This book consists of seven chapters containing multiple questions of the global socially epistemological situation in science and higher education. Despite the progress of techno-sciences, we are facing blind flaws in leading systems of knowledge and perception. The global era, in a paradox way, connects the new knowledge of economics, postpolitics, postdemocracy, and biopolitical regulation of live and unpresentable forms of the global geo-located violence. Techno-optimism and techno-dictatorship in the twenty-first century coincide with the ideology of market, biopolitics of mandatory (...) satisfaction, religious revivalism, and collapse of higher education. In order for sciences to recover, it is necessary to make a globally epistemological and moral turn toward the truth. The book shows that, when joint desires of the new economics of knowledge and technology erase epistemology (in a way to assign definitions of knowledge and rules and practices of the public usage of the mind), then the time for epistemology is on its way"--https://www.intechopen.com/books/epistemology-and-transformation-of-knowledge-in-global-age, accessed 06/07/2020. (shrink)

Departing from Levinas, this paper will address the significance of shame in contemporary discourse in order to approach what could be called its ethical intrigue. Focusing on its political, social and phenomenological implications, I intend to reconsider the experience of shame as it has been appropriated within the politics of affect and account for its relation to ethics, which alone can reveal its transformative possibilities. Shame will emerge as an affect of proximity whose basic structure of being exposed is an (...) attestation of our constitutive openness to others that towers above the politics of interest and the structures of economy that advance the drama of the Ego. (shrink)

Departing from what Levey and Sznaider (2002) in their seminal work ‘Memory Unbound’ refer to as ‘cosmopolitan memory’ that emerges as one of the fundamental forms ‘collective memories take in the age of globalization’, this article will consider the underlying ethical implications of global memory formation that have yet to be adequately theorized. Since global disseminations of local memory cultures and the implicit canonization of its traumas are intimately related to the concept of archive, I will first focus on what (...) Derrida (1996) in Archive Fever calls ‘archival violence’ and will show its inherent relation to the formation of cosmopolitan memory. Another related concept that I will use and that will problematize the transformation of living, embodied memory into archival, cultural memory upon which the formation of cosmopolitan memory depends is the witness. Using Agamben’s writing (2002) in this context that in Remnants of Auschwitz focuses on the foundational (im)possibilities of bearing witness, I will show that this transformation that determines the very possibility of cosmopolitan memory is far from unproblematic and readily accessible as Levy and Sznaider seem to assume. What will emerge as the most distinctive concern of global memory formation is the ethical material of difference as that which both makes its imperatives historically and politically exigent and that which signifies the difficulties of its unified articulation. Solidarity with the suffering of the other that mobilizes the very formation of cosmopolitan memory is also what should solicit vigilance against the universalistic ritualizations of its prerogatives. (shrink)

The notion of strictly primitive recursive realizability is further investigated, and the realizable prenex sentences, which coincide with primitive recursive truths of classical arithmetic, are characterized as precisely those provable in transfinite progressions over a fragment of intuitionistic arithmetic. The progressions are based on uniform reflection principles of bounded complexity iterated along initial segments