We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.
This paper offers a reconstruction of Alessandro Piccolomini's philosophy of mathematics, and reconstructs the role of Themistius and Averroes in the Renaissance debate on Aristotle's theory of proof. It also describes the interpretative context within which Piccolomini was working in order to show that he was not an isolated figure, but rather that he was fully involved in the debate on mathematics and physics of Italian Aristotelians of his time. The ideas of Lodovico Boccadiferro and Sperone Speroni will be (...) analysed. This paper demonstrates that Piccolomini's attack on the certitude of mathematics was a product of discussions between Aristotelians. (shrink)
Alessandro Ferrara’s The Democratic Horizon: Hyperpluralism and the Renewal of Political Liberalism poses an important challenge to recent defenders of ‘realism’ in political theory and shows that a renewal of Rawlsian ideal theory is possible. Ferrara focuses on the contemporary condition of ‘hyperpluralism’, in which every comprehensive worldview and religion has to admit the equal validity of at least one other conception, and claims that only a ‘pluralist justification of pluralism’ can lead to a genuine revival of the democratic (...) horizon. Naming such a project of democracy the ‘multivariate’ polity, he uses Rawls’ method of conjecture to show how such a justification strategy is possible. I argue that the multivariate polity may attain pluralism but not stability and may fail in securing democratic respect among equal citizens for each other’s point of view. (shrink)
Among the various attempts that have been undertaken today to reformulate critically the idea of European modernism, Alessandro Ferraras book certainly represents one of the most radical. In contrast to other approaches, which rather depart from a competition of various sources of ideas, Ferrara sets forth a single principle that should be able to provide us with an appropriate and future-regarding self-under-standing of the intellectual situation of present modernity. Its key concept is authenticity that, in opposition to all other (...) principles of validity so far, possesses a priority since it brings most clearly to expression who we actually want to be (p. 162ff.). Before I briefly discuss a few questions that are connected with this thesis, I want first to try to understand the claims underpinning the project as a whole. Only then will I thereby be in a position to lay out those points of view that place doubt upon on the whole project. (shrink)
This comment on Alessandro Ferrara’s Democratic Horizon raises questions about his development of ‘conjectural reasoning’ and the democratic virtue of openness as responses to what he calls ‘hyperpluralism’. In order to probe these questions, the article offers an alternative reading of these ideas.
continent. 1.4 (2011): 286—310. This mad play of writing —Stéphane Mallarmé Somewhere in between mathematics and theory, light and dark, physicality and projection, oscillates the poetry of Alessandro De Francesco. The texts hold no periods or commas, not even a capital letter for reference. Each piece stands as an individual construction, and yet the poetry flows in and out of the frame. Images resurface from one poem to the next, haunting the reader with reincarnations of an object lost in (...) the grass or a representation of a pear in a Dutch still life, embedded in cycles of cinematic close ups and multiple dimensions. As a whole, De Francesco’s oeuvre suggests, to use the title of one of his works, a redefinition —linguistic, epistemological, personal. The poem The End (un’agenda) (The End (an agenda)) opens with a quote by literary theorist Maurice Blanchot, which may be translated as follows: Speaking is not seeing. Speaking frees thought from this optical imperative that in the Western tradition, for thousands of years, has subjugated out approach to things, and induced us to think under the guaranty of light or under the threat of its absence. In writing, De Francesco seeks to redefine our approach to things. His poems, like Blanchot’s writings, speak to both illuminate and to obscure. The reader hangs in an absence of reality within language that necessitates an attempt at interpretation, yet renders such a search ultimately futile. De Francesco draws the anonymous images that appear in this poem from the city of Paris, his current home. The fragmented narrative depicts an inner doubt of realness, calling for a confirmation of a physical existence beyond verbalization and cogitation. Cyclical references to film throw into question the reliability of the reality he creates. The light, sometimes red and safe, other times absent and murky, cannot necessarily be trusted as a guaranteed means of illumination. Blanchot’s distinction between language and visualization, and the relationship of each to reality, though linked specifically to The End (un’agenda) , can be a lens through which to read any of the three works that follow. assente obliqua (absent oblique) is composed of descriptions of six still life paintings, ranging from Dutch masterpieces of the seventeenth century to 1960s minimalism. The actual images of the paintings