Logicism

How do philosophical accusations of talking nonsense relate to the layperson’s notions of meaning and meaningfulness?  If one were to explain carefully what philosophical nonsense was supposed to be, would one be greeted with incredulity?  How do people react to being accused to talking nonsense themselves?  Is anything analogous to an illusion of meaning recognised in everyday life?  In dream-reports perhaps?  Or in the utterances of schizophrenics or those under the influence of drugs?  Or in certain jokes and hoaxes?  Are contradictions felt to be meaningless?  I argue that, though it is clear that experimental philosophy could shed some light on these questions, their subject matter creates special difficulties.  First, it is more difficult than usual to formulate questions and produce ‘vignettes’ that do not subtly encourage certain responses at the expense of others.  Second, the fact that philosophical nonsense is a metaphilosophical concept ensures that its investigation is going to be more indirect than would be that of knowledge or intention, for example.

Presentación que usé por primera vez en una charla sobre el logicismo de Russell que di en el congreso internacional de filosofía "Identidad y Diferencia".

Nota: La versión anterior de esta presentación, que tenía más de 6 años de antiguedad, contenía diversos errores que han sido corregidos en la versión actual.

"Michel Weber and Will Desmond, (eds.), Handbook of Whiteheadian Process Thought, Frankfurt / Lancaster, ontos verlag, Process Thought X1 & X2, 2008. (695 p. + 726 p. ; ISBN 978-3-938793-92-3 ; 398 €)
Gathering 115 entries written by 101 internationally renowned experts in their fields, the Handbook of Whiteheadian Process Thought aims at interpreting Whitehead secundum Whitehead, at canvassing the current state of knowledge in Whiteheadian scholarship and at identifying promising directions for future investigations through (internal) cross-elucidation and (external) interdisciplinary and crossdisciplinary development.
Table of Contents
Introduction
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II. Anthropology
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V. Education
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IX. Language
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XIX. Biographical entries
XX. Critical Apparatus

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This book is an introduction in a double sense. It is intended to introduce beginners in philosophy to the idea of philosophical nonsense and the problems it raises. But it is also addressed to professional philosophers, most of whom seem virtually unaware of the issue.

Certain philosophers, here called ‘nonsensicalists’, believe that much philosophy (philosophical questions as well as assertions) is simply nonsense in the strict sense of being meaningless. They proceed as though it were an established fact that there is such a thing as philosophical nonsense and the notion were quite unproblematic. By contrast, many other philosophers proceed as though either they had never heard of it or it were quite obvious that there is no such thing.

There can be little doubt that what the nonsensicalists are saying is of great importance – if they are right. But there are at least eight questions that must be addressed before anyone is in a position to start hunting down philosophical nonsense and they have all been woefully neglected.

The idea of philosophical nonsense goes back to Thomas Hobbes at least and yet its history remains largely unresearched.

In view of the neglect of the problems raised by the notion of philosophical nonsense, even by professional philosophers, it is not unduly optimistic to suggest that it is a topic to which relative newcomers to the subject might make a contribution.

Ludwig Wittgenstein thought that good philosophy unties the knots in our thinking that bad philosophy has put there and must make movements as complicated as the knots it unties. Is the notion of philosophical nonsense an essential aid to this – as Wittgenstein himself thought – or just another knot?

Russell's main academic achievements consist in the fields of logic and analytic philosophy. His contributions to logic include: in order to avoid paradoxes, he put forward the principle of vicious circle, developed simple type theory and branched type theory; basing on his type theory, he established propositional logic, first-order predicate logic, theory of identity, theory of descriptions, etc.; he insisted on a logicist project to use logic to guarantee the consistency and reliability of mathematics, and deduced a lot of mathematical theories in his logical system. His contributions to analytic philosophy include: he rejected theory of internal relations with theory of external relations, thus rebelling against Kant's and Hegel's idealistic philosophy; he distinguished knowledge of truths from knowledge of things, knowledge by acquaintance from knowledge by description, primitive truths from derived truths, and his epistemology has a strong empiricist and skeptic flavor; he maintained logical atomist philosophy, asserting that there is a structural parallel between (ideal) language and the external world; he developed his theory of logical constructions based on sense-data, trying to eliminate too many ontological settings of natural language and retaining "the robust sense of reality" even in abstract research. Because of his creative works and significant academic influence, Russell has been a master and giant in the fields of logic and analytic philosophy.

