In §8 of his Begriffsschrift (1879), Gottlob Frege discusses issues related to identity. Frege begins his most famous essay, “On Sense and Denotation” (1892), published 13 years later, by criticizing the view advocated in §8. He returns to these issues in the concluding paragraph. Controversies continue over these important passages. We offer an interpretation and discuss some alternatives. We defend that in the Begriffsschrift, Frege does not hold that identity is a relation between signs. §8 of the Begriffsschrift is motivated (...) by the conflict between two different criteria for sameness of conceptual content of sentences. To resolve that conflict, Frege introduces ‘≡’ in §8 and, thus, circumstances with names as constituents. To the same end, in “On Sense and Denotation,” Frege introduces senses and Thoughts and abandons both ‘≡’ and circumstances. He solves what we call the Co-instantiation problem, and disregards, but does not solve, the Name problem. (shrink)

This paper is dedicated to developing a formalism that takes rejection seriously. Bilateral notation of signed formulas with force indicators is adopted to define signed consequences which can be viewed as the bilateral counterpart of Tarskian consequence relations. Its relation to some other bilateral approaches is discussed. It is shown how David Nelson’s logic N4 can be characterized bilaterally and the corresponding completeness result is proved. Further, bilateral variants of three familiar notions are considered and investigated: that of a fragment, (...) of definitional equivalence, and of a conservative extension. (shrink)

There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berry's Paradox, Heterologicality, Russell's Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, and (...) should be replaced with Hilbert and Bernays' conservative extension. Standard second-order logic, and quantified propositional logic also must be substantially modified, to incorporate, in the first place, nominalizations of predicates, and whole sentences. And further modifications must be made, so as to insist that predicates are parts of sentences rather than forms of them, and that truth is a property of propositions rather than their sentential expressions. In all, a thorough reworking of what has been called 'logic' in recent years must be undertaken, to make it more fit for use. (shrink)

MEANING POSTULATES REINSTATED If I am right in agreeing with Cresswell that the "logicarrlexicaT distinction is one of degree rather than one of kind, that in turn impugns the distinction between the official truth-rules that define logical ...

Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...) formalizations of arithmetic. In Peano's formalization the domain is a restricted class of individuals, while the universe of discourse is the unrestricted class of all individuals. In Gödel's formalization the domain is a restricted class of individuals as in Peano's formalization, but the universe of discourse coincides with the domain. In Whitehead-Russell's formalization the domain is a class of logical notions in Tarski's sense, that are necessarily not individuals, whereas the universe of discourse is the unrestricted class of individuals as in Peano's formalization. The present approach emphasizes the viewpoint that the universe of discourse of a given discourse is important in determining which propositions are expressed by which sentences. (shrink)

In this paper we introduce a theoretical framework and a logical application for analysing the semantics and pragmatics of contrastive conjunctions in natural language. It is shown how expressions like although, nevertheless, yet, and but are semantically definable as connectives using an operator for implication in natural language and how similar pragmatic principles affect the behaviour of both contrastive conjunctions and indicative conditionals. Following previous proposals, conditions on contrast in a conjunction are analysed as presuppositions of die conjunction. Further linguistic (...) evidence leads to a distinction between restrictive and non-restrictive connectives of contrast, and consequently between direct and indirect contrast, which are given a precise definition. A general interface for a theory of contrast using possible world semantics for implication is then presented. As a test case, we show how this interface is applicable to the semantics for conditionals that was introduced by Veltman in his article 'Data semantics and the pragmatics of indicative conditionals' (1986). This application yields an extension of Veltman's Data Logic, called Contrastive Data Logic Once appropriate modifications are added to Veltman's pragmatic considerations, we show that contrastive data logic provides an adequate tool for the analysis of substantial linguistic data concerning contrast and implication in natural language. (shrink)

Book reviewed in this article:F.H. Bradley, Collected Works Volumes 1–5.

By a seemingly strange twist of fate, the formalist approach to language became popular after Hilbert’s project of providing a formalist foundation for mathematics foundered on G¨odel’s famous incompleteness theorems. Even in September 1930, during the congress in K¨onigsberg, where G¨odel presented his results for the first time, Carnap still defended logicism against the intuitionist and formalist views on the foundations of mathematics. Furthermore in linguistics, the formalist approach to syntactic issues had only become disseminated in the 1930s, due to (...) the distributionists of Bloomfield’s school, and found its paramount expression in Hjelmslev’s Prolegomena to a Theory of Language : according to Hjelmslev, both the linguistic theory and the grammar of a given language are nothing more than a calculus. (shrink)

