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)

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)

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)

A detailed interpretation is provided of the ‘Gray's Elegy’ passage in Russell's ‘On Denoting’. The passage is suffciently obscure that its principal lessons have been independently rediscovered. Russell attempts to demonstrate that the thesis that definite descriptions are singular terms is untenable. The thesis demands a distinction be drawn between content and designation, but the attempt to form a proposition directly about the content (as by using an appropriate form of quotation) inevitably results in a proposition about the thing (...) designated instead of the content expressed. In light of this collapse, argues Russell, the thesis that definite descriptions are singular terms must accept that all propositions about a description's content represent it by means of a higher-level descriptive content, so that knowledge of a description's content is always ‘by description’, not ‘by acquaintance’. This, according to Russell, renders our cognitive grip on definite descriptions inexplicable. Separate responses on behalf of Fregeans and Millians are offered. (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)

In his celebrated 'Good and Evil' (l956) Professor Geach argues as against the non-naturalists that ‘good’ is attributive and that the predicative 'good', as used by Moore, is senseless.. 'Good' when properly used is attributive. 'There is no such thing as being just good or bad, [that is, no predicative 'good'] there is only being a good or bad so and so'. On the other hand, Geach insists, as against non-cognitivists, that good-judgments are entirely 'descriptive'. By a consideration of what (...) it is to be an A, we can determine what it is to be a good A, even where the ‘A’ in question is ‘human being’. These battles are fought on behalf of naturalism, indeed, of an up-to-date Aristotelianism. Geach plans to 'pass' from the 'purely descriptive' man to good/bad man, and from human act to good/bad human act. I argue: (l) That the predicative 'good' does have a genuine sense and that it is a mistake to suppose that ‘good’ is a purely attributive adjective. This does not entail that the predicative good (as used by Moore) denotes a non-natural property, but his mistake, if any is metaphysical or ontological not conceptual. (2) That the attributive 'good' cannot be used to generate a naturalistic ethic. It is difficult to extract a set of biologically based requirements out of human nature that are a) reasonably specific; b) rationally binding or at least highly persuasive; and c) morally credible. -/- On the way I protest against Geach’s tendency to try to win arguments by affecting not to understand things. -/- My views to some extent anticipate those of Kraut in *Against Absolute Goodness*. (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)

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)

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)

ABSTRACT. Fodor characterizes concepts as consisting of two dimensions: one is content, which is purely denotational/broad, the other the Mentalese vehicle bearing that content, which Fodor calls the Mode of Presentation (MOP), understood "syntactically." I argue that, so understood, concepts are not interpersonally sharable; so Fodor's own account violates what he calls the Publicity Constraint in his (1998) book. Furthermore, I argue that Fodor's non-semantic, or "syntactic," solution to Frege cases succumbs to the problem of providing interpersonally applicable functional roles (...) for MOPs. This is a serious problem because Fodor himself has argued extensively that if Fregean senses or meanings are understood as functional/conceptual roles, then they can't be public, since, according to Fodor, there are no interpersonally applicable functional roles in the relevant senses. I elaborate on these relevant senses in the paper. (shrink)

The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...) categorial grammar, and also on the ground of its extension to the bi-level, intensional and extensional semantic-pragmatic theory ST for L. In T, according to the token-type distinction of Ch.S. Peirce, L is characterized first as a language of well-formed expression-tokens (wfe-tokens) - material, concrete objects - and then as a language of wfe-types - abstract objects, classes of wfe-tokens. In ST the semantic-pragmatic notions of meaning and interpretation for wfe-types of L of intensional semantics and the notion of denotation of extensional semanics for wfe-types and constituents of knowledge are formalized. These notions allow formulating a postulate (an axiom of categorial adequacy) from which follow all the most important conditions of the language adequacy, including the above, and a structural one connected with three principles of compositionality. (shrink)

