A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, (...) a goal of the present paper is to argue that his success in securing the objectivity of arithmetic depends on a less contentious commitment to numbers as objects than either he or his critics have supposed. As such, this paper is an articulation and defense of both Frege's analysis of arithmetic and Kreisel's observation. (shrink)

A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, (...) a goal of the present paper is to argue that his success in securing the objectivity of arithmetic depends on a less contentious commitment to numbers as objects than either he or his critics have supposed. As such, this paper is an articulation and defense of both Frege's analysis of arithmetic and Kreisel's observation. (shrink)

According to platonists, entities such as numbers, sets, propositions and properties are abstract objects. But abstract objects lack causal powers and a location in space and time, so how could we ever come to know of the existence of such impotent and remote objects? In Knowledge, Cause, and Abstract Objects, Colin Cheyne presents the first systematic and detailed account of this epistemological objection to the platonist doctrine that abstract objects (...) exist and can be known. Since mathematics has such a central role in the acquisition of scientific knowledge, he concentrates on mathematical platonism. He also concentrates on our knowledge of what exists, and argues for a causal constraint on such existential knowledge. Finally, he exposes the weaknesses of recent attempts by platonists to account for our supposed platonic knowledge. This book will be of particular interest to researchers and advanced students of epistemology and of the philosophy of mathematics and science. It will also be of interest to all philosophers with a general interest in metaphysics and ontology. (shrink)

This is a dialogue in which five characters are involved. Various issues in the philosophy of mathematics are discussed. Among those issues are these: numbers as abstract objects, our knowledge of numbers as abstract objects, a proof as showing a mathematical statement to be true as opposed to the statement being true in virtue of having a proof.

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

In lieu of an abstract, here is a brief excerpt of the content:Martin Heidegger and OntologyEmmanuel Levinas (bio)The prestige of Martin Heidegger 1 and the influence of his thought on German philosophy marks both a new phase and one of the high points of the phenomenological movement. Caught unawares, the traditional establishment is obliged to clarify its position on this new teaching which casts a spell over youth and which, overstepping the bounds of permissibility, is already in vogue. For (...) once, Fame has picked one who deserves it and, for that matter, one who is still living. Anyone who has studied philosophy cannot, when confronted by Heidegger’s work, fail to recognize how the originality and force of his achievements, stemming from genius, are combined with an attentive, painstaking, and close working-out of the argument—with that craftsmanship of the patient artisan in which phenomenologists take such pride. In this study, it is important for us to understand, above all, the true intentions of our author, to illuminate what he thinks really needs to be said, and to surmise what is most critical for him.To get to the heart of Heidegger’s system, it seems fitting to begin with a problem that is generally familiar. We choose the problem of knowledge, a deeper understanding of which takes us to the very threshold of Heidegger’s thought. For this problem, central to modern philosophy, is one of the main obstacles of modern philosophy that Heidegger wishes to surmount. Neo-Kantianism, which takes knowledge as the philosophical problem of the first rank, is the movement against which Heidegger rebels with all his strength. We have, thus, every chance of gaining access to his thought by the main door, so to speak. Once inside the system we will try to trace its outlines, 2 reserving, for a second part of our work, the determination of Heidegger’s place in the history of ideas, especially in the phenomenological movement, as well as of his relations with the philosopher to whom he owes so much—Edmund Husserl. 31In its most general form, the problem of the theory of knowledge has a critical significance. It consists in delineating a domain where knowledge can be certain and in determining the criteria for the legitimate scope of knowledge. But this problem, as normal and as simple as it may appear, has deeper roots. That knowledge should need a criterion at all presupposes that truth is not identical to all that is known and that the course [End Page 11] of things can fail to correspond with the course of thought. “How does knowledge correspond to being?” is a more profound formulation of the problem of knowledge.But we are not going to touch anymore on the primordial phenomenon that generates the problem. The problem of correspondence between thing and thought presupposes a free activity of thought and its isolation in relation to the object. It is precisely this presupposition which renders their harmony and even their contact problematic. “How does the subject take leave of itself to attain the object?” is what the problem of knowledge, in the last analysis, boils down to. Its true source is thus the concept of “subject” as elaborated by modern philosophy. The cogito presided over the subject’s birth. The cogito was the affirmation of the privileged nature of the subject’s immanent sphere, of its unique place in existence; hence, the cogito was the specificity of the subject’s connection to the rest of reality, the sui generis nature which opens up the passage from immanence to transcendence, the passage from ideas contained in the thinking substance to 4 their “formal existence.”The concept of the subject, understood as a substance having a specific position in the entire domain of being, presents us with difficulties of two kinds. First, how do we understand this leave-taking from the self which the thinking substance brings about and which displays an entirely original aspect? Indeed, we could say that thought, in reaching out toward objects, does not actually take leave of itself, since its objects—considered as ideas and contents of thought—are, in a certain sense, already within it. In order to make sense of this paradox, Descartes... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Locke on the Knowledge of Material Things ROBERT FENDEL ANDERSON IT IS nOT John Locke's intention, in his Essay Concerning Human Understanding, to deal with matter and material substance nor with how these are able to affect the mind. These are considerations for natural philosophy; Locke counts himself rather among the moral philosophers. He does not propose, therefore, to meddle with the physical aspects of the mind, (...) nor with the physical production of sensations through the organs, nor with the production of ideas in the understanding, nor even with whether ideas depend upon matter for their source. He defers to the wisdom of such men as Boyle, Sydenham, Huygens and Newton in these considerations, and finds it "... ambition enough to be employed as an under-labourer in clearing the ground a little, and removing some of the rubbish that lies in the way to knowledge....,, 1 It is true that Locke's Essay is characterized chiefly not by an interest in matter and the mechanics of perception but rather by an interest in epistemology and in the ordering and assessment of our knowledge. Because of the very nature and emphasis of this epistemology, however, Locke finds that he must, from time to time, at least mention the nature of matter and how it affects us. Finally, it becomes apparent, certain changes or ambiguities in his point of view regarding the mode of our knowledge and its certainty are consequences of his understanding of matter. It is a demonstration of these elements of his doctrine, which seem not to have obtained the full attention of such scholars as Aaron, Fraser, and Gibson, that I shall attempt in this paper. Fundamentally, Locke's theory of matter appears to be that of Democritus and Epicurus. Like the Greek atomists, he conceives of matter as consisting of particles or corpuscles infinite in number. At least some of these are so minute as to be individually insensible, and probably he intends that all are, although, to my knowledge, he never states that this is so. In the aggregate, in any case, particles do constitute perceptible bodies. As for the Greeks, so also for Locke, the particles arc all extended, having size and shape. They are said also to possess motion or rest, although he takes care to say that matter cannot produce motion in itself,e Locke frequently mentions other properties as being "primary" or "really in" material things. Some of these are solidity, texture, cohesion of parts, situation, and number. Apparently some of these may be ranked under others since, as he 1"Epistle to the Reader," Vol. I, p. 14. All footnotes refer to passages in John Locke's An Essay Concerning Human Understanding, collated and annotated, with prolegomena, biographical, critical, and historical by Alexander Campbell Fraser, in two volumes (New York, Dover Publications, Inc., 1959). Large Roman numerals refer to books of the Essay; small Roman numerals refer to chapters of the books; Arabic numerals refer to sections of the chapters. 2 IV, x, 10. [205] 206 HISTORY OF PHILOSOPHY remarks, figure presupposes extension, and receiving or communicating motion through impact presupposes solidity. The influences of these particles upon one another are treated by Locke under the topic of "powers," a notion which includes in it some kind of "secret relation of parts." 3 The capacities in any substance to give alterations of primary qualities are active powers; the capacities to receive such alterations are passive powers. This alteration must be accomplished by impact or impulse since this, Locke says, is the only way in which bodies can be conceived to operate. Sensation in the percipient being then is to be understood as a special case of this impact of particles upon others. It is evident to Locke that from external obiects some motion must be conveyed by some parts of our bodies to the brain or seat of sensation to produce in our minds the particular ideas we have of these external objects. We are able by sight to perceive at a distance the primary qualities of bodies of observable size. Locke reasons that therefore "... some singly imperceptible bodies must come from them to the eyes, and thereby convey to... (shrink)

