"On Reduplication is a study of the logical properties of reduplicative propositions, that is, of propositions having qualifications, like 'Christ "qua God is a ...

Leibniz presents himself, especially in his late correspondence with Remond, as a concordist: in other philosophical views, even distant and ancient ones, he sets out to discover «traces of truth» that are already present there. According to the concordist programme, Leibniz claims, philosophers are right in what they affi rm, and wrong in what they deny. This paradoxical asymmetry is given a logical explanation in the paper, in connection with the topic of «reduplication», i. e. the introduction of qualifi (...) cations in otherwise simple categorical propositions. In order to be right in affi rming a complex disjunctive proposition, it is enough for one of the disjuncts to be true; but in order to be right in negating a complex disjunctive proposition, it is required for all of them to be false. Meanwhile, if one may «qualify» propositions by different reduplications of their terms, in principle one of those qualifi ed propositions is bound to be true. On such presuppositions concordism can be expected to be quite effective as a meta-philosophical perspective. (shrink)

Aristotle’s presentation of ontology advanced at the beginning of the fourth book of Metaphysics is universally known: “there is a science which studies being qua being...”. Needless to say, this is a familiar sentence: unfortunately, it is also quite an odd one. Why Aristotle does not simply say that ontology is the theory of being? Is there any difference between ‘theory of being’ and ‘theory of being qua being’? In brief, the problem is to decide whether the two expressions ‘the (...) study of being’ and ‘the study of being qua being’ are equivalent. If they are, the ‘qua’ does not play any interesting role. On the contrary, if the two expressions are different, that is to say, if there is a difference between the study of being (simpliciter) and the study of being qua being, we should study the role played by the (operator) ‘qua’. (shrink)

The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis also consistent.After the discovery (...) of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions. Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [2], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all. (shrink)

The third chapter gives an account of the debates over Cartesianism outlined below, which shifted from the University of Utrecht to Leiden, where the new philosophy was introduced by Adriaan Heereboord in the early 1640s, and was carried on by Johannes de Raey at the end of the decade. In Leiden, the quarrels over Cartesianism were prompted by the intervention of the theologian Jacob Revius, criticising Descartes’s philosophy as a source of Pelagianism in 1647. This gave rise to a series (...) of attacks, replies, and counter-replies which would dominate Dutch Cartesianism well into the 1650s: Revius’s Methodi cartesianae consideratio theologica (1648), Statera philosophiae cartesianae (1650), and Cyriacus Lentulus’s Nova Renati Descartes sapientia (1651) offered a full-blown critique of Descartes’s philosophy, focusing on his metaphysics, method and on their uses in academia. Such critiques are analysed in this chapter as they brought about the first foundation of Cartesian philosophy after Descartes himself, namely, the development of a ‘Cartesian Scholastic’ by Johannes Clauberg, professor at Herborn and Duisburg. In fact, Clauberg’s defence and foundation of a Cartesian academic philosophy was not the effort of one philosopher, but was coordinated with De Raey and with other members of the Cartesian network in the Netherlands and in Germany (including Abraham Heidanus, Tobias Andreae and Christopher Wittich), as a means to avoid the bans on Cartesianism and to provide a decisive answer to the theologians. This coordinated strategy of defence is revealed by two letters of De Raey to Clauberg: their contents shed light on the background of Clauberg’s foundation, which constitutes the first, Cartesian reworking of the academic curriculum. In his works, indeed, Clauberg maintained a metaphysical foundation embodying rational-theological arguments, while providing at the same time a logical theory of the method for natural philosophy, as well as for law, theology and medicine. Yet, his concerns with the traditional structure of the curriculum led him to develop, besides a Cartesian first philosophy, also an ontosophia, whose object is being as such. This is considered by Clauberg not only in the light of the ‘first notions’ of mind and body, but also of those abstracted from concrete realities, as ‘unity’, ‘goodness’, ‘truth’, and so on. This ultimately results in the reduplication of metaphysics, which will be reduced by Clauberg’s followers – dealt with in the next chapters. (shrink)

I EXPLORE ONE WAY IN WHICH THE THEORY OF RELATIVE IDENTITY (DEVELOPED ALONG LINES SUGGESTED BY GEACH’S WRITINGS) CAN BE USED TO UNDERSTAND THE WAY LANGUAGE FUNCTIONS IN TRINITARIAN DOCTRINE. THIS INCLUDES A DISCUSSION OF REDUPLICATIVE PROPOSITIONS.

