In contemporary natural languages semantics one will often see the use of special brackets to enclose a linguistic expression, e.g. ⟦carrot⟧. These brackets---so-called denotation brackets or semantic evaluation brackets---stand for a function that maps a linguistic expression to its "denotation" or semantic value (perhaps relative to a model or other parameters). Even though this notation has been used in one form or another since the early development of natural language semantics in the 1960s and (...) 1970s, Montague himself didn't make use of this notation in his series of groundbreaking papers on semantics. That raises the question: When was the ⟦.⟧-notation introduced to semantics? This note answers that question. (shrink)

The paper is Part III of the large research, dedicated to both the revision of the system of basic logical categories and the generalization of modern predicate logic to functional logic. We determinate and contrapose modern Fregean logistics and proposed by the author ultra-Fregean logistics, next we describe values and arguments of functions, arguments of relations, relations themselves, sets (classes), and subsets (subclasses) as derivative categories (concepts) of ultrafregean logistics. Logistics is a part of metalogic, independent of semantics. Fregean logictics (...) is a metalogical theory, based on the quadruple <particular (individual), predicate, equality, sequence>; it generates predicate logic. Ultrafregean logictics is based on the quadruple <particular, function, representation, sequence>, where the notion of a function is a generalization of the notion of a predicate and the notion of representation is a generalization of the notion of equality; this logictics generates functional logic. For the completely correct denotation of the functional values, we need the Churchian symbolics with parenthesis. Predicates are usually identified with relations. A relation is the derived and even definable category of ultra-Fregean logictics. Namely, relations are representations by functions (of one of their arguments). We show that Frege could really establish this definition and the notion (category) of representation but, unfortunately, rejected this course of thought. Next, we show that every n-ary relation can be resolved for some of its arguments via some (n-1)-ary function. A set, or class, is a derived and not definable category of ultra-Fregean logistics. The universal way to introduce the sets is Frege’s abstraction principle. We formulate this principle for functional logic and show that the notion of a set is quantified, so there is the dual existential notion of a nonempty subset, involved by the same abstraction principle. (shrink)

Moral value as it was understood by Nicolai Hartmann and by Max Scheler belongs uniquely to volitions or willings, to dispositions to will and to persons as beings capable of willing. Moreover, as understood in this paper as well as by Hartmann, Scheler, and Husserl, every volition necessarily involves if not actual valuings then reference to retained valuings and potential valuings as well as to cognitive mental phenomena. As used here, the terms 'volition' and 'willing' denote mental traits, such as (...) lived experiences and habits insofar as they either do or can occur actively. A trait of a mind or "monad" can have moral value — in contrast to utility, for example — only (would belong) insofar as it is or can be or could have been engaged in and so performed by the person or ego to whose mind the trait belongs . The classification of lived experiences as voluntary or not voluntary cuts across the three-fold classification of mental processes as cognitive, affective, or conative. This seems to be the most appropriate way of distinguishing the voluntary from the involuntary. Voluntary mental phenomena are characterized by the engagement of the ego in some lived experience occurring in the flux of its lived experiences, i.e., by taking position. " within the text below by numbers. End notes are referred to within square brackets [] linked to the notes and these link back to the text loci. Text printed in sepia has been emended. The brief passage in the text that occurs in angle brackets and in the same color as this introductory note has been added to state more pointedly an important issue>. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

In this article, following on from earlier debates in the journal regarding the ‘thorny issue’ of epochē and bracketing in sociological phenomenological research, we consider more generally the challenges of engaging in reflexivity and bracketing when undertaking ethnographic ‘insider’ research, or research in familiar settings. We ground our discussion and illustrate some of the key challenges by drawing on the experience of undertaking this research approach with a group of competitive swimmers, who were participating in a British university performance swimming (...) programme at the time of the doctoral study. The primary researcher was highly familiar with the phenomenon of competitive swimming, having been both a competitive swimmer and swimming coach. Some of the key elements of a sociological phenomenological approach to studying physical-cultural embodiment are first delineated, before addressing the considerable challenges of engaging in sustained reflexivity and bracketing, using the swimming research for illustrative purposes. We suggest some practical ways in which researchers in sport and physical cultures might approach epochē and bracketing in ethnographic ‘insider’ research. -/- KEYWORDS: Sociological phenomenology, competitive swimming, insider research, epochē/bracketing. (shrink)