In this paper I will discuss the philosophical implications of Dedekind's introduction
of natural numbers in the central section of his 1888 foundational
writing "Was sind und was sollen die Zahlen?", particularly as opposed to the
approach to numbers to be found in Gottlob Frege's writings (above all, the
"Grundlagen der Arithmetik" (1884) and both volumes of the "Grundgesetze
der Arithmetik" (1893, 1903)). This comparison will be crucial not only to
highlight Dedekind's value as a philosopher, but also to discuss crucial issues
regarding the introduction of new mathematical objects, about their nature
and our access to them.

This paper provides a study and assessment of the neo-logicist view that mathematical knowledge is essentially logical knowledge, as advanced by Hale and Wright. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism - a general conception of the relation between language and reality; (2) the method of abstraction - a particular method for introducing concepts into language; (3) the scope of 2nd order logic - second order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explored and assessed. The issues discussed included reductionism, rejectionism, the Julius Caesar objections, and the charge that second order logic is set theory in disguise.

There are passages in Wittgenstein where he compares his method to psychotherapy and one or two where he seems to suggest that the ‘patient’ has the last word on his ‘illness’ and ‘cure’.  This paper tries to take these seriously, especially in connexion with the idea that victims of philosophical confusion talk nonsense.

Philosophical accusations of talking nonsense made in a polemical spirit are bound to fail, since the only way one can effectively criticise another’s utterance is by attaching some meaning to it.  But if the other acknowledges the possibility that his puzzlement arises from his having been taken in by nonsense, then perhaps a co-operative investigation of this suggestion might be fruitful.  Indeed self-diagnosis ought in principle to be possible.  Ought it not to have happened at least once in the history of philosophy if philosophical nonsense has ever been exposed? 

But there are difficulties.  For example:
a) We must ask whether or not philosophical nonsense, when exposed as such, is supposed to lose all appearance of meaningfulness.  Either answer is problematic.
b) The acknowledged similarity of the methodology under investigation to that of psychoanalysis exposes it to many of the familiar objections to the methodology of psychoanalysis, especially those that draw attention to the misleading influence of suggestion by an authority-figure.
c) The proposal that relentless cross-questioning of a suspected nonsense-talker will eventually lead her to ‘dry up’ (if she really is talking nonsense) seems to involve a version of the so-called Socratic Fallacy.

This paper looks at the history of the problem of individuation from Plato to Whitehead. Part I takes as its point of departure Reiner Wiehl’s interpretation of the different meanings of “abstract” in the metaphysics of Alfred North Whitehead and arrives at a corresponding taxonomy of different ways things can be called concrete.  Part II compares the way philosophers in different periods understand the relation between thought and intuition.  The view mostly associated with ancient philosophy is that thought and sense-perception target different kinds of objects.  The view mostly associated with modern philosophy (although it was introduced by the Stoics) is that thought and sense-perception are different ways of targeting the same objects.  These differences have specific consequences for theories of individuation, which are assessed historically in Part III and then applied to Whitehead’s difficult texts in part IV.

Resumen: Esta nota tiene como propósito introducir a los estudiantes interesados en el logicismo. Nuestro objetivo no es mostrar ninguna nueva interpretación o tesis sobre el logicismo o sobre su renacimiento entre los años 60 y 80 del siglo pasado. Lo que haremos es mostrar sistemáticamente la evolución del logicismo desde Frege hasta Russell-Whitehead, con mayor énfasis en este último desarrollo, y abordar algunos problemas que surgen en el seno de dicho movimiento, como por ejemplo: Las paradojas lógicas y el principio de comprehensión intuitiva, la definiciones impredicativas y las paradojas semánticas, la jerarquía ramificada y los números reales, el axioma de reducibilidad y la imposibilidad de la reducción de la matemática a la lógica, etc. Palabras clave: Logicismo, Matemática, Paradojas, Teoría de tipos, Axioma de Reducibilidad. Abstract: The following note has on purpose to introduce interested students to logicism. Our objective is not to show any new interpretation or thesis about logicism or its rebirth between the 60s and 80s of the last century. What we will do is systematically show the evolution of logicism from Frege to Russell-Whitehead, with greater emphasis on this latest development, and approach some problems that arise within that movement, for example: The logical paradoxes and the principle of intuitive comprehension, the impredicative definitions and the semantic paradoxes, the Ramified Hierarchy and real numbers, the axiom of reducibility and the impossibility of reducing mathematics to logic, etc.