In this paper I highlight certain logical and metaphysical issues which arise in the characterisation of functionalism-in particular its ready coherence with a physicalist ontology, its structuralism and the impredicativity of functionalist specifications. I then utilise these points in an attempt to demonstrate fatal flaws in the functionalist programme. I argue that the brand of functionalism inspired by David Lewis fails to accommodate multiple realisability though such accommodation was vaunted as a key improvement over the identity theory. More standard accounts (...) of functionalism allow, by contrast, for far too much multiple realisability. Specifically, functionalist structures will be massively reduplicated in the human brain; so functionalism yields the absurd consequence that each human harbours large numbers of minds and exemplifies virtually all mental states. (shrink)

English summary: It was not until the publication of Schelling''s Munich and Berlin lectures that we learned the decisive source for his theory of an identity of identity or identity doubled in itself. Schelling referred to what he called an older logic that was still acquainted with the figure of reduplication, for instance in Leibniz and Wolff. Philosophers in this tradition employed this term to refer to the specification of an aspect under which the subject-term is being considered. (...) An often quoted example: As consul, Fabius Maximus has authority over his father, but as son he stands under his fathers authority. Schelling gave the following turn to reduplication: Nature as nature does not coincide with the mind; and the mind as mind does not coincide with nature. Both have different truth conditions, so as to integrate an essential moment of difference into the identity formula. There is an X, however, which is strictly (seamlessly) identical with itself (the absolute subject = X) while transitively being both of them in turn; and it is only via X that the relata (nature and mind) are indirectly identified with each other: X is B and X is A (and X is strictly identical to itself). In addition to this, Schelling held a view of predication as kind of identification. He became acquainted with this view at the Tubingen Seminary through his teacher Gottfried Ploucquet. This insight helps us understand why Schelling reasonably thought that the identity-formula A=A is the genuine matrix of all veridical judgments. Taken together with his conviction that judging (Kant''s relative position) is a minor (or inferior) form of existential being (Kant''s absolute position) sheds light on why in 1806 Schelling made the radical contention in his Aphorisms: The strict sense of being (absolutely posited seamless self-sameness) is taken over by the looser sense of the copulative is which identifies subject and predicate; yes, this copula alone is existence itself and nothing else. Why should Schelling''s conception of nature-mind identity interest recent philosophers of mind? Because Schelling presents an ontologically neutral solution: Identity is a symmetrical relation that does not favor mind or matter, and prevents the idealistic reduction of nature to the mind. Nor can we conceive of the nature-mind identity as a fact inwardly disclosed to the mind (McGinn, Levine). Consciousness remains an enigma for itself; so does its identity with nature. Schelling teaches us that identity theories are not justified by self-evidence, but by an inference to the best explanation. German description: Nie ist genau erklart worden, was Schelling unter Identitat von Natur und Geist verstand. Dabei hat er sein reifes Denken Identitatssystem genannt und sich zeitlebens um kein zweites Problem begrifflich ahnliche Muhe gegeben. Da er aber seine Uberlegungen in Schriften verpackte, deren grosser systematischer Ausgriff sie schier erdruckte, ist, was er bis hinein in die Weltalter-Periode daruber herausfand, kaum eigens gewurdigt oder auch nur klar benannt worden. Die Schellingliteratur arbeitete entweder historisch oder liess sich vom Systemgedanken oder einzelnen in die Augen springenden Problemen blenden (z. B. Natur, Organismus, Freiheit, Existenz). Dabei ist Schellings Starke in einzelnen entscheidenden Argumenten versteckt, die, waren sie bekannt, die gegenwartige, auch analytische Diskussion durchaus zu inspirieren vermochten. Wir konnen heute urteilen, dass schon der junge Schelling in seiner Schrift Form der Philosophie eine differenzsensitive Form der Identitat im Sinn hatte, die er in den kommenden Jahrzehnten immer genauer auszubuchstabieren unternahm. Seine eigentlichen Quellen hat er kunstvoll verborgen. Es sind erstens die Identitatstheorie der Pradikation seines Universitatslehrers Ploucquet, die den Stiftlern in Tubingen eingeblaut wurde und die ihre merkwurdige Fixierung auf die ganz unkantische Auffassung vom Urteil als Subjekt-Pradikat-Identifikation (mit quantifiziertem Pradikator) erklart. Und zweitens Schellings Entdeckung einer alteren Logik, die mit der Figur der reduplicatio arbeitete. - So auch das Absolute: Als Geist ist es nicht Natur (und umgekehrt; Aussagen uber beide haben unterschiedliche Wahrheitsbedingungen), aber Geist und Natur werden beide vom Absoluten gewesen (transitiv ins Sein gehoben), und dies Absolute ist im striktest denkbaren Sinne mit sich identisch. So lasst sich die Schelling''sche Formel von der Identitat der Identitat und Differenz dem gesunden Menschenverstand vermitteln und Schellings aufrichtiger Jugendgedanke (Marx) aktualisieren. Er schneidet respektabel ab im Wettbewerb mit allerlei heutigen Leib-Seele-Identitatstheorien. (shrink)