Bertrand Russell’s _Principles of Mathematics_ (1903) gives rise to several interpretational challenges, especially concerning the theory of denoting concepts. Only relatively recently, for instance, has it been properly realised that Russell accepted denoting concepts that do not denote anything. Such empty denoting concepts are sometimes thought to enable Russell, whether he was aware of it or not, to avoid commitment to some of the problematic non-existent entities he seems to accept, such as the Homeric gods and chimeras. In this paper, (...) I argue first that the theory of denoting concepts in _Principles of __Mathematics_ has been generally misunderstood. According to the interpretation I defend, if a denoting concept shifts what a proposition is about, then the aggregate of the denoted terms will also be a constituent of the proposition. I then show that Russell therefore could not have avoided commitment to the Homeric gods and chimeras by appealing to empty denoting concepts. Finally, I develop what I think is the best understanding of the ontology of _Principles of __Mathematics_ by interpreting some difficult passages. (shrink)

This article considers a novel approach to researching sporting embodiment via what has been termed ‘autophenomenography’. Whilst having some similarities with autoethnography, autophenomenography provides a distinctive research form, located within phenomenology as theoretical and methodological tradition. Its focus is upon the researcher’s own lived experience of a phenomenon or phenomena. This article examines some of the key elements of a sociological phenomenological approach to studying sporting embodiment in general before portraying how autophenomenography was utilised specifically within two recent research projects (...) on distance running. The thorny issues of epoche and bracketing within phenomenological and autophenomenographical research are addressed and some practical suggestions tentatively posited. (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating (...) any two senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

In this paper, I critically approach the essence of Dewey’s philosophy: his method. In particular, it is what Dewey termed as denotative method is at the center of my attention. I approach Dewey’s denotative method via what I call the “genealogical deconstruction” that is followed by the “pragmatic reconstruction.” This meta-approach is not alien to Dewey’s philosophy, and in fact was employed by Dewey himself in Experience and Nature. The paper consists of two parts. In Part 1, I genealogically deconstruct (...) the philosophical foundation of the denotative method: the doctrine of immediate empiricism. The latter was originally stated in Dewey’s 1905 seminal “The Postulate of Immediate Empiricism” article, and fully developed twenty years later in his Experience and Nature. I claim that Dewey’s immediate empiricism is essentially incompatible with his pragmatism (instrumentalism) and with pragmatism overall. In Part 2, I pragmatically reconstruct Dewey’s denotative method from the perspective of what I term as the “hermeneutic empiricism” which is grounded in Dewey’s 1896 “The Reflex Arc Concept in Psychology” article. As opposed to the immediate empiricism’s main thesis “things are what they are experienced as,” the motto of the hermeneutic empiricism would be “things are what they are interpreted as”/“things are experienced what they are interpreted as.” The above-mentioned pragmatic reconstruction also leads to the transformation of the notion of “common sense” which is vital to Dewey’s method, into the notion of sound reason. (shrink)

I present and discuss three previously unpublished manuscripts written by Bertrand Russell in 1903, not included with similar manuscripts in Volume 4 of his Collected Papers. One is a one-page list of basic principles for his “functional theory” of May 1903, in which Russell partly anticipated the later Lambda Calculus. The next, catalogued under the title “Proof That No Function Takes All Values”, largely explores the status of Cantor’s proof that there is no greatest cardinal number in the variation of (...) the functional theory holding that only some but not all complexes can be analyzed into function and argument. The final manuscript, “Meaning and Denotation”, examines how his pre-1905 dis­tinction between meaning and denotation is to be understood with respect to functions and their arguments. In them, Russell seems to endorse an extensional view of functions not endorsed in other works prior to the 1920s. All three manuscripts illustrate the close connection between his work on the logical paradoxes and his work on the theory of meaning. (shrink)

There is an inconsistency among claims made (or apparently made) in separate articles by Alonzo Church concerning Frege's distinction between sense and denotation taken together with plausible assertions by Frege concerning his notion of ungerade Sinn-i.e., the sense that an expression allegedly takes on in positions in which it has ungerade Bedeutung, denoting its own customary sense. As with any inconsistency, the difficulty can be avoided by relinquishing one of the joint assumptions from which contradiction may be derived. Yet (...) what seems the most plausible resolution, in light of Church's own arguments, involves abandoning the theory of sense and denotation, in the form in which it has been staunchly advocated by both Frege and Church. That theory has come under sustained criticism from several quarters. Whereas the present difficulty supplements the case against the theory, it is unlike more familiar criticisms, since it is not framed from the perspective of an alternative theory (or picture) but is based instead on an internal conflict, and therefore has special force. (shrink)