Transcendent realism is a theistic philosophical system which holds that reality comprises physical and metaphysical entities, including morally conscious souls and God, as the creative and sustaining explanation of the being of beings ("Being") and moral obligation. The three central theses of the philosophy are that (1) Being and the intelligibility of Being are self-same, reducible to logic, and logically necessary, (2) absolute nothingness is incoherent because it entails the absence of the rules of its own conception, and (3) human rational experience is not materially reducible and includes direct and inferential experience of metaphysical Being. Some of the ideas developed in this summary are: (A) that the presuppositions of objective reason include a self-transcendent, knowing soul and the logicality of Being; (B) humankind is a self-concerned, substantive, psychosomatic unity whose Being is being-toward-God, whose soul exists not in, but alongside, the external world, and whose body is the physical manifestation of the soul's relation to the external world; (C) the logicality of Being implies the existence of the one and only God as its Supreme Principle and as Agape (unqualified good will), the definitionally good, self-intending source of the moral obligation of self-transcending souls; and (D) humankind's fundamental obligation, as the agent of God's self-intending good will and the being who brings morality into the world, is to act with agape to all.

L’A. présente la pertinence anthropologique de la thèse d’indétermination de la traduction de Quine, en suggérant qu’elle joue contre le relativisme, mais aussi contre une certaine forme d’universalisme : c’est ce que montre une analyse de la notion de prélogicité, critiquée par Quine qui invente à cette occasion le « principe de charité ». L’examen des usages et de la portée d’un tel principe, et sa confrontation aux thèses de Lévy-Bruhl, permet, au-delà de Quine, de repenser l’invocation devenue trop courante et indéterminée d’une anthropologie en philosophie.

What is at stake for Russell in espousing logicism? I argue that Russell's aims are chiefly epistemological and mathematical in nature. Russell develops logicism in order to give an account of the character of mathematics and of mathematical knowledge that is compatible with what he takes to be the uncontroversial status of this science as true, certain and exact. I argue for this view against the view of Peter Hylton, according to which Russell uses logicism to defend the unconditional truth of mathematics against various Idealist positions that treat mathematics as true only partially or only relative to a particular point of view.

بحران حاصل از منطق‌گرایی و نابسنده‌بودن پیشنهاده‌های آن برای پایة تحلیل امور یکی از مهم‌ترین دغدغه‌های معرفت‌شناسی، به‌خصوص از اوایل قرن بیستم میلادی به این‌سو است. لوی‌برول با بررسی کارکردهای ذهنی اقوام ابتدایی از زاویه‌ای جدید، به ضرورتِ قائل‌شدن به ذهنیتی دیگر در جوار ذهنیت علمی-منطقی به‌منظور تحلیل بسندة سازوکار متفاوت آن اذهان تأکید می‌کند. او این ذهنیت را، که متضمن زیست عرفانی است، پیش‌منطقی می‌نامد. ذهنیت پیش‌منطقی، بر خلاف ذهنیت علمی-منطقی، نسبت به قانون امتناع تناقض بی‌اعتناست و بر اساس قانون آمیختگی عمل می‌کند. وی به همزیستی این دو سنخ متمایز و مستقل اشاره می‌کند. یلمزلف با پذیرش پیشنهادة لوی‌برول، ایده‌های او را در ساحتی معرفت‌شناختی حول مسئلة کلی تحلیل ساختارها پی می‌گیرد. او با گسترش ابژة بررسی به زبان و نشانگان، به نظام زیرمنطقی که ممکن‌کنندة منطق و پیش‌منطق است نایل می‌شود. یلمزلف با بهره‌گیری از قانون آمیختگی تأکید می‌کند که تقابل پایه‌ای در تحلیل نظام‌ها (زبانی و نشانگانی) تقابل میان A (جزء) و A + (non-A) (کل) است، نه چنان که منطق‌گرایی پیشنهاد می‌کند، تقابل میان A و non-A (تناقض). بر این اساس، او در نظریة (یا علم) گلوسم‌شناسی، هنگام تحلیل نظام‌ها یا همان مفصل‌بندی مقولات معطوف به پیوندهای تقابلی، دستگاه محاسباتی صوری زیرمنطقی را به عنوان بدیلی برای منطق (که در نظریة بسیاری چون لوی‌استروس، یاکوبسون و چامسکی پایة تحلیل است) صورت‌بندی می‌کند. خود نظام‌های منطقی به عنوان وضعیت‌هایی از نظام‌های زیرمنطقی امکان ثبت‌شدن می‌یابند. زیرمنطق (و آمیختگی) یکی از ارکان بدیعی است که یلمزلف از طریق آن در گلوسم‌شناسی، که هدف‌اش تأویل و تحلیل انسان-جهان به‌مثابة متن است، امکانات معرفت‌شناختی جدیدی را می‌گشاید. در این جستار، ما این دو نظریه را به عنوان پیشنهادهایی بدیل برای منطق‌گرایی مورد بررسی قرار می‌دهیم و خط‌وربط‌شان را می‌سنجیم.