Noam Chomsky claims that we know the grammatical principles of our languages in pretty much the same sense that we know ordinary things about the world (e.g. facts), a view about linguistic knowledge that I term ''cognitivism''. In much recent philosophy of linguistics (including that sympathetic to Chomsky's general approach to language), cognitivism has been rejected in favour of an account of grammatical competence as some or other form of mental mechanism, describable at various levels of abstraction (''non-cognitivism''). I (...) argue for cognitivism and against non-cognitivism. First, I show that the distinction between competence and performance in current linguistics is as clearly made as ever it was, in spite of recent interest in linguistic processing modules. Second, I use these facts about the practice of theoretical linguistics to refute various proposals for a non-cognitivist construal of grammatical competence, and to support cognitivism by reflecting on the inapplicability of a multi-level account of linguistic competence. Cognitivism is then defended against several objections centring around the problems of rational integration and conceptualization of grammatical knowledge. Finally, the conception of competence argued for in relation to linguistics is placed in the larger context of cognitive science research and its implications for philosophy of mind. (shrink)

This paper is an attempt to clarify our talk about minds and thoughts—our own minds and the thoughts which run through them and which we know directly, as well as the minds of other people and the thoughts with which we credit them. We do so in order to be able to characterize satisfactorily our whole performance in talking about minds and thoughts, the rules according to which such talk operates and the goals it purports to reach. We also hope (...) to evaluate, in the light of such a characterization, a number of more elaborate ways of speaking about minds and thoughts, so as to become clear as to their advantages or disadvantages in comparison with more ordinary ways of speaking. The whole investigation is well worth undertaking, since it has long been evident that our talk about mind and thought is, to a peculiar extent, liable to become the seat of certain deep perplexities, which do not arise when we deal with unusual material on the borderlines of knowledge, but which tend, rather, to obtrude themselves in commonplace situations, and to trouble our grasp of the most obvious notions and the most evident truths. Such perplexities, broadly covered by the word “philosophical,” are rendered very stubborn by their objects and their origin. For when we are dealing with things remote, strange and intricate, we have at least a firm foothold in the well-known, simple and near, and a clear set of terms to talk with; but we hardly seem to have a perch to hop to, or any intelligible language left to talk in, when the obvious itself begins to present difficulties. And it is also characteristic of most of the difficulties we are considering that in them the burning zone of perplexity seems to shift erratically from issue to issue, that each expedient adopted to meet them involves us in new problems, that men cannot ever agree as to the best expedient or the least serious difficulty, and that, in the outcome, they resemble nothing so much as a set of sleepers under inadequate coverings, some of whom prefer exposure in one place, while others prefer it in another. (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. This paper considers how the doctrine of symbolism and the philosophers' different commitments to the laws of logic, especially the Law of Non-Contradiction (LNC), enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's *Grundgesetze*. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal (...) axiom that (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege's conception of numbers and logical objects. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, (...) numbers, propositions, and degrees is considerably more marginal than generally held. (shrink)

In this dissertation I explore Frege’s conception of truth. In particular I defend the thesis that Frege in his mature career takes truth to be an object, i.e., the True qua the reference of true sentences. In the literature on truth Frege has been usually taken to be a truth deflationist or a truth primitivist. Indeed Frege leaves a number of comments that sound like typical deflationist claims and his famous indefinability argument is the most discussed argument for primitivism. However, (...) Frege is neither a deflationist nor a primitivist. His deflationist remarks and the indefinability argument are rather his arguments that truth is an object. -/- For Frege judging—and its verbal counterpart asserting—is always acknowledging the truth of a truth-bearer. Thus, if truth is an object for him, his conception of judgment ought to also be adjusted accordingly. Indeed Frege shows how we can understand judgment qua acknowledgment of truth if truth is an object. Specifically, judging that p is identifying the True with the reference of ‘p’ non-judgmentally, i.e., without judging that p is identical with the reference of ‘p’. Frege’s conception of judgment impacts his conception of knowledge because the act of judging is that of producing knowledge. In a nutshell our act of judging and the knowledge we produce by it are epistemically grounded in our objectual knowledge of the True. If we take this point into account, we can develop a new reading of Frege’s claim that logic is the science of truth. -/- The suggested reading of Frege’s conception of truth and related notions can make a contribution to contemporary philosophical problems. First, Frege’s conception of judgment can cope with Peter Hanks’s recent criticisms of the Fregean picture of judgment in general. Secondly, his conception of assertion can explain the connection between truth and assertion in a novel way. Lastly, Frege’s conception of knowledge can be developed into a new theory of knowledge where objectual knowledge is more fundamental than propositional knowledge. (shrink)

The relationship between language and conceptual thought is an unresolved problem in both philosophy and psychology. It remains unclear whether linguistic structure plays a role in our cognitive processes. This special issue brings together cognitive scientists and philosophers to focus on the role of language in numerical cognition: because of their universality and variability across languages, number words can serve as a fruitful test case to investigate claims of linguistic relativism.

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambigu-ity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argu-ment’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambi-guity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argument’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

The field of numerical cognition provides a fairly clear picture of the processes through which we learn basic arithmetical facts. This scientific picture, however, is rarely taken as providing a response to a much‐debated philosophical question, namely, the question of how we obtain number knowledge, since numbers are usually thought to be abstract entities located outside of space and time. In this paper, I take the scientific evidence on how we learn arithmetic as providing a response to (...) the philosophical question of how we obtain number knowledge. I reject the view that numbers are abstract entities located outside of space and time and, alternatively, derive from the scientific evidence a novel account of the nature of numbers. In this account, numbers are reifications of the counting procedure and arithmetic statements are seen as describing the functioning of counting and calculation techniques. (shrink)

This thesis is concerned with explaining how a subject can acquire a priori knowledge of arithmetic. Every account for arithmetical, and in general mathematical knowledge faces Benacerraf's well-known challenge, i.e. how to reconcile the truths of mathematics with what can be known by ordinary human thinkers. I suggest four requirements that jointly make up this challenge and discuss and reject four distinct solutions to it. This will motivate a broadly Fregean approach to our knowledge of arithmetic and (...) mathematics in general. Pursuing this strategy appeals to the context principle which, it is proposed, underwrites a form of Platonism and explains how reference to and object-directed thought about abstract entities is, in principle, possible. I discuss this principle and defend it against different criticisms as put forth in recent literature. Moreover, I will offer a general framework for implicit definitions by means of which - without an appeal to a faculty of intuition or purely pragmatic considerations - a priori and non-inferential knowledge of basic mathematical principles can be acquired. In the course of this discussion, I will argue against various types of opposition to this general approach. Also, I will highlight crucial shortcomings in the explanation of how implicit definitions may underwrite a priori knowledge of basic principles in broadly similar conceptions. In the final part, I will offer a general account of how non-inferential mathematical knowledge resulting from implicit definitions is best conceived which avoids these shortcomings. (shrink)

Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 (Cambridge University Press, New York) is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic (“intuition” in the specific sense of Kant and Hilbert). Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic structure is (...) the so-called ‘intuitive model’ of arithmetic realized by Hilbert’s strings of strokes. This paper argues that Hilbert’s strings, considered as given in intuition, cannot play the role Parsons assigns to them: the criteria of identity of these strings do not have the sharpness that Parsons wants to see in them, and Parsons inadvertently projects abstract structures into his ‘intuitive model’. This diagnosis is exemplified with respect to (a) Parsons’ distinction between addition and multiplication on the one hand and exponentiation on the other and (b) his analysis of arithmetical knowledge in simple cases like “7 + 5 = 12”. All in all, it is claimed that Parsons book contains many important insights with respect to, for example, different versions structuralism, the notion of “natural number” and its uniqueness, induction, predicativity and other things, for which he is rightly famous, but that his way of drawing on the notion of intuition leaves too many questions unanswered. (shrink)

