Axiomathes DOI 10.1007/s10516-014-9248-5 ORIGINAL PAPER

On Essentialism and Existentialism in the Husserlian Platonism: A Reflexion Based on Modal Logic Carlos Lobo • Cleverson Leite Bastos Carlos Eduardo de Carvalho Vargas

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Received: 22 July 2014 / Accepted: 29 September 2014  Springer Science+Business Media Dordrecht 2014

Abstract Departing from modal logic, Jean-Yves Girard, as a logician interested in philosophy, presented a distinction between essentialism and existentialism in logic. Carlos Lobo reflected about the Girard’s concept to reinterpret the Husserlian Platonism in regard of the status of logical modalities. We start rescuing the notion of modal logic in the Edmund Husserl’s works, especially Formal and Transcendental Logic and First Philosophy. Developing this reflexion, we propose a new contribution to this discussion, reinterpreting the platonic influence in the Husserlian notions of eidos and science, light of some readings of Lee Hardy and Johanna M. Tito. As a conclusion of this dialogue between Husserl and Girard, the method of eidetic variation is presented as a tool to review the idea of science, in a manner consistent with the phenomenological approach. Keywords Philosophy of logic
Phenomenology
Edmund Husserl
Jean-Yves Girard
Modal logic
Platonism

1 Starting from the Modal Logic Carlos Lobo presented at the 45th Meeting of the Husserl Circle a paper on Husserl and Girard on Modal Logic and Platonism. The author not only contributes to C. Lobo Directeur de Programme, Colle`ge International de Philosophie, Paris, France e-mail: [email protected] C. L. Bastos
C. E. de C. Vargas (&) Postgraduate Program in Philosophy, Pontifical Catholic University of Parana´, School of Education and Humanities, 80215-901, Rua Imaculada Conceic¸a˜o, 1155, Prado Velho, Curitiba, Parana´, Brazil e-mail: [email protected] C. L. Bastos e-mail: [email protected]

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history of philosophy, but also enriches the history of logic. He is interested in phenomenology, but he considers that there is a partial influence of Husserl’s investigations in the development of mathematical logic. Edmund Husserl was a mathematician who devoted himself to philosophy, referring to logic in his different phases, even in the development of his phenomenological methodology (Bastos and Vargas 2013). In this paper, we will comment Lobo’s reflexions in the perspective of Lee Hardy’s contributions to the understanding of the Husserlian epistemology, starting from the question about modal logic. One can also observe that in the phenomenological context, the theme of modal logic was developed by Oskar Becker, the first German mathematician to investigate the matter from a vindicated phenomenological point of view. Becker studied philosophy with Edmund Husserl, looking for the phenomenological foundations of geometry and natural science, including special and general relativity theory, as presented by Weyl (1919). In 1930, Becker published On the logic of modalities in the Yearbook of Philosophy and Phenomenological Research, proposing a modal interpretation of the intuitionistic logic from Arend Heyting and some incentive modifications of C. I. Lewis systems of modal logic (S4 and S5). The theme of modality was also analyzed in the phenomenological context, by Hermann Weyl, seeking for a phenomenological foundation of logic and mathematics, especially in natural sciences. In the paper The ghost of modality (from 1937), Weyl (1981) analyzed the ‘‘appearance’’ of the ‘‘modal problem’’ from the development of logic with Clarence I. Lewis. Having referred to the origins of contemporary logic with Gottlob Frege, but also addressed the formalization developed by Bertrand Russell and Alfred N. Whitehead (Principia Mathematica), he presented a philosophical interpretation of the symbolic manipulation by logic. Presenting a dialogue between Hilbert’s formalism and Brower’s intuitionism, he traces the emergence of the modal ghost in probability theory, topology and quantum logic f. On 10th April 1918, Edmund Husserl wrote a letter to Hermann Weyl recognizing a common direction in their research, and declared that he had been seeking for years a philosophically grounded mathesis universalis, claiming the design of a new formal logic (van Dalen 1984). Interpreting the correspondence between Husserl and Weyl, Lobo (2010) that the extension of the concept of logic presented by Husserl, requires a clarification of fundamental concepts of modal dimension, especially the notion of analytical ability. However, this task falls more specifically under philosophical phenomenology than under formal logic. It requires the development of the consequences resulting from accepting the modal dimension as constitutive of the logical content. Nuno Nabais (1999) and Guillermo Rosado Haddock (1997) highlighted the importance of the contribution of the Edmund Husserl’s philosophy to modal logic, but the contributions of Husserl belong more to a philosophical understanding of logic rather than to a formally developed new logic. Claire Ortiz Hill (2008, p. xiii) recalled the letter that Husserl wrote on 18th February 1905, to Heinrich Gomperz highlighting the theoretical and methodological developments that occurred in the lessons taught in Go¨ttingen, especially those on theory of signification, in 1908 (Husserl 1987). In Formal and Transcendental Logic, the author criticized the stance taken in the Prolegomena, where no explicit modal dimension was recognized to pure logic. In