From the first decades of the 20th century, the crisis of Logicism and its inappropriate propositions for the general basis of the analysis of all the facts is among the most problematic epistemological issues. By studying the specific mental functions of primitive societies from a new angle, Lévy-Bruhl shows that if we want to have an appropriate analysis of their fundamentally different mind and life, it would be necessary to introduce a mentality other than our scientific-logical one. He calls it "mystic mentality"; a mentality which, instead of logic, is based on "prelogic". The prelogical system is indifferent to the law of non-contradiction and is formed based on the law of "participation". He claims that these two distinct and independent types of mentality coexist. Hjelmslev basically accepts Lévy-Bruhl's proposal and takes advantage of the epistemological consequences of his ideas as a support for dealing with the general problem of structural analysis. Taking the most general concept of language (or semiotic) as the object of his special immanent theory, he introduces the "sublogical system" as a ground from which the logic and prelogic can be derived. He refers to the law of participation and claims that the basic opposition in a semiotic is that between A and A+(non-A), and not, as logic assumes, the one between A and non-A (contradiction). Regarding this hypothesis, Hjelmslev establishes a formal sublogical calculus in the procedure of his Glossematics while treating the analysis of systems (or the articulation of categories concerning oppositions). It should be considered as an alternative to the logical proposal which is established as the basis of the analysis in many theories such as those of Jakobson, Lévi-Strauss, Chomsky, and so on. In the present study, we intended to explain Lévy-Bruhl's prelogic and Hjelmslev's sublogic and their relations, and to cast light on an important possible response to the epistemological problem of the inadequacy of logicism.

Is a logicist bound to the claim that as a matter of analytic truth there is an actual infinity of objects? If Hume's Principle is analytic then in the standard setting the answer appears to be yes. Hodes's work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. We re-explore this idea and discover that in the setting of the potential infinite one can interpret first-order Peano arithmetic, but not second-order Peano arithmetic. We conclude that in order for the logicist to weaken the metaphysically loaded claim of necessary actual infinities, they must also weaken the mathematics they recover.

The paper discusses Husserl’s criticism of Frege in Philosophy of Arithmetic (1891) and then his later attitude towards logicism as expressed in Logical Investigations (1900-01). In Philosophy of Arithmetic Husserl holds that logicists offer needless and artificial definitions of notions such as equivalence and number. Frege criticized Husserl’s approach in Philosophy of Arithmetic as psychological, thus shifting the focus of the debate away from logicism. However, Frege’s criticism could be seen to lead Husserl to his later transcendental phenomenological concept of correlation and, with it, to a more developed criticism of logicism. In this regard the division of labor between mathematics and philosophy established in Prolegomena to the Logical Investigations (1900) is central. It implies that in Husserl’s view formal methods fail to shed philosophical insight into the essence of mathematics. In his picture the central notions in need of philosophical clarification are, instead of number and quantity, the notions that are central to abstract structural mathematics. Contrary to Frege who can only elucidate the primitive concepts, Husserl engages in detailed description of their constitution.

This article provides the first English translation of Tanabe’s early essay, “The Limit of Logicism in Epistemology: A Critique of the Marburg and Freiburg Schools” (1914). The key notion that the young Tanabe seeks to define in relation to his detailed analyses of contemporary Neo-Kantian epistemology is the notion of “pure experience” presented in Nishida’s philosophy. The general theory of epistemology shared among the thinkers from these two prominent schools of philosophy in early 20th century Germany aimed to eliminate the empirical residues in Kant’s theory of knowledge while opposing naïve empiricism and the uncritical methodology of positive science. Their “logicistic” approach, according to Tanabe, seems to contradict Nishida’s notion of pure experience, for it cannot allow any vestige of empiricism in its systematic framework, which is specifically designed to ground scientific knowledge. Yet given that the Neo-Kantian configuration of epistemology does not create the object of knowledge, it must face sensation or representational content as its limiting instance. Thus, to ground a Neo-Kantian theory of knowledge while
taking account of this limit of logicism involves explaining their understanding of the unity of subject and object in human knowing. For this, Tanabe argues, recourse to Nishida’s notion of pure experience is
indispensable.

