to are basically taken from different Upaniṣads. For example, “Aham Brahmāsmi” is from Bṛhadāraṇyaka Upanisad, and “Tattvamasi” is from Chāndogya Upaniṣad. Śrī Śaṅkarācārya has written extensively. His main works include his Commentary on Brahma-Sūtras, on major Upaniṣads, and on ŚrīmadBhagavadGītā, called Bhāṣyas of them, respectively. Almost all these works are available in English translation published by Advaita Ashrama, 5 Dehi Entally Road, Calcutta, 700014.) On the other hand, the ‘Incompleteness’ of Gödel is due to the intervening G-sentence, which has an adverse self-referential element. Gödel’s incompleteness theorem in its mathematical form with an elaborate introduction by R.W. Braithwaite can be found in Meltzer (Kurt Gödel: on formally undecidable propositions of principia mathematica and related systems. Oliver & Boyd, Edinburgh, 1962). The present author believes first that semantic content cannot be substituted by any amount of arithmoquining, (Arithmoquining or arithmatization means, as Braithwaite says,—“Gödel’s novel metamathematical method is that of attaching numbers to the signs, to the series of signs (formulae) and to the series of series of signs (“proof-schemata”) which occur in his formal system…Gödel invented what might be called co-ordinate metamathematics…”) Meltzer (1962 p. 7). In Antone (2006) it is said “The problem is that he (Gödel) tries to replace an abstract version of the number (which can exist) with the concept of a real number version of that abstract notion. We can state the abstraction of what the number needs to be, [the arithmoquining of a number cannot be a proof-pair and an arithmoquine] but that is a concept that cannot be turned into a specific number, because by definition no such number can exist.”.), especially so where first-hand personal experience is called for. Therefore, what ultimately rules is the semanticity as in a first-hand experience. Similar points are voiced, albeit implicitly, in Antone (Who understands Gödel’s incompleteness theorem, 2006). (“…it is so important to understand that Gödel’s theorem only is true with respect to formal systems—which is the exact opposite of the analogous UTM (Antone (2006) webpage 2. And galatomic says in the same discussion chain that “saying” that it ((is)) only true for formal systems is more significant… We only know the world through “formal” categories of understanding… If the world as it is in itself has no incompleteness problem, which I am sure is true, it does not mean much, because that is not the world of time and space that we experience. So it is more significant that formal systems are incomplete than the inexperiencable ‘World in Itself’ has no such problem.—galatomic”) Antone (2006) webpage 2. Nevertheless galatomic certainly, but unwittingly succeeds in highlighting the possibility of experiencing the ‘completeness’ Second, even if any formal system including the system of Advaita of Śaṅkara is to be subsumed or interpreted under Gödel’s theorem, or Tarski’s semantic unprovability theses, the ultimate appeal would lie to the point of human involvement in realizing completeness since any formal system is ‘Incomplete’ always by its very nature as ‘objectual’, and fails to comprehend the ‘subject’ within its fold. (shrink)

Hedonism claims that all and only pleasure is intrinsically good. One worry about Hedonism focuses on the “only” part: Are there not things other than pleasure, such as personal projects and relationships, that are intrinsically good? If so, it can be objected that Hedonism is incomplete. In this paper, I defend Hedonism against this objection by arguing for a distinction between goodness and desirability that understands “desirability” as a deontic concept, in terms of “reason to desire”, but goodness as (...) an evaluative concept. Based on this distinction, I attempt to show that Hedonists should accept that things other than pleasure, such as personal projects and relationships, are desirable for their own sakes but deny that these things are intrinsically good. (shrink)

The division of cognitive labor is fundamental to all cultures. Adults have a strong sense of how knowledge is clustered in the world around them and use that sense to access additional information, defer to relevant experts, and ground their own incomplete understandings. One prominent way of clustering knowledge is by disciplines similar to those that comprise the natural and social sciences. Seven studies explored an emerging sense of these discipline‐based ways of clustering of knowledge. Even 5‐year‐olds could cluster (...) knowledge in a manner roughly corresponding to the departments of natural and social sciences in a university, doing so without any explicit awareness of those academic disciplines. But this awareness is fragile early on and competes with other ways of clustering knowledge. Over the next few years, children come to see discipline‐based clusters as having a privileged status, one that may be linked to increasingly sophisticated assumptions about essences for natural kinds. Possible mechanisms for this developmental shift are examined. (shrink)

In Mental Acts Professor Peter Geach asserts that “‘The same’ is a fragmentary expression, and has no significance unless we say or mean ‘the same X’, where ‘X’ represents a general term … ” In Reference and Generality Geach interjects the following note: “I maintain that it makes no sense to judge whether x and y are ‘the same’, or whether x remains ‘the same’, unless we add or understand some general term ‘the same F’.” Here, as in Mental Acts, (...) he goes on to say that not any general term will serve to complete ‘the same’ constructions; only substantival terms will suffice for this purpose. Finally, in his article, “ldentity,” Geach asserts that “When one says ‘x is identical with y’, this … is an incomplete expression; it is short for ‘x is the same A as y’, where ‘A’ represents some count noun understood from the context of utterance—or else, it is just a vague expression of a half-formed thought.” (We should not, incidently, conclude from this last remark that Geach thinks all and only count nouns are substantival terms. (shrink)