Reductive, naturalistic psychosemantic theories do not have a good track record when it comes to accommodating the representation of kinds. In this paper, I will suggest a particular teleosemantic strategy to solve this problem, grounded in the neurocomputational details of the cerebral cortex. It is a strategy with some parallels to one that Ruth Millikan has suggested, but to which insufficient attention has been paid. This lack of attention is perhaps due to a lack of appreciation for the severity of (...) the problem, so I begin by explaining why the situation is indeed a dire one. One of the main tasks for a naturalistic psychosemantic theory is to describe how the extensions of mental representations are determined. (Such a theory may also attempt to account for other aspects of the “meaning” of mental representations, if there are any.) Some mental representations, e.g. the concept of water, denote kinds (I shall be assuming this is non-negotiable). How is this possible? Unfortunately, I haven’t the space to canvass all the theories out there and show that each one fails to accommodate the representation of kinds, but I will point out the major types of problems that arise for the kinds of theories that, judging by the literature, are considered viable contenders.1 In general, the theories either attempt and fail to account for the representation of kinds, or they fall back on something like an intention to refer to a kind – not exactly the most auspicious move for a reductive theory. There are a number of problems that prevent non-teleosemantic theories from explaining how it is possible to represent kinds. A concept of a kind K must.. (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)

In this paper, I offer a new solution to the old problem of how best to understand the meaning of the word ‘logos’ in the extant writings of Heraclitus, especially in fragments DK B1, B2 and B50. On the view I defend, Heraclitus was neither using the word in a perfectly ordinary way in these fragments, as some have maintained, nor denoting by it some kind of general principle or law governing change in the cosmos, as many have claimed. (...) Rather, I argue, Heraclitus deliberately traded on the ordinary use of the word in his time (to refer to a written or spoken presentation of things as ‘thus and so’) to denote the world’s constant presentation of itself as ‘thus and so’ to all of us in our experience – a kind of cosmic self-revelation. I show how this captures the sense in which ‘the logos’ is said to be ‘common’ (xunos) and to be the kind of thing most people fail to comprehend even before hearing Heraclitus’ own account, all without detaching Heraclitus’ use of the word from its ordinary contemporary meaning. This interpretation suggests Heraclitus was a thinker more centrally concerned with human (mis)understanding than with speculative cosmology. (shrink)

Traditionally, ‘that’-clauses occurring in attitude attributions are taken to denote the objects of the attitudes. Prior raised a famous problem: even if Frege fears that the Begriffsschrift leads to a paradox, it is unlikely that he fears a proposition, a sentence or what have you as the alleged object denoted by the ‘that’-clause. The usual way out is to say that ‘that’-clauses do not contribute the objects of the attitudes but their contents. I will show that, if we accept this (...) answer, either we’d better stop working on attitude attributions or we’d better work harder on them. (shrink)

This paper analyzes the determinants of women’s representation on boards of directors based on a panel of all privately owned or listed Danish firms with at least 50 employees observed during the period 1998–2010. We focus on the directors who are not elected by the employees and test three hypotheses on female board representation that we denote the female-led hypothesis, the tokenism hypothesis, and the pipeline hypothesis, respectively. We find evidence rejecting the female-led hypothesis. Firms with a female chairperson on (...) the board of directors tend to have significantly fewer other non-employee-elected female board members. We also find clear evidence of a tokenism behavior in Danish companies. The likelihood of enlarging the share of non-employee-elected female board members is significantly smaller if one, two, or more women have sat on the board of directors. Finally, the pipeline hypothesis is partly confirmed. The relation between the female pipeline of potentially qualified directors and female directors is weaker than the similar relation for males. Our findings offer insights to policy makers interested in promoting gender diversity within boardrooms. Our empirical evidence suggests that an important way to increase the female proportion of non-employee-elected board members is that more women reach top executive positions. (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...) semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

