In Mathematics is megethology Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis’work is very attractive. However, the alleged (...) innocence of mereology and plural quantification is highly controversial and has been criticized by several authors. In the present paper we propose a new approach to megethology based on the theory of plural reference developed in To be is to be the object of a possible act of choice. Our approach shows how megethology can be grounded on plural reference without the help of mereology. (shrink)
Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification (, ) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite (...) à la Dedekind, as the unique non-logical axiom. We will also sketch a virtual interpretation of the classical continuum involving no other infinite than a countable plurality of individuals. (shrink)
In Mathematics is megethology. Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed (...) in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification. (shrink)
In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification (...) are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, ifMPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)
In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification . Instead, in the mereological case: (Lewis, 1991, p. 87). The aim of the paper is to (...) argue that one—an innocence thesis similar to that of plural reference is defensible. To give a precise account of plural reference, we use the idea of plural choice. We then propose a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. (shrink)
In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal provability (...) and, on the other, by means of the operator K of epistemic logic. Intuitionistic logic, as reconstructed within this perspective, turns out to be a part of epistemic logic, so that it loses its traditional foundational role, antithetic to that of classical logic. In section 3 we uphold the view that certain consequences of the adoption of atemporal notion of truth, despite their apparent oddity, are quite acceptable from an antirealist point of view. (shrink)
This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) we propose our \ logic. Finally, we show how \ supports the dialetheic solution of the liar paradox. (shrink)
In Parts of Classes [Lewis 1991] David Lewis attempts to draw a sharp contrast between mereology and set theory and to assimilate mereology to logic. He argues that, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain objects, no further ontological commitment is required for the existence of their sum. On the contrary, by accepting set theory, given certain objects, a further commitment is required for the existence of the set of them. The latter – (...) unlike the sum of the given objects – seems to be an abstract entity whose existence is not directly entailed by the existence of the objects themselves. The argument for the innocence of mereology is grounded on the thesis of “Composition as identity”. Lewis analyses two different versions of the thesis: the first is the Strong composition thesis, according to which certain objects are their sum, where the use of “are” would mean that composition is literally identity. The second version is the Weak composition thesis, according to which composition is analogous, under some aspects, to identity. He criticises the first version of the thesis and argues for the second one. In the paper we argue that (T1) arguments for the ontological innocence of mereology are not conclusive. An obvious objection to the Strong composition thesis is that – given certain objects Xs – they cannot be their sum because none of them is the sum. One could reply to this objection by observing that the “are” in the sentence “The Xs are their sum” is to be understood collectively and not distributively. But the crux is that the collective reading fails to generate a new entity, whereas mereology, in particular in Lewis’ use for the reconstruction of set theory as “megethology”, needs to consider sums as real objects. Besides, we contend that Lewis’ argument for the innocence of mereology based on the Weak composition thesis is a petitio principii. The reason is that the aspects of the analogy between composition and identity, which Lewis emphasises, obtain under the presupposition of the existence of sums. But this is just what a denier of innocence would refuse. (T2) Some arguments against the ontological innocence of mereology show a certain ambiguity in the innocence thesis itself. Some defences of the innocence seem to implicitly presuppose that the sum of certain objects Xs is not a genuine entity. Speaking of the sum of the Xs would be just another way of speaking plurally of the Xs. However, the relevant use of sums in mereology treats them as well determined objects. The relevant innocence thesis takes for granted that, though sums are genuine objects, nevertheless their existence does not require any further commitment. (T3) The innocence thesis, apart from Lewis’ defence, seems to depend on a general conception of the nature of objects and on how the notion of ontological commitment is understood. We think that the thesis is the manifesto of a realistic conception of parts and sums. This conception consists of the following clauses: (i) given any object x, it is well determined which parts it possesses; these are in turn objects whose existence is a necessary consequence of the existence of x. (ii) However any objects Xs are given, they automatically constitute a well determined object x which is their sum; (iii) We can refer singularly and plurally to parts and sums of given objects. Obviously, one might wonder if such a conception is really ontologically innocent. One could object that it is not innocent because clauses (i) – (iii) are not. For example, clause (i) could be considered as an ontological commitment to the existence of sums. But the innocence at issue does not concern the above-sketched conception. The innocence is embedded in the conception