Quantifiers in Frege's Grundgesetze like are not well-defined because the part Fx & Gx stands for a concept but the yoking conjunction is horizontalised and must stand for a truth-value. This standard interpretation is rejected in favor of a substitutional reading that, it is argued, both conforms better to the text and is well-defined. The theory of the horizontal is investigated in detail and the composite reading of Frege's connectives as made up of horizontals is rejected. The sense in which (...) the Grundgesetze has a many-valued but classical logic is explained by proving that its propositional fragment (under the standard interpretation) and Bochvar's 3-valued logic are instances of the same metatheoretic methods. Historically, the paper argues for a more naive but well-defined reading of the text. Theoretically, it provides a formally adequate statement of that semantics, as well as developing the abstract metatheory which embraces Bochvar's language and the Fregean fragment. (shrink)

The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the (...) paper then goes on to indicate the lines on which formal logic—and also the lambda calculus and set theory—needs to be restructured, to remove the difficulties. Throughout the study of what have come to be known as first-, second-, and higher-order languages, what has been primarily overlooked is that these languages are abstractions. Many well known paradoxes, we shall see, arose because of the elementary level of simplification which has been involved in the abstract languages studied. Straightforward resolutions of the paradoxes immediately appear merely through attention to languages of greater sophistication, notably natural language, of course. The basic problem has been exclusive attention to a theory in place of what it is a theory of, leading to a focus on mathematical manipulation, which ‘brackets off’ any natural language reading. (shrink)

A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of theirrespective explanatory powers. After a briefsurvey of such a comparison, we argue (...) that anextended form of conceptual realism provides themost coherent formal ontology and, as such, canbe used to defend the view of logic as language. (shrink)