In recent work Allan Gibbard claims to be both a local quasi-realist, in Blackburn’s sense, and a global expressivist. His local quasi-realism rests on an argument that for naturalistic discourse but not ethical discourse, the semantic relation of denotation and the causal relation of tracking can and should be identified; that denoting simply is tracking, for naturalistic vocabulary. I argue that Gibbard’s case for this conclusion is unconvincing, and poorly motivated by his own expressivist standards. I also argue that (...) even if it were successful, it is doubtful whether the resulting position would count as global expressivism, as Gibbard and I both use that term. (shrink)

The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence (...) G (I), X1, X2, … is the identity, then G (I) is nilpotent. (shrink)

This paper is a critical investigation of Gottlob Frege's and Bertrand Russell's views on the sense or meaning of singular terms. In his famous "On denoting" Russell erects his case on objections that he raises against Frege. I suggest that Russell's criticisms of Frege are seriously misguided, due in large measure to the uneven applications of his terminology when addressing Frege's views.

This paper argues that Wolff’s rejection of Leibnizian monads is rooted in a disagreement concerning the general notion of substance. Briefly, whereas Leibniz defines substance in terms of activity, Wolff retains a broadly scholastic and Cartesian conception of substance as that which per se subsists and sustains accidents. One consequence of this difference is that it leads Wolff to interpret Leibniz’s concept of a constantly striving force as denoting a feature of substance separate from its static powers, and not (...) as their replacement. For Wolff, powers are essential possibilities of acting in subjects suited for independent existence. Force is a further ingredient that provides a reason for the contingent operation of powers. Unlike Leibniz, Wolff conceives force narrowly as a principle of actuality, which he calls the “nature” of substance, as distinct from its principle of possibility, or essence. (shrink)

The aim of this critical note is to discuss Heraclitus' use of analogy as a pattern of thought not only with argumentative value but also ontological and epistemological status. Heraclitus' analogy is of two kinds and is expressed in the use of the adverbs ὥσπερ ("as") and ὅκωσπερ ("just as"). The first is used as an explanatory device, while the second denotes the ontological homogeneity of logos. Analogy reveals not only the inherent opposition of logos in each single thing, but (...) also the interdependent common interrelation between things. (shrink)

Ecological economics is an interdisciplinary science that is primarily concerned with developing interventions to achieve sustainable ecological and economic systems. While ecological economists have, over the last few decades, made various empirical, theoretical, and conceptual advancements, there is one concept in particular that remains subject to confusion: critical natural capital. While critical natural capital denotes parts of the environment that are essential for the continued existence of our species, the meaning of terms commonly associated with this concept, such as ‘non-substitutable’ (...) and ‘impossible to substitute,’ require a clearer formulation then they tend to receive. With the help of equations and graphs, this article develops new definite account of critical natural capital that makes explicit what it means for objective environmental conditions to be essential for continued existence. The second main part of this article turns to the question of formally modeling the priority of conserving critical natural capital. While some ecological economists have maintained that, beyond a certain threshold, critical natural capital possesses absolute infinite value, absolute infinite utility models encounter significant problems. This article shows that a relative infinite utility model provides a better way to model the priority of conserving critical natural capital. (shrink)

Self-respect is an aspect of human personality. It denotes showing respect to oneself. In other words, self-respect is a quality or characteristic of an individual that he always wants to maintain in his life. It assists a man to acquire self-confidence, self-satisfaction, and self-realization. In the history of contemporary philosophy, applied philosophy deals with human rights, euthanasia, feminism, abortion, animal rights, bonds, self-respect, and so on. Elizabeth Telfer is a notable name in the history of contemporary applied philosophy. Telfer discusses (...) self-respect from a moral viewpoint. She explains the conative and estimative aspects of self-respect and the value of self-respect. Likewise, Telfer, I will also place more emphasis on the conative aspects of self-respect. And finally, I will offer arguments for showing the significance of self-respect in this paper. (shrink)

