"La gente dice una y otra vez que la filosofía no progresa realmente, que todavía estamos ocupados con los mismos problemas filosóficos que los griegos. Pero la gente que dice esto no entiende por qué tiene que ser así. Es porque nuestro lenguaje ha permanecido igual y nos sigue seduciendo para que hagan las mismas preguntas. Mientras siga habiendo un verbo "ser" que parezca como si funciona de la misma manera que "comer y beber", siempre y cuando todavía tengamos (...) los adjetivos "idénticos", "verdaderos", "falsos", "posibles", siempre y cuando sigamos hablando de un río de tiempo, , de una extensión de espacio, etc., etc., la gente seguirá tropezando con las mismas dificultades desconcertante y se encontrará mirando a algo que ninguna explicación parece capaz de aclarar. Y lo que es más, esto satisface un anhelo de lo trascendente, porque, en la medida en que la gente cree que puede ver el ‘límites de la comprensión humana ́, creen, por supuesto, que pueden ver más allá de estos. ' ' Esta cita es de Ludwig Wittgenstein que redefinió la filosofía hace unos 70 años (pero la mayoría de la gente todavía tiene que averiguarlo). Dennett, aunque ha sido un filósofo desde hace unos 40 años, es uno de ellos. También es curioso que tanto él como su antagonista principal, John Searle, estudiaron bajo los famosos Wittgensteinianos (Searle con John Austin, Dennett con Gilbert Ryle) pero Searle Más o menos consiguió el punto y Dennett no, (aunque se está estirando cosas para llamar Searle o Ryle Wittgensteinianos). Dennett es un determinista duro (aunque intenta escabullirse de la realidad en la puerta trasera), y tal vez esto se deba a Ryle, cuyo famoso libro ́el concepto de la mente ́ (1949) continúa siendo reimpreso. Ese libro hizo un gran trabajo de exorcizar al fantasma, pero dejó la máquina. A Dennett le gusta cometer los errores que Wittgenstein, Ryle (y muchos otros desde entonces) han expuesto en detalle. Nuestro uso de las palabras consciencia, elección, libertad, intención, partícula, pensamiento, determina, oleada, causa, ocurrió, evento (y así sucesivamente) raramente son una fuente de confusión, pero tan pronto como dejamos la vida normal y entramos en la filosofía (y cualquier discusión separada del entorno en el que el lenguaje evolucionó— es decir, el contexto exacto en el que las palabras tenían sentido) reina el caos. Como la mayoría, Dennett carece de un marco coherente - que Searle ha llamado la estructura lógica de la racionalidad. Me he expandido en este considerablemente desde que escribí esta reseña y mis artículos recientes muestran en detalle lo que está mal con el enfoque de Dennett a la filosofía, que uno podría llamar scientismo en esteroides. Permítanme terminar con otra cita de Wittgenstein--́la ambición es la muerte del pensamiento ́. Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna Doe Sistemas Punto de Vista puede consultar mi libro 'La estructura lógica de la filosofía, la psicología, la mente y lenguaje en Ludwig Wittgenstein y John Searle ' 2nd ED (2019). Los interesados en más de mis escritos pueden ver 'Monos parlantes--filosofía, psicología, ciencia, religión y política en un planeta condenado--artículos y reseñas 2006-2019 3rd ED (2019) y delirios utópicos suicidas en el siglo 21 4a Ed (2019) y otras. (shrink)

Personal AI assistants are now nearly ubiquitous. Every leading smartphone operating system comes with a personal AI assistant that promises to help you with basic cognitive tasks: searching, planning, messaging, scheduling and so on. Usage of such devices is effectively a form of algorithmic outsourcing: getting a smart algorithm to do something on your behalf. Many have expressed concerns about this algorithmic outsourcing. They claim that it is dehumanising, leads to cognitive degeneration, and robs us of our freedom and autonomy. (...) Some people have a more subtle view, arguing that it is problematic in those cases where its use may degrade important interpersonal virtues. In this article, I assess these objections to the use of AI assistants. I will argue that the ethics of their use is complex. There are no quick fixes or knockdown objections to the practice, but there are some legitimate concerns. By carefully analysing and evaluating the objections that have been lodged to date, we can begin to articulate an ethics of personal AI use that navigates those concerns. In the process, we can locate some paradoxes in our thinking about outsourcing and technological dependence, and we can think more clearly about what it means to live a good life in the age of smart machines. (shrink)

