Frege and the rigorization of analysis

This paper has three goals: (i) to show that the foundational program begun in theBegriffsschrift, and carried forward in theGrundlagen, represented Frege's attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence ofintuitive reasoning were not in question. (ii) To place Frege's logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to pursue the goal of autonomy within the framework of the system of second-order logic of theBegriffsschrift. (iii) To address certain criticisms of Frege by Parsons and Boolos, and thereby to clarify what was and was not achieved by the development, in Part III of theBegriffsschrift, of a fragment of the theory of relations.     

Zwischen Berechenbarkeit und Nichtberechenbarkeit. Die Thematisierung der Berechenbarkeit in der aktuellen Physik komplexer Systeme

Between Calculability and Non-Calculability. Issues of Calculability and Predictability in the Physics of Complex Systems. The ability to predict has been a very important qualifier of what constitutes scientific knowledge, ever since the successes of Babylonian and Greek astronomy. More recent is the general appreciation of the fact that in the presence of deterministic chaos, predictability is severely limited (the so-called ‘butterfly effect’): Nearby trajectories diverge during time evolution; small errors typically grow exponentially with time. The system obeys deterministic laws and still is unpredictable, seemingly a paradox for the traditional viewpoint of Laplacian determinisms. With the concept of deterministic chaos the epistemological issue about an adequate understanding of predictability is no longer just a mere philosophical topic. Physicists on the one hand recognize the limits of (long term) predictability, computability and even of scientific knowledge, on the other hand they work on concepts for extending the horizon of predictability. It is shown in this paper that physics of complex systems is useful to clarify the jungle of different meanings of the terms ‘predictability’ and ‘computability’ — also with philosophical implications for understanding science and nature. Today, from the physical point of view, the relevance of the concepts of predictability seems to be underestimated by philosophers as a mere methodological topic. In the paper I analyse the importance of predictability and computability in physics of complex systems. I show a way how to cope with problems of unpredictability and noncomputability. Nine different concepts of predictability and computability (i.e. open solution, sensitivity/chaos, redundancy/chance) are presented, compared and evaluated. This revised version was published online in August 2006 with corrections to the Cover Date.     

The flesh of all that is: Merleau-Ponty, Irigaray, and Julian’s ‘showings’

Julian of Norwich (b. 1342) anticipated the ontological and epistemological work on sexed embodiment pioneered in the work of Merleau-Ponty and Irigaray in the 20th century. Her epistemology of sensual ‘showings’ helped reconfigure women’s embodiment and speech acts (‘bodytalk’): by recognizing cognitive emotions and the knowledge-producing body; and by envisioning the intertwining of human flesh with All That Is. The paper next examines Merleau-Ponty’s somatic discourse on the chiasmic flesh, which leads to a discussion of Irigaray’s work on poetic mimesis.     

Sensible Atoms: A Techno-aesthetic Approach to Representation

This essay argues that nano-images would be best understood with an aesthetical approach rather than with an epistemological critique. For this aim, I propose a ‘techno-aesthetical’ approach: an enquiry into the way instruments and machines transform the logic of the sensible itself and not just the way by which it represents something else. Unlike critical epistemology, which remains self-evidently grounded on a representationalist philosophy, the approach developed here presents the advantage of providing a clear-cut distinction between image-as-representation and other modes of existence of images, such as the one of ‘imaginaction’ that I draw from a comparison between far-field and near-field microscopies. Once this regime of imaginaction is distinguished from representation, I focus on nanotechnological percepts and argue that they follow a transmodal logic. I then draw the implications of this enquiry in terms of a new sensible condition that changes the way we think of non-living objects. Finally, I conclude that if techno-aesthetics dares to posit and articulate sensibility beyond the privileged sphere of subject/object relationships, it simultaneously engages us to consider the political character of our responsibilities towards the design of nano-engineered sensorial spaces.     