Medieval theologians discussed the logical structure of reduplicative propositions in the midst of their discussions of the Incarnation and the Trinity. Aquinas has the usual medieval analyzes of reduplicative propositions: the specificative and the strictly reduplicative. But neither analysis resolves successfully the problems of the consistency of the statements about God while avoiding making the Trinity or the Incarnation a merely accidental feature of Him. However, Scotus introduces another analysis: abstractive. I shall conclude that Scotus’s view of reduplication, one, (...) if not invented by him, as least stressed and developed by him, offers a better solution of the consistency of the Incarnation and the Trinity than that of Aquinas. (shrink)

The paper examines Beuchot's approach and agrees that there are many coincidences between medieval Aristotelianism and analytical philosophy. Both pursue philosophical inquiry in an argumentative manner. Nowadays analytical philosophy also tends to recognize as genuine such traditional metaphysical problems as were debated by the Scholastics. The paper's only criticism at Beuchot's views concerns analogy and reduplicative as-clauses. It argues that on that issue the cleavage between medieval and analytical philosophy lies in the latter's tending to favor complete equivocality of the (...) word «being». However, an alternative is possible, namely univocism, as implemented in combinatory logics, which while also rejecting reduplicative clauses is free from the ineffableness attendant upon equivocism. (shrink)

'De syllogismis' is the fifth treatise of John Buridan's 'Summulae dialecticae', a textbook he wrote for his logic course in the Faculty of Arts at the University of Paris. 'De syllogismis' contains material related to Aristotle's Analytica Priora and Boethius's 'De hypotheticis syllogismis'. The textbook discusses inferences involving not only propositions de inesse, but also propositions featuring oblique, reduplicative and infinite terms. Buridan displays a keen interest in modal inferences and inferences involving propositional attitudes. Buridan's De syllogismis continues along (...) the lines of his nominalist conception of the relations between mind, language and reality. (shrink)