We argue that intentions are beliefs—beliefs that are held in light of, and made rational by, practical reasoning. To intend to do something is neither more nor less than to believe, on the basis of one’s practical reasoning, that one will do it. The identification of the mental state of intention with the mental state of belief is what we call strong cognitivism about intentions. It is a strong form of cognitivism because we identify intentions with beliefs, rather than maintaining (...) that beliefs are entailed by intentions or are components of them. (shrink)

Five experiments demonstrate the central role of knowledge attributions in social evaluations. In Experiments 1–3, we manipulated whether an agent believes, is certain of, or knows a true proposition and asked people to rate whether the agent should perform a variety of actions. We found that knowledge, more so than belief or certainty, leads people to judge that the agent should act. In Experiments 4–5, we investigated whether attributions of knowledge or certainty can explain an important finding on how people (...) act based on statistical evidence, known as “the Wells effect”. We found that knowledge attributions, but not certainty attributions, mediate this effect on decision making. 2018 APA, all rights reserved). (shrink)

Many policies and ethical guidelines recommend developing “trustworthy AI”. We argue that developing morally trustworthy AI is not only unethical, as it promotes trust in an entity that cannot be trustworthy, but it is also unnecessary for optimal calibration. Instead, we show that reliability, exclusive of moral trust, entails the appropriate normative constraints that enable optimal calibration and mitigate the vulnerability that arises in high-stakes hybrid decision-making environments, without also demanding, as moral trust would, the anthropomorphization of AI and thus (...) epistemically dubious behavior. The normative demands of reliability for inter-agential action are argued to be met by an analogue to procedural metacognitive competence (i.e., the ability to evaluate the quality of one’s own informational states to regulate subsequent action). Drawing on recent empirical findings that suggest providing reliability scores (e.g., F1-scores) to human decision-makers improves calibration in the AI system, we argue that reliability scores provide a good index of competence and enable humans to determine how much they wish to rely on the system. (shrink)

A principal conclusion supported by convergent evidence from cognitive science, life science, and philosophy is that knowledge is a central norm of assertion—that is, according to the rules of the practice, assertions should express knowledge. That view has recently been challenged with new experiments. This paper identifies a critical confound in the experiments. In the process, a new study is reported that provides additional support for the view that knowledge is a central norm of assertion.

We think we have lots of substantial knowledge about the future. But contemporary wisdom has it that indeterminism prevails in such a way that just about any proposition about the future has a non-zero objective chance of being false.2, 3 What should one do about this? One, pessimistic, reaction is scepticism about knowledge of the future. We think this should be something of a last resort, especially since this scepticism is likely to infect alleged knowledge of the present and past. (...) One anti-sceptical strategy is to pin our hopes on determinism, conceding that knowledge of the future is unavailable in an indeterministic world. This is not satisfying either: we would rather not be hostage to empirical fortune in the way that this strategy recommends. A final strategy, one that we shall explore in this paper, is one of reconciliation: knowledge of a proposition is compatible with a subject’s belief having a non-zero objective chance of error.4 Following Williamson, we are interested in tying knowledge to the presence or absence of error in close cases, and so we shall explore the connections between knowledge and objective chance within such a framework. We don’t want to get tangled up here in complications involved in attempting to formulate a necessary and sufficient condition for knowledge in terms of safety. Instead, we will assume the following rough and ready necessary condition: a subject knows P only if she could not easily have falsely believed P.5 Assuming that easiness is to be spelt.. (shrink)