SUMMARY1 The rational soul becomes the constant and dimensionless Euclidean point in all experience - defining the situations in which it finds itself, but itself undefined and undefinable in any situation. It is in nature but not of nature. Just as the dimensionless Euclidean point can occupy infinite positions on a line and yet remain unaltered, so the immortal, active intellect remains unaffected by the world in which it finds itself. It is not influenced by age, sense data, sickness or (...) death. It is the knower whose nature is pure knowing or reason. This is in great part the basic assumption that runs through the history of Aristotelean and modern symbolic logics24.The rational soul grasps identity, reasons consistently, and knows objectively for though it is in the world it is not of the world. Thus it is unnecessary and impossible to relate its truth to time or place or condition. As the source of understanding it need not be understood. It understands in that it knows. It is this which places the objective knower and observer outside of all systems of knowledge that it creates in philosophy, science and theology, and frees it from subjective interpretation. It is the absolute observer beyond self-observation.252 Language, values, and meanings reflect the absolute viewpoint of the dimensionless observer beyond the necessity of observation. The task of this observer is to know trie world just as the task of the animal and plant soul is motion and reproduction. The rational soul performs its task beyond nature as surely as animals and plants perform their tasks in nature. This is why it is possible to discuss the necessary evolution of living organisms in nature, but unnecessary to discuss the necessary or unnecessary nature of the evolution of this discussion. This is one of the reasons why determinism or predestination which seem so clearly applicable to nature, need not be applied to theories of determinism and predestination. These are principles grasped in reality beyond nature and totally inapplicable to the non-natural spirit that comprehends their essences. Thus self-reflexive questions about the questioner are as irrelevant as would be questions historically of “in what sense might the definition of dimensionless point itself be dimensioned or dimension-less?”26 Questions, on the other hand, that relate to the observed world are important for they can be truly answered (where questions as to the nature of the questioner cannot). In this view reality is not nature, but rather it is from reality that the objective observer, philosopher, scientist, and theologian understands and controls nature.3 Logic, the science of reason, is the science of all sciences. It reflects the pure and innate rational nature of the knowing intellect or soul. It is pure form beyond nature. Its realm is that of first principles or axioms. These too are in the world but not of it, as with Plato's eidos and Aristotle's universals. They are clear, true and self-evident. This explains the on going use of axiomatized revelations in studies in the natural and social sciences, the arts and the humanities. In symbolic logics, natural languages are in and of the world, but meta-languages are the constructs of pure intellectual activity and thus not natural. The abstract tends to become the more real, the less it can be found in nature. Rational souls, however, share a common reality that is as universal for Frege as it was for Aristotle.274 The occidental object tradition in general breaks out of the nature continuum by withdrawing into reality where the intellect knows and manipulates the world in philosophy, science, and theology from its position in and understanding of reality. Nature is a sub-set of reality and not vice versa. Axioms are the laws and determinants of nature and logic, but they are not nature.28 This means that at the basis of the occidental continuum of nature there is a qualitative and irreducible dichotomy of reality vs. nature. This has been most useful in the history of occidental science, but it produces a world view in which nature may lose the race with reality. SUMMARY IIIn the first portion of my paper, I discussed the implications of the Euclidean egg for philosophy and science as nature is understood and manipulated from reality. I shall now turn to what I see as the implications of the three-legged chicken view that the human intellect is in and of nature and that reality is a perspective in nature and is not simply the other of an irreducible qualitative dichotomy. Although there are an endless number of such implications that I could explore, the following, it seems to me are the most important:1 In the natural continuum there is no “dimensionless real” which can serve either as the locus of an external observer or a fixed position in nature. There is no perspective which is not an aspect of that upon which it is a perspective. The Chinese sage, for example, is one who sees himself/herself as one with or within natural process. This is expressed in a number of ways. Fung Yu-lan speaks of the difference between having no knowledge and having no-knowledge.34 Within such a continuum there can be no abstracting out of the absolute and unchanging. The nameless is the source of the named. First principles are the process itself and these principles are the alternation of opposites:“The Nameless is the origin of Heaven and Earth;The Named is the mother of all things.Therefore let there always be non-being so we may see their subtlety, And let there always be being so we may see their outcome. The two are the same.“352 An empty mind is not a blank mind. Where Aristotle viewed the mind as a blank tablet at birth to be filled by sense experience, Hsun Tzu speaks of its emptiness. It is the emptiness of the Tao itself:“The mind is constantly storing up things, and yet it is said to be empty. The mind is constantly marked by diversity, and yet it is said to be unified. The mind is constantly moving, and yet it is said to be still. Inevitably it will see things for itself. And although the objects it perceives may be many and diverse, if its acuity is of the highest level, it cannot become divided within itself.”36The nature in which and of which the mind is both perspective and aspect remains a totality. Being a totality, it is empty of itself just as any part of a whole, while a part of the whole, is empty of the whole. My ideas of myself are both of myself and empty of myself. This point can be illustrated with the simple example of knowing and speaking about two hands – one of which is mine, and the second of which belongs to someone else. 1 can objectify the second hand and fill my blank mind with information and observations about it, but I continue to remain outside of it –the arbiter in my statements of its nature and reality. However, in knowing my own hand, the hand known is also the knower and what I know represents a perspective upon an aspective of a totality of which “I–my–hand” are aspects. Being an aspect of the whole is being empty of the whole. If mind is in and of nature, any perspective on nature is an aspect of the whole. A blank mind is an unnatural mind outside of nature, filling up with impressions of nature. An empty mind is nature viewing nature as aspect and perspective. The occidental would be ashamed to reach old age and still have a blank mind. The Chinese sage would be ashamed to reach old age and still not recognize that the mind is empty.3 If mind is in nature and like nature, then language too reflects natural flow and change and process. It is one thing for me to talk about myself and another for me to talk about someone else. In the case of the latter, I may insist that objectively this other subject fits into this or that category and even administer tests to determine that it does do indeed so. But when I talk about myself, the speaker and the object of speech are one and the same. The terms I select do represent a dichotomy of sorts, but it is one of aspect and perspective and not subject and object. When I say “this is my hand” for example, the words create distinctions which are aspects of awareness but do not create an / that is or is not my hand. Language does not model or even represent reality as opposed to nature. It makes reality possible as something that nature says or thinks. Reality through language is an aspect of nature and thus a perspective upon itself as aspect. This is an important distinction that translators often miss.4 Logic in this natural continuum is concerned with distinctions in a very different sense. As a consequence of the unity of nature and mind, three kinds of distinction in experience are manifested: (a) Those distinctions which come into being as aspects of the changing world.The 10,000 things are in this sense aspects and not separate “identities” as some philosophers and scientists presuppose.37 (b) Those distinctions which come into being as aspects of the human mind. These are impressions of and thoughts about the infinite distinctions of which the restless mind is capable, (c) Those distinctions which come into being by way of the mind's use of symbols. These are the distinctions which permit us to stabilize and store our experiences, preserve the answers to our questions, and name the world into compartments and relationships.Implicit in these three assumptions which connect the distinguishing mind to the unity of a nature of'10,000‘ aspects, is an inferential process of aspect to perspective to knowledge to understanding to attitude to action/response. The reasoning mind synthesizes some aspect of experience in nature with a perspective upon this aspect. This synthesis, in turn, is an aspect of mind and the reasoning process proceeds from it to a perspective upon it which is knowledge and understanding. Knowledge and understanding in turn are aspects of thinking and the reasoning process proceeds from them to a perspective upon them which is an attitude. Attitude in turn is an aspect of thinking and the reasoning process proceeds from it to a perspective upon it which is reflected in the reasoning individual's actions and responses. This inferential process is a continuum which proceeds from aspects of experience to perspectives in thought to action and response. In this sequence an aspect is always connected by a perspective which becomes an aspect, until action/non-action, response occurs. This is as applicable to the details of life as it is to mastering life as a whole. When this inference process is incomplete many problems may result, ranging from action without understanding to the confusion of aspect and perspective with one another or to “obsession with distinctions.”38In practice this is a logic of paradox. The human being is aware that he or she is a living-dying aspect of nature, but an aspect which is also a perspective upon nature's aspects of living and dying. This paradox is the process around which a profound logic of aspect/perspective is developed by the sage. This view of logic within a continuum does not mean that there is no principle of identity, contradiction or excluded middle present – as some Chinese and European philosophers assume.These principles are also implicit in the knowing of my hand versus the knowing of the hand of another. However, the content, meaning, and application of these principles may vary just as when I say propriety, I mean propriety, and when the Chinese says li he means li but the context, meaning and application of the term may differ in each case.5 Aspect logic as it relates mind to nature in a cosmological totality is a series of syntheses in a cyclic continuum organizing thinking in phases. Each phase is an aspect/perspective synthesis which becomes an aspect of a further aspect/perspective synthesis. This progression might be described thusly: The synthesis of nature/human which is Tao (non-being) translates into the aspects of being (the 10,000 things), and as such is a synthesis of aspect and perspective. This synthesis of aspect and perspective translates into an aspect of ideas and as such is a synthesis of perception and conception. This synthesis of perception and conception translates into an aspect of knowledge, and as such is a synthesis of knowledge and understanding (understanding is a perspective upon knowledge) i.e., no-knowledge. This synthesis of knowledge and understanding translates into an aspect of purpose, and as such is a synthesis of purpose and action. The perspective here on action is aesthetic and/or moral. This synthesis of purpose and actions translates again into an aspect of nature and as such is a synthesis beyond individual aspects and perspective, i.e. Tao. Thus there is a cyclic dynamic in the system which remains open to further development.Tai Chen in his Inquiry Into Goodness connects this cycle of syntheses with wisdom and benevolence:Because there are mind and intelligence, the superior man knows that the perfection of the Way of Man depends completely upon nature. When he looks at the signs of the natural (Cheng), he knows the beginning of things; when he cherishes the virtue of supreme illumination, (Shen-ming), he knows the end of things. Proceeding from mind and intelligence to the attainment of the virtue of supreme intelligence, [the superior man] in his treatment of things in the world will cause the world to return to [the principles of] benevolence; and in his treatment of the capability inherent in things, he will cause the world to follow wisdom (Chih).39. (shrink)