Resumen Este volumen de Metatheoria incluye traducciones al castellano de los tres famosos trabajos sobre las escuelas de fundamentos de la matemática, el logicismo, el intuicionismo y el formalismo, expuestos en el Simposio de Königsberg sobre Fundamentos de la Matemática en septiembre de 1930, y que fueron finalmente publicados en la revista Erkenntnis en 1931. Los tres constituyeron un hito en la filosofía de la matemática del siglo pasado. En esta introducción a las traducciones, los compiladores del volumen esbozan el contexto histórico en el cual se concibieron los trabajos originales e incluyen detalles de su publicación original. También ponen de relieve el papel decisivo que tuvieron en la filosofía de la matemática del siglo pasado. Se hace un resumen de sus contenidos, y se discuten las ideas subyacentes del Círculo de Viena acerca de la naturaleza de la matemática y el impacto de los teoremas de Gödel en los programas de fundamentos. Además, se hace una breve introducción a las contribuciones originales que siguen en el volumen a las traducciones. Palabras clave: fundamentos de la matemática-filosofía de la matemática del siglo XX-Círculo de Viena-teoremas de Gödel Abstract This volumen of Metatheoria includes translations into Spanish of the three famous papers on the schools in foundations of mathematics, logicism, intuitionism and formalism, presented at the Königsberg's Symposium on Foundations of Mathematics in September 1930 and finally published in the journal Erkenntnis in 1931. The three papers constituted a milestone in the Philosophy of Mathematics of the last century. In this introduction to the translations, the editors of the volume outline the historical context in which the original papers were conceived and they include some details concerning their original publication. They also stress the decisive role played by the papers in the philosophy of mathematics in the last century. A summary of them is provided and the underlying ideas of the Vienna Circle on the nature of mathematics and the impact of Gödel theorems in the foundations programs are discussed. Moreover, they briefly introduce the original contributions to the volume that follow the translations.

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, contextualism, and pluralism.
  Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. One rather conspicuous example is that the process of refining logical terminology has reached a critical mass. Future logic students will no longer be burdened by obscure terminology and they will be better able to read, think, talk, and write about logic in a more careful and more rewarding manner.
  Closely related is increased use and study of variable-enhanced natural language as in “Every proposition x that implies some proposition y that is false also implies some proposition z that is true”.
  Another welcome development is the culmination of the slow demise of logicism. No longer is the teacher blocked from using examples from arithmetic and algebra fearing that the students had been indoctrinated into thinking that every mathematical truth was a tautology and that every mathematical falsehood was a contradiction.
  A fifth welcome development is the separation of laws of logic from so-called logical truths, i.e., tautologies. Now we can teach the logical independence of the laws of excluded middle and non-contradiction without fear that students had been indoctrinated into thinking that every logical law was a tautology and that every falsehood of logic was a contradiction. This separation permits the logic teacher to apply logic in the clarification of laws of logic.
  This lecture expands the above points, which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”.

En este ensayo me concentraré en discutir la posibilidad de la naturalización de la epistemología en respuesta a problemas planteados por Quine (1969). Para poder hacer eso es necesario discutir algunas nociones preliminares i.e. i) ¿Qué entendemos por la naturalización de una disciplina filosófica?; ii) ¿Qué entendemos por la naturalización de la epistemología? Y iii) ¿Qué sería que la naturalización de la epistemología fuese posible? Me ocupo de ello en la primera sección.

En la segunda sección abordo específicamente los argumentos de Quine en favor de la naturalización de la epistemología. Motivo esta sección con algunas observaciones acerca del programa epistemológico de los empiristas lógicos, desde un punto de vista general, así como el de los logicistas, específicamente Russell. Argumento que las objeciones de Quine al proyecto a priori en epistemología, en la medida en que están fundamentadas en su crítica a estos proyectos, fracasan.  Acto seguido, con el objetivo de vulnerar otras supuestos del argumento de Quine, discuto a grandes rasgos las estrategias abiertas para el epistemólogo a priori en respuesta al reto escéptico clásico (helénico). Esta sección contiene la parte más robusta de la discusión.