Deleuze is prominent among those philosophers who pronounce that difference must be understood as ontologically prior to identity. He teaches that identity is a surface effect of difference, so to understand the basis of logico-mathematical idealities we must uncover their genesis in the fecundity of differentiation. Deleuze wants to offer a foundation of number and mathematics as a subversive, creative force, an affirmation of Nietzsche’s eternal return as the ‘roll of the dice’. But he begins too late. For Deleuze, virtual (...) intensities (Eternal Return) generate the logical , conceptual, theoretical, lawful principles for empirical domains, and then are held steady in the background, beyond the reach of the conceptual and logical patterns, which cancel them by freezing and isolating them. Applying Heidegger’s deconstruction of Nietzschean subjectivity to Deleuze’s project reveals intensities to function as subjective enframings of the species and parts that develop from them. Intensive processes posit , set in place and represent the qualities that steadily remain throughout the calculation of difference in degree. Deleuze does not appear to recognize that the iteration of extensive quantity is devoid of meaningful sense. His failure to make this distinction leads him to confuse mathematical with non-mathematical idealities and prevents him from locating the fundamental sense of extensive duration. What Husserl, and Heidegger after him, recognized is that numeration never counts anything but its own self-iteration, devoid of sense and meaning outside of the empty ‘same thing, different time’. To experience an object as meaningful beyond this ‘how much’ is to no longer attend to it as calculative, countable iteration, as persisting self-identical presence. What holds only for intensities in Deleuze’s understanding of the structure of time, that every change in degree is simultaneously a difference in kind, constitutes the irreducible, absolute essence of all duration. (shrink)

The paper defends a variant of the material implication approach to the meaning of conditional sentences against some arguments that are considered to be widely subscribed to and/or important in the philosophical, psychological and linguistic literature. These arguments are shown to be wrong, debatable, or to miss their aim if the truth conditions defining material implication are viewed as determining nothing but the denotation of conditional sentences and if the function of conditional sentences in deduction (logic) is focused on (...) rather than in inferencing (reasoning). It is shown that some ‘paradoxes of material implication’ are due to inconsistent premises of deductions introduced by semantic relations between clauses constituting the premises, a fact which does not invalidate the approach. Other ‘paradoxes’ are shown to arise because they are based on uninformative deductions, violating a basic pragmatic principle. In addition, the paper introduces the distinction between the set of possible states of a mental model of the actual world and of alternative worlds. It is argued that material implication determines the denotation of an indicative conditional as a subset of the former set and the denotation of a subjunctive conditional as a subset of the latter set, thus unifying these two types of conditionals. (shrink)

The paper argues that philosophers commonly misidentify the substitutivity principle involved in Russell’s puzzle about substitutivity in “On Denoting”. This matters because when that principle is properly identified the puzzle becomes considerably sharper and more interesting than it is often taken to be. This article describes both the puzzle itself and Russell's solution to it, which involves resources beyond the theory of descriptions. It then explores the epistemological and metaphysical consequences of that solution. One such consequence, it argues, is that (...) Russell must abandon his commitment to propositions. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction (...) system of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

A recent and growing discussion in philosophy addresses the construction of models and their use in scientific reasoning by comparison with fiction. This comparison helps to explore the problem of mediated observation and, hence, the lack of an unambiguous reference of representations. Examining the usefulness of the concept of fiction for a comparison with non-denoting elements in science, the aim of this paper is to present reasonable grounds for drawing a distinction between these two kinds of representation. In particular, my (...) account will suggest a demarcation between fictional and non-fictional discourse as involving two different ways of interpreting representations. This demarcation, leading me to distinguish between fictional and non-fictional forms of enquiry, will provide a useful tool to explore to what extent the descriptions given by a model can be justified as making claims about the world and to what degree they are a consequence of the model’s particular construction. (shrink)

Bracket out the wrong of committing a wrong, or conspiring or colluding or conniving with others in their committing one. Suppose you have done none of those things, and you find yourself merely benefiting from a wrong committed wholly by someone else. What, if anything, is wrong with that? What, if any, duties follow from it? If straightforward restitution were possible — if you could just ‘give back’ what you received as a result of the wrongdoing to its rightful owner (...) — then matters are morally more straightforward. But in real-world cases that is often impossible, and questions of ‘how much, from whom and to whom?’ become far more vexing. The beneficiary disgorging all benefits of the wrong is part of the story, but where that is not possible or will not suffice to compensate the victim of wrongdoing we discuss various ways of allocating the cost of making the victim whole, including supplementation from public coffers. (shrink)