This paper connects recent findings from experimental epistemology to several major themes in classical Indian epistemology. First, current evidence supports a specific account of the ordinary knowledge concept in contemporary anglophone American culture. According to this account, known as abilism, knowledge is a true representation produced by cognitive ability. I present evidence that abilism closely approximates Nyāya epistemology’s theory of knowledge, especially that found in the Nyāya-sūtra. Second, Americans are more willing to attribute knowledge of positive facts than of negative (...) facts, especially when such facts are inferred and even when the positive and negative “facts” are logically equivalent. Similar suspicions about knowledge of negative facts seemingly occur in classical Indian epistemology, suggesting that the asymmetry might not be an American quirk but instead reflect a cross-culturally robust tendency in knowledge attributions. Each of these themes—abilism and the positive/negative asymmetry—presents an exciting opportunity for further research in experimental cross-cultural epistemology. (shrink)

Influentially, Pamela Hieronymi has argued that any account of forgiveness must be both articulate and uncompromising. It must articulate the change in judgement that results in the forgiver’s loss of resentment without excusing or justifying the misdeed, and without comprising a commitment to the transgressor=s responsibility, the wrongness of the action, and the transgressed person=s self-worth. Non-articulate accounts of forgiveness, which rely on indirect strategies for reducing resentment (for example, reflecting on the transgressor’s bad childhood) are said to fail to (...) explain forgiveness. I argue that the articulateness condition is not a necessary condition for forgiveness. I respond to numerous objections advanced against non-articulate accounts, including the claim that the resentment-mitigating practices they involve amount to excusing. Appealing to P.F. Strawson=s distinction between objective and participant attitudes, I argue that forgivers can take transgressors to be detrimentally causally shaped by their past while holding him them to be morally responsible. (shrink)

This paper proposes a novel experimental approach that would help to determine whether perspectival shapes, such as the elliptical profile of a tilted plate or coin, are part of perceptual experience. If they are part of perceptual experience, then it should be possible to identify these shapes simply by attending appropriately to them. Otherwise, in order to identify perspectival shapes they must first be constructed in the visual imagination. We propose that these accounts of perspectival identification can be tested by (...) measuring the interference between visual and verbal working memory load, respectively, and the identification of perspectival shapes in the appearance of a 3D object. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

In a recent very interesting and important challenge to tracking theories of knowledge, Williams & Sinhababu claim to have devised a counter-example to tracking theories of knowledge of a sort that escapes the defense of those theories by Adams & Clarke. In this paper we will explain why this is not true. Tracking theories are not undermined by the example of the backward clock, as interesting as the case is.

The evolution of life on Earth has produced an organism that is beginning to model and understand its own evolution and the possible future evolution of life in the universe. These models and associated evidence show that evolution on Earth has a trajectory. The scale over which living processes are organized cooperatively has increased progressively, as has its evolvability. Recent theoretical advances raise the possibility that this trajectory is itself part of a wider developmental process. According to these theories, the (...) developmental process has been shaped by a yet larger evolutionary dynamic that involves the reproduction of universes. This evolutionary dynamic has tuned the key parameters of the universe to increase the likelihood that life will emerge and produce outcomes that are successful in the larger process (e.g. a key outcome may be to produce life and intelligence that intentionally reproduces the universe and tunes the parameters of ‘offspring’ universes). Theory suggests that when life emerges on a planet, it moves along this trajectory of its own accord. However, at a particular point evolution will continue to advance only if organisms emerge that decide to advance the developmental process intentionally. The organisms must be prepared to make this commitment even though the ultimate nature and destination of the process is uncertain, and may forever remain unknown. Organisms that complete this transition to intentional evolution will drive the further development of life and intelligence in the universe. Humanity’s increasing understanding of the evolution of life in the universe is rapidly bringing it to the threshold of this major evolutionary transition. (shrink)

The Double Content view is the first comprehensive theory of art that is able to satisfactorily explain the nature of all kinds of artworks in a unified way — whether paintings, novels, or musical and theatrical performances. The basic thesis is that all such representational artworks involve two levels or kinds of representation: a first stage in which a concrete artifact represents an artwork, and a second stage in which that artwork in turn represents its subject matter. "Dilworth applies his (...) theory across the arts and to a variety of issues, demonstrating that it has far-reaching implications for our philosophical understanding of the nature of art.” - Stephen Davies, Associate Professor of Philosophy, University of Auckland.. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