When reusing existing ontologies for publishing a dataset in RDF (or developing a new ontology), preference may be given to those providing extensive subcategorization for important classes (denoted as focus classes). The subcategories may consist not only of named classes but also of compound class expressions. We define the notion of focused categorization power of a given ontology, with respect to a focus class and a concept expression language, as the (estimated) weighted count of the categories that can be built (...) from the ontology’s signature, conform to the language, and are subsumed by the focus class. For the sake of tractable initial experiments we then formulate a restricted concept expression language based on existential restrictions, and heuristically map it to syntactic patterns over ontology axioms (so-called FCE patterns). The characteristics of the chosen concept expression language and associated FCE patterns are investigated using three different empirical sources derived from ontology collections: first, the concept expression pattern frequency in class definitions; second, the occurrence of FCE patterns in the Tbox of ontologies; and last, for class expressions generated from the Tbox of ontologies (through the FCE patterns); their ‘meaningfulness’ was assessed by different groups of users, yielding a ‘quality ordering’ of the concept expression patterns. The complementary analyses are then compared and summarized. To allow for further experimentation, a web-based prototype was also implemented, which covers the whole process of ontology reuse from keyword-based ontology search through the FCP computation to the selection of ontologies and their enrichment with new concepts built from compound expressions. (shrink)

A common understanding of the role of a game developer includes establishing (or at least partially establishing) what is interactively and perceptually available in (video)game environments: what elements and behaviors those worlds include and allow, and what is – instead – left out of their ‘possibility horizon’. The term ‘possibility horizon’ references the Ancient Greek origin of the term ‘horizon’, ὄρος (oros), which denotes a frontier – a spatial limit. On this etymological foundation, ‘horizon’ is used here to indicate the (...) spatial and operational boundaries that a (video)game environment affords its players. This book chapter discusses a particular feeling that emerge in relation to playful encounters with the ‘possibility horizons’ of videogames. I am referring here to the realization, as a player, that a game environment can be experientially exhausted and is, as such, ultimately banal. In other words, I will examine how our deliberate engagement with the interactive environments of digital games can trigger sensations that are analogous to what Romantic authors referred to as Weltschmerz (‘world-weariness’). (shrink)

Alberto Coffa used the phrase "the Copernican turn in semantics" to denote a revolutionary transformation of philosophical views about the connection between the meanings of words and the acceptability of sentences and arguments containing those words. According to the new conception resulting from the Copernican turn, here called "the Copernican view", rules of use are constitutive of the meanings of words. This view has been linked with two doctrines: (A) the instances of meaning-constitutive rules are analytically and a priori true (...) or valid; (B) to grasp a meaning is to accept its rules. The pros and cons of different versions of the Copernican view, ascribable to Wittgenstein, Carnap, Gentzen, Dummett, Prawitz, Boghossian and other authors, will be weighed. A new version will be proposed, which implies neither (A) nor (B). (shrink)

Frege supposedly believes that vague predicates have no referent (Bedeutung). But given other things he evidently believes, such a position would seem to commit him to a suspect nihilism according to which assertoric sentences containing vague predicates are neither true nor false. I argue that we have good reason to resist ascribing to Frege the view that vague predicates have no Bedeutung and thus good reason to resist seeing him as committed to the suspect nihilism. In the process, I call (...) attention to several under-appreciated texts in which Frege suggests that a vague predicate, though lacking a Bedeutung of its own, can come to acquire a Bedeutung in certain contexts. The upshot of this suggestion is that vague predicates can serve the purposes of ordinary communication quite well, even if they are useless for logical purposes. (shrink)

With regard to the importance and position of phone for thought and language in Aristotle, and his brief account of it in Περὶ Ψυχῆς / De Anima, here I am going to paraphrase his brief mentioning in the chapter eight of the second book of the mentioned treatise. When we read the pertinent section of 4201b - 421a, we see that Aristotle examines it in connection with “hearing” as a sense that is embedded in his wide discussion about “soul”. But (...) when we go into details under this general topic, we see that phone definition is connected with three concepts such as sound, phantasia and semantic. In other words, Aristotle considers human phone in a unit that consists of “hearing, sound, phantasia and semantic” and all of these within a broader specific discussion about human “soul” denotes to the texture and nature of his account. (shrink)

Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement Φ: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆[2,f(7)]. Let B denote the system of equations: {x_j!=x_k: i,k∈{1,...,9}}∪{x_i⋅x_j=x_k: i,j,k∈{1,...,9}}. The system of equations {x_1!=x_1, x_1 \cdot x_1=x_2, x_2!=x_3, x_3!=x_4, x_4!=x_5, x_5!=x_6, x_6!=x_7, x_7!=x_8, x_8!=x_9} has exactly two solutions in positive integers x_1,...,x_9, namely (1,...,1) and (f(1),...,f(9)). No known system S⊆B with a finite (...) number of solutions in positive integers x_1,...,x_9 has a solution (x_1,...,x_9)∈(N\{0})^9 satisfying max(x_1,...,x_9)>f(9). For every known system S⊆B, if the finiteness/infiniteness of the set {(x_1,...,x_9)∈(N\{0})^9: (x_1,...,x_9) solves S} is unknown, then the statement ∃ x_1,...,x_9∈N\{0} ((x_1,...,x_9) solves S)∧(max(x_1,...,x_9)>f(9)) remains unproven. Let Λ denote the statement: if the system of equations {x_2!=x_3, x_3!=x_4, x_5!=x_6, x_8!=x_9, x_1 \cdot x_1=x_2, x_3 \cdot x_5=x_6, x_4 \cdot x_8=x_9, x_5 \cdot x_7=x_8} has at most finitely many solutions in positive integers x_1,...,x_9, then each such solution (x_1,...,x_9) satisfies x_1,...,x_9≤f(9). The statement Λ is equivalent to the statement Φ. It heuristically justifies the statement Φ . This justification does not yield the finiteness/infiniteness of P(n^2+1). We present a new heuristic argument for the infiniteness of P(n^2+1), which is not based on the statement Φ. Algorithms always terminate. We explain the distinction between existing algorithms (i.e. algorithms whose existence is provable in ZFC) and known algorithms (i.e. algorithms whose definition is constructive and currently known). Assuming that the infiniteness of a set X⊆N 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) No known algorithm with no input returns the logical value of the statement card(X)=ω. (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. *** Conditions (2)-(5) hold for X=P(n^2+1). The statement Φ implies Condition (1) for X=P(n^2+1). The set X={n∈N: the interval [-1,n] contains more than 29.5+\frac{11!}{3n+1}⋅sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. 501893∈X. Condition (1) holds with n=501893. card(X∩[0,501893])=159827. X∩[501894,∞)= {n∈N: the interval [-1,n] contains at least 30 primes of the form k!+1}. We present a table that shows satisfiable conjunctions of the form #(Condition 1) ∧ (Condition 2) ∧ #(Condition 3) ∧ (Condition 4) ∧ #(Condition 5), where # denotes the negation ¬ or the absence of any symbol. 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 this assumption. (shrink)

In this paper, we turn to the philosophy of Jean-Luc Nancy. In his work La Création du Monde ou la Mondialisation of 2002 the French philosopher analyses the process of globalisation. Rather than denoting a new homogeneity, the term refers to a world horizon characterized in its interpalpable multiplicity of cultural, socio-economical, ideological and politico-moral content. According to Nancy, globalisation refers to ag-glome-ration: the decay of what once was a globe and now nothing more than a glome. On the (...) one hand, Nancy indicates that the world has changed by an unknown increase of techno-science, the worsening of inequalities between growing populations and by the changing and disappearing of given certainties, views and identities of the world and of man. On a large scale, this deformation is due to the relation between the capitalist evolution and the capitalising of worldviews. On the other hand, due to the inter-palpability of the multiplicity, this means that on our planet there is only space for one world. The world gradually becomes the only world. In this paper we will investigate what Nancy means with the becoming-world of the world and how this relates to our being in the world. For Nancy globalisation reveals two possible destinies of our relation with the world. In La Création du Monde ou la Mondialisation he discerns globalisation from mondialisation to analyze these two possibilities. We will investigate this distinction of Nancy and its consequences for everyday life. (shrink)