are absent, and the text is the sole source and object of a virtual reality created around the artwork. “Absent oblique” refers to the light source placed outside of the frame, which both informs and distracts viewing of the scene. Although mere description can be unreliable and unsatisfying in its necessary limitation, the representational act of description is shown as more than just a human want. It is a need, a means by which to grapple with an unsure reality. As the illustrations progress, they descend into abstraction and chaos. The precariously placed plate triggers the movement: the bottle bursts and the objects collapse into the movement of a tracking film camera. corpo estraneo in moto ascensionale (foreign body in ascending motion) is prose poetry in action. Its objective tone of description is skewed by the subjectivity of the narrative as horrific images are relayed in fragmented but matter-of-fact manner. A “foreign body” is both a mass of cancerous cells, and a corporeal description, and the poem takes the reader on a journey back and forth between the two, destination unclear. Beyond a questioning of the real, corpo estraneo in moto ascensionale is an examination of the possible. De Francesco’s poetry becomes a camera obscura through which to observe the constant flux of light and dark that blurs our reality. His work is colored by the idea of apo koinou , a Greek term meaning “from the common” that involves a construction of two clauses with a shared word or phrase. Through such melting of meaning, De Francesco creates a fluid ambiguity that is nonetheless grounded in bodily concepts. In assente obliqua , the reader is confronted with a description of a still life that rapidly transforms into a more chilling scene: the membrane of the mushroom in the basket emerges behind the white cloth a body could hide itself that asks for help In the realm of pure description, there is a mushroom that peeks out from behind a white cloth in a basket. Behind the white cloth, too, there could be a body, hiding, asking for help. Such an elision elicits disorienting mistrust in temporality, but also expands the planar possibilities of syntactical meaning. A white cloth is not merely a construct in still life painting, but veil that both shields and reveals potential mysteries. It is a proposed alternative to a traditional Western binary of subjectivity and objectivity. The apo koinou construction is rare in modern English, having slipped out of use after its resurgence in Old English poetry. De Francesco reintroduces this blur of object and subject relations into a modern light. He draws inspiration from a device used by Gruppo 63 founder and avant-garde poet Antonio Porta tended toward repetition of phrases in third person perspective. In Italian, it is perfectly grammatically correct to omit the subject, including only a verb conjugation. Gender, even humanity unknown, the subject dissolves into the action, thus giving to the poetry the power to change the reader’s perception of who or what is actually acting. To further push the relative boundaries of experience, De Francesco expands his written poetry into what he calls “reading environments.” In these sound experiments, De Francesco’s voice reading his poetry is manipulated by real time digital voice processing. The written is transformed to the spoken, and then injected with currents of electric sound. “At each activation of word in the darkness,” (from The End (un’agenda) ) language is permutated into a nonphysical yet all-encompassing being. In these projects, realized all over Europe, De Francesco continues his examination of the word’s potency beyond the page and into an “n-dimensional space,” where the lines between nature and affect are intertwined. To publish excerpts of De Francesco’s oeuvre is to show screen shots of full-length film, to read pull quotes from a philosophy treatise. In these poems, there are questions, not to be answered, but to be questioned again. The words will oscillate in and out of the square construction found in his poems, out of the borders of the page, out of the rectangle of the laptop screen. NOTES (1) Blanchot, Maurice. The Infinite Conversation . Trans. Susan Hanson. Minneapolis: University of Minnesota Press, 1993. 27. EDITORS' NOTE The .pdf above contains about twenty pages of translation and the original Italian poetry. Below we provide only a brief account. The End (an agenda) Parler, ce n’est pas voir. Parler libère la pensée de cette exigence optique qui, dans la tradition occidentale, soumet depuis des millénaires notre approche des choses et nous invite à penser sous la garantie de la lumière ou sous la menace de l’absence de lumière. —Maurice Blanchot in this n-dimensional space i could spy on myself from the cracks while going back and forth from the summer to the wardrobe from the night to the parking lot but something filters in through the half-closed shutters becomes an event enunciation we stay without explanation like parallel curves on the back of a solid growing older she enters the garden always repeats certain phrases the elevator to be redone the neighbor’s music the steps the pavement furls like the leaves of a fern when touched she is framed from