I explain what Aristotle means when, after puzzling about the matter of motion in incomplete animals (those without sight, smell, hearing), he suggests in De Anima III 11.433b31-434a5 that just as incomplete animals are moved indeterminately, desire and phantasia are present in those animals, but present indeterminately. I argue that self-motion and its directing faculties in incomplete animals differ in degree but not in kind from those of complete animals. I examine how an object of desire differs (...) for an incomplete animal. Using a comparison with Aristotle’s account of recollection, especially in unfavorable circumstances, I describe indeterminate self-motion. Finally, I discuss implications for our understanding of Aristotle’s accounts of the faculties of the soul and incomplete animals. (shrink)

Current mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through GOdel's two incompleteness theorems, and in doing so demonstrates how influential GOdel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, while GOdel's theorems are able to predict (...) their limitations for more accurate analysis and understanding of national and international events. This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science. (shrink)

Shortly after Kurt Gödel had announced an early version of the 1st incompleteness theorem, John von Neumann wrote a letter to inform him of a remarkable discovery, i.e. that the consistency of a formal system containing arithmetic is unprovable, now known as the 2nd incompleteness theorem. Although today von Neumann’s proof of the theorem is considered lost, recent literature has explored many of the issues surrounding his discovery. Yet, one question still awaits a satisfactory answer: how did von Neumann achieve (...) his result, knowing as little as he seemingly did about the 1st incompleteness theorem? In this article, I shall advance a conjectural argument to answer this question, after having rejected the argument widely shared in the literature and having analyzed the relevant documents surrounding his discovery. The argument I shall advance strictly links two of the three letters written by von Neumann to Gödel in the late 1930 and early 1931 (i.e. respectively that of November 20, 1930 and that of January 12, 1931) and finds the key for von Neumann’s discovery in his prompt understanding of the Gödel sentence A – as the documents refer to it – as expressing consistency for a formal system that contains arithmetic. (shrink)

In this essay, I focus on Recanati's treatment of 'What is said' in his book Literal Meaning. I discuss Recanati's conception of Minimalism, his views on propositional completeness, and his understanding of the processes governing the semantic interpretation of meaning-controlled contextuality. In the final sections, I draw some conclusions pertaining to Recanati's assessment of the interface between pragmatic and semantic processes. /// En este ensayo me enfoco en el trato que le da Recanati a "lo que se dice" en (...) su libro Literal Meaning. Discuto su concepción del minimismo, su posición sobre la completud proposicional y su comprensión de los procesos que rigen la interpretación semántica de la contextualidad controlada por el significado. En las secciones finales, extraigo algunas conclusiones acerca de la evaluación que Recanati hace de la interfase entre procesos semánticos y pragmáticos. (shrink)

The familiar idea of a gap between theory and practice cannot be understood in terms of distinctions such as general-particular or abstract-concrete. A "gap" suggests a more fundamental difference. The underlying distinction is that between two incomplete and incompatible models of morality, a doctrine model and a practice model. Morality can be described in terms of interaction, a practice, and it can be described as a set of precepts, an ethical doctrine. This distinction may help us to understand various (...) debates and problems in ethics. It explains why there is so little progress in methodological discussions on reflective equilibrium. In a doctrine perspective, reflective equilibrium is a method to attain moral truth; in a practice perspective it is a process of continuous critical reflection. The distinction also explains conflicting views on moral expertise. In a practice perspective, moral philosophers are not moral experts, whereas in a doctrine perspective they are. (shrink)

Despite his place as one of the most original thinkers of the Middle Ages, the legacy of Joachim of Fiore has eluded clear comprehension in at least two areas, those of texts and transmission. That is, Joachim studies have, until most recently, been limited by a lack of modern editions for Joachim’s works, and by an incomplete understanding of how the revolutionary ideology inspired by a twelfth-century abbot from Calabria ultimately came to be appropriated by disparate groups such (...) as the Spiritual Franciscans, the Münster Anabaptists, and Spanish missionaries in colonial Latin America. Yet there has been much scholarship, of exacting standards and of immense value, which has pushed forward our knowledge of... (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not (...) be thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