A set D subset of V(G) is a dominating set of a graph G if for all x ϵ V(G)\D, for some y ϵ D such that xy ϵ E(G). A dominating set D subset of V(G) is called a connected dominating set of a graph G if the subgraph <D> induced by D is connected. A connected domination number of G, denoted by γ_c(G), is the minimum cardinality of a connected dominating set D. The triple repetition sequence denoted by (...) {S_n:n ϵ Z+} is a sequence of positive integers which is repeated thrice, i.e., {S_n}={1,1,1,2,2,2,3,3,3, ...}. In this paper, we construct a combinatorial explicit formula for the triple repetition sequence of connected domination numbers of a triangular grid graph. (shrink)

As the word demos denotes, the democracy is generally considered as the rule or governance based on the general base of people in which monarchy or oligarchy form is excluded. We have a classical view about the four forms of government, which was proposed by Platonic concepts. Most idealistic form of government, in his prongs, could be found in Crete and Sparta, which was nevertheless not a democratic form. His accolade of these two nations, which, of course, would be a (...) kind of God’s product so to be most benevolent, humanly appealing, efficient and philanthropic. This means the democratic form of government is not best, but most favored alternative to police the society. The political terms, henceforth, would supervene the concept of democracy, and, for many reasons and on historical wake, democracy is generally accepted as practically most desired form of rule or governance. While some modern scholar revealed, a mini-republic can be a niche to contest the merits of various forms of governance. We can gauge a scope of elements we value through the governance process, human intrinsic, efficiency, equality, welfare and even individual happiness. As the time is a small city community, called a polis, in Plato and Socrates, a mini republic can be well envisaged in understanding the Platonic Republic. In that case, most benevolent ruler may be superior to any other form of governance, which can be a philosopher’s Republic. The ideal ruler would behave and govern with mighty intelligence and concomitant power to rule. It is idealistic to produce maximum happiness of polis constituents. The worst contras, however, a tyranny, comes that the constituents legitimately expel their ruler by a collective vote. This extreme contrast and the way of process also could be ascertained in the ancient form of oriental monarchy. The dynasty could be legitimately revoked to restore new heritage of emperor or Kings where a kind of rebellion, as elucidated by Locke, is well justified in the name of heaven’s command. Given the size of polis or governed territory, there are separate ways to redress the evils of tyranny while the Oriental culture has not recognized the kind of formal vote methods. Any means to expel the tyranny could be embraced to rebel. For our purpose of grasp through this working paper, I would theorize on the traditional elements of public policy and democratic form of government. (shrink)

This article addressed historical aspects of the political economy involving sustained forest ecology in Sierra Leone as a whole, with emphasis on the Freetown Peninsula and its surrounding communities. Attention is paid to cultural, social and economic aspects involving forest livelihoods of residents on the Freetown Peninsula and far afield. The term 'Political Economy' is used in this situation to denote the relationship between the economics of people's livelihoods and public policy (in relation to the management of legislative procedures) in (...) ensuring that resources in the forest environment is sustainably managed to cater for the livelihood needs of people in Sierra Leone, while at the same time maintaining a balance in protecting the forest ecosystems. The paper has provided a critical review of the political economy of forest ecology in the country on the basis of scholarly discourses, and its applicability in adapting to the fragile political administrative management Sierra Leone have (and is continuing to) experienced. (shrink)