By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: Every natural number, n, has a (...) successor, n + 1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language‐specific counting routines (e.g., the rules in English that represent base‐10 structure). We tested 4‐ and 5‐year‐old children’s knowledge of counting with three tasks, which we then related to (a) children’s belief that 1 can always be added to any number (the successor function) and (b) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge was not directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as 4 years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Simulation, Subjective Knowledge, and the Cognitive Value of Literary NarrativeScott R. Stroud (bio)IntroductionLiterary narrative holds the power to move individuals to thought, reflection, action, and belief. According to a longstanding view of literature, it is this impact on the reader that leads to literary narrative being valued so highly in our culture and in others. What exactly is the value of literature? Humanists such as Peter Lamarque (...) and Stein Olsen1 argue for this value in terms of perennial themes that literature allows one to "grapple with," as opposed to cognitivist accounts that discuss the value of literary narrative in terms of conveyed truths or knowledge. One particularly important position that explains the cognitive value of literature can be labeled the "Subjective Knowledge Theory" (SKT). Such an account of literature places its value in the subjective perspectives or experiences the narrative opens up to the reader. Thus, one can gain knowledge of "what it is like" to be caught in the throes of jealousy, endangered by an opposing army, or captivated by the lure of magical prowess. Lamarque and Olsen, however, argue that SKT is fundamentally flawed in its analysis of knowledge derivable from the literary narrative and in terms of its account of literary practice.I wish to defend a version of SKT in this article. In order to do so, I make and defend the following claims. First, Lamarque and Olsen's critique of SKT relies on a conflation of two distinct types of knowledge—the knowledge provided by the simulated subjective experience and its appropriation/ generalization to forms useful for the reader's real life activities. I will argue that the former of these outcomes is due strictly to the aesthetic features of the literary narrative, whereas the second involves a non-necessary psychological reaction to the text (that is, judgments of the veracity or usefulness of the text for one's own purposes). By conflating both of these into the cognitive knowledge derivable from the text, Lamarque and Olsen's critique can [End Page 19] gain its purchase against SKT. If these two processes and the resultant sorts of knowledge are separated, then the SKT account does seem to show how literature holds value in itself and in relation to the reader's moral activities/ judgments. Second, the process of simulation is the primary means by which one can gain any type of subjective knowledge from a literary narrative. This type of knowledge will be gained by virtue of the literary narrative's aesthetic qualities, which result in a certain type of activity in the reader. Third, I will argue that the second sort of knowledge—that derived from the simulated subjective experience—results from the process of reader identification with the values, beliefs, and/or behaviors of the simulated agent. This sense of identification involves selective appropriation and generalization and will be shown not to be subject to the critiques of simple identification offered by Noël Carroll.2 It is at this stage that individuals learn what they believe they ought to value, how they ought to act, and what they should believe from their experience of simulation in reading the literary narrative. Notice that this knowledge is separate from the first sort of knowledge, which is knowledge of what it is like to experience x through y's eyes.As I elucidate and defend these claims, I hope it will become clear that this is an account that does justice to the value resident in literature and in the activities readers do after they partake in the aesthetic object of the literary narrative. Thus, I will conclude by showing how this account does not fall prey to the conflation that both critics and supporters of SKT commit in muddling the different types of knowledge available from and in relation to a literary narrative.Before I proceed, it is important that some basic concepts are clearly set forth. A narrative can be defined as any representation of two or more events over time. The number of events and the relationship among them can be as simple or complex as one likes, but the crucial aspect is that the representation supplies the... (shrink)

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is (...) to explore the relationship between the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

The traditional conception of knowledge as justified true belief has collapsed under weighty objections. Some of these are well known; but others, though equally weighty and puzzling, have attracted comparatively little attention, and still demand careful study. Only through such study can we approach correct understanding of propositional knowledge.

In lieu of an abstract, here is a brief excerpt of the content:382 HISTORY OF PHILOSOPHY the spiritual effort of all mankind. Many so-called historic events, he was convinced, will in the end be "as written in water," but the work of the human "spirit," however limited at any given time, is accumulative and helps prepare a better future. It seems fitting to close this review with the concluding words of high commendation addressed to him by the Argentinian Society (...) of Writers on the occasion of the appearance of the Theory of Man: "Se premia a un hombre, a una obra, a una conducta." (We are paying homage to a man, a work, a noble conduct.) COR~ELI~:S KRUS~ Wesleyan University The Knowledge o] Man. Selected Essays. By Martin Buber. Edited with an Introduction by Maurice Friedman. Translated by Maurice Friedman and Ronald Gregor Smith. (New York: Harper Torchbooks, The Cloister Library, TB 135H. Pp. 186. $1.45.) The present volume contains the English translations, previously published, of six anthropological essays of Martin Buber, which had appeared originally in German. They are: Distance and Relation (1950), Elements of the Interhuman (1954), What is Common to All (1956), The Word that is Spoken (1960), Guilt and Guilt Feelings (1957), Man and his Image-Work (1955). As an Appendix has been added the unpublished text of a discussion between the late Martin Buber and the psychologist Carl R. Rogers, in April 1957. An introductory Essay by Maurice S. Friedman intends to set these essays in the context of Buber's philosophy of dialogue and "to show their interrelations and their significance for other fields of thought" (p. 7). Both the Introductory Essay and the translated texts had been seen by Buber before going to the press. Broadly speaking, these essays concern the distinctive features of man, and the reality of the dazwischen (p. 12), translated as "there in-between," "the between" or "betweenness" (p. 107): between man and reality (art), and between man and man (the interhuman in dialogue, word and language, guilt and psychotherapy). No specific texts on religion and knowledge have been included in this collection, its purpose being to present Buber's "philosophical anthropology" (p. 7). One may speak of a synthesis of Buber's view of man, as it comes out in this volume. Man is constituting "a special category of being" (60), by being capable of entering into living relations; this happens in the sphere of "the between," in particular the interhuman, the unfolding of which is "the dialogicaI" (p. 75). Here the "spokenness" of the word has its place (p. 112), here are found the different forms of encounter from which the human "selves" emerge after "a bold swinging...into the life of the other" (p. 81) and making each other "present" through "imagining" the real in each other (p. 70). There is the permanent "temptation to... take refuge in the pseudo security of the world of It, the world of ordered objectivity and private subjectivity" (Friedman, p. 23). But there is also the "common world" (cosmos) as built by "common speech-with-meaning" (logos) (Friedman, p. 40); this is the world of the We (pp. 107-108). Buber dismisses the annihilation of the human person in the dream and sleep of the East (pp. 91-96), the "situationless" and "uncommunal" chemical holidays of Aldous Huxley (p. 100), the solipsism and panpsychism of C. G. Jung (p. 124-125) : by all of these "the pure duty and responsibility of waking togetherness" (p. 91) has been forsaken. Of particular interest are Friedman's pages concerning Buber's view of the unconscious (pp. 32-38): they replace an essay which Buber had intended to write on the subject. In this connection the essay on existential guilt to oneself and to others is illuminating ; this guilt is "as something of an ontic character" (p. 123), and only a--"for the man of our age" (p. 138)--difficult self-illumination can hereby give insight and open the door into "the identity of the human person as such with himself" (p. 147). Also, the discussion on psychotherapy should be mentioned, where Buber puts his finger on "this dialogue bounded by tragedy" (p. 174) in which "You are not equals and cannot... (shrink)

This paper aims to construct a picture of knowledge out of Frege’s comments on truth, judgment, assertion, and knowledge. Frege takes truth to be an object, and the act of judgment to be the act of non-judgmental identification of truth qua an object with the reference of a sentence. For him, the propositional knowledge that p is the non-propositional knowledge of the identity between truth and |p|. Propositional knowledge thusly understood is produced by our (...) class='Hi'>knowledge of truth qua an object, which is constituted by our abilities to identify truth as such. The Fregean picture of knowledge provides a tight connection between knowledge-how, objectual knowledge, and propositional knowledge. (shrink)