The fifth chapter is a study of the emergence of ‘radical Cartesianism’ as an actor’s category in 1660s and 1670s, which prompted a further development of foundationalism as a reflection on the limits and proper method of philosophy. The key figure in this double process was De Raey, who in the late 1660s started to develop a new logic or metaphysics, intended to counter, on the one hand, the uses of Descartes outside natural philosophy and metaphysics itself, and on (...) the other, the erosion of Descartes’s metaphysical tenets. His writings thus turn out to be relevant as he offers a mapping of the interpretations of Cartesianism covering its uses in theology (as by Meijer and Spinoza) and the spreading of Hobbes’s materialist philosophy in the Low Countries. Moreover, his logical-metaphysical theories embody a novelty in determining the aim of these disciplines, both with respect to the Cartesian tradition (i.e. to Clauberg and Geulincx) and to the Scholastic one, and start to assume a reflective role as they assess the limits of scientific knowledge. In his hands, logic and metaphysics become one discipline, as they have the same function, i.e. the definition of the principles of scientific knowledge (viz. the notions of physical and mental realities), and of its scope and applications. On the one hand, therefore, he can overcome the reduplication of metaphysics and ontology of Clauberg, and the introductory or didactic function that logic played both in Clauberg’s and Geulincx’s philosophy. On the other, his logical and metaphysical systematisation can be read as the result of a long-standing debate over the objects of these disciplines (either mere concepts, or entities existing outside mind), in which De Raey places himself by dealing with the theories of Burgersdijk and Ramus. This chapter thus works as a junction in the account of the establishment of Cartesianism as the philosophy of the university, and its challenges by emerging, alternative worldviews, interpretations and uses. Together, these converging theoretical and historical factors shaped a new, reflective function for logic and metaphysics. (shrink)

Following Freud’s analysis of the fragile line between the uncanny double and its comic redoubling, I identify the doubling of the double found in critical moments of Hegelian dialectic as producing a kind of comic effect. It almost goes without saying that two provides greater pleasure than one, the loneliest number. Many also find two to be preferable to three, the tired trope of dialectic as a teleological waltz. Two seems to offer lightness, relieving one from her loneliness and lacking (...) the complications of a third who comes in between. And yet, we learn through Marx and Freud that the double (even the double of tragedy and farce) borders on something closer to horror than comedy. -/- In the following, I would like to explore why four is funnier than two in my staging of dialectic as the doubling of the double or, to borrow a movie title from Laurel and Hardy, “Twice Two” (Roach et al. 1933a). I will begin by exploring the formulations of the double in the form of a pair of opposites and in the form of a pair of twins. The literary tropes of the double as the odd couple, on one side, and the twins, on the other, appear to serve very different narrative functions, which incite different kinds of affective responses from the audience. However, the form of the opposed double sometimes conceals the realization that the empty or fragmented content of the first is only reduplicated in the second. The “straight man” of the odd couple cannot see himself in his counterpart “the comic.” The redoubling of the double, however, forces not only the audience, but the original double on stage to confront what was already present, but unrealized, from the beginning. To illustrate this redoubling of the double within the opening of Hegel’s Science of Logic, I consider two short films by Laurel and Hardy in which the comic duo redoubles itself. The formula (2 x 2) produces a comic excess through the dialectical redoubling of there uncanny double. (shrink)

In this paper I highlight certain logical and metaphysical issues which arise in the characterisation of functionalism-in particular its ready coherence with a physicalist ontology, its structuralism and the impredicativity of functionalist specifications. I then utilise these points in an attempt to demonstrate fatal flaws in the functionalist programme. I argue that the brand of functionalism inspired by David Lewis fails to accommodate multiple realisability though such accommodation was vaunted as a key improvement over the identity theory. More standard accounts (...) of functionalism allow, by contrast, for far too much multiple realisability. Specifically, functionalist structures will be massively reduplicated in the human brain; so functionalism yields the absurd consequence that each human harbours large numbers of minds and exemplifies virtually all mental states. (shrink)

A recombinationist like the earlier Armstrong (1989) claims that logically possible worlds are recombinations of items found in the actual world, with some items reduplicated if need be and others deleted. An immediate consequence of this is that if an..

A recombinationist like the earlier Armstrong (1989) claims that logically possible worlds are recombinations of items found in the actual world, with some items reduplicated if need be and others deleted. An immediate consequence of this is that if an alien property is a property that could only be defined in terms of fundamental properties that are actually uninstantiated, then it is logically impossible that an alien property be instantiated as no recombination of the items in the actual world can (...) yield a world with an entity having such a property. Recombinationism immediately implies that S5 is false. To see this, suppose for simplicity, as I will throughout this paper, that electric charge is a fundamental property--otherwise, a different example would have to be used. Then, let w be a possible world lacking any charged objects. At w, then, it is true that it is logically impossible that there be a charged particle since no recombination of the entities in w yields a charged particle. Therefore, contrary to S5, what is possible at w differs from what is possible at the actual world, since charged particles are actual and hence logically possible at the actual world. While this argument may make one sceptical of recombinationism, the recombinationist will say that it is not surprising that if we follow out the Aristotelian intuition that possibility is to be grounded in actually existing entities, then what is possible will depend on what is actual. Henceforth I will no longer assume S5, and so logical possibilities will have to be relativized to worlds if recombinationism is true: it is logically possible at the actual world for charged particles to exist, but at a world at which there are no charged particles it is logically impossible for charged particles to exist... (shrink)