itself. In other words, someone who argues for clauses (i) – (iii) takes a point of view from which mereology appears to be innocent. For, such a point of view forces us to consider as well determined the parts of any object and does not allow us to separate the existence of certain objects form the existence of their sum. (T4) is the claim that the alleged innocence of mereology is subject to Quine’s notorious criticisms of the set-theoretical interpretation of second order logic. To the purpose, we construct a mereological model of a substantive fragment of set theory, i.e. the one that grounds the principal model semantics of second order logic. First, we construct a mereological model under the assumption of the existence of infinitely many atoms. Then, we replace this assumption with that of the existence of any infinite object (with or without atoms). Finally, let us make a general point about the innocence thesis of mereology. A conclusive argument for that would be a refutation of the thesis that there are only denumerably many entities. For, since the parts of an infinite object constitute a non-denumerable infinity, such an argument would entail that there could be no infinite without a non-denumerable infinity. However, the thesis that any genuine infinity is a denumerable one has had some important advocates. So, a conclusive argument for the innocence of mereology seems to be highly implausible. (shrink)
In Parts of Classes David Lewis attempts to draw a sharp contrast between mereology and set theory and he tries to assimilate mereology to logic. For him, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain objects, no further ontological commitment is required for the existence of their sum. On the contrary, by accepting set theory, given certain objects, a further commitment is required for the existence of the set of them. The latter – unlike (...) the sum of the given objects – seems to be an abstract entity whose existence is not directly entailed by the existence of the objects themselves. The argument for the innocence of mereology is grounded on the thesis of composition as identity. In our paper we argue that: arguments for the ontological innocence of mereology are not conclusive. Some arguments against the ontological innocence of mereology show a certain ambiguity in the innocence thesis itself. The innocence thesis seems to depend on a general conception of the nature of objects and on how the notion of ontological commitment is understood. Specifically, we think that the thesis is the manifesto of a realistic conception of parts and sums. Quine‟s notorious criticism of the set-theoretical interpretation of second order logic seems to be reproducible against Lewis‟defence of mereology. To the purpose we construct a mereological model of a substantive fragment of set theory, adequate to ground the set-theoretical semantics of second order logic. (shrink)
The present paper deals with natural intuitionistic semantics for intuitionistic logic within an intuitionistic metamathematics. We show how strong completeness of full first order logic fails. We then consider a negationless semantics à la Henkin for second order intuitionistic logic. By using the theory of lawless sequences we prove that, for such semantics, strong completeness is restorable. We argue that lawless negationless semantics is a suitable framework for a constructive structuralist interpretation of any second order formalizable theory (classical or intuitionistic, (...) contradictory or not). (shrink)
The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not “fall foul” of Curry’s Paradox by invalidating an inference rule called “Absorption” (or “Contraction”) and the classical logical theorem called “Assertion”. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priest’s counterexamples to Absorption and Assertion use (...) in the metalanguage a dialetheically unacceptable principle. Furthermore, we show that the rejection of Assertion undermines Priest’s claim that the entailment connective expresses the notion of logical consequence. (shrink)
This paper investigates the question of how we manage to single out the natural number structure as the intended interpretation of our arithmetical language. Horsten submits that the reference of our arithmetical vocabulary is determined by our knowledge of some principles of arithmetic on the one hand, and by our computational abilities on the other. We argue against such a view and we submit an alternative answer. We single out the structure of natural numbers through our intuition of the absolute (...) notion of finiteness. (shrink)
We introduce an epistemic version of validity and completeness of first order logic, based on the notions of ideal agent and fictional model. We then show how the perspective here considered may help to solve an epistemic puzzle arising from Gödel's second incompleteness theorem.
Brouwer's theorem of 1927 on the equivalence between virtual and inextensible order is discussed. Several commentators considered the theorem at issue as problematic in various ways. Brouwer himself, at a certain time, believed to have found a very simple counter-example to his theorem. In some later publications, however, he stated the theorem in the original form again. It is argued that the source of all criticisms is Brouwer's overly elliptical formulation of the definition of inextensible order, as well as a (...) certain ambiguity in his terminology. Once these drawbacks are removed, his proof goes through. (shrink)
In To be is to be the object of a possible act of choice the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as a theory of logical concepts. (...) Within this theory, we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege’s traditional logicism. (shrink)
MartinoEnrico.* * Intuitionistic Proof Versus Classical Truth, The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics. Logic, Methodology and the Unity of Science; 42. Springer, 2018. ISBN: 978-3-319-74356-1 ; 978-3-030-08971-9, 978-3-319-74357-8. Pp. xiii + 170.