Scientists are often bemused by the efforts of philosophers essaying a theory of colour: colour science sports a huge array of facts and theories, and it is unclear to its practitioners what philosophy can or is trying to contribute. Equally, philosophers tend to be puzzled about how they can fit colour science into their investigations without compromising their own disciplinary identity: philosophy is supposed to be an a priori investigation; philosophers do not work in psychophysics labs – not in their (...) professional capacity, anyway.These inter-disciplinary barriers arise out of misunderstanding. Philosophers should not so much attempt to contribute to empirical theories of colour, as to formulate philosophical theories of colour. Philosophy is concerned with appearance and reality, object and property, function and representation, and other such fundamental categories of ontology and epistemology. Philosophical theories attempt to fit colour into these categories; such theories do not compete with colour science. However, fitting colour into philosophical theories means dealing with colour as it really is – and one cannot know what it is without consulting the psychologists. That is why philosophers need an up-to-date understanding of psychological theories of colour. (shrink)

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the (...) vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity, while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic. Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the~$\omega$-rule or to the non-computability and non-continuity of probability assignments. Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments, such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated. In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abstract General Ideas in Hume George S. Pappas Hume followed Berkeley in rejecting abstract general ideas; that is, both of these philosophers rejected the view that one could engage in the operation or activity ofabstraction — a kind ofmental separation ofentities that are inseparable in reality —as well as the view that the alleged products of such an activity — ideas which are intrinsically general — (...) really exist. What has not been clear to commentators on either of these two philosophers has been why they each were so opposed to abstraction and abstract general ideas. The provision of an answer to this question is the main thrust of this paper. The nature of the question should be clarified at the outset. I am notasking the psychological question, whatwere BerkeleyandHume's actual intentions when they were moved to reject abstraction and abstract general ideas. Though I regard this question as one of great interest and importance, I am presently aiming to answer a somewhat different one, viz., what role, what philosophical role, does the rejection of abstraction and abstract general ideas play in the philosophies ofBerkeley and Hume? The answer to this latter question is apt to have some bearing on the right way to answer the first question; but, for present purposes, it is important to keep the two questions distinct. The maincontentionofthe paperis thattherejectionofabstraction and abstract general ideas lies at the very heart of the philosophy of Berkeley, and that pretty much the same may be said for Hume. Berkeley's defense ofa kind ofidealism stands or falls with the success ofhis attack on abstract general ideas, and Hume's critique ofinfinite divisibility in matters pertaining to space and time, along with his destructive critique ofvarious metaphysical notions, crucially depends on the successful denial of abstract general ideas. I. Berkeleyan Idealism Berkeley's most extended treatment of abstract ideas comes in the introduction to the Principles ofHuman Knowledge, first published in 1710. However, since he does not take up the topic in any systematic way later in the same book, nor in the Three Dialogues Between Hylas and Phihnous (1713), it has seemed to many commentators that Berkeley's attack on abstract ideas is a local matter, one having only to do with issues concerning language use and a somewhat isolated criticism of Locke. That this is the wrong way to look at things is Volume XV Number 2 339 GEORGE S. PAPPAS perhaps best indicated by a couple of passages from the Principles. In section 5 ofthat work Berkeley says: If we thoroughly examine this tenet it will, perhaps, be found at bottom to depend on the doctrine of abstract ideas. For can there be a nicer strain of abstraction than to distinguish the existence of sensible objects from there being perceived, so as to conceive them existing unperceived? The tenet Berkeley is here referring to is to the effect that sensible objects such as trees and chairs exist independently ofperception. This allusion is made clear when we notice that in the immediately preceding passage Berkeley says: It is indeed an opinion strangely prevailing among men that houses, mountains, rivers, and in a word all sensible objects, have an existence, natural or real, distinct from their being perceived by the understanding. But, with how great an assurance and acquiescence soever this Principle may be entertained... whoever shall find in his heart to call it in question may... perceive it to involve a manifest contradiction. For, what are the aforementioned objects but the things we perceive by sense? and what do we perceive besides our own ideas or sensations? and is it not plainly repugnant that any one of these, or any combination of them, should exist unperceived? (Principles 4) The claim that sensible objects exist independently ofall perception is the very denial of Berkeley's esse is percipi thesis regarding such objects. For the latter thesis holds that each sensible object is such that it exists if and only if it is perceived. So, in the first-quoted passage from Principles 5, Berkeley is saying that the denial of esse is percipi 'depends on' the doctrine of abstract ideas. Surely, the esse is percipi thesis is part ofthe core ofBerkeley's... (shrink)

Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 (Cambridge University Press, New York) is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic (“intuition” in the specific sense of Kant and Hilbert). Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic structure is (...) the so-called ‘intuitive model’ of arithmetic realized by Hilbert’s strings of strokes. This paper argues that Hilbert’s strings, considered as given in intuition, cannot play the role Parsons assigns to them: the criteria of identity of these strings do not have the sharpness that Parsons wants to see in them, and Parsons inadvertently projects abstract structures into his ‘intuitive model’. This diagnosis is exemplified with respect to (a) Parsons’ distinction between addition and multiplication on the one hand and exponentiation on the other and (b) his analysis of arithmetical knowledge in simple cases like “7 + 5 = 12”. All in all, it is claimed that Parsons book contains many important insights with respect to, for example, different versions structuralism, the notion of “natural number” and its uniqueness, induction, predicativity and other things, for which he is rightly famous, but that his way of drawing on the notion of intuition leaves too many questions unanswered. (shrink)