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reworking his philosophy of logic, Husserl realized the need for an expansion of pure logic in relation to the notion of modality (Husserl 1974, pp. 99–100). If Carlos Lobo (2008, 2009) and Suzanne Bachelard (1957) emphasized the importance of modal dimension in Husserl’s work, Vigo (2004, p. 157) also noted that the issue of the modalities of judgment had become crucial to the philosophy of Husserl from Ideas I onward. Husserl criticized the sources of validity of the logical concepts. Analyzing the relation between objectivity and subjectivity, he opened a new domain with his phenomenological description. He discovered a potential of logical functions that are waiting for formalization. Lobo (2014) questioned: what are the others unexploited resources of the Husserlian passive and actives syntheses that could help the understanding the logical structures? Husserl wanted to reform the logic and needed, first, to investigate the general requirements of the formalization and the notion of form. Considering modal logic, Mitsuhiro Okada (2004, 2008) also found connections between Girard (2011) and Husserl (1984). Okada used modal logical to compare linear and classical logic. In the context of the discussion on the intuitionistic philosophy of mathematics, from elements of linear logic, Okada (2004) suggested that we should relate categorial intuition (Husserl 1984) and modal logic, which can be associated with the discussion promoted by Lobo (2009) about the meaning of eidos in Husserl’s philosophy. Lobo retakes the Okada’ suggestion that the modal operator ‘‘h’’ play the same role in the understanding of logic and linguistic activity, as the objectivization act in the phenomenology. It is possible to think the relations of modal logic with the particular sciences, as suggested Lanciani (2008), who proposed an epistemological revision of the theory of probability. In the context of pure logic, inspired maybe by Johannes von Kries (1886), Husserl seems to indicate another path in the treatment of probability distinct from Kolmogorov’s axiomatization. Referring to Third Logical Investigation, Lanciani insisted on the importance of the concept of Fundierung and its relations to the axiomatic of the probability theory. As stressed by Rota (1997), ‘‘of great scientific interest is the relation of Fundierung, which rank among Husserl’s greatest logical discoveries’’ (Rota 1992, p. 171). Another important discussion regards the intersubjective constitution of modal logic, related to the noematical traits acquired by logical items. Girard’s paper, Truth, Modality and Intersubjectivity, discusses the logical foundation of the quantum physics: ‘‘instead of teaching logic to nature, it is more reasonable to learn from her’’ (2007, p. 4). Jean-Yves Girard underlined the role of subjectivity and intersubjectivity in logic from a point of view based on the discovery of the quantum phenomena. This subjective aspect of logic, but is by no means subjectivistic. Husserl presented a reform of logic that questions the notion of ideality. Following Formal and Transcendental Logic, we can see that Husserl does not accept the illusory manipulation of idealities as real data. Lobo (2014) shows that Husserl escapes the dilemma between subjectivism and objectivism: the modal core of logic is a product of objectivization, but it is sustained by a subjective sedimentation. Far from being a psychologist, the phenomenologist scrutinizes intersubjective and subjective activities in a transcendental ‘‘history’’, that of the constitutive genesis.