In the present paper we discuss different issues concerning the Philosophy of India. We examine, in the first place, the current situation of the area in Argentinean universities and, more specifically, in the programme of the Licenciaturas in Philosophy taught in our country. We assess, with this purpose, the programme of the thirty two degrees in Philosophy offered by national private and public universities. In the second place, we provide a brief discussion of the up-to-date specialized bibliography about the dilemma (...) concerning the existence or not of philosophy in India. We consider, thus, the possitions of a few authors who try to deconstruct centenary and rooted conceptions about the absence of philosophy in India. We evaluate, as well, the stances of contemporary specialists in Indian thought who defend the presence of philosophy in classical Indian culture arguing from a sistematic and methodologically honest knowledge of this tradition. Our inquiry tries to show, in such a way, that approaching the (meta)philosophical dilemma regarding the presence or absence of philosophy in India requires and implies a (self-)critical and specialized tradition of research in the area, and that in our country this tradition exists only in an very incipient stage. (shrink)
Is it possible to speak of a Husserlian phenomenology of the animal? In his phenomenological analyses, Husserl thematizes animals as a case of “abnormality” in order to investigate the subjectivity that constitutes the human world as a normal world. With respect to other perspectives—such as the Heideggerian one—which imply a drastic separation from animality, Husserl’s standpoint has the advantage of keeping a path of communication open between the phenomenological and the scientific investigation of the problem, in the multifarious forms taken (...) on today by the latter. However, what is the original contribution of phenomenology on this issue, in comparison with that of the empirical sciences? Phenomenology addresses the experience of lifeworld as its own field of activity and as the implicit ground for every scientific observation and reconstruction. Phenomenology, thus, provides a new approach to animal life, avoiding naive ontological assumptions about it. (shrink)
El presente trabajo está dedicado a rastrear la influencia del pensamiento plotiniano sobre el revival de la lírica irlandesa bajo la pluma de su más célebre poeta: William Butler Yeats. Los escritos del Irlandés, en efecto, contienen alusiones directas al filósofo neoplatónico que constituyen la ‘punta del iceberg’, por así decirlo, de una impronta profunda y trascendente de la filosofía eneádica sobre la literatura yeatseana. Nuestro trabajo, por lo tanto, procura examinar el significado de este ascendiente e intenta poner de (...) manifiesto los caracteres propios de la relación personal, textual y conceptual que Yeats establece con Plotino en sus escritos. (shrink)
1. EI dilema de Jørgensen. 2. La salución propuesta. 3. Breve historia de un prejudicio filosófico. 4. Normas sin lógica. 4.1. Imperativos sin lógica. 4.2. Normas y proposicienesnormativas. 4.3. Proposiciones normativas y normas verdaderas. 4.4. Mundos posibles. 4.5. Validez e invalidez. 4.6. La racionalidad del legislador. 5. La noción abstracta, sintáctica y semántica de consecuencia. 5.1. La noción abstracta de consecuencia. 5.2. La noción sintáctica de consecuencia. 5.3. La noción semántica de consecuencia. 5.4. EI sentido dado por las reglas de (...) uso en un contexto. 5.5. Qué operadores para la lógica. 5.6. Solo en un contexto la parte cobra sentido. 6. La lógica deóntica. 7. De donde la solución del dilema interesa a toda la lógica. 8. Consecuendas para la informática. (shrink)
Two of the constitutive elements of Plotinus’ philosophy are mysticism and the exegesis of the philosophers that preceded him. These two aspects, however, are interpreted in different ways by scholars. Due to these facts, in the present paper we try to show and explain Plotinus’ exegesis of some Middle Platonic ideas. Furthermore, we evaluate the impact that these ideas together, with his mystical experiences, had on his metaphysical doctrine. We offer, in the last place, an interpretation of the relationship that (...) mysticism and exegesis have in the Enneads, reconsidering the way in which scholars understand it. (shrink)
“Philosophy and Exegesis in the Enneads . The Wings of the Plotinean Soul in his reading of Plato’s Phaedrus ”. In the present paper, we examine the role exegesis plays in the philosophy of the Enneads and, in particular, the way in which Plotinus interprets Plato. With this purpose we analyze, in the first place, some revealing passages of Porphyrius’ Life of Plotinus in order to understand, on the one hand, how late Greek thinkers conceived the exegetic endeavour and, on (...) the other hand, the way in which plotinian philosophy was considered by his contemporaries. In the second section of this work, we examine the treatise IV 8 of the Enneads and try to show some peculiar aspects of Plotinus’ exegetic procedure as well as of his reading of Plato’s Phaedrus. (shrink)
Are urban societies unsustainable per se? So far most analyses of urbanization have been ethno and temporocentric, concentrating on modern industrial and post-industrial cities of the West. The potential sustainability of cities should not be determined with reference to correct consumption patterns, and the structures of capitalism and industrialism, nor under an autarkic view. To answer the urban sustainability question the characteristics of urban societies need to be defined and isolated.