WHAT IS PERHAPS the most influential of all theories of knowledge maintains that the content of knowledge and the known are identical in nature. The view goes back to Pythagoras, with his doctrine that reality is at once constituted of and known by means of geometrized numbers. Over the course of time, these numbers have been replaced by other equally startling candidates. The Platonic Idea, the Leibnizian Simple, the Berkeleyan Notion, the Humean Impression, the Peircean Third, (...) and the Whiteheadean Feeling differ from one another in origin, range and career, but like Pythagoras' numbers, all function both as the content of knowledge and the content of the known. Let us term this the "Pure Identity Theory." A "Partial Identity Theory" can be obtained by supposing that the content of knowledge is a fainter version of the content known, or that the content known offers a blurred version of the content of knowledge. In the end, I think, we must hold an Identity Theory. But we must first radically alter the way it has been traditionally viewed and used. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.3 (2004) 19-35 [Access article in PDF] Moderate Formalism As a Theory of the Aesthetic Glenn Parsons Art history and art criticism explore, classify, and critique artworks from a number of perspectives. Their cultural, political, and moral significance are all of interest in this regard. This variety of perspectives notwithstanding, one way of considering artworks retains a central position for these disciplines. Despite (...) perennial shifting in conceptions of the purpose and nature of art, the aesthetic appreciation of art remains at the center of our practices for classifying and evaluating it. Without claiming that the aesthetic dimension of art is the only proper focus of its appreciation or that the aesthetic is a very clearly understood notion, we may say that some degree of contact with the aesthetic is what makes our consideration of an artwork an appreciation of it as art, rather than as historical artifact, manifestation of cultural ideology, and so on.In light of the central position of aesthetic appreciation in art history and criticism, an important concern regarding aesthetic education is what sort of knowledge, if any, is required for appropriate aesthetic appreciation of an artwork. Is knowledge of the historical context of an artwork required for appropriate aesthetic appreciation of it, or is its historical dimension a separate matter, perhaps worthy of appreciation in its own right but not relevant to the appreciation of the artistic achievement of the work? Virtually all modern theories of the aesthetic agree that in order to appreciate an artwork aesthetically, we need to perceive attentively certain of its perceptual properties, such as its shape and color. They differ, however, on whether such attentive perception is sufficient for appropriate aesthetic appreciation. On the one hand we have cognitivist views, which assert that, in addition to this sort of attentive perception, certain kinds of knowledge about the object of appreciation are required for appropriate aesthetic appreciation. On the other hand we have non-cognitivist views, which deny that such knowledge is necessary for appropriate aesthetic appreciation. According to the latter, the aesthetic qualities of an artwork, such as its gracefulness, [End Page 19] are formal in the sense that they depend only upon those perceptual properties, such as color, shape, and size, that constitute the "sensory surface" of the work.1 These properties, apparent to the attentive observer, are the only properties of the object to which one need attend in order to appreciate its gracefulness. Other properties of the painting, such as its depicting German peasants or having been rendered by a communist, are irrelevant to its aesthetic qualities, and knowledge about them is not required for its appropriate aesthetic appreciation. Today this non-cognitivist position is generally called formalism.2In the twentieth century, philosophical aesthetics largely rejected such views in favor of models of aesthetic appreciation with a richer cognitive element. This movement away from formalism has a number of dimensions, including the efforts of feminists to establish the aesthetic value of activist art, the desire to make sense of well-established practices of art appreciation, a growing awareness of the role that beliefs play in our aesthetic responses, the effort to do justice to the aesthetic character of the natural environment, and conceptual difficulties internal to formalism itself.3 Recently, however, some philosophers have revived the spirit, if not the letter, of formalism. Acknowledging widespread criticism of early formalists, such as Clive Bell, they concede that these theorists overstated the case when they claimed that all aesthetic qualities depend on nothing beyond the sensory surface of the object.4 The new formalists, in contrast, claim only that some aesthetic qualities are of this character. They call this doctrine moderate formalism, in contrast to the extreme formalism defended by earlier formalists.5By adopting this more modest position, moderate formalists can accommodate many of the criticisms that led to the decline of extreme formalism. However, if it turns out that only a handful of relatively unimportant aesthetic qualities are formal in nature, then moderate formalism would hardly make an impressively "formalist" theory of the... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.3 (2004) 19-35 [Access article in PDF] Moderate Formalism As a Theory of the Aesthetic Glenn Parsons Art history and art criticism explore, classify, and critique artworks from a number of perspectives. Their cultural, political, and moral significance are all of interest in this regard. This variety of perspectives notwithstanding, one way of considering artworks retains a central position for these disciplines. Despite (...) perennial shifting in conceptions of the purpose and nature of art, the aesthetic appreciation of art remains at the center of our practices for classifying and evaluating it. Without claiming that the aesthetic dimension of art is the only proper focus of its appreciation or that the aesthetic is a very clearly understood notion, we may say that some degree of contact with the aesthetic is what makes our consideration of an artwork an appreciation of it as art, rather than as historical artifact, manifestation of cultural ideology, and so on.In light of the central position of aesthetic appreciation in art history and criticism, an important concern regarding aesthetic education is what sort of knowledge, if any, is required for appropriate aesthetic appreciation of an artwork. Is knowledge of the historical context of an artwork required for appropriate aesthetic appreciation of it, or is its historical dimension a separate matter, perhaps worthy of appreciation in its own right but not relevant to the appreciation of the artistic achievement of the work? Virtually all modern theories of the aesthetic agree that in order to appreciate an artwork aesthetically, we need to perceive attentively certain of its perceptual properties, such as its shape and color. They differ, however, on whether such attentive perception is sufficient for appropriate aesthetic appreciation. On the one hand we have cognitivist views, which assert that, in addition to this sort of attentive perception, certain kinds of knowledge about the object of appreciation are required for appropriate aesthetic appreciation. On the other hand we have non-cognitivist views, which deny that such knowledge is necessary for appropriate aesthetic appreciation. According to the latter, the aesthetic qualities of an artwork, such as its gracefulness, [End Page 19] are formal in the sense that they depend only upon those perceptual properties, such as color, shape, and size, that constitute the "sensory surface" of the work.1 These properties, apparent to the attentive observer, are the only properties of the object to which one need attend in order to appreciate its gracefulness. Other properties of the painting, such as its depicting German peasants or having been rendered by a communist, are irrelevant to its aesthetic qualities, and knowledge about them is not required for its appropriate aesthetic appreciation. Today this non-cognitivist position is generally called formalism.2In the twentieth century, philosophical aesthetics largely rejected such views in favor of models of aesthetic appreciation with a richer cognitive element. This movement away from formalism has a number of dimensions, including the efforts of feminists to establish the aesthetic value of activist art, the desire to make sense of well-established practices of art appreciation, a growing awareness of the role that beliefs play in our aesthetic responses, the effort to do justice to the aesthetic character of the natural environment, and conceptual difficulties internal to formalism itself.3 Recently, however, some philosophers have revived the spirit, if not the letter, of formalism. Acknowledging widespread criticism of early formalists, such as Clive Bell, they concede that these theorists overstated the case when they claimed that all aesthetic qualities depend on nothing beyond the sensory surface of the object.4 The new formalists, in contrast, claim only that some aesthetic qualities are of this character. They call this doctrine moderate formalism, in contrast to the extreme formalism defended by earlier formalists.5By adopting this more modest position, moderate formalists can accommodate many of the criticisms that led to the decline of extreme formalism. However, if it turns out that only a handful of relatively unimportant aesthetic qualities are formal in nature, then moderate formalism would hardly make an impressively "formalist" theory of the... (shrink)

This book was inadvertently published with the addition of the editor’s name, C. J. Posy, as co-author of the chapter. His name has been removed now and the author’s name Saul A. Kripke has been updated in the chapter.

In accord with the theme of the present volume on , it is not so much the aim of this essay to provide a detailed account of particular lines of argument, as it is to suggest something of the manner in which so-called 'Buddhist idealism' unfolded as a tradition not just for Buddhists, but within Indian philosophy more generally. Seen from this perspective, Buddhist idealism remained a current within Indian philosophy long after the demise of Buddhism in India, in about (...) the twelfth century, and endured in some respects at least until the Mughal age, when the last thinker to be examined here, the Jain teacher Yaśovijaya, was active. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.3 (2004) 19-35 [Access article in PDF] Moderate Formalism As a Theory of the Aesthetic Glenn Parsons Art history and art criticism explore, classify, and critique artworks from a number of perspectives. Their cultural, political, and moral significance are all of interest in this regard. This variety of perspectives notwithstanding, one way of considering artworks retains a central position for these disciplines. Despite (...) perennial shifting in conceptions of the purpose and nature of art, the aesthetic appreciation of art remains at the center of our practices for classifying and evaluating it. Without claiming that the aesthetic dimension of art is the only proper focus of its appreciation or that the aesthetic is a very clearly understood notion, we may say that some degree of contact with the aesthetic is what makes our consideration of an artwork an appreciation of it as art, rather than as historical artifact, manifestation of cultural ideology, and so on.In light of the central position of aesthetic appreciation in art history and criticism, an important concern regarding aesthetic education is what sort of knowledge, if any, is required for appropriate aesthetic appreciation of an artwork. Is knowledge of the historical context of an artwork required for appropriate aesthetic appreciation of it, or is its historical dimension a separate matter, perhaps worthy of appreciation in its own right but not relevant to the appreciation of the artistic achievement of the work? Virtually all modern theories of the aesthetic agree that in order to appreciate an artwork aesthetically, we need to perceive attentively certain of its perceptual properties, such as its shape and color. They differ, however, on whether such attentive perception is sufficient for appropriate aesthetic appreciation. On the one hand we have cognitivist views, which assert that, in addition to this sort of attentive perception, certain kinds of knowledge about the object of appreciation are required for appropriate aesthetic appreciation. On the other hand we have non-cognitivist views, which deny that such knowledge is necessary for appropriate aesthetic appreciation. According to the latter, the aesthetic qualities of an artwork, such as its gracefulness, [End Page 19] are formal in the sense that they depend only upon those perceptual properties, such as color, shape, and size, that constitute the "sensory surface" of the work.1 These properties, apparent to the attentive observer, are the only properties of the object to which one need attend in order to appreciate its gracefulness. Other properties of the painting, such as its depicting German peasants or having been rendered by a communist, are irrelevant to its aesthetic qualities, and knowledge about them is not required for its appropriate aesthetic appreciation. Today this non-cognitivist position is generally called formalism.2In the twentieth century, philosophical aesthetics largely rejected such views in favor of models of aesthetic appreciation with a richer cognitive element. This movement away from formalism has a number of dimensions, including the efforts of feminists to establish the aesthetic value of activist art, the desire to make sense of well-established practices of art appreciation, a growing awareness of the role that beliefs play in our aesthetic responses, the effort to do justice to the aesthetic character of the natural environment, and conceptual difficulties internal to formalism itself.3 Recently, however, some philosophers have revived the spirit, if not the letter, of formalism. Acknowledging widespread criticism of early formalists, such as Clive Bell, they concede that these theorists overstated the case when they claimed that all aesthetic qualities depend on nothing beyond the sensory surface of the object.4 The new formalists, in contrast, claim only that some aesthetic qualities are of this character. They call this doctrine moderate formalism, in contrast to the extreme formalism defended by earlier formalists.5By adopting this more modest position, moderate formalists can accommodate many of the criticisms that led to the decline of extreme formalism. However, if it turns out that only a handful of relatively unimportant aesthetic qualities are formal in nature, then moderate formalism would hardly make an impressively "formalist" theory of the... (shrink)