In this paper, I attempt to clarify the heart of Dewey’s philosophy: his method (denotative method (DM) / pattern of inquiry (PI)). Despite the traditional understanding of Dewey as anti-foundationalist, I want to show that Dewey did have metaphysical foundations for his method: the principle of continuity or theory of emergentism. I also argue that Dewey’s metaphysical position is better named as ‘cultural emergentism’, rather than his own term ‘cultural naturalism’. What Dewey called ‘common sense’ in his Logic, Husserl termed (...) as the ‘life-world’ in his Crisis. I compare two perspectives of dealing with the phenomenon and conclude that for Dewey, the difference between natural sciences and the common sense inquiry is that of subject-matter but not of method. Thus, the goal is to find the unified method to be applied in both domains. Whereas Husserl was more pessimistic: for him, the difference was not only in subject-matter, but in the very methods. Following that discussion, I also attempt to reformulate the hard problem of consciousness in Deweyan terms. In the end, I compare Dewey’s DM / PI with Popper’s understandings of scientific method and conclude that there is no significant difference between the two and that Dewey’s method could also be looked at as hypothetic-deductive method, with the only difference in emphases. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

This paper proposes an extensionalist analysis of computer simulations (CSs). It puts the emphasis not on languages nor on models, but on symbols, on their extensions, and on their various ways of referring. It shows that chains of reference of symbols in CSs are multiple and of different kinds. As they are distinct and diverse, these chains enable different kinds of remoteness of reference and different kinds of validation for CSs. Although some methodological papers have already underlined the role of (...) these various relationships of reference in CSs and of cross-validations, this diversity is still overlooked in the epistemological literature on CSs. As a consequence, a particular outcome of this analytical view is an ability to classify existing epistemological theses on CSs according to what their authors choose to select and put at the forefront: either the extensions of symbols, or the symbol-types, or the symbol-tokens, or the internal denotational hierarchies of the CS or the reference of these hierarchies to external denotational hierarchies. Through the adoption of this extensionalist view, it also becomes possible to explain more precisely the reasons why some complete reduction of CSs to classical epistemic paradigms such as “experiment” or “theoretical argument” remains doubtful. On this last point, in particular, this paper is in agreement with what many epistemologists already have acknowledged. (shrink)

Propositional attitude sentences, such as "John believes that snow is white," are traditionally taken to express the holding of a relation between a subject and what ‘that’-clauses like ‘that snow is white’ denote, i.e. propositions. On the traditional account, propositions are abstract, mind- and language-independent entities. Recently, some have raised some serious worries for the traditional account and thought that we were mistaken about the kind of entities propositions are. Over the last ten years there has then been a boom (...) of accounts of propositions in terms of mental acts. But Friederike Moltmann has recently suggested that in accounting for attitudes we should forget about mindand language-independent entities and acts and follow Twardowski in focusing instead on attitudinal objects, which are the products of our mental life. In this paper, I will focus on some semantic problems that any product-based account seems to face. Moreover, I will show that product-based accounts may be also criticised on ontological grounds. My conclusion will be that we lack a reason to think that in accounting for propositional attitudes we should focus on the alleged products of our mental lives. (shrink)

The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and (...) upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed. (shrink)

One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functor-function defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

Now that complex Agent-Based Models and computer simulations spread over economics and social sciences - as in most sciences of complex systems -, epistemological puzzles (re)emerge. We introduce new epistemological tools so as to show to what precise extent each author is right when he focuses on some empirical, instrumental or conceptual significance of his model or simulation. By distinguishing between models and simulations, between types of models, between types of computer simulations and between types of empiricity, section 2 gives (...) conceptual tools to explain the rationale of the diverse epistemological positions presented in section 1. Finally, we claim that a careful attention to the real multiplicity of denotational powers of symbols at stake and then to the implicit routes of references operated by models and computer simulations is necessary to determine, in each case, the proper epistemic status and credibility of a given model and/or simulation. (shrink)

The aim of this paper is to discuss the “Framework for M&S with Agents” (FMSA) proposed by Zeigler et al. [2000, 2009] in regard to the diverse epistemological aims of agent simulations in social sciences. We first show that there surely are great similitudes, hence that the aim to emulate a universal “automated modeler agent” opens new ways of interactions between these two domains of M&S with agents. E.g., it can be shown that the multi-level conception at the core of (...) the FMSA is similar in both contexts: notions of “levels of system specifi cation”, “behavior of models”, “simulator”and “endomorphic agents” can be partially translated in the terms linked to the “denotational hierarchy” (DH) recently introduced in a multi-level centered epistemology of M&S. Second, we suggest considering the question of “credibility” of agent M&S in social sciences when we do not try to emulate but only to simulate target systems. Whereas a stringent and standardized treatment of the heterogeneous internal relations (in the DH) between systems of formalisms is the key problem and the essential challenge in the scope of Agent M&S driven engineering, it is urgent too to address the problem of the external relations (and of the external validity, hence of the epistemic power and credibility) of such levels of formalisms in the specific domains of agent M&S in social sciences, especially when we intend to introduce the concepts of activity tracking. (shrink)