In this paper I reconstruct and discuss Antonio Rubio (1546-1615)’s theory of the composition of the continuum, as set out in his Tractatus de compositione continui, a part of his influential commentary on Aristotle’s Physics, published in 1605 but rewritten in 1606. Here I attempt especially to show that Rubio’s is a significant case of Scholastic overlapping between Aristotle’s theory of infinitely divisible parts and indivisibilism or ‘Zenonism’, i.e. the theory that allows for indivisibles, extensionless points, lines, and surfaces, which (...) are supposed to take part in the composition of the continuum. Even if such a syncretic tendency was, in many different ways, already developing in the medieval period and then at the end of the sixteenth century, Rubio’s position is indeed peculiar. He maintains that indivisibles are real and actual, infinite in act, really distinct from each other, and that, although they indwell in substance, indivisibles do not contribute directly to the constitution of the continuum. In this reconstruction, I emphasize notably Rubio’s usage of mereological notions like those of part, whole, completeness and incompleteness. (shrink)

'God needs no instruments to act', Malebranche writes in Search 6.2.3; 'it suffices that He wills in order that a thing be, because it is a contradiction that He should will and that what He wills should not happen. Therefore, His power is His will' (450). After nearly identical language in Treatise 1.12, Malebranche writes that '[God's] wills are necessarily efficacious ... [H]is power differs not at all from [H]is will' (116). God's causal power, here, clearly traces only to His (...) volitions - not merely to the fact that He wills, but specifically to the content of His volitions ('"what" He wills'). Yet despite the obviously key role the ordinary notion of volitional content plays for Malebranche, recent writers have paid surprisingly little attention either to it or its exegetical implications. I hope to rectify this situation here. The plan of this paper is this: first, to borrow current work in the philosophy of mind to sketch the notion of an incomplete volition, i.e. one whose content is 'incomplete' in a sense to be explained; second, to show that Malebranche clearly allows and uses something like this notion; third, to apply the notion to Malebranche's doctrine of human freedom. In so doing, I believe, we can understand this doctrine in a new way, and one which: (i) is clearly consistent with his texts, and (ii) unlike other interpretations makes coherent sense out of the conflicting streams in his heroic attempt to reconcile his occasionalism - the doctrine that no finite substances have genuine causal powers - with our freedom; fourth, Contrast my interpretation with those of two recent writers: Sleigh et al. (1998) and Schmaltz (1996); and Fifth, Summarize the major results. (shrink)

Individuals regaining reliable day-to-day walking function after incomplete spinal cord injury report persisting unsteadiness when confronted with walking challenges. However, quantifiable measures of walking capacity lack the sensitivity to reveal underlying impairments of supra-spinal locomotor control. This study investigates the relationship between intramuscular coherence and corticospinal dynamic balance control during a visually guided Target walking treadmill task. In thirteen individuals with iSCI and 24 controls, intramuscular coherence and cumulant densities were estimated from pairs of Tibialis anterior surface EMG recordings (...) during normal treadmill walking and a Target walking task. The approximate center of mass was calculated from pelvis markers. Spearman rank correlations were performed to evaluate the relationship between intramuscular coherence, clinical parameters, and center of mass parameters. In controls, we found that the Target walking task results in increased high-frequency intramuscular coherence, which negatively related to changes in the center of mass movement, whereas this modulation was largely reduced in individuals with iSCI. The impaired modulation of high-frequency intramuscular coherence during the Target walking task correlated with neurophysiological and functional readouts, such as motor-evoked potential amplitude and outdoor mobility score, as well as center of mass trajectory length. The Target walking effect, the difference between Target and Normal walking intramuscular coherence, was significantly higher in controls than in individuals with iSCI [F = 13.042, p < 0.001]. Intramuscular coherence obtained during challenging walking in individuals with iSCI may provide information on corticospinal gait control. The relationships between biomechanics, clinical scores, and neurophysiology suggest that intramuscular coherence assessed during challenging tasks may be meaningful for understanding impaired supra-spinal control in individuals with iSCI. (shrink)

The General Data Protection Regulation (GDPR) of the EU confirms the protection of personal data as a fundamental human right and affords data subjects more control over the way their personal information is processed, shared, and analyzed. However, where data are processed by artificial intelligence (AI) algorithms, asserting control and providing adequate explanations is a challenge. Due to massive increases in computing power and big data processing, modern AI algorithms are too complex and opaque to be understood by most data (...) subjects. Articles 15 and 22 of the GDPR provide a modest regulatory framework for automated data processing by, among other things, mandating that data controllers inform data subjects about when it is being used, and its logic and ramifications. Nevertheless, due to the phrasing of the articles and the numerous exceptions they allow, doubts have arisen about their effectiveness. In this paper, we empirically evaluate the quality and effectiveness of AI disclosures as mandated by the GDPR. By means of an online survey (N = 835), we investigated how data subjects expect to be informed about the automated processing of their data. We then conducted a content analysis of the AI disclosures of N = 100 companies and organizations. The combined findings reveal that current GDPR-mandated disclosures do not meet the expectations and needs of data subjects. Explanations drawn up following the guidelines of the generic formulations of the GDPR differ widely and are often vague, incomplete and lack transparency. In our conclusions we identify a path towards standardizing and optimizing AI information notices. (shrink)