According to mathematical platonism, mathematical entities (e.g. numbers) exist as abstract objects. If numbers are abstract objects, then I doubt our ability to know of their existence.objects lack causal powers and spatio-temporal location. On the other hand, we human knowers exist within the causal nexus and are wholly spatio-temporal. So our epistemic isolation from abstract objects is total and unbridgeable (Benacerraf 1973, Cheyne 2001). Any version of mathematical platonism that is worth (...) taking seriously must claim that we can and do know of the existence of abstract objects. Since I deny that knowledge of the existence of abstract objects is possible, I reject mathematical platonism. (shrink)

This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and (...) algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society. (shrink)

In this essay, I show how Thomas Aquinas circumscribes epistemological questions concerning both the possibility and character of our knowledge of God within a larger eschatological framework that acknowledges the beatific vision as the ultimate good that we desire as well as the ultimate end for which we were created. Thus, knowledge of God is possible and actual on Aquinas's view because it is eternally rather than merely temporally indexed—that is, properly attributable to the blessed in heaven and (...) only derivatively attributable to persons of faith. I further argue that interpreting Aquinas's account of faith in the light of his account of the beatific vision allows us to carve out polemical space for the theologically realist claim that there can be and in fact is objectivity in our knowledge of God, whether that knowledge comes through faith (in this life) or the beatific vision (in the next life). (shrink)

Many formalisms for reasoning about knowing commit an agent to be logically omniscient. Logical omniscience is an unrealistic principle for us to use to build a real-world agent, since it commits the agent to knowing infinitely many things. A number of formalizations of knowledge have been developed that do not ascribe logical omniscience to agents. With few exceptions, these approaches are modifications of the possible-worlds semantics. In this paper we use a combination of several general techniques for building non-omniscient (...) reasoners. First we provide for the explicit representation of notions such as problems, solutions, and problem solving activities, notions which are usually left implicit in the discussions of autonomous agents. A second technique is to take explicitly into account the notion of resource when we formalize reasoning principles. We use the notion of resource to describe interesting principles of reasoning that are used for ascribing knowledge to agents. For us, resources are abstract objects. We make extensive use of ordering and inaccessibility relations on resources, but we do not find it necessary to define a metric. Using principles about resources without using a metric is one of the strengths of our approach.We describe the architecture of a reasoner, built from a finite number of components, who solves a puzzle, involving reasoning about knowing, by explicitly using the notion of resource. Our approach allows the use of axioms about belief ordinarily used in problem solving – such as axiom K of modal logic – without being forced to attribute logical omniscience to any agent. In particular we address the issue of how we can use resource-unbounded (e.g., logically omniscient) reasoning to attribute knowledge to others without introducing contradictions. We do this by showing how omniscient reasoning can be introduced as a conservative extension over resource-bounded reasoning. (shrink)

Part of Frege's concern about whether number words are properties of objects was that if they could be construed as such it would lend support to the view that truths of arithmetic were empirical truths. Such concern is ill-founded. Even if number words do apply to objects as predicates, this does not entail that numerical truths would be empirical, any more than the fact that ‘bachelor’ and ‘unmarried’ are predicates of objects entails that their relationship is an (...) empirical one. The account of number words as predicates given here, consequently, should not be taken as supportive of any one particular theory concerning arithmetic truth rather than another.The view of number words that emerges above from the criticism of Frege's arguments is that sentences containing number words can and do say something about objects in a collective and syncategorematic way. That is, they say something about classes of objects, when it is clear what is to count as an object. Whether this view commits us to accepting certain ontological entities, classes of individuals, above and beyond individuals themselves, I am not prepared to say, and at any rate this question falls beyond the intended scope of this essay. To those who would eschew abstract entities, however, it may be noted that the ontological problems that arise are not peculiar to this view; they seem no more or less severe than those that arise in connection with other collective predicate statements, as, for example, “Blue whales are becoming extinct.”The view presented here also does not pretend to be a fatal criticism of the logicist program. Taking our cue from the above noted fact that syncategorematic predicates share in a common ‘partial’ abstract sense, it seems reasonable to say that it is just the set of such partial senses of number words, and the relationships that hold between such senses, that the logicist and the pure number theorist investigate. (shrink)

Bertrand Russell’s philosophy around 1914 is often interpreted as phenomenalism, the view that sensations are not caused by but rather constitute ordinary objects. Indeed, prima facie, his 1914 Our Knowledge of the External World reduces objects to sense-data. However, Russell did not think his view was phenomenalist, and he said that he never gave up either the causal theory of perception or a realist understanding of objects. In this paper I offer an explanation of why Russell (...) might have undertaken the constructionist project of his 1914 work while not considering the resulting position that objects can be constructed out of sense-data to be phenomenalist. (shrink)

This article sets out to analyse some of the most basic elements of our number concept - of our awareness of the one and the many in their coherence with multiplicity, succession and equinumerosity. On the basis of the definition given by Cantor and the set theoretical definition of cardinal numbers and ordinal numbers provided by Ebbinghaus, a critical appraisal is given of Frege’s objection that abstraction and noticing (or disregarding) differences between entities do not produce the concept (...) of number. By introducing the notion of subject functions, an account is advanced of the (nominalistic) reason why Frege accepted physical, kinematic and spatial properties (subject functions) of entities, but denied the ontic status of their quantitative properties (their quantitative subject function). With reference to intuitionistic mathematics (Brouwer, Weyl, Troelstra, Kreisel, Van Dalen) the primitive meaning of succession is acknowledged and connected to an analysis of what is entailed in the term ‘Gleichzahligkeit’ (‘equinumerosity’). This expression enables an analysis of the connections between ordinality and cardinality on the one hand and succession and wholeness (totality) on the other. The conceptions of mathematicians such as Frege, Cantor, Dedekind, Zermelo, Brouwer, Skolem, Fraenkel, Von Neumann, Hilbert, Bernays and Weyl, as well as the views of the philosopher Cassirer, are discussed in order to arrive at an assessment of the relation between ordinality and cardinality (also taking into account the relation between logic and arithmetic) - and on the basis of this evaluation, attention is briefly given to the definition of an ordered pair in axiomatic set theory (with reference to the set theory of Zermelo-Fraenkel) and to the defmition of an ordered pair advanced by Wiener and Kuratowski. (shrink)