Posteriormente, en la sección III, observo algunos problemas con la propuesta positiva de Quine: específicamente sostendré que Quine pide la cuestión respecto a la posibilidad de naturalizar la epistemología con respecto al problema de la normatividad. Finalmente, argumento brevemente en favor de la posibilidad de una naturalización parcial de la epistemología desde algunos programas posteriores. [Faltan referencias] [NO CITAR]

How do philosophical accusations of talking nonsense relate to the layperson’s notions of meaning and meaningfulness?  If one were to explain carefully what philosophical nonsense was supposed to be, would one be greeted with incredulity?  How do people react to being accused of talking nonsense themselves?  Is anything analogous to an illusion of meaning recognised in everyday life?  In dream-reports perhaps?  Or in the utterances of schizophrenics or those under the influence of drugs?  Or in certain jokes and hoaxes?  Are contradictions felt to be meaningless?  I argue that, though it is clear that experimental philosophy could shed some light on these questions, their subject matter creates special difficulties.  First, it is more difficult than usual to formulate questions and produce ‘vignettes’ that do not subtly encourage certain responses at the expense of others.  Second, the fact that philosophical nonsense is a metaphilosophical concept ensures that its investigation is going to be more indirect than would be that of knowledge or intention, for example.

Phenomenology is an approach to understanding internal and external phenomena as they appear to us. As part of the project of phenomenology, Husserl's pure logical grammar suggests that linguistic structures are ultimately based on logic. Thus, phenomenology offers modern linguistics a viewpoint more profound than Saussurean structuralism which limits its scope to the interaction of meaning and form. Phenomenology proposes that structures of meaning arise from cognitive structures that are founded on the logic of composition. This insight helps to avoid biologistic claims that have been made in generative grammar and cognitive linguistics. The present paper proposes solutions to help apply pure logical grammar in general and applied linguistics. To increase phenomenology's compatibility with structural linguistics, it introduces a principle of learnability as an adjustment to 'double articulation'. It also proposes an adjustment to the standard model of the social construction of language to cater for an intentional intersubjective theory. Finally, brief counter-criticisms to previous conceptions of pure logical grammar are provided.

This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and Principia Mathematica.

“Logicism and the Recursion Theorem”, In R. Honzík & O. Tomala (eds.), Logica Yearbook 2006 ,Filosofia, Praha 2007, pp. 127–136

This paper has two aims. The first is to portray Frege's logicism in the spirit of Lakatos' logic of mathematical discovery as a bold conjecture eventually rejected. The second aim consists in showing that this rejection was based on different and more serious reasons than we are usually told. What I maintain is that one can agree with the neologicists that Frege's system is not so badly affected by Russell's paradox as was once thought, but still claim that this is not enough to render the whole project successful according to Frege's own standards. So the second aim of my paper is to indicate why – contrary to the neologicists' plan – the logicist idea cannot be saved and rendered compatible with Frege's original intentions, which, in my opinion, are quite sound. The recursion theorem and its role in the early foundational development turn out to be central to both parts of my argument.

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, contextualism, and pluralism.
  Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. One rather conspicuous example is that the process of refining logical terminology has been productive. Future logic students will no longer be burdened by obscure terminology and they will be able to read, think, talk, and write about logic in a more careful and more rewarding manner.
  Closely related is increased use and study of variable-enhanced natural language as in “Every proposition x that implies some proposition y that is false also implies some proposition z that is true”.
  Another welcome development is the culmination of the slow demise of logicism. No longer is the teacher blocked from using examples from arithmetic and algebra fearing that the students had been indoctrinated into thinking that every mathematical truth was a tautology and that every mathematical falsehood was a contradiction.
  A fifth welcome development is the separation of laws of logic from so-called logical truths, i.e., tautologies. Now we can teach the logical independence of the laws of excluded middle and non-contradiction without fear that students had been indoctrinated into thinking that every logical law was a tautology and that every falsehood of logic was a contradiction. This separation permits the logic teacher to apply logic in the clarification of laws of logic.
  This lecture expands the above points, which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”.