I argue for an egalitarian conception of modesty. Modesty is a virtue because an apt expression of what is, and is not, morally salient in our attitudes toward persons and is important because we are prone to arrogance, self-importance, and hero worship. To make my case, I consider 3 claims which have shaped recent discussions: first, that modesty is valuable because it obviates destructive social rankings; second, that modesty essentially involves an indifference to how others evaluate one's accomplishments; and third, (...) the widespread but normatively fraught assumption that the modest person is deserving of credit. Although the first 2 features identify something significant about modesty, they fail to ground it. I argue that appeals to deserved credit bear a larger explanatory burden than has been supposed; they can smuggle in the illegitimate social hierarchies that modesty is supposed to counter. I make my case for modesty as an excellence in moral perspective by arguing that prominent, nonegalitarian, accounts of modesty allow for or promote illegitimate forms of social privilege. Modesty is valuable because it expresses a commitment to fair distribution of basic moral recognition and a skillful response to unjust social hierarchies at odds with this fair distribution. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...) of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

Elijah Chudnoff’s case for irreducible cognitive phenomenology hinges on seeming to see the truth of a mathematical proposition (Chudnoff 2015). In the following, I develop an augmented version of Chudnoff’s case, not based on seeming to see, or intuition, but based on being in a state with presentational phenomenology of high-level content. In contrast to other cases for cognitive phenomenology, those based on Strawson’s case (Strawson 2011), I argue that the case presented here is able to withstand counterarguments, which attempt (...) to reduce cognitive phenomenology to sensory phenomenology. To support my argument, I present findings from Bowden and Jung-Beeman’s experiments with the Aha! Experience (Bowden & Jung-Beeman 2004), and argue that the Aha! Experience is a species of the experience of understanding presented here. I interpret the results of these experiments to provide further evidence for irreducible cognitive phenomenology. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...) that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless without rigor and objectivity. The logician urging us to be dispassionate is in resonance and harmony with the ethicist urging us to be compassionate.

I argue that the physical marks on a canvas resulting from an artist's intentional, stylistic and expressive acts cannot themselves be the artist's expression, but instead they serve to signify or indicate those acts. Thus there is a kind of indicative content associated with a picture that is distinct from its subject matter (or 'representational content'). I also argue that this kind of indicative content is closely associated with the specific artistic medium chosen by the artist as her expressive medium, (...) for which reason I call this kind of content medium content (or medium-related content). (shrink)

In Languages of Art, Nelson Goodman presents a general theory of symbolic notation. However, I show that his theory could not adequately explain possible cases of natural language notational uses, and argue that this outcome undermines, not only Goodman's own theory, but any broadly type versus token based account of notational structure.Given this failure, an alternative representational theory is proposed, in which different visual or perceptual aspects of a given physical inscription each represent a different letter, word, or other notational (...) item. Such a view is strongly supported by the completely conventional relation between inscriptions and notation, as shown by encryption techniques etc. (shrink)

This paper raises obvious questions undermining any residual confidence in Mates work and revealing our embarrassing ignorance of true nature of Stoic deduction. It was inspired by the challenging exploratory work of JOSIAH GOULD.

This paper questions the idea that theism can function as an explanatory hypothesis to account for the nature and origins of the cosmos. Invoking God cannot dissolve the mystery of existence, and the characteristic religious response here is one of awe and humility. I then address David E. Cooper’s challenge of showing how a ”doctrine of mystery’ can have any discursible content. It is argued that certain aspects of our human experience afford us glimpses of the divine nature -- intimations (...) of the transcendent, which shine through from the ineffable source of our being to the human world we inhabit. (shrink)

It is generally accepted that Picasso might have used a different canvas as the vehicle for his painting Guernica, and also that the artwork Guernica itself necessarily represents a certain historical episode—rather than, say, a bowl of fruit. I argue that such a conjunctive acceptance entails a broadly propositional view of the nature of representational artworks. In addition, I argue—via a comprehensive examination of possible alternatives—that, perhaps surprisingly, there simply is no other available conjunctive view of the nature of representational (...) artworks in general. CiteULike Connotea Del.icio.us What's this? (shrink)