The new Chomskian orthodoxy denies that our linguistic competence gives us knowledge *of* a language, and that the representations in the language faculty are representations *of* anything. In reply, I have argued that through their intuitions speaker/hearers, (but not their language faculties) have knowledge of language, though not of any externally existing language. In order to count as knowledge, these intuitions must track linguistic facts represented in the language faculty. I defend this idea against the objections Collins (...) has raised to such an account. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.3 (2003) 78-98 [Access article in PDF] Aesthetic Understanding as Informed Experience:The Role of Knowledge in Our Art Viewing Experiences Richard Lachapelle, Deborah Murray, and Sandy Neim [Figures] Thinking calls for images, and images contain thought. Therefore, the visual arts are a homeground of visual thinking. 1A common misconception about the nature of art and of aesthetic appreciation is that these activities (...) are essentially a question of "feeling," as if tuning in to the right feeling will automatically lead to a full understanding of the work of art. Another widespread misunderstanding essentially reduces art viewing to a simple question of perception, as if looking long and hard isalways enough to apprehend the work of art's message. Fortunately, a growing body of research into adults' art viewing experiences is debunking these widely held beliefs as oversimplifications of the art viewing process. We can now assert, with a good degree of certainty, that our art viewing experiences solicit four key areas: the affective, perceptual, communicative, and cognitive dimensions of human experiencing. 2 Therefore, we would be hard-pressed not to agree with Rudolph Arnheim's reflections, presented above, on the important role of thought in shaping our artistic and aesthetic experiences.While acknowledging at the outset the essential roles of affect, perception, and communication in our art viewing experiences, this paper focuses more specifically on aspects of the intellectual dimension of this experience. First, we will present and discuss a model that we have developed over the last several years. This model identifies the kinds of knowledge and learning involved in art viewing activities. Second, we will present the results of an empirical study conducted to provide support for the model. Finally we will briefly discuss the model's usefulness for the purposes of aesthetic education. [End Page 78] The Model of Aesthetic Understanding as Informed Experience The Model of Aesthetic Understanding as Informed Experience provides an explanation of the process of understanding and appreciating a work of art from an educational perspective: it identifies the types of knowledge involved and it also pinpoints the kinds of learning at each stage in the process leading to an understanding of the aesthetic object.In this model, the process of viewing and understanding a work of art is visualized as a two-phased type of informed experience. Through a process of experiential learning, the viewer first encounters the work of art and formulates an initial interpretation. Then, through a process involving theoretical learning, the viewer compares his or her first interpretation with a related body of external, scientific information. This second step in the learning process leads to a reconstruction of knowledge about the work of art. Tandem use of the two processes assists the viewer in furthering his or her understanding of the art object; it also promotes growth in his or her art viewing skills. In the course of each new encounter with an aesthetic object, the interplay of experiential and theoretical learning leads to additional development of the viewer's background knowledge in art, resulting in better preparedness to successfully engage the next work of art. 4 Theoretical Foundations of the Model Three different theories informed the development of the model. 5 By using anecdotal evidence obtained from a group of fifty-two museum professionals, Mihaly Csikszentmihalyi and Rick E.Robinson were able to identify the four major dimensions of aesthetic experience: intellect, communication, perception, and emotion. Each one of these dimensions constitutes, to some extent, a challenge that the work of art addresses to the viewer. According to these researchers, the intellectual dimension of aesthetic experience consists of all aspects of the viewer's attempts to use knowledge in order to find meaning in the work of art (TAS, 27-71). Csikszentmihalyi and Robinson also propose a model that describes the aesthetic encounter in terms of an interaction between the viewer, the work of art, and the artist. To this encounter, the viewer brings his skills in aesthetic appreciation; these may be... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.3 (2003) 78-98 [Access article in PDF] Aesthetic Understanding as Informed Experience:The Role of Knowledge in Our Art Viewing Experiences Richard Lachapelle, Deborah Murray, and Sandy Neim [Figures] Thinking calls for images, and images contain thought. Therefore, the visual arts are a homeground of visual thinking. 1A common misconception about the nature of art and of aesthetic appreciation is that these activities (...) are essentially a question of "feeling," as if tuning in to the right feeling will automatically lead to a full understanding of the work of art. Another widespread misunderstanding essentially reduces art viewing to a simple question of perception, as if looking long and hard isalways enough to apprehend the work of art's message. Fortunately, a growing body of research into adults' art viewing experiences is debunking these widely held beliefs as oversimplifications of the art viewing process. We can now assert, with a good degree of certainty, that our art viewing experiences solicit four key areas: the affective, perceptual, communicative, and cognitive dimensions of human experiencing. 2 Therefore, we would be hard-pressed not to agree with Rudolph Arnheim's reflections, presented above, on the important role of thought in shaping our artistic and aesthetic experiences.While acknowledging at the outset the essential roles of affect, perception, and communication in our art viewing experiences, this paper focuses more specifically on aspects of the intellectual dimension of this experience. First, we will present and discuss a model that we have developed over the last several years. This model identifies the kinds of knowledge and learning involved in art viewing activities. Second, we will present the results of an empirical study conducted to provide support for the model. Finally we will briefly discuss the model's usefulness for the purposes of aesthetic education. [End Page 78] The Model of Aesthetic Understanding as Informed Experience The Model of Aesthetic Understanding as Informed Experience provides an explanation of the process of understanding and appreciating a work of art from an educational perspective: it identifies the types of knowledge involved and it also pinpoints the kinds of learning at each stage in the process leading to an understanding of the aesthetic object.In this model, the process of viewing and understanding a work of art is visualized as a two-phased type of informed experience. Through a process of experiential learning, the viewer first encounters the work of art and formulates an initial interpretation. Then, through a process involving theoretical learning, the viewer compares his or her first interpretation with a related body of external, scientific information. This second step in the learning process leads to a reconstruction of knowledge about the work of art. Tandem use of the two processes assists the viewer in furthering his or her understanding of the art object; it also promotes growth in his or her art viewing skills. In the course of each new encounter with an aesthetic object, the interplay of experiential and theoretical learning leads to additional development of the viewer's background knowledge in art, resulting in better preparedness to successfully engage the next work of art. 4 Theoretical Foundations of the Model Three different theories informed the development of the model. 5 By using anecdotal evidence obtained from a group of fifty-two museum professionals, Mihaly Csikszentmihalyi and Rick E.Robinson were able to identify the four major dimensions of aesthetic experience: intellect, communication, perception, and emotion. Each one of these dimensions constitutes, to some extent, a challenge that the work of art addresses to the viewer. According to these researchers, the intellectual dimension of aesthetic experience consists of all aspects of the viewer's attempts to use knowledge in order to find meaning in the work of art (TAS, 27-71). Csikszentmihalyi and Robinson also propose a model that describes the aesthetic encounter in terms of an interaction between the viewer, the work of art, and the artist. To this encounter, the viewer brings his skills in aesthetic appreciation; these may be... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 407-436 [Access article in PDF] Dilthey's Epistemology of the Geisteswissenschaften: Between Lebensphilosophie and Wissenschaftstheorie James Reid A great part of my life's work has been devoted to formulating a universally valid science which should provide the human sciences with a firm foundation and a unified internal coherency.... I am neither an intuitionist, nor a historicist, nor a skeptic. Dilthey to (...) Husserl, 29 June 1911 To show life as it is, that is what we strive for. To describe life: that is our goal.... We want to make life visible in its unfathomable depths, and in its unfathomable nexus. Dilthey, Gesammelte Schriften 19: 330 In the dedication of the first volume of the Einleitung in die Geisteswissenschaften to his friend and philosophical interlocutor Count Yorck, Dilthey famously named what would become his lifelong philosophical preoccupation a Kritik der historischen Vernunft, the overarching aim of which is to provide "an epistemological foundation for the human sciences" that would "determine the interconnections among the particular human sciences, the limits within which knowledge is possible in these sciences, and the relation of their truths to one another." 1 For Dilthey, the liberation of historical consciousness from the "grey cobweb of abstract essences" spun by traditional metaphysics constituted one of the [End Page 407] major intellectual achievements of the nineteenth century. 2 However, as important as the concrete historical investigations of Ranke, Droysen, and Mommsen undoubtedly are, the Historical School nevertheless failed in Dilthey's eyes to grasp the essence of historical consciousness—its scope, limits and objective validity: Its study and evaluation of historical phenomena remain unconnected with the analysis of facts of consciousness; consequently, it has no grounding in the only knowledge which is ultimately secure; it has in short no philosophical foundation. 3A critique of historical reason, grasped as an epistemological analysis of "the capacity of man to know himself and the society and history which he has produced," is needed in order to provide for the Geisteswissenschaften a foundation equivalent to the one furnished by Kant for mathematical natural science in the Kritik der reinen Vernunft. 4The epistemological dimension of Dilthey's project took shape as the elaboration of a basic science (Grundwissenschaft) identified, in the Einleitung at least, with descriptive psychology. 5 In an effort to delimit the province of the Geisteswissenschaften, Dilthey came to distinguish between outer experience and its objects and various levels of inner experience. Although Dilthey's thought developed considerably in the years after 1900, most notably in the direction [End Page 408] of a refinement of the relation between inner and outer experience, the distinction between these two fundamental modes of givenness remained central to his conception of the structure and methodology of the human sciences. 6 In a number of manuscripts, some published in Dilthey's lifetime, others (by far the majority) published after his death by former students, Dilthey envisages a comprehensive theory of consciousness and its objectifications that would shed light on the origins and ultimate validity of our knowledge of the historical world.As several commentators have pointed out, however, the epistemological dimension of Dilthey's project fails to capture the entire breadth of his achievement. 7 Dilthey's interest in the objective validity of historical investigation was subservient to broader concerns about the nature of human existence and its historicity, what Dilthey often referred to simply as Leben. 8 Life as it is revealed in the human sciences is the medium in which self-consciousness and self-knowledge, scientific and practical activity originate, and remains the abiding concern of the human sciences. At the most fundamental level of epistemological reflection, we encounter life as it is lived in pre-scientific and pre-reflective experience (Erlebnis). 9 Life, Dilthey consistently maintained, is the "prius" of thought: Knowledge (Erkenntnis) cannot go behind life, of which it is a function. Life always remains the presupposition of knowledge, i.e., of the consciousness or knowledge (Wissen) contained in life. As a presupposition of knowledge (des Erkennens) itself, life is [End... (shrink)