Abstract Frank Thomas Sautter:
In this paper Chateaubriand's approach to solve some problems related to the nature of logic is confronted with the traditional approaches. It is shown that his hierarchy of logical types opens up new possibilities to characterize logical properties and logical truths and that it also sheds some new light on the foundations of mathematics. The order in which a system is exhibited almost always does not correspond to the order in which it has been elaborated. The system proposed by Oswaldo Chateaubriand is no exception (see Chateaubriand 2001). Since it contains many original ideas and original interpretations of traditional ideas which were initially developed to refute the slingshot-argument, especially the variant formulated by Gödel, the first chapter of the book with regard to the order of elaboration is the fourth chapter with regard to the order of exhibition. The diverse parts of the system form an organic whole making it difficult to apprehend them in isolation; this explains also the recurrence of some ideas.

Abstract response:
In §1 I examine the connections between my account of logical properties and Tarski’s account of logical notions. In §2 I briefly present some of my views on modality and the basis for my claim that there are intensional as well as extensional relations between properties. In §3 I compare my views on the nature of logic and of mathematics with Gödel’s views.

Abstract Abel Lassalle Casanave:
In his doctoral dissertation, O. Chateaubriand favored Dedekind's analysis of the notion of number; whereas in Logical Forms, he favors a fregean approach to the topic. My aim in this paper is to examine the kind of logicism he defends. Three aspects will be considered: the concept of analysis; the universality of arithmetical properties and their definability; the irreducibility of arithmetical objects.

Abstract response:
In §1 I discuss Dedekind and Frege on the logical and structural analysis of natural numbers and present my view that the logical analysis of the notion of number involves a combination of their analyses. In §2 I answer some of the specific questions that Abel raises in connection with Chapter 9 of Logical Forms.

I put forward a new interpretation of Frege's use of the formal system developed in Begriffsschrift, the concept-script. In contrast with the commonly-held view, I argue that this use suggests that he did not articulate a logicist programme in 1879. Two lines of argument support this claim. First, I show that between 1879 and 1882 Frege presented the concept-script of Begriffsschrift as a tool for arithmetic, and not as a logical theory from which to deduce arithmetical theorems. Second, I consider Frege's results in Begriffsschrift and conclude that they do not imply an endorsement of his later logicist programme.

Sažetak: problemu na lini psihologizma (mentalizma) tj. pravca koji se poziva na psihološke argumente pri rješavanju filozofijskih (spoznajno-teorijskih) problema, gdje se vidi svojevrsna nadređenost psihologije filozofiji i (uvjetno uzevši) logicizma koji zakone matematičkog i logičkog mišljenja sagledava kao transcendentalno postavljene, neovisne u subjektivnim mentalnim stanjima, pokušat ću se približiti genealoškim ocrtavanjem šire historiografije tj. geneze odnosa na liniji psihologizam/ logicizam. Potom ću prikazati osnovne crte psihologizma, poglavito u radu J.S. Milla, zatim ću ocrtati fenomenološku kritiku psihologističkog učenja od strane E. Husserla, te ću naposljetku kontrastirat Husserla naspram M. Heideggera i M. Schelera (u sasvim osnovnim crtama) kao svojevrsne kritičke odmake od "ortodoksne" husserlovske fenomenologije.

According to Quine, Charles Parsons, Mark Steiner, and others, Russell's logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as a prioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell's explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on recent work by Andrew Irvine and Martin Godwyn, I argue that Russell thought a systematic reduction of mathematics increases the certainty of known mathematical theorems (even basic arithmetical facts) by showing mathematical knowledge to be coherently organized. The paper outlines Russell's theory of coherence, and discusses its relevance to logicism and the certainty attributed to mathematics.

Ce travail propose une reevaluation du schisme phenomenologico-analytique a la lumiere des textes de Husserl et de Carnap qui en constituent l’un des fondements et qui cependant emergent d’un contexte philosophique et scientifique similaire. L’idee carnapienne de constitution comme « reconstruction rationnelle » et arbitraire du monde peut en effet paraitre s’opposer terme a terme au «se-constituer» des choses que deploie la phenomenologie husserlienne, mais l’emploi par Carnap du vocabulaire de la constitution nous impose d’interroger le lien que l’entreprise de l’Aufbau entretient avec la constitution idealiste transcendantale. La these de ce travail revient a affirmer que l’opposition Husserl/Carnap ne peut etre interpretee dans les termes d’une opposition entre phenomenologie et analyse logique, ni non plus sur la base des concepts d’idealisme transcendantal, de logicisme ou de phenomenalisme. Comprendre l’opposition entre les deux auteurs (et donc plus lointainement entre les d...