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2 About Essentialism in Logic In The Blind Spot, before exposing his linear logic, Jean-Yves Girard (2011) proposes an introduction, in philosophical terms, describing the conflict between existentialism and essentialism in logic. According to him, are essentialists ‘‘those who think that everything is already there, that one can but repeat archetypes’’. To define existentialism, Girard explains that: ‘‘the existentialist world is a lawless world, in which contestation is total and constant; which is not viable. This viewpoint takes substance only as a reaction against the essentialist haughtiness’’ (Girard 2011, pp. 4–5). Taking Saul Kripke in consideration, Girard (2011, p. 11) criticizes the essentialist dimension of his modal logic. Nonetheless ‘‘linear logic reduces essentialism to an opaque modal kernel, especially when one keeps in mind that modality is a creation of essentialist logicians’’ (Girard 2011, p. 11). Although Girard criticizes the ‘‘arbitrariness’’ of modal logic, linear logic also allows variations in the modality treatments (di Cosmo and Miller 2010, p. 9). Contrary to logical essentialism, linear logic rejects the assumption of universe of ‘‘unique, well-defined actions’’ (Girard 2011, p. 13). In the case of the modal part of linear logic, Girard insists on the ‘‘imperfection’’ of exponentials, which he calls ‘‘heterodox’’ (Girard 2011, pp. 14, 357). Systems of linear logic are atypical in the sense that, for example, they cannot be exhausted by the theory of sets.

3 About Platonism 3.1 A Dialogue Between Husserlian Philosophy and Platonism Lobo (2014) notes that Girard’s anti-essentialism is not necessarily an antiplatonism. Lobo says that Husserl and Girard are Platonists in the way they think the modal substructure of logic. Jean-Yves Girard, being anti-essentialist, counts the historical platonic epistemology related to logic among the real existentialist attitudes. The science, according to Girard (2011), is not ossified, nor immobile and the Platonist pays attention to science that changes. Edmund Husserl has his originality, but he also depends upon a philosophical tradition (Hardy 1992, 2013; Tito 1987, 1990). Husserl departed from the classical idea of science and proposed, with phenomenology, some methodological prerequisites to sustain philosophically the traditional idea: ‘‘Husserl does not merely want to repeat Plato, but wishes to reinterpret him’’ (Tito 1987, p. 14). In Formal and Transcendental Logic, Husserl explicitly takes up ‘‘the old Platonic idea’’ of science, ‘‘the idea of genuine science as science grounded on an absolute foundation,’’ as the guiding idea of philosophy. Similarly, in the Crisis, Husserl represents phenomenology as the fulfillment of the ancient ideal of philosophy as a universal science, initiated by Plato and renewed by Descartes. As such, phenomenology is to fulfill the sense of philosophy’s

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‘‘primal establishment as the universal and grounding science’’ (Hardy 2013, p. 40). The Husserlian theory of science can be explicitly associated with Plato’s classical tradition. As Plato, Husserl wants a genuine science with an absolute foundation. He searched, with phenomenology, the ‘‘true sense of science’’ and thought that Plato found a theory of science: ‘‘In Plato, logic (dialectic) is concerned with the theory of science. Logic is the discipline the task of which it is to seek the sense of science and to guide its development in light of this sense’’ (Tito 1987, p. 10). Plato (1997), in the Republic (533c), thought the science as a deductive system with self-evident first principles (Bachelard 1957, p. xxxiii; Plato 1997; Tito 1987, p. 12): Rationality, in that high and genuine sense of which alone we are speaking, the primordial Greek sense which in the classical period of Greek philosophy had become an ideal, still requires, to be sure, much clarification through selfreflection; but it is called in its mature form to guide [our] development (Husserl 1976, English tr., p. 337). Phenomenology searches an idea implicit in the philosophical tradition, that ‘‘was originally and always sought in philosophy’’ (Husserl 1976, English tr., p. 16), with ‘‘the unity of mind and world in reason’’ (Tito 1987, p. 23). Phenomenology seeks to properly understand the rationality with ultimate insight of clarity. Husserl aimed to reestablish sciences according the ideal of self-responsibility, selfjustification and self-understanding. From the perspective of Johanna Maria Tito (1990), the main difference between the Husserlian philosophy and Platonism is the conception of the relationship between fact and eidos, because Husserl (1976) approximates reason and life: ‘‘Husserl’s theory is distinct from Plato’s. After all, the new theory of rationality that Husserl is trying to put forth is one which unites life and reason, fact with idea, while on many readings of Plato, fact and idea are separate’’ (Tito 1987, p. 26). Thus Plato was set on the path to the pure idea. Not gathered from the de facto sciences but formative of pure norms, his dialectic of pure ideas — as we say, his logic or his theory of science — was called on to make genuine science possible now for the first time, to guide its practice. And precisely in fulfilling this vocation the Platonic dialectic actually helped create sciences (Husserl 1974, English tr., p. 2). 3.2 Revising the Platonic Notion of Eidos in a Modal Perspective Carlos Lobo (2009) associated the criticism of Husserl’s Formal and Transcendental Logic with Husserl ‘s critique of the Platonic logic on First Philosophy (Husserl 1956, pp. 17–24), reviewing the absence of modality in the Prolegomena, from the sphere of what is defined there as pure logic. Husserl, in his critical reflection on the history of ideas, commented the limitations of the concept of Platonic eidos. For Lobo, the notion of eidos had been conceived in the Prolegomena as a pole of objectivity and identity that left no room for the modal dimension.