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

In this paper I argue against a deflationist view that as representational vehicles symbols and models do their jobs in essentially the same way. I argue that symbols are conventional vehicles whose chief function is denotation while models are epistemic vehicles whose chief function is showing what their targets are like in the relevant aspects. It is further pointed out that models usually do not rely on similarity or some such relations to relate to their targets. For that referential (...) relation they reply instead on symbols (names and labels) given to them and their parts. And a Goodmanian view on pictures of fictional characters reveals the distinction between symbolic and model representations. (shrink)

Bertrand Russell in his essay On Denoting [1905] presented a theory of description developed in response to the one proposed by Gottlob Frege in his paper Über Sinn und Bedeutung [1892]. The aim of our work will be to show that Russell underestimated Frege three times over in presenting the latter’s work: in relation to the Gray’s Elegy argument, to the Ferdinand argument, and to puzzles discussed by Russell. First, we will discuss two claims of Russell’s which do not do (...) justice to Frege: that we speak of a sense by means of quotation marks, and that all Frege does to cope with phrases that might denote nothing is define an arbitrary object as their reference. Second, we will show that Russell omitted the fact that Frege’s theory provided some answers for the puzzles presented by Russell in his essay. (shrink)

Fregeans face the difficulty finding a notation for distinguishing statements about the sense or meaning of an expression as opposed to its reference or denotation. Famously, in "On Denoting", Russell rejected methods that begin with an expression designating its denotation, and then alter it with a "the meaning of" operator to designate the meaning. Such methods attempt an impossible "backward road" from denotation to meaning. Contemporary neo-Fregeans, however, have suggested that we can disambiguate _with_, rather than _against_, (...) the grain, by using a notation that begins with expressions designating senses or meanings, and then alters them with a "the denotation of" operator to designate the denotation. I show that in his manuscripts of 1903–05, Russell both considered and rejected a similar notation along with the metaphysical suppositions underlying it. This discussion sheds light on the evolution of Russell's thought, and may yet be instructive for ongoing debates. (shrink)

Many differences exist between the logical relations “equality” and “equivalence”. In this monograph I point out differences that concern definition, linguistics, computational gates and tables, denotation, application, negation of terms, negation of the relation, relations to other relations, the laws of symmetry, transitivity and reflexivity, the laws of commutation and permutation, the law of tautology, the law of distribution, the law of association, propositional meaning, and “genesis”. I also point out a form of “symmetry breaking”: the negation of some (...) equality may yield some non-equality, while the negation of that non-equality might not yield the same equality. (For full access: use the website link of the title page. -- Copyright License: CC BY-NC-ND. -- DOI: 10.17026/dans-zh3-h2b2 --). (shrink)

The analysis method and paradigm of film have become a controversial topic in the data-driven era. Film, is not only an attractive industry that can achieve filmmakers’ imagination but has become a perfect stimulus to understand human being’s mental activity. The core research in this study is to examine the impact of filmmaking experience and the role of narrative denoters from filmmakers’ construction to audiences’ interpretation. Based on previous studies and integrating cognitive approaches, the thesis re-explores the nature and essence (...) of film and proposes an alternative term - narrative denoter - which can be used as the indication of message exchanging between filmmakers and audiences. Using a released film that has a complete story to do the experiment, this study investigates the relationship between major, film interpretations, event segmentation, and audience’s preference. The result showed that filmmaking experience does not impact the interpretation of film; however the identification of the narrative denoter played an important role in film perception and cognition; apart from these, the audience’s preference did not correlate with film interpretation. With respect to this result, the narrative denoter can be indicator to demonstrate the message transitions from filmmaker to audience. Suggestions were made for future cognitive film studies on using the narrative denoters as a new analysis unit. (shrink)

‘Complexics’ denotes the meta-transdisciplinary field specifically concerned with giving us suitable cognitive tools to understand the world’s complexity. Additionally, the use of the adjective ‘complexical’ would avoid the common confusion caused by the adjective ‘complex’, which belongs to everyday usage and already has its own connotations of complication and confusion. Thus, ‘complexical’ thinking and ‘complexical’ perspective would provide clearer terms, be freer of confusion, and refer more precisely to epistemic elements in contrast to the ‘complexity’ typical of many phenomena of (...) reality. In short, the world would be ‘complex’, but our way of looking at the world would be ‘complexical’. As a meta-transdiscipline, ‘complexics’ would carry on the perspective of cybernetics: “Cybernetics deals with all forms of behaviour insofar as they are regular, or determinate, or reproducible. The materiality is irrelevant… The truths of cybernetics are not conditional on their being derived from some other branch of science. Cybernetics has its own foundations” (Ashby, 1956:1). Thus, it has a distinctly transdisciplinary mission to provide concepts, schema and possibilities of thinking and representation able to express the multidimensional and systemic interwovenness and interdependence of the many, highly significant phenomena of reality that have these characteristics. On the level of theory, complexics needs to provide a set of principles, concepts and conceptual landscapes that can be applied transversally to distinct areas of knowledge and phenomena of reality, enabling us to gain a much firmer grasp of the complex aspects of their existence than we currently have. For this reason, our aim needs to be, as Morin says, not “to reduce complexity to simplicity, [but] to translate complexity into theory” (1994:315). (shrink)