A concrete proposal is presented as to how semantics should be naturalized. Rather than attempting to naturalize propositions, they are treated as abstract entities that index concrete cognitive states. In turn the relevant concrete cognitive states are identified via perceptual classifications of worldly states, with the aid of an interactive theory of perception. The approach enables a broadly realist theory of propositions, truth and cognitive states to be preserved, with propositions functioning much as abstract mathematical constructs do in the nonsemantic (...) sciences, but with a much more specific propositional indexing scheme than previous naturalistic proposals were able to achieve. (shrink)

ABSTRACT: In its strongest unqualified form, the principle of wholistic reference is that in any given discourse, each proposition refers to the whole universe of that discourse, regardless of how limited the referents of its non-logical or content terms. According to this principle every proposition of number theory, even an equation such as "5 + 7 = 12", refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. This principle, its history, (...) and its relevance to some of Oswaldo Chateaubriand's work are discussed in my 2004 paper "The Principle of Wholistic Reference" in Essays on Chateaubriand's "Logical Forms". In Chateaubriand's réplica (reply), which is printed with my paper, he raised several important additional issues including the three I focus on in this tréplica (reply to his reply): truth-values, universes of discourse, and formal ontology. This paper is self-contained: it is not necessary to have read the above-mentioned works. The principle of wholistic reference (PWR) was first put forth by George Boole in 1847 when he espoused a monistic fixed-universe viewpoint similar to the one Frege and Russell espoused throughout their careers. Later, Boole elaborated PWR in 1854 from the pluralistic multiple-universes perspective. (shrink)

I propose a distinction between design intentions, activities and products, as opposed to artistic intentions, activities and artworks. Examples of design products would include a specific type of car (or any other invention or device) as well as closer relatives of art such as decorative wall designs. In order to distinguish artistic from design intentions, I present an example in which two sculptors independently work on a single object to produce two sculptures, which are distinct just because the artistic intentions (...) of the sculptors are distinct. This case is then contrasted with an attempted parallel example for design intentions, which fails to produce two correspondingly distinct design products in spite of the different design intentions of its designers. I argue that this failure occurs because designs are types, for which any single token of a given type could not simultaneously be a token of some other type of the same general kind; whereas the possibility of my sculptural 'double artwork' example shows that such artworks cannot be types. I then further investigate the concept of a design, and conclude by arguing that an extension of my sculptural example shows that literary artworks also cannot be types. (shrink)

There is some intuitive plausibility to the idea that composers create musical works by indicating sonic types in a historical context. But the idea is technically indefensible as it stands, requiring a thorough representational reform that also eliminates the type-theoretic commitments of current versions. On the reformed account, musical 'indication' is an operation of high level representational interpretation of concrete sounds, that can both explain the creativity of composers, and the often successful interpretations of their listeners. This approach also bypasses (...) contentious issues regarding the status of both indicated and 'initiated' types, as extensively discussed in the BJA. (shrink)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...) of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

Our modern egalitarian and individualistic age is suspicious of authority, and in recent times there have been almost daily reports in the press of cases where trust in various authorities, including financial, governmental, political and religious, has been found to have been abused or misplaced. Such disappointments seem to bolster the case for withholding trust in external authority and falling back on one’s own resources. But if the lessons from Linda Zagzebski’s groundbreaking work are accepted, 1 self- reliance turns out (...) to be a confused and probably incoherent ideal ; and the rational and self-reflective person is committed to believing and acting on authority. In the second half of this short discussion paper I shall raise some possible concerns about Zagzebski’s positive case for reliance on authority, focussing on the moral and religious spheres. First however, let me say something about the negative part of Zagzebski’s work, her critique of self-reliance. Since I find this wholly convincing, I shall confine myself to some supplementary observations, mainly to do with the historical context in which her critique is located. (shrink)