Venerable tradition allies the Torah with Wisdom, a “tree of life.”2 The tree of life is an ancient mythic symbol of the earth mother. This essay demonstrates the capacity of the Torah to facilitate a reintegrative return to the mother when, as now, the religious narratives falter that once seemed to ensure the unity of man made in the image of God conceived only as the Father. Participating in the process of this return one discovers beneath the Torah's fractured narrative (...) surface a reduplicative pattern based on the logic of the unconscious, which is founded on the repressed prelinguistic bond with all life formed at the maternal breast. This pattern reflects the recombinant properties that the unconscious shares with the earth, which breaks down and regenerates dead matter as the unconscious breaks down and regenerates the meaning of words. Folded into rhetorical tropes as into a single letter, the Torah's regenerative pattern repeatedly recalls to man what it means to be human, unique among but also one with all the diverse life of the earth. (shrink)

I give an analysis of the logical structure of statements describing duties in social roles. Role terms like ‘doctor’ should not be treated as simple predicates, as natural kind terms, like ‘human being’, are. When role terms are treated as simple predicates, fallacies may result. Rather, treat role terms (M) as complex predicates with a simple subject, a person (S), as a base; ‘S qua M’, and then analyze their reduplicative structure. I illustrate and support this analysis by considering sophisms, (...) traditionally known as committing the fallacy of secundum quid et simpliciter, about conflicts of duties in different roles. I end with some remarks about personal integrity. (shrink)

I give an analysis of the logical structure of statements describing duties in social roles. Role terms like ‘doctor’ should not be treated as simple predicates, as natural kind terms, like ‘human being’, are. When role terms are treated as simple predicates, fallacies may result. Rather, treat role terms (M) as complex predicates with a simple subject, a person (S), as a base; ‘S qua M’, and then analyze their reduplicative structure. I illustrate and support this analysis by considering sophisms, (...) traditionally known as committing the fallacy of secundum quid et simpliciter, about conflicts of duties in different roles. I end with some remarks about personal integrity. (shrink)

In this book, Bäck dedicates himself to the logical properties of the qua connective, that is, to put it as does the Leibniz scholar Benson Mates, to “that treacherous little word ‘as’”. This connective is represented in ordinary language by expressions such as “insofar as,” “in virtue of,” “in the sense that,” translating the Greek ᾗ, and the Latin ut, prout, inquantum. Bäck reminds us that, traditionally, “a use of this connective was called reduplication”. The goal of the book (...) is thus to “trace the development of the theory of reduplication... [which] has its roots in various passages where Aristotle discusses qua propositions. Islamic and Latin medieval philosophers then contributed to the topic. From all this there arose a theory of qua propositions, or a theory of reduplication, in the high medieval period ”. Bäck adds that the views of the different philosophers who dealt with reduplication in that period are extremely similar, so that “it makes sense to talk of the rise of a single theory of reduplication”. In fact, quite correctly, he points out that the similarity of these views is due to the use of Aristotle’s work as a common reference point. All these authors “heed what Aristotle says about qua propositions, and attempt to offer analyses that demonstrate the truth of those qua propositions that Aristotle asserts and the validity of inferences involving qua propositions that he maintains”. The problem lying at the heart of all this is that of determination, that is, of the qualification of a sentence by a modifier. Among its applications are the fallacy of secundum quid et simpliciter, the ἔκθεσις of reduplicative propositions, the conversion of reduplicative propositions, the reduplicative syllogistic, and the supposition of terms in qua propositions. (shrink)