Constructive Dialogical Pluralism: A Context of Interreligious Relations

This article presents current philosophical reflections on religious diversity and concomitant attitudes towards the interreligious situation. The motive behind this presentation is to show that in order to deal more efficiently with the phenomenon of religious plurality, there is a need for a development of the philosophy of religion, where new perspectives are opened up and explored. The very concept of religion as a belief system is put into question, since it has caused philosophical reflections on religious diversity to be confined to certain metaphysical and epistemological concerns. Instead of focusing on the noun ‘religion’, the article suggests a way to understand the adjective ‘religious’ and view religious plurality as a plurality of ways of being religious. This opens up a certain context of interreligious relations and interreligious dialogue, where this very dialogue itself can contribute to the development of philosophical tools, concepts and categories for dealing with the fact of plurality. I call this context constructive dialogical pluralism.     

Why Dichotomies can be Misleading while Dualities Fit the Analysis of Complex Phenomena

Humans’ tendency to classify and categorize is definitely overspread, but it can be misleading at all fields, including epistemology, ontology, theory, and analysis of scientific knowledge construction itself. Sanchez and Loredo (IPBS: Integrative Psychological & Behavioral Science 43:4, 2009—DOI ) in their article on classification of contemporary constructivists fall exactly into such pitfall- even as their effort to make sense of many outstanding theorists is impressive and intriguing. A further analysis, however, points at the theoretical trap posed by such endeavor, for models arisen from different epistemological standpoints cannot be compared along the lines of a simplistic polarity between “objectivism” and subjectivism”. There is much more to be taken into account when a intrinsically complex subject like constructivism and constructionism epistemological approach and their welcome different versions—perspectives—are submitted to analysis and critical evaluation.     

Is Historical Epistemology Part of the ‘Modernist Settlement’?

Bruno Latour, as part of his advocacy of science studies urges us to move beyond what he calls ‘the Modernist Settlement’ that, among other things, separated science from politics and subject from object. As part of this project he has frequently called for the abolition of epistemology, including quite specifically the historical epistemology/epistemological history of Gaston Bachelard and Georges Canguilhem. Pierre Bourdieu, on the other hand, deploys the resources of historical epistemology, to dismiss Latour’s science studies. After examining the charges against historical epistemology and their rebuttal, I rule in favor of the defense. However, I also suggest that Latour raises genuine concerns about how to equip ourselves to tackle problems such as those associated with climate change; these are problems that require engagement with the politics of nature, with the politics of the sciences of nature and with the epistemological challenges associated with the need to deploy multiple disciplines in the service of complex, practical, policy-relevant problem solving.     

Williamson’s Woes

This is a reply to Timothy Williamson’s paper ‘Tennant’s Troubles’. It defends against Williamson’s objections the anti-realist’s knowability principle based on the author’s ‘local’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson’s purported Fitchian reductio, involving the unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson’s attempt to cause problems for the anti-realist by means of a supposed rigid designator generates a contradiction with arithmetic right away, upon instantiating the obviously relevant theorem that every natural number is provably odd or provably even. The paper also explains and formulates a globally restricted knowability principle, which likewise blocks the attempted reductio.     

Conquering the quarters: Religion and politics in Hinduism

Conclusion Our understanding of South Asian society and history is sometimes muddled by the rigid distinctions we make between ‘religion’ and ‘politics.’ The resurgent appeal of Hindu nationalism, the involvement of Hindu renouncers in contemporary Indian politics, and the continuing relevance of religious issues to political discourse throughout South Asia, show that such a distinction is of limited utility. In this essay, I have examined the notion of digvijaya in some detail, in an attempt to show that this ‘most important Indian concept with regard to sovereignty’ was always both a ‘religious’ and a ‘political’ phenomenon. When it was performed by Hindu kings in the classical period, the ‘political’ dimension of digvijaya was foregrounded, while in the medieval and modern periods, when it was associated primarily with Hindu renouncers, its ‘religious’ aspects were paramount. But neither ‘political’ nor ‘religious’ aspects were ever absent from any of the digvijayas discussed here because religion and politics were mutually entailed in the digvijaya at all times, just as kings and renouncers were—and still are—alter-egos of each other. I am tempted to conclude that the digvijaya melded religious and political domains. Yet perhaps even to speak of ‘melding’ religion and politics is a peculiarly modern kind of discourse. Perhaps we need to rethink our categories and recognize that politics always has a religious element, while religion is always a political force.     