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On First Philosophy, the main criticism to the logic eidos is that the Aristotelian and Stoic logic of non-contradiction, considered as complete, has impeded the development of a logic of truth, in Husserl’s sense, i.e. distinct from the morphology of meanings and the logic of consequence. In Husserl (1956), the exclusion of the modal dimension in the definition of truth intended to preserve it from possible contradictions. Lobo (2009) examined Husserl’s thoughts on designing ideation, understood as the apodeictic intuition of the eidos. In terms of formal logic, Husserl’s criticism refers to the exclusion of the concepts of necessity, possibility and impossibility of the analysis of the concept of truth in the logic of noncontradiction. However, in criticizing traditional logic (die alte Logik, as Husserl called it sometimes), rather than analyzing the history of logic, Husserl applies a distinction between logic of truth and logic of non-contradiction to the earlier thinkers, showing theirs philosophical limitations. Regarding the history of logic, it may be necessary to make some reservations and further distinguish the contributions of Platonic, Aristotelian and Stoic logic in relation to the modal dimension of knowledge (Bastos and Oliveira 2012). Despite this, Husserl concluded his review by stating that the logic inherited from the Greeks contributed to consider the modalities as secondary qualitative determinations, just as if they belonged to a psychological logic. For the author, it was an error to relegate the modal variants to the realm of psychological or empirical subjectivity. From the comments by Lobo (2009), we can recognize that Husserl (1956) proposes, in First Philosophy, a logic that, without becoming historical or empirical, is able to explore various aspects of ‘‘life’’, including cases involving the intellectual conditions. Such ideas seem to anticipate the philosophical proposal that has been developed, on the basis of on the notion of ‘‘life-world’’ (Lebenswelt), but it would have been difficult to understand it in the context of the Prolegomena. 3.3 The Method of Eidetic Variation and the Platonic Idea of Science As Carlos Lobo (2014) noted, the Husserlian Platonism is ambiguous. He explains that the mathematician is not psychologist because he takes seriously the pure unrealities of his searches, being a species of spontaneous Platonist. This is a solution that reminds ‘‘The Blind Spot’’, when Girard (2011) states: ‘‘all good mathematicians […] should be considered as Platonists in as much as they believe in what they does’’. We remember a Rosado Haddock’s paper, who gives a Husserlian flavor to his Platonism: ‘‘If asked, most mathematicians would probably agree in considering themselves as intuitive Platonists’’ (Haddock 2007). Thinking about the Husserlian Platonism in logic and mathematics, Lobo (2014) offers an explanation that seems to reconcile Husserl’s phenomenology with Girard’s existentialism, which is grounded on linear logic: The modal core of logic and formal ontology, and in general the modal core of the formal is always the product of an objectivization and its solidity is sustained by a complex sedimentation of subjective (constitutive) activity. […] This hidden logical dimension was not a sphere of unclosed actually