In this paper I argue that Bykvist’s recent challenges to the fitting-attitude account of value (FA) can be successfully met. The challenge from solitary goods claims that FA cannot account for the value of states of affairs which necessarily rule out the presence of favouring subjects. I point out the modal reasons why FA can account for solitary goods by appealing to contemplative attitudes. Bykvist’s second challenge, the ‘distance problem’, questions the ability of FA to match facts about the intensity (...) of fitting attitudes and facts about value, particularly in the case of solitary goods. I argue that this challenge can be met by including the notion of a veil of ignorance in the formulation of FA, and understanding its role as bracketing the relevance of certain facts when determining the fittingness of attitudes to states of affairs. (shrink)

K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent, publicly available, and contains theorems both from formal and constructive mathematics. Any theorem of any mathematician from past or present forever belongs to K. Mathematical statements with known constructive proofs exist in K separately and form the set K_c⊆K. We assume that mathematical sets are atemporal entities. They exist formally in ZFC theory although their (...) properties can be time-dependent (when they depend on K) or informal. The true statement "K is non-empty" is outside K forever because K is not a formal set. Paul Cohen proved in 1963 that the equality 2^{\aleph_0}=\aleph_1 is independent of ZFC. Before 1963, the statement "There is a known constructively defined integer n⩾1 such that 2^{\aleph_0}=\aleph_n" was outside K. Since 1963, this statement is outside K forever. The true statement "There exists a set X⊆{1,...,49} such that card(X)=6 and X never occurred as the winning six numbers in the Polish Lotto lottery" refers to the current non-mathematical knowledge and is outside K forever. In Martin-Löf's terminology, every currently known theorem is actually true whereas every theorem (known or unknown) is potentially true. Actual truth is knowledge dependent and tensed. Potential truth is knowledge independent and tenseless. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. For every such statement, its truth concerning the current mathematical knowledge is implied by a true statement of the form: (the conjunction of i conditions of the form α∈K)∧(the conjunction of j conditions of the form β∉K)∧(the conjunction of k conditions of the form γ∈K_c)∧(the conjunction of l conditions of the form δ∉K_c), where i,j,k,l∈N and α,β,γ,δ are mathematical statements. In constructive mathematics and the traditional Brouwerian intuitionism, the truth of a mathematical statement means that we know a constructive proof. Therefore, the truth of a mathematical statement depends on time, where the statement is formally stated in the classical mathematics without the predicate K. In this article, mathematical statements on decidable sets X⊆N refer to time because they refer to the current mathematical knowledge on X. They cannot be formally stated in the classical mathematics without the predicate K and their logical values may change in time. For a set X⊆N whose infiniteness is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(X)=ω" is outside K. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove the assumption of the above statement. We prove that the set X={n∈N: the interval [-1,n] contains more than 29.5+(11!/(3n+1))∙sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. We present a table that shows satisfiable conjunctions of the form #(Condition1)∧(Condition 2)∧#(Condition 3)∧(Condition 4)∧#(Condition 5), where # denotes the negation ¬ or the absence of any symbol. We prove that there exists a naturally defined set C⊆N which satisfies the following conditions (6)-(11). (6) A known and simple algorithm for every k∈N decides whether or not k∈C. (7) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(C)=ω" is outside K. (8) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(N\C)=ω" is outside K. (9) It is conjectured, though so far unproven, that C is infinite. (10) For every known algorithm A with no input, the statement "A returns an integer n satisfying card(C)<ω ⇒ C⊆(-∞,n]" is outside K. (11) For every known algorithm A with no input, the statement "A returns an integer m satisfying card(N\C)<ω ⇒ N\C⊆(-∞,m]" is outside K. The set C={k∈N: 2^{2^k}+1 is composite} is naturally defined and satisfies conditions (6)-(11). (shrink)