Space Cannot Be Cut—Why Self-Identity Naturally Includes Neighbourhood

Psychology is not alone in its struggle with conceptualizing the dynamic relationship between space and individual or collective identity. This general epistemological issue haunts biology where it has a specific focus in evolutionary arguments. It arises because of the incompatibility between definitive logical systems of ‘contradiction or unity’, which can only apply to inert material systems, and natural evolutionary processes of cumulative energetic transformation. This incompatibility makes any attempt to apply definitive logic to evolutionary change unrealistic and paradoxical. It is important to recognise, because discrete perceptions of self and group, based on the supposition that any distinguishable identity can be completely cut free, as an ‘independent singleness’, from the space it inescapably includes and is included in, are a profound but unnecessary source of psychological, social and environmental conflict. These perceptions underlie Darwin’s definition of ‘natural selection’ as ‘the preservation of favoured races in the struggle for life’. They result in precedence being given to striving for homogeneous supremacy, through the competitive suppression of others, instead of seeking sustainable, co-creative evolutionary relationship in spatially and temporally heterogeneous communities. Here, I show how ‘natural inclusion’, a new, post-dialectic understanding of evolutionary process, becomes possible through recognising space as a limitless, indivisible, receptive (non-resistive) ‘intangible presence’ vital for movement and communication, not as empty distance between one tangible thing and another. The fluid boundary logic of natural inclusion as the co-creative, fluid dynamic transformation of all through all in receptive spatial context, allows all form to be understood as flow-form, distinctive but dynamically continuous, not singularly discrete. This simple move from regarding space and boundaries as sources of discontinuity and discrete definition to sources of continuity and dynamic distinction correspondingly enables self-identity to be understood as a dynamic inclusion of neighbourhood, through the inclusion of space throughout and beyond all natural figural forms as configurations of energy. Fully to appreciate and communicate the significance of this move, it is necessary to widen the linguistic, mathematical and imaginative remit of conventional scientific argument and explication so as to include more poetic, fluid and artistic forms of expression.     

Transzendentalpragmatik und Diskursethik. Elemente und Perspektiven der Apelschen Diskursphilosophie