The Quine/Putnam indispensability approach to the confirmation of mathematical theories in recent times has been the subject of significant criticism. In this paper I explore an alternative to the Quine/Putnam indispensability approach. I begin with a van Fraassen-like distinction between accepting the adequacy of a mathematical theory and believing in the truth of a mathematical theory. Finally, I consider the problem of moving from the adequacy of a mathematical theory to its truth. I argue that the prospects for justifying this (...) move are qualitatively worse in mathematics than they are in science. (shrink)

This paper makes a Fregean analysis of certain expressions which, according to the way they are constructed, can refer, firstly, to events and, secondly, to the results of these events. This paper intends to show that –if we take into account the above mentioned expressions and use Fregean notions such as meaning, reference, function, argument and concept– it is possible to consider events as objects. To do this we need to articulate developments made both from a linguistic perspective and a (...) philosophical one. In this particular case, we take into account the Fregean ontology; we try to analyze ontologically the linguistic phenomena called nominalization and arrive to interesting conclusions about the ontological and semantic behavior of the expressions that contain event and result nominalizations. (shrink)

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in this paper (...) have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims atproviding an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic hasfewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations. It introduces the notion of -space for a sentence A as the basis of logical model theory, and the notion of P A /, functioning as a `private' subuniverse for A/A. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. PPC3 and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of PPC3 as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: 1a for the conjoined presuppositions of a, ã for the complement of a within 1a, and â for the complement of 1a within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