The concept of facticity denotes conditions of experience whose necessity is not logical yet whose contingency is not empirical. Although often associated with Heidegger, Fichte coins ‘facticity’ in his Berlin period to refer to the conclusion of Kant’s metaphysical deduction of the categories, which he argues leaves it a contingent matter that we have the conditions of experience that we do. Such rhapsodic or factical conditions, he argues, must follow necessarily, independent of empirical givenness, from the I through a process (...) of ‘genesis.’ I reconstruct Fichte’s argument by tracing the origin of his neologism, presenting his Jena critique of Kant’s rhapsodic appeal to the forms of judgment, and illustrating the Jena period’s continuity with the Berlin period’s genetic method, while noting a methodological shift whereby Fichte directs his critique against his own doctrine of intellectual intuition in order to eliminate its ‘factical terms.’. (shrink)

Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final (...) analysis. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

Aristotle is essentially human; that is, for all possible worlds metaphysically consistent with our own, if Aristotle exists, then he is human. This is a claim about the essential property of an object. The claim that objects have essential properties has been hotly disputed, but for present purposes, we can bracket that issue. In this essay, we are interested, rather, in the question of whether properties themselves have essential properties (or features) for their existence. We call those who suppose they (...) do “property essentialists”; those who do not, “property anti-essentialists,” or “quidditists.” We offer two complementary arguments. Our total argument is under-girded by two assumptions: transworld identity theory and “received view” counterfactual semantics, a la David Lewis. We then argue that, if one presumes that these are true, then one risks running headlong into paradox if one also accepts property anti-essentialism. That's the first argument. By contrast, if one accepts these same assumptions in conjunction with property essentialism, then the paradox is avoided. This is the second argument. We take it that our arguments work to show that, between property essentialism and quidditism, the property essentialist is on better footing. Plausibly, properties themselves do have essential properties for their existence. (shrink)

Let ‘warrant’ denote whatever precisely it is that makes the difference between knowledge and mere true belief. A current debate in epistemology asks whether warrant entails truth, i.e., whether (Infallibilism) S’s belief that p is warranted only if p is true. The arguments for infallibilism have come under considerable and, as of yet, unanswered objections. In this paper, I will defend infallibilism. In Part I, I advance a new argument for infallibilism; the basic outline is as follows. Suppose fallibilism is (...) true. An implication of fallibilism is that the property that makes the difference between knowledge and mere belief (which I dub ‘warrant*’) is the conjunctive property being warranted and true . I show that this implication of fallibilism conflicts with an uncontroversial thesis we have learned from reflection on Gettier cases: that nonaccidental truth is a constituent of warrant*. It follows that infallibilism is true. In the second part of the paper, I present and criticize a new argument against infallibilism. The argument states that there are plausible cases where, intuitively, the only thing that is keeping a belief from counting as knowledge is the falsity of that belief. Furthermore, it is plausible that such a belief is warranted and false. So, the argument goes, infallibilism is false. I show that this argument fails. (shrink)

The standard view of "believes" and other propositional attitude verbs is that such verbs express relations between agents and propositions. A sentence of the form “S believes that p” is true just in case S stands in the belief-relation to the proposition that p; this proposition is the referent of the complement clause "that p." On this view, we would expect the clausal complements of propositional attitude verbs to be freely intersubstitutable with their corresponding proposition descriptions—e.g., "the proposition that p"—as (...) they are in the case of "believes." In many cases, however, intersubstitution of that-clauses and proposition descriptions fails to preserve truth value or even grammaticality. These substitution failures lead some philosophers to reject the standard view of propositional attitude reports. Others conclude that propositional attitude verbs are systematically ambiguous. I reject both these views. On my view, the that-clause complements of propositional attitude verbs denote propositions, but proposition descriptions do not. (shrink)

We often get reason to doubt the reliability of some of our own reasoning. The rational response to such evidence would seem to depend on how reliable one should estimate that reasoning to be. Independence principles constrain that reliability-assessment, to prevent question-begging reliance on the very reasoning being assessed. But this has consequences some find disturbing: can it be rational for an agent to bracket some of her reasons—which she may, after all, be assessing impeccably? So several arguments have been (...) offered against the very idea of an Independence principle. This paper argues that looking closely at these arguments actually strengthens the case for Independence, and yields some guidance in meeting a formidable challenge for Independence-defenders: formulating the principle in an adequate way. (shrink)

This paper offers a systematic classification and characterization of speech acts and their norms. Recently, the normative approach has been applied to various speech acts, most notably to constatives. I start by showing how the work on the norms of assertion has influenced various approaches to the norms of other speech acts. I focus on the fact that various norms of assertion have different extensions, i.e., they denote different clusters of illocutions as belonging to an assertion. I argue that this (...) has consequences for theorising about norms of other speech acts and generates certain arbitrary divisions. In the central part, I analyse two groups of speech acts. Firstly, ordinary speech acts, like predictions or retractions. Secondly, I indicate how the normative view can be extended to so-called ancillary speech acts, like presuppositions or implicatures. I end with a discussion of possible extensions of the normative approach, focusing on the debate on lying. (shrink)