Transcendental Pragmatics and Discourse Ethics. Elements and Perspectives of Apel's Discourse-Philosophy. The author follows Apel's intellectual biography and shows the conception of a critique of meaning qua ‘reflection upon the discourse within the discourse’ to be the centre of Apel's language-pragmatic ‘Transformation of Philosophy’ (Frankfurt a.M. 1973). Beginning with an explication of the situation of a speaker/thinker, especially of the situation of a philosophising speaker/thinker, Apel reconstructs a two fold apriori of communication: Every thought is situated within the context of a particular, historically evolved, community of language and interaction. At the same time, however, the validity-claims of thoughts transcend the context of their origin towards an unlimited community of argumentation. On the basis of the first apriori Apel criticises the methodical solipsism as well as the objectivism of modern philosophy and theory of science. Drawing upon the second apriori he develops a universalist critique of meaning of relativism and contextualism. In the sixties and seventies Apel worked out a differentiated theory of the – more or less – communicatively cognizing humanities and set it apart from the theory of the causal-explanatory natural sciences, thus challenging the objectivism of a Theory of Unified Science. Building upon this work Transcendental Pragmatics, as developed by Apel and others, sets philosophy primarily two tasks: firstly, a (fallible) internal reconstruction of argumentative discourse as the (logical) situation of speech and thought which seeks to elucidate the conditions of the meaningfulness, i. e. the presuppositions, of discourse. These presuppositions comprise, thus Apel with Habermas, the four validity-claims to intelligibility, sincerety/credibility, truth and normative rightness/legitimacy. Their moral content consists, thus Apel, not only in the recognition of the equality of all beings capable of discursive reasoning but also in their recognition of a co-responsibility for the realizability of discourses and of responsibility. The author argues that the existence of a co-responsibility of this kind is indisputable because the discursive claims to validity are intertwined with a set of ‘primordial promises of dialogue’. Only with the elucidation and explication of these promises can the reconstruction of the internal conditions of discourse be completed.The second task of a pragmatics of argumentation isthe strict resp. actual reflection of the thinker upon the presuppositions of the discourse in which he currently engages. This reflection has a Socratic character and can only be done in the form of discussion and debate (‘Auseinandersetzungen’, Apel, Frankfurt a.M. 1998) with critics of the reconstruction. In this context, the author proposes a method of Socratic reflection upon the presuppositions of dialogue which suspends the usual, theoretically oriented, attitude of the scientist and the philosopher in favour of an actual reflective attitude. Within a dialogue with a sceptic who doubts one of the results of the internal reconstruction of dialogical presuppositions, say X, it is tested whether his doubt as to the unrestricted validity of X can be understood as a sincere contribution to the current dialogue or whether this particular sceptical thesis does not make sense, because it is incompatible with the role of a sincere participant of argumentation which, after all, the sceptic cannot refuse to claim for himself.Finally the author explains Apel's characterization of the tension between “Discourse and Responsibility” (Frankfurt a.M. 1988). In the course of discussions with Max Weber, Lawrence Kohlberg, Hans Jonas et al., Apel formulates and justifies an ethics of responsibility and gives an affirmative answer to the crucial question of whether the fulfilment of the moral obligations connected with the recognition of co-responsibility can be demanded within the non-dialogical circumstances of social reality. Apel's answer employs the idea of counter-strategies which are morally legitimate in virtue of their being worthy of argumentative consensus. This revised version was published online in August 2006 with corrections to the Cover Date.     

What is Classical and Non-Classical Knowledge?

Mamardašvili’s ‘classical’ paradigm of knowledge is seen to be minimally based on extrapolations from Descartes’ classical philosophy to which Mamardašvili attributes features that rather anticipate his own post-classical ontology. The latter is oriented towards the primacy of perception as a subjective process, in which the self-conscious subject constructs the world, not as illusion, but as a ‘picture’ or ‘model’ (Wittgenstein’s Bild). By examining Mamardašvili’s definition of the ‘phenomenon’ against the␣background of Husserl’s ‘reduction’, Wittgenstein’s ‘object’ and the Freudian and post-structuralist psychoanalytic model of subjectivity, the paper arrives at the inference that Mamardašvili is essentially a post-Structuralist thinker who appropriates concepts from various critical and philosophical disciplines to construct his own multi-disciplinary theory of consciousness and perception.     

Trustworthiness in explanation: The obligation to explain well

‘Scientific integrity’ certainly requires that data and references be beyond reproach. However, issues within the theory of scientific explanation suggest that there may be more to it than just this. While it is true that some contemporary, pragmatic analyses of explanation suffer from the ‘problem of relevance’ (an inability to ensure that explanations which are paradigmatic technically are relevant to the question being posed), it does not seem to be true that the addition of formal, metaphysical constraints is necessary to solve this problem. I argue that, when viewed as requests for help with an epistemic problem, explanation-seeking questions reveal the existence of a set of moral criteria centered in trust which, when satisfied, prevent trivial or irrelevant explanations from being offered, thereby broadening the concept of ‘scientific integrity’.     

The transmission of support: a Bayesian re-analysis

Crispin Wright’s discussion of the notion of ‘transmission-failure’ promises to have important philosophical ramifications, both in epistemology and beyond. This paper offers a precise, formal characterisation of the concept within a Bayesian framework. The interpretation given avoids the serious shortcomings of a recent alternative proposal due to Samir Okasha.     