Having briefly sketched the aims of our paper, namely, to logically analyse the ascription of propositional attitudes to somebody else in terms, not of Fregean senses or of intensions-with-s, but of the intentional object of the person spoken about, say, the believer or intender (Section 1), we try to introduce the concept of an intentional object as simply as possible, to wit, as coming into view whenever two (or more) subjective belief-worlds strikingly diverge (Section 2). Then, we assess the pros (...) and cons of Frege’s view that the indirect reference of an expression is nothing but its customary sense (Sections 3–4), and call the reader’s attention to the fact that in belief ascriptions de re we take it for granted that the believer’s intentional object is at the same time a ‘citizen’ of the belief ascriber’s subjective world (or, for that matter, the real word), and that the idea of such a ‘dual citizenship’ is even more obviously presupposed in the cases of true belief and propositional knowledge (Section 5). Then, we try to argue that it is more fertile to take the belief ascriber’s intentional object to be, not the whole state of affairs the believer has in mind and thinks to exist, but the latter’s intentional object as such, that is, as being his intentional object (Section 6). Finally, we discuss the intricate and mostly neglected question of whether an intentional object’s inhabiting two or more subjective belief-worlds should be considered to be sort of a ‘transmundane identity’ in the numerical sense or rather in some deviant sense of the term, which can be specified as a momentous subcase of a ‘categorial difference’ (Section 7). (shrink)

Brahmānanda Sarasvatī has written an elaborate comment on the following inference cited in Advaitasiddhi: attribute etc. are identical to and different from attributee etc. since they are co-referential. There he wants to prove that every significant case of attribution is a case of identity that coexists with a difference between two demarcators. The identity that coexists with difference is called ‘equality’. This paper will argue that in each case of equality, the realist ontology chooses either identity over difference or the (...) reverse. In the case of ‘the black pot’, the realist ontology prefers difference over identity. In the case of ‘the qualified object is the mere object’, the same ontology prefers identity over difference. Accordingly the ontological ‘entity’ gets projected. This is perhaps because the realist ontology is guided by Ockham’s razor and the grammatical classification of objects. (shrink)

Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent logicism is compatible with intuitionism.

L'Existence de choses telles que des propositions, conc,ues comme distinctes des phrases qui les expriment et dont elles constituent comme le sens — cela que l'on comprend en entendant une phrase — a été mise en question, par Quine, en particulier, et aussi défendue. Ce débat fera l'objet de ce texte.La proposition, comme on l’entendra ici, se définit essentiellement comme une synthèse de concepts. Cette définition en a été donnée par G.E. Moore, un peu avant que Russell ne la reprenne (...) dans trois grands articles publiés dans Mind en 1904, sous le titre de « Meinong’s Theory of Complexes and Assumptions ». (shrink)

This article discusses and develops some recent debates in feminist epistemology, by outlining the concept of an ‘emancipatory value’. It outlines the optimum conditions that a ‘community’ of knowers must satisfy in order that its members have the best chance of producing knowledge claims. The article thus covers general ground in epistemology. The article also argues that one of the conditions that any ‘emancipatory community’ must satisfy is that its underlying values should not oppress women. It is related to feminist (...) debates, therefore, in two ways: first, it develops its arguments by drawing on those debates; and second, after developing the general concepts of emancipatory value and epistemic community, it argues that feminist values are one set of emancipatory values to which an epistemic community should pay regard. (shrink)

Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation (...) to its crucial differences with a set-theoretic foundational perspective. This should also spread some light on a question arisen by J. Hintikka and G. Sandu in a widely discussed paper, namely whether Frege should or should not be credited with the notion of arbitrary function underlying our standard interpretation of second-order logic. In section 1, I account for Lagrange's notion of function. In section 2, I advance some remarks on connected historical matters. This will provide an appropriate framework for discussing the role played by the notion of function in Frege's Grundgesetze. Section 3 is devoted to this. Some concluding remarks will close the paper. (shrink)

In British and American anthropological literature, the ethnology of Central and Eastern European countries has shared in the plight of descriptions of this part of the world: it was seen as exotic, foreign, remote, a backwater, focused on sideline problems and situated on the periphery of this field of science. This state of affairs has been the case since at least the beginning of the Cold War as the descriptions of the national characters of Eastern Bloc communities, drafted by American (...) scholars. The ethnography of these countries was automatically aligned with the same categories of description which were applied to the characteristics of these communities. This was, in part, an effect of entirely different research traditions in the subject matter, objectives and methods of these remote parts of the science. The differences of ’cultural wholes’ did have a decisive impact on the image of ethnology. Like all these communities, Polish ethnology was perceived as a homogeneous whole, which it never was. (shrink)