We defend a functionalist approach to emotion that begins by focusing on emotions as central states with causal connections to behavior and to other cognitive states. The approach brackets the conscious experience of emotion, lists plausible features that emotions exhibit, and argues that alternative schemes are unpromising candidates. We conclude with the benefits of our approach: one can study emotions in animals; one can look in the brain for the implementation of specific features; and one ends up with an (...) architecture of the mind in which emotions are fully accommodated through their relations to the rest of cognition. Our article focuses on arguing for this general approach; as such, it is an essay in the philosophy of emotion rather than in the psychology or neuroscience of emotion. (shrink)

Although Husserlian phenomenology appears to require that practitioners bracket all metaphysical questions and claims, this requirement runs against the evidence of experience in which objects themselves are presented as constituents of experience. Moreover, to completely bracket metaphysical considerations would suggest that phenomenology is compatible with metaphysical views it should in principle deny. Nonetheless, permitting metaphysical claims threatens to contravene the critical limits of phenomenology, to invite claims that would require a perspective different in kind than our own to verify. These (...) tensions raise an important question, namely, what are the metaphysical implications of the phenomenologically intuitive claim that objects themselves are constituents of experience? To answer this question, I draw on a broad swath of thought on transcendental idealism and phenomenology. I argue that a modest metaphysics of appearance is warranted within the critical limits of Husserlian phenomenology. Through discussing and addressing the problems that typically plague transcendental arguments, I show that Husserlian phenomenology permits stronger claims about objects of experience than deflationary accounts allow but does not permit claims about intrinsic properties allowed by some forms of transcendental idealism. (shrink)

This paper focuses on the puzzling question of what motivates the radical epistemological shift necessary for engaging in transcendental phenomenology. Husserl touches on the problem of motivation on many occasions, but it becomes an explicit issue in Fink’s bold reimagining of the transcendental theory of method, as presented in the Sixth Cartesian Meditation. In the first section, I briefly introduce the problem as it appears in Husserl. The second section of the paper discusses Fink’s Hegelian dissolution of it. Finally, I (...) point to several historical, practical, and ethical aspects of transcendental phenomenology, and argue that a good account of motivation for phenomenology ought to find a way to address these without hastily bracketing them. (shrink)

Building on past constructive criticism, the present study provides further methodological development focused on the elimination of bias that may occur during first-person observation. First, various sources of errors that may accompany introspection are distinguished based on previous critical literature. Four main errors are classified, namely attentional, attributional, conceptual, and expressional error. Furthermore, methodological recommendations for the possible elimination of these errors have been determined based on the analysis and focused excerpting of introspective scientific literature. The following groups of methodological (...) recommendations were determined: 1) a better focusing of the subject’s attention to their mental processes, 2) providing suitable stimuli, and 3) the sharing of introspective experience between subjects. Furthermore, the potential of adjustments in introspective research designs for eliminating attentional, attributional, conceptual, and expressional error is discussed. (shrink)

“Passive fear” denotes a certain type of response to a perceived threat; what is distinctive about the state of passive fear is that its behavioral outlook appears to qualify the emotional experience. I distinguish between two cases of passive fear: one is that of freezing in fear; the other is that of fear-involved tonic immobility. I reconstruct the explanatory strategy that is commonly employed in the field of emotion science, and argue that it leaves certain questions about the nature of (...) passive fear unanswered. I subsequently propose an account of passive fear that builds upon a phenomenological theory of emotions, placing emphasis on the interpretation of current research into human tonic immobility. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

It is not uncommon in educational research and social science in general either to eschew the word truth or to put it in scare quotes in order to signify scepticism about it. After the initial wave of relativism in the philosophy of natural science, a second wave has developed in social science with the rise of postmodernism and poststructuralism. The tendency here is to relativise truth or to bracket out questions of truth. In contradistinction, this paper revindicates the metaphysical nature (...) of truth. Truth is a transcendental precondition of educational inquiry and is best understood as a formal, regulative norm. Realism about truth enjoins a defence of the correspondence theory, which is provided here. At the same time, however, the development of realism in the social sciences has ironically followed the postmodernists in its scepticism about truth and its rejection of the correspondence theory. This paper critically appraises such recent developments, since all research is unintelligible without realism about the social world and whether our substantive knowledge-claims correspond with it. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...) means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)