The information in intuitionistic logic

Issues about information spring up wherever one scratches the surface of logic. Here is a case that raises delicate issues of ‘factual’ versus ‘procedural’ information, or ‘statics’ versus ‘dynamics’. What does intuitionistic logic, perhaps the earliest source of informational and procedural thinking in contemporary logic, really tell us about information? How does its view relate to its ‘cousin’ epistemic logic? We discuss connections between intuitionistic models and recent protocol models for dynamic-epistemic logic, as well as more general issues that emerge.     

Realismbei Frege: Reply to Burge

Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings — interpretations on which these claims receive a very different reading. In Frege on Knowing the Third Realm, Tyler Burge attempts to undermine this trend. Burge argues that Frege is the very Platonist most have thought him — that revisionist interpretations of Frege's Platonism, mine among them, run afoul of the words on Frege's pages. This paper is a response to Burge's criticisms. I argue that my interpretation is more faithful than Burge's to Frege's texts.     

Buddhist Idealism,Epistemic and Otherwise: Thoughts on the Alternating Perspectives of Dharmakīrti

Some influential interpreters of Dharmakīrti have suggested understanding his thought in terms of a ‘sliding scale of analysis.’ Here it is argued that this emphasis on Dharmakīrti's alternating philosophical perspectives, though helpful in important respects, obscures the close connection between the two views in play (identified by later commentators as ‘Sautrāntika’ and ‘Yogācāra’). Indeed, with respect to these perspectives as Dharmakīrti develops them, the epistemology is the same either way. Insofar as that is right, John Dunne's characterization of Dharmakīrti's Yogācāra as ‘epistemic idealism’ may not, after all, distinguish this perspective from Sautrāntika; indeed, epistemic idealism can be understood as just the view these positions share. Thus, what distinguishes the ‘Yogācāra’ section of Dharmakīrti's texts is simply his making explicit that epistemological commitments the Sautrāntika does (or at least can coherently) hold are already compatible with idealism. Sautrāntika and Yogācāra thus differ only when one turns to the metaphysical arguments that (on the idealist's view) additionally show that only such mental things as sense data could be real.

Portraits in painting and photography

In this paper, we offer an analysis of ‘group intentions.’ On our proposal, group intentions should be understood as a state of equilibrium among the beliefs of the members of a group. Although the discussion in this paper is non-technical, the equilibrium concept is drawn from the formal theory of interactive epistemology due to Robert Aumann. The goal of this paper is to provide an analysis of group intentions that is informed by important work in economics and formal epistemology.     

Beyond Descartes: Panpsychism Revisited

For some two millennia, Western civilization has predominantly viewed mind and consciousness as the private domain of the human species. Some have been willing to extend these qualities to certain animals. And there has been a small but very significant minority of philosophers who have argued that the processes of mind are universal in extent, and resident in all material things – the concept of panpsychism. The traditional ‘man-alone’, or ‘man-and-higher-animals’, views of mind have come under increasing criticism of late, and their philosophical weaknesses seem increasingly insurmountable. This has caused some thinkers to reexamine the ancient and venerable concept of panpsychism, and to apply it anew in contemporary theories of mind. The present essay reintroduces panpsychism, and demonstrates something of its legacy in Western thought.     

Ernst Cassirer as cultural scientist

The article investigates Cassirer’s developing interest in the cultural sciences to display how his Philosophy of Symbolic Forms constitutes a philosophy of culture. The core concept in such a philosophy of culture is the symbolic formation that both possesses a structured-structuring dimension and appears as an historical process in which culture shows itself as a temporal creation. The philosophy of culture displays ‘life in meaning’, that is reality as it exhibits human reality manifested in and through the medium of linguistic, artistic, religious, scientific “and so on” action and behaviour. This reality, therefore, is mediation between culture and nature through human spirit. Cassirer’s philosophy of culture connects back to Kant’s transcendental idealism by emphasizing that any concept of reality establishes itself through a modalization of reality, e.g. that reality constitutes itself in the mode of interpretation. This makes the basis for Cassirer’s characteristic understanding of hermeneutics where cultural development is regarded as drama.