behind while she moves rocking she covers distances slowly a bag overflows from the wardrobe something stirs inside but then the suitcase comes open not even by my hand it’s the objects that are starting to filter out the little red haired monster watches idling the appointments written on one of your agendas two years old still seem urgent each letter holds itself upright on the page with flourishes and arabesques each angle has its own geography i’m trying to describe the path the fingers trace on the carpet the zipper takes the opposite route we are suspended on the stairs above the water in the center is the summer seen from above the darkness of the city passes from one headlight to the next the surfaces of our arms cohere and are shiny underneath the blinking of a sign each pore is an open expanse the body dreams the hair gives form to the possible some daring swimmers were throwing themselves into the seine they swam upstream up to the first quay look there could exist behind the screen a room where even when the lamp is out and the curtains drawn even when the suitcase wasn’t closed everything seemed red everything calm construction of a four-dimensional tetrahedron by R. Courant – H. Robbins, What is Mathematics? Oxford University Press, 1941  . (shrink)
[Does the gymnosophist’s reply to Alexander’s question on the origin of time indeed reflect an Indian doctrine?] The episode of Alexander’s interview with the gymnosophists has come down to us in several versions, among which the one in Plutarch’s Vita Alexandri is the most renowned. In this connection, the question arises whether the solutions given by the naked philosophers to the puzzles propounded by Alexander can be shown to reflect genuine Indian doctrines. Challenging Dumézil’s reply in the affirmative, the author (...) contends that they cannot. While most questions and answers are scarcely relevant to the investigation, as being of little (if any) philosophical import, the analysis concentrates on the more significant ones, and especially on the solution offered to the question as to which of the two — day or night — came first. According to Dumézil, the gymnosophist’s answer reported by Plutarch, i. e. that the day came first, by one day, reflects the vedic doctrine of the primeval cosmogonic role of Dawn and Light. Against this may be argued in the first place that such doctrine does not enjoy any prominent status in the Vedas themselves — quite to the contrary, it stands up disadvantegeously to many all-important texts, such as the Nāsadīyasūkta, which assign the primeval status to Darkness — and cannot therefore be regarded as being specifically Indian any more than its opposite. Secondly, it is shown that the Greek tradition is at great variance on this very point, to the extent that all logically conceivable solutions (i. e., precedence of day by one day / day by one night / night by one day / night by one night) are represented in some version or other. This inconsistency appears to stem from the fact that no particular doctrine (Indian or whatever) was envisaged; according to the present author, we have reason to believe that the gymnosophist’s reply was rather meant to set off by means of a paradox the sheer impossibility of a solution (all four alternatives being equivalent to that effect). This interpretation is reinforced by the gymnosophist’s own remark confessing the aporetical nature of his reply, and finally by a further recourse to paradox — this time a variant of the well-known “paradox of the liar” — which the author lays bare in the otherwise inexplicable dénouement of the anecdote. (shrink)
This volume presents thirteen essays on intentionality, with a strong focus on historical issues—nine articles deal with the concepts of intentionality in Spinoza, Leibniz, Bolzano, Brentano, Marty, Husserl, and Pfänder—but also taking into consideration some contemporary issues about intentionality, especially from the perspective of externalism and on the question of collective intentionality. The wide variety of topics, historical periods, and perspectives presented in this volume bears witness to the fact that intentionality is widely acknowledged as a central phenomenon in philosophy (...) of mind, despite the fact that there has thus far been no consensus on the methodology of investigation of this phenomenon—neither in the historical development of the concept, nor in its contemporary use. This may be one reason why the editor refuses to take a stand on how the concept historically developed and on the role played by this concept in contemporary issues. As the editor contends, the his .. (shrink)
In this article I explore the character and importance of a democratic ethos. Ferrara develops such a concept around the idea of ‘openness’ as part of his broader ideal of seeking to foster exemplary expansions of political identity with the goal of better accommodating the ‘hyperpluralism’ polities face today. I argue that ‘openness’ has several drawbacks that hinder its possible functioning in such a role, contending rather that ‘presumptive generosity’ is to be preferred. The latter can contribute more effectively than (...) the former to enhancing Ferrara’s notion of exemplarity. (shrink)