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eternally existing realities and progressively disclosed by the efforts of generations of mathematical work […], but an ideal sphere stuffed with layers of unrealities issued from subjective and intersubjective activities, layers indicating to a close scrutiny periods of a ‘‘transcendental history’’, a ‘‘constitution genesis’’. The phenomenologist is the historian or surveyor of this stratified activities (Lobo 2014, p. 16). The essentialism’s question is related to the understanding of the essence, which is an important issue to Husserl. Lee Hardy (1992, 2013) also researched the Husserlian conception of science, considering the method of eidetic variation and concluded that the apprehension of the essences, by the ‘‘intuition’’ (Anschauung) could not be secured once and for all (Husserl 1977, p. 13): It became clear that the apprehension of eidetic states of affairs is not achieved in an instant; rather, it is an open-ended process involving the imaginative variation of endless possibilities. The method of eidetic variation is in principle inductive. It is an induction not over individual facts, but over imagined possibilities. For this reason, as Elisabeth Stro¨ker has pointed out, the method of eidetic variation can never establish eidetic claims once and for all (Hardy 2013, pp. 36–37). Lee Hardy discovered that the Husserlian idea of science, although foundationalist and inspired by Plato and Aristotle, is not ‘‘dogmatic’’. The ‘‘absolute’’ certainty, with adequate evidence, searched to found the genuine science, is the final aim, but is not an accomplished fact (Husserl 1956, p. 221; 1973, p. 49; 1976, p. 113). The scientific reason should actualize the ‘‘genuine’’ cognition by its criticism (Husserl 1974, p. 246). As Husserl taught, we need to explain knowledge, without being psychologists and relativists: ‘‘this does not mean that all truth is relative, in the sense that one truth claim is just as good as any other. For although all truth-claims necessarily fall short of the ideal of adequate evidence, this ideal remains as criterion for the criticism of extant truth-claims’’ (Hardy 2013, p. 37). As Hardy (2013) points out, the development of the method of eidetic variation had consequences for the understanding of science and logic. The critique of reason developed from reflection on modal logic can also interfere in understanding Husserl’s thought as a whole. By summarizing some reflections on his relationship with the philosophy of logic, one could infer two directions for interdisciplinary deepening of these relationships resulting from Husserl suggestions. On the one hand, philosophers could phenomenologically clarify the logical concepts, but, on the other hand, it would also be possible to identify in Husserl’s philosophy logical elements and draw them logically (Simons 1982).

4 Conclusion Considering the change of perspective in the Husserl’s logic, opening the modal problem, one might question the division of labor between scientists and philosophers (Husserl 1975, § 71). It is not the case to mix up improperly the

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various areas of research, which would lead us back to psychologists errors criticized in the Prolegomena (Husserl 1975). However, one can observe a complementarity between the logical and phenomenological philosophy. Husserl criticized the sources of validity of the traditional logical concepts. Analyzing the relations between objectivity and subjectivity, he opened, with your phenomenological description, a new domain. The author of Logical Investigations discovered a potential of logical functions that are awaiting for formalization. We cannot ignore the philosophical task of clarifying concepts, including that of logical and mathematical notions. Husserl cannot be considered an essentialist if we assume his epistemology of knowledge of the essence. Lobo (2014), inspired by Girard (2011), found that one can be Platonist without being essentialist—in Girard’ sense. We add, now, that one can be Platonist without being dogmatic in Hardy’ sense. The influence of Plato is fundamental, but Husserl has its own phenomenological philosophy (Tito 1987, 1990). Thus, the ‘‘Husserlian Platonism’’ needs to be reviewed with the method of eidetic variation. In this sense, Lobo’s response offers an appropriate and coherent approach to the issue, because it does not exclude the importance of Platonic origin of the idea of science, and does justice to the phenomenological attention to the life of reason. Overcoming the dichotomy between subjectivity and objectivity, we should insist, with Husserl, on the necessity of a renewed philosophical reflection on the relation between facts and ideas. Acknowledgments This research was made possible by a Grant from CAPES and PUC-PR to develop a thesis project. We are also grateful to the participants of the 45th Annual Meeting of the Husserl Circle for their insightful suggestions.

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