The norm of assertion, to be in force, is a social norm. What is the content of our social norm of assertion? Various linguistic arguments purport to show that to assert is to represent oneself as knowing. But to represent oneself as knowing does not entail that assertion is governed by a knowledge norm. At best these linguistic arguments provide indirect support for a knowledge norm. Furthermore, there are alternative, non-normative explanations for the linguistic data (as in recent (...) work from Van Elswyk). Direct arguments would rely on normative judgments about the permissibility or impermissibility of assertions with and without the speaker knowing the content asserted. John Turri's work experimental results purport to show that our norm of assertion is factive, and probably knowledge. But as a number of recent experimentalists (Kneer, Reuter and Broessel, Marsili and Wiegmann) have shown, Turri's results rely on the problemmatic use of 'should' as in 'Maria should assert that she owns a 1990 watch.' Correcting for this, these experimentalists provide strong evidence that our norm of assertion is not factive. The standard reply to evidence like this from the assertion of unlucky falsehoods is the excuse maneuver. But Marsili and Wiegmann, following Turri's protocol for testing for excuse validation, show that participants who judge that assertions unlucky falsehoods are permissible are not guilty of excuse validation. Given our current understanding of the experimental evidence, knowledge is not our norm of assertion. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 407-436 [Access article in PDF] Dilthey's Epistemology of the Geisteswissenschaften: Between Lebensphilosophie and Wissenschaftstheorie James Reid A great part of my life's work has been devoted to formulating a universally valid science which should provide the human sciences with a firm foundation and a unified internal coherency.... I am neither an intuitionist, nor a historicist, nor a skeptic. Dilthey to (...) Husserl, 29 June 1911 To show life as it is, that is what we strive for. To describe life: that is our goal.... We want to make life visible in its unfathomable depths, and in its unfathomable nexus. Dilthey, Gesammelte Schriften 19: 330 In the dedication of the first volume of the Einleitung in die Geisteswissenschaften to his friend and philosophical interlocutor Count Yorck, Dilthey famously named what would become his lifelong philosophical preoccupation a Kritik der historischen Vernunft, the overarching aim of which is to provide "an epistemological foundation for the human sciences" that would "determine the interconnections among the particular human sciences, the limits within which knowledge is possible in these sciences, and the relation of their truths to one another." 1 For Dilthey, the liberation of historical consciousness from the "grey cobweb of abstract essences" spun by traditional metaphysics constituted one of the [End Page 407] major intellectual achievements of the nineteenth century. 2 However, as important as the concrete historical investigations of Ranke, Droysen, and Mommsen undoubtedly are, the Historical School nevertheless failed in Dilthey's eyes to grasp the essence of historical consciousness—its scope, limits and objective validity: Its study and evaluation of historical phenomena remain unconnected with the analysis of facts of consciousness; consequently, it has no grounding in the only knowledge which is ultimately secure; it has in short no philosophical foundation. 3A critique of historical reason, grasped as an epistemological analysis of "the capacity of man to know himself and the society and history which he has produced," is needed in order to provide for the Geisteswissenschaften a foundation equivalent to the one furnished by Kant for mathematical natural science in the Kritik der reinen Vernunft. 4The epistemological dimension of Dilthey's project took shape as the elaboration of a basic science (Grundwissenschaft) identified, in the Einleitung at least, with descriptive psychology. 5 In an effort to delimit the province of the Geisteswissenschaften, Dilthey came to distinguish between outer experience and its objects and various levels of inner experience. Although Dilthey's thought developed considerably in the years after 1900, most notably in the direction [End Page 408] of a refinement of the relation between inner and outer experience, the distinction between these two fundamental modes of givenness remained central to his conception of the structure and methodology of the human sciences. 6 In a number of manuscripts, some published in Dilthey's lifetime, others (by far the majority) published after his death by former students, Dilthey envisages a comprehensive theory of consciousness and its objectifications that would shed light on the origins and ultimate validity of our knowledge of the historical world.As several commentators have pointed out, however, the epistemological dimension of Dilthey's project fails to capture the entire breadth of his achievement. 7 Dilthey's interest in the objective validity of historical investigation was subservient to broader concerns about the nature of human existence and its historicity, what Dilthey often referred to simply as Leben. 8 Life as it is revealed in the human sciences is the medium in which self-consciousness and self-knowledge, scientific and practical activity originate, and remains the abiding concern of the human sciences. At the most fundamental level of epistemological reflection, we encounter life as it is lived in pre-scientific and pre-reflective experience (Erlebnis). 9 Life, Dilthey consistently maintained, is the "prius" of thought: Knowledge (Erkenntnis) cannot go behind life, of which it is a function. Life always remains the presupposition of knowledge, i.e., of the consciousness or knowledge (Wissen) contained in life. As a presupposition of knowledge (des Erkennens) itself, life is [End... (shrink)

In Fredericks (2018b), I argued that we can be morally responsible for our concepts if they are mental representations. Here, I make a complementary argument for the claim that even if concepts are abstract objects, we can be morally responsible for coming to grasp and for thinking (or not thinking) in terms of them. As before, I take for granted Angela Smith's (2005) rational relations account of moral responsibility, though I think the same conclusion follows from various other (...) accounts. My strategy is to focus on the relations that can obtain between concepts (understood as abstract objects) and morally responsible agents. I conclude by discussing some of the reasons why my arguments matter, which have to do with consequential choices between conceptual options, purposefully seeking out concepts that are new to us, and moral education. (shrink)