Comment on “Dependency distance: a new perspective on syntactic patterns in natural language” by Haitao Liu et al

Whitehead’s special relativistic reformulation of Einstein’s general relativistic theory of gravitation is quite close to Einstein’s 1915–1916 original with regard to mathematical formulae and empirical tests. Only highly sophisticated contemporary tests (such as the ones highlighted by Gary Gibbons and Clifford Will1 ) reveal that the two theories are not empirically equivalent, and justify physicists to favor Einstein’s theory with regard to experimental success. However, Whitehead’s 1920–1922 alternative came out of season for the physicist, and hence, it never played a significant role in the history of physics. Allowing for a common sense interpretation, its importance is mainly philosophical, but the philosophical interpretation of Whitehead’s theory is not included in the scope of the present paper.

Bourbaki nos enseñó el potencial que guarda el concepto de estructura matemática para reorganizar, sistematizar y unificar el entramado matemático. Pero la evolución de la matemática, en las últimas décadas deja patente las limitaciones de este enfoque. En este artículo analizamos las contribuciones de Bourbaki a lo que denominamos fundamentación “interna” de la matemática y señalamos, a su vez, las que a nuestro juicio son sus principales carencias. A continuación bosquejamos brevemente algunas evidencias sobre las que sustentamos la perspectiva denominada funcionalismo estructuralista. Según ésta, la noción general de morfismo caracteriza la naturaleza dinámica de la matemática actual.

In the early twentieth century, L.E.J. Brouwer pioneered a new philosophy of mathematics, called intuitionism. Intuitionism was revolutionary in many respects but stands out -mathematically speaking- for its challenge of Hilbert’s formalist philosophy of mathematics and rejection of the law of excluded middle from the ‘classical’ logic used in mainstream mathematics. Out of intuitionism grew intuitionistic logic and the associated Brouwer-Heyting-Kolmogorov interpretation by which ‘there exists x’ intuitively means ‘an algorithm to compute x is given’. A number of schools of constructive mathematics were developed, inspired by Brouwer’s intuitionism and invariably based on intuitionistic logic, but with varying interpretations of what constitutes an algorithm. This paper deals with the dichotomy between constructive and non-constructive mathematics, or rather the absence of such an ‘excluded middle’.

In this article we analyze the key concept of Hilbert’s axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert’s foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert’s ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call “Frege’s Problem”, form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

In one perspective, the central problem pursued in this research is that of the inverse problem in the context of general rough sets. The problem is about the existence of rough basis for given approximations in a context. Granular operator spaces were recently introduced by the present author as an optimal framework for anti-chain based algebraic semantics of general rough sets and the inverse problem. In the framework, various subtypes of crisp and non crisp objects are identifiable that may be missed in more restrictive formalism. This is also because in the latter cases the concept of complementation and negation are taken for granted. This opens the door for a general approach to dialectical rough sets building on previous work of the present author and figures of opposition. In this paper dialectical rough logics are developed from a semantic perspective, concept of dialectical predicates is formalized, connection with dialethias and glutty negation established, parthood analyzed and studied from the point of view of classical and dialectical figures of opposition

Rome had always been the eternal caput mundi, after all, and almost three millennia of history had attested to the fact of the city’s grandeur. The idea of Rome finds itself imbued within the works of countless poets, philosophers, monarchs, and theologians, writing and thinking throughout the passing ages. Saint Augustine in the fifth century, sitting in his study in Hippo and listening with dread to the war cries of the approaching Vandal hordes, fought to his last breath to understand the collapsing Roman world around him. Charlemagne, a Germanic king of the Franks, accepted nothing short of a revived Rome, and became the progenitor of a political body in the year 800 that turned out to be a non-holy, non-Roman, non-empire, despite its name. Dante voyaged both in literature and life at the outset of the fourteenth century, and shed tears at the fact that the Roman poet Virgil could never join him in the heavenly realm.

The problem of present is analyzed as a reality given to man. First, the impersonal character of time is studied in its contradictory condition of opening place of giving: when present appears, there is not a giver, nor a receiver. In the second place, by considering the etymological sense of the French word “maintenant”, it is showed that the “now” is a nullity between past and future, a dual interstice in which everything is reached or lost. Following the Kantian conception of time and the Derridian notion of “donation”, the author highlights that the “now” is immediate receptivity, intuitive and not conceptual: in the present, man gives himself to himself and receives himself from himself. The present, at the same time that it constitutes the space of identity, it is also the vector of difference: when it becomes a sign to himself of himself, the present appears as his own alterity.

There is a surprising variety of programs in the philosophy and foundations of mathematics that have found mereology a useful and, in some cases, an indispensable tool. After emphasizing a number of key relevant features of mereology, we will brie.y examine four such programs, including (1) Goodman and Quine.s efforts to recover syntax of mathematical language as part of a .nitist, formalist philosophy of mathematics; (2) Field.s and Burgess.”synthetic mechanics” as an effort to recover nominalistically certain applications of mathematics in physics inspired by synthetic geometry; (3) Lewis.attempt to ground set theory on a combination of mereology and plural logic, which he called “megethology” (theory of size); (4) Hellman.s modal-structuralism employing the same machinery as (3) Together with modal logic, but to provide an eliminative structuralist alternative to platonist, face-value readings of abstract mathemtical theories.

The present discussion concerning certain fundamental physical theories (such as string theory and multiverse cosmology) has reopened the demarcation problem between science and non-science. While parts of the physics community see the situation as a beginning epistemic shift in what defines science, others deny that the traditional criterion of empirical testability can or should be changed. As demonstrated by the history of physics, it is not the first time that drastic revisions of theory assessment have been proposed. Although historical reflection has little to offer modern physicists in a technical sense, it does offer a broader and more nuanced perspective on the present debate. This paper suggests that history of science is of some indirect value to modern physicists and philosophers dealing with string theory, multiverse scenarios, and related theoretical ideas.