Aristotle’s major work on psychology was De anima. Nevertheless, Parva naturalia, also known as De sensu et sensato, played a prominent role among Arabs and Western thinkers. In the present essay, we aim to show how the Arabic translation of this last work was used by Avicenna, Ibn Bâjjia and, under his influence, by Averroes. In Averroes’s Epitome De Sensu one can notice, for example, that the theoretical principles are Aristotelian, but they are contaminated by the term “spiritual”, which is (...) not used by the Greek philosopher. In the Latin West, Averroes’s reading will have influence on Albertus Magnus and Thomas Aquinas. KEY WORDS – Parva naturalia. De anima. Arabic and Western philosophy of mind. Averroes. Spiritual perception. (shrink)
El Yoga constituye uno de los legados de la India a la humanidad que Occidente haadoptado con mayor aceptación y entusiasmo. Conociendo innumerables transformaciones, la práctica del Yoga ha sido incorporada a la vida occidental de diversas maneras, ya sea como profesión, como entretenimiento, como técnica de relajación, como preparación física eincluso, en algunos casos, como técnica de liberación. Pero el carácter mudable o „camaleónico‟, podríamos decir, del Yoga es tan antiguo como el Yoga mismo y ya en la India (...) antigua es posible atestiguar diferentes expresiones de su práctica y de su contenidofilosófico. (shrink)
This paper examines the position of international human rights law towards missionary or proselytizing activities with a special focus on the American context. By evaluating UN legal acts such as the 1948 Universal Declaration of Human Rights, the 1960 Arcot Krishnaswami Study and the 1981 Declaration on the Elimination of All Forms of Intolerance and Discrimination Based on Religion or Belief and the American Convention of Human Rights, it investigates the extent to which such activities fall within the scope of (...) the right to free speech and to freedom of religion for religious organizations. This is exemplified by looking at two Evangelical religious organizations founded for the purpose of luring away groups of believers from their original religious communities: “Mission to Amish People”, targeting the Amish People, and “Jews for Jesus”, aimed at the Jewish community. The clash of one religious community which considers mission a fundamental element of its religion with a religious community who is highly skeptical about mission constitute the extreme test case of the right to free speech and to corporate freedom of religion. Given the highly various importance which mission can play in different religions, the article suggests to solve each case individually by carefully examining the content of each religious doctrine. (shrink)
O que é considerado "teoria" nos estudos de Comunicação? Este texto busca delinear uma resposta a partir dos programas de ensino de "Teoria da Comunicação" de 31 universidades. O exame indica que os debates epistemológicos da área são condensados em um pequeno núcleo de teorias, não havendo consenso a respeito do que constitui uma 'teoria da comunicação'.
La tensión entre fidelidad a la tradición e innovación presente en el pensamiento plotiniano se manifiesta de modo patente en su propuesta metafísica. La ontología expuesta en las Enéadas, en efecto, es un claro ejemplo de la labor exegética mediante la cual Plotino toma las concepciones metafísicas platónico-pitagóricas precedentes y las sintetiza infundiendo nueva vitalidad en ideas antiguas. Para llevar a cabo su exégesis utiliza, incluso, conceptos aristotélicos que integra de un modo peculiar a su pensamiento platonizante. En el presente (...) trabajo, pues, nos proponemos esclarecer el procedimiento interpretativo que Plotino lleva a cabo en la formulación de su doctrina de lo Uno y de la relación entre esta hipóstasis y la Inteligencia. En nuestro análisis examinamos las nociones metafísicas que nuestro filósofo toma como punto de partida y brindamos una interpretación de la transformación que opera sobre ellas para arribar al sistema que dio origen a una nueva corriente de pensamiento platónico. The tension between innovation and fidelity to tradition present in the thought of Plotinus manifests itself clearly in his metaphysical conception. The ontology put forward in the Enneads, in fact, is a fine example of the exegetical work by which our thinker takes the preceding platonic-pythagorean metaphysics and synthesizes it, bringing new vitality into ancient ideas. To accomplish his exegesis he even employs Aristotelian concepts incorporating them in a peculiar way to his Platonizing thought. In the present paper, hence, we intend to elucidate the interpretive procedure that Plotinus carries out to arrive at his conceptions of the One and of the relationship between this hypostasis and Intelligence. In our analysis, we examine the metaphysical notions that our philosopher takes as starting points and we offer an interpretation of the transformation he operates upon them to reach the system that gave birth to a new current of Platonic thought. (shrink)