The paper deals with the problem of logical adequacy of language knowledge with cognition of reality. A logical explication of the concept of language knowledge conceived of as a kind of codified knowledge is taken into account in the paper. Formal considerations regarding the notions of meta-knowledge (logical knowledge about language knowledge) and truth are developed in the spirit of some ideas presented in the author’s earlier papers (1991, 1998, 2001a,b, 2007a,b,c) treating about the notions of meaning, denotation and truthfulness (...) of well-formed expressions (wfes) of any given categorial language. Three aspects connected with knowledge codified in language are considered, including: 1) syntax and two kinds of semantics: intensional and extensional, 2) three kinds of non-standard language models and 3) three notions of truthfulness of wfes. Adequacy of language knowledge to cognitive objects is understood as an agreement of truthfulness of sentences in these three models. (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)

What Ivan Illich regarded in his Medical Nemesis as the ‘expropriation of health’ takes place on the surfaces and in the spaces of the screens all around us, including our cell phones but also the patient monitors and (increasingly) the iPads that intervene between nurse and patient. To explore what Illich called the ‘age of the show’, this essay uses film examples, like Creed and the controversial documentary Vaxxed, and the television series Nurse Jackie. Rocky’s cancer in his last film (...) (submitting to chemo to ‘fight’ cancer) highlights what Illich along with Petr Skrabanek called the ‘expropriation of death’. In contrast to what Illich denotes as ‘Umsonstigkeit’ – i.e., a free gift, given undeservedly, i.e., gratuitously – medical science tends to be tempted by what Illich terms scientistic ‘black magic’, taking over (expropriating) the life and the death of the patient in increasingly technological ways, a point underscored in the concluding section on the commercial prospects of xenotransplants using factory farm or mass-produced (and already for some time) human-pig mosaics or chimeras. (shrink)

The paper discusses a prominent one of Kratzer's (1986, 1991, 2012) arguments against material implication analyses of the denotation of (indicative) conditional sentences. This is the argument based on the sentence _Most of the time, if a man buys a horse, he pays cash for it_. It is shown that material implication makes a prediction that does conform to speakers' intuitions, contrary to Kratzer's claim. The paper also argues that Lewis's (1975) attack on material implication analyses of conditional sentences based (...) on examples where the conditional is embedded under the adverbials _sometimes_ and _never_ does not have much force given that the interpretation of such sentences is subject to inferential pragmatic operations in addition to the recovery of their denotation. (shrink)

The aim of this paper is to draw the attention of those conducting research on imagery to the different kinds of visual information deployed by expert drawers compared to non-expert drawers. To demonstrate this difference I draw upon the cognitive science literature on vision and imagery to distinguish between three different ways that visual phenomena can be represented in memory: structural descriptions, denotative descriptions, and configural descriptions. Research suggests that perception and imagery deploy the same mental processes and that the (...) drawing of one's imagery would require the simultaneous deployment of these very processes. I reason that drawing a picture of one's imagery is not possible. I hypothesize that when required to draw a picture from memory, both expert and non-expert drawers access their denotative description of the object rather than their imagery. I then suggest how my hypothesis could be tested and if accurate, how this finding would impact upon the design and interpretation of experiments on imagery when drawing is involved. I also suggest why the constraints that perception places upon the simultaneous deployment of imagery appear not to cause the same constraints in autistic savant drawers and visual agnosia patients. (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)