On a traditional or default view of the grasping or understanding of a singular proposition by an individual, it is assumed to be a unitary or holistic activity. However, naturalistic views of cognition plausibly could analyze propositional thinking in terms of more than one distinctive functional stage of cognitive processing, suggesting at least the potential legitimacy of a non-unitary analysis of propositional grasping. We outline a novel dual-component view of this kind, and show that it is well supported by current (...) cognitive science research. (shrink)

Howard Gardner's theory of Multiple Intelligences has had a huge influence on school education. But its credentials lack justification, as the first section of this paper shows via a detailed philosophical analysis of how the intelligences are identified. If we want to make sense of the theory, we need to turn from a philosophical to a historical perspective. This is provided in the second section, which explores how the theory came to take shape in the course of Gardner's intellectual development. (...) The third section looks at changes in the theory since its inception in 1983 and at problems with its applications to education. The paper concludes with a response to Gardner's critical comments on the argument to this point. (shrink)

Upon first hearing sinewaves, all that can be discerned are beeps and whistles. But after hearing the original speech, the beeps and whistles sound like speech. The difference between these two episodes undoubtedly involves an alteration in phenomenal character. O’Callaghan (2011) argues that this alteration is non-sensory, but he leaves open the possibility of attributing it to some other source, e.g. cognition. I discuss whether the alteration in phenomenal character involved in sinewave speech provides evidence for cognitive phenomenology. I defend (...) both the existence of cognitive phenomenology and the phenomenal contrast method, as each concerns the case presented here. (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...) weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

Excerpts and paraphrases of this memoir appeared in 2008 and 2009. I posted it in full here in happy memory of Peter Hare and my joyful years with him. -/- 2008. Remembering Peter Hare 1935–2008. Philosophy Now. Co-authors: T. Madigan and A. Razin. Issue 66 March/April 2008. Pages 50–2. PDF -/- 2009. Remembering My Life with Peter Hare. Remembering Peter Hare 1935–2008. Ed. J. Campbell. Society for the Advancement of American Philosophy. pp. 9–16. http://american-philosophy.org/documents/RememberingPeterHare_final.pdf -/- Peter H. Hare, Distinguished Professor (...) Emeritus of Philosophy at the University of Buffalo (SUNY at Buffalo), died peacefully in his sleep on Thursday, January 3, 2008. I would like to share my memories of my life with him. Others have eulogized him, enumerated his virtues and accomplishments, and written his obituaries. I am revisiting my personal relationship with him. These memories are as much about me as about him. (shrink)

Utilitarian (U.) theories must be capable of being applied in practical reasoning, or they would have no value as a guide to rational conduct. However, I show that epistemic extensions to U. theories produce logical confusion. Basic questions about what one needs to know in order to apply a U. analysis embroil one in an infinite regress. And attempts to incrementally apply U. either are no help at all (leaving one entirely 'in the dark'), or in general constitute arbitrary gambles (...) which no practical reasoner could defend taking. These problems are serious enough to completely discredit U. theories as having any relevance to practical reasoning. (shrink)

In the performing arts, including music, theater, dance and so on, theoretical issues both about artworks and about performances of them must be dealt with, so that their theoretical analysis is inherently more complex and troublesome than that of nonperforming arts such as painting or film, in which primarily only artworks need to be discussed. Thus it is especially desirable in the case of the performing arts to look for defensible broad theoretical simplifications or generalizations that could serve to unify (...) and potentially comprehensively explain these difficult cases. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...) using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .

There are no unicorns, but there are representations of them, hence motivating an explanation of discourse about the property 'unicorn' in terms of discourse about representations of unicorns. I show how to extend this strategy to apply to any kind or property terms. References to property instances may be explained as references to comprehensive representations of them, which represent all of the (supposed) properties of such an instance--unlike 'ordinary' representations, which are distinctive in that they represent only some limited subset (...) of such properties, through use only of some proper subset of their own (supposed) properties. This representationalist approach results in a very economical naturalist ontology, which has no need for properties. (shrink)

I propose a new kind of meta-ethical theory, grounded in a theory of interests and of the modifications required in order to render interests compatible with each other. The theory hence is called "Interest Compatibilism" (IC). A basic account of the nature of interests, and of possible relations between them, is also included. Ethical values turn out to be those involved in optimally desirable forms of harmonization and control of interests and their associated values. The theory is presented and developed (...) with the aid of specific comparisons to more standard deontological and consequentialist ethical theories and views. Utilitarian consequentialist views are particularly criticised, and suggestions for an improved consequentialist view incorporating aspects of the IC approach are developed. Whether or not the IC theory is acceptable as a whole, I argue that some such alternative consequentialist theory is desperately needed. My account of interests should be independently acceptable also. (shrink)

This largely expository lecture deals with aspects of traditional solid geometry suitable for applications in logic courses. Polygons are plane or two-dimensional; the simplest are triangles. Polyhedra [or polyhedrons] are solid or three-dimensional; the simplest are tetrahedra [or triangular pyramids, made of four triangles]. -/- A regular polygon has equal sides and equal angles. A polyhedron having congruent faces and congruent [polyhedral] angles is not called regular, as some might expect; rather they are said to be subregular—a word coined for (...) this lecture. To repeat, a subregular polyhedron has congruent faces and congruent [polyhedral] angles. A subregular polyhedron whose faces are all regular polygons is regular—using standard terminology. -/- Geometers before Euclid showed that there are “essentially” only five regular polyhedra: every regular polyhedron is a tetrahedron (4 faces), a hexahedron or cube (6 faces), an octahedron (8 faces), a dodecahedron (12 faces), or an icosahedron (20 faces). -/- The first question is whether there are subregular polyhedra that are not regular. For example, are there tetrahedra having congruent angles and congruent triangular faces but whose faces are not equilateral triangles? -/- Another question is the classification of subregular polyhedra if they exist. For example, considering the fact that the regular tetrahedra all have equilateral triangles as faces, we ask which triangles other than equilaterals are faces of subregular tetrahedra. Similarly, considering the fact that the regular hexahedra all have squares as faces, we ask which quadrangles other than squares are faces of subregular hexahedra. -/- After introductory remarks that include historical and philosophical points, we concentrate on tetrahedra. A triangle that is congruent to each of the four faces of a tetrahedron is called a generator of the tetrahedron. The main result proved is that every acute triangle is a generator of a subregular tetrahedron. The proof includes an algorithm –implementable with scissors and paper –that constructs from any given acute triangle a subregular tetrahedron whose faces are congruent to the given triangle. -/- Algorithm: Given any acute triangle. Construct a similar triangle whose sides are double the sides of the given triangle. Draw the three lines connecting the three midpoints of the sides (making four triangles congruent to the given triangle—a central triangle surrounded by three peripheral triangles). Make three “hinges” along the lines connecting the midpoints. “Fold” the peripheral triangles together (into a tetrahedron). [LIGHTLY EDITED VERSION OF PRINTED ABSTRACT] Acknowledgements: William Lawvere, Colin McLarty, Irvin Miller, Frango Nabrasa, Lawrence Spector, Roberto Torretti, and Richard Vesley. -/- . (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...) weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself.Em sua forma mais forte e geral, o princípio da referência universalista afirma que toda proposição refere-se ao universo completo do discurso propriamente dito, independentemente de quão limitados sejam os referentes de seus termos não-lógicos ou com conteúdo. Embora Boole mudasse de um modelo monístico de universo-fixo nos seus trabalhos iniciais de 1847 e 1848 para um modelo pluralista de universo-múltiplo no seu tratado maduro de 1854, ele nunca hesitou em sua aceitação franca do princípio da referência universalista, possivelmente em uma forma ligeiramente mais fraca. De fato, ele considerou este princípio como um acompanhamento essencial para a sua teoria de formação de conceitos e de proposições. Visões semelhantes são encontradas em lógicos posteriores, e algumas das mais recentes formulações da lógica clássica de primeira ordem parecem estar de acordo com uma forma deste, se é que elas não implicam, de fato, o próprio princípio. (shrink)