The main aim of this study was to evaluate the effects of school heads’ new normal leadership on collaborative school culture. To achieve this aim, the researcher conducted a survey to a number of school principals and teachers inFukuoka and Hiroshima Prefectures during the school year 2020-2021. The data were collected and processed using the Statistical Packages for Social Sciences. Results indicated that the three (3) variables of new normal leadership of school heads affect the collaborative school culture in varying (...) extent as shown by the obtained B Coefficients 1.170 (adaptability), 1.132 (decision-making), 0.430 (planning and implementation). This means that for every unit improvement in the new normal leadership mentioned could generate a 1.170, 1.132, 0.430 increase on collaborative school culture. A closer look at the obtained Beta Coefficients, one could infer that of the 3 variables of school new normal leadership, it was the ‘adaptability’ that exert a greatest influence (Beta=1.170) on the collaborative school culture. The R able to denote multiple correlation coefficient between the different variables as a predictor of the dependent variable. It could be noted that the R is .895 which indicated a level of prediction while R2 figure is a statistical measure on closeness of the data in regression line as the coefficient of determination or simply the coefficient of multiple determination for multiple regression. It can be indicated that the explanatory powers of the dependent variable of 0.698 implies that 69.8% or 70% of the variation in new normal leadership is accounted by changes in the collaborative school culture. Furthermore, results of analysis of variance revealed an F ratio equal to 1.642 with an associated probability equal to .000.Since the p-value is lower than the significance level set at 0.05, the null hypothesis is rejected. It may be safely concluded that the new normal leadership of school heads produce significant combined effects on collaborative school culture. (shrink)

In this paper I try to show that semantics can explain word-to-world relations and that sentences can have meanings that determine truth-conditions. Critics like Chomsky typically maintain that only speakers denote, i.e., only speakers, by using words in one way or another, represent entities or events in the world. However, according to their view, individual acts of denotations are not explained just by virtue of speakers’ semantic knowledge. Against this view, I will hold that, in the typical cases considered, semantic (...) knowledge can account for the denotational uses of words of individual speakers. (shrink)

Recently, the term ‘aphantasia’ has become current in scientific and public discourse to denote the absence of mental imagery. However, new terms for aphantasia or its subgroups have recently been proposed, e.g. ‘dysikonesia’ or ‘anauralia’, which complicates the literature, research communication and understanding for the general public. Before further terms emerge, we advocate the consistent use of the term ‘aphantasia’ as it can be used flexibly and precisely, and is already widely known in the scientific community and among the general (...) public. (shrink)

It is sometimes claimed that in his 1912 work, "The Problems of Philosophy" (POP), and possibly as early as “on Denoting”, Russell conceives of the mind's acquaintance with sense-data as providing an indubitable or certain foundation for empirical knowledge. However, although he does say things suggestive of this view in certain of his 1914 works, Russell also makes remarks in POP that conflict with any such broadly "Cartesian" interpretation of this work. This paper attempts to resolve this apparent tension, (...) while also offering a close examination of Russell's views on the nature of acquaintance and their relationship to certain ideas in William James. (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his (...) rejection of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

Some contemporary semantic views defend an asymmetry thesis concerning defi-nite descriptions and indexicals. Semantically, indexicals are devices of singular refer-ence; they contribute objects to the contents of the speech acts made with utterances including them. Definite descriptions, on the other hand, are generalized quantifiers, behaving roughly the way Russell envisaged in “On Denoting”. The asymmetry thesis depends on the existence of a sufficiently clear-cut distinction between semantics and pragmatics, because indexicals and descriptions are often used in ways that apparently (...) contradict the asymmetry thesis; the semantics/pragmatics distinction is invoked to see behind the appearances. The paper critically examines arguments by Schiffer against the asymmetry thesis, based on referential uses of incomplete descriptions. (shrink)

"This 'paper' is meant to be an introduction to three other papers of mine, namely: 'The "Emergence" of Existence' (cf. http://www.academia.edu/4310644/The_Emergence_of_Existence_-_from_Pregeometry_to_Prephysics), 'Names and Objects' (cf. http://www.academia.edu/4310705/Names_and_Objects_-_Outlines_of_an_Essentialist_Nominalism), and 'Information Monism' (cf. http://www.academia.edu/4310969/Information_Monism_-_and_its_Concepts_of_Substance_Attributes_and_Em ergent_Modes). In this introduction also some light shall be shed on the mutual dependence and interrelatedness of these mentioned papers. It also includes a hefty attack on Russell's 'On Denotation' with respect to his alleged refutation of Meinong's Gegenstandstheorie (objectology aka theory of objects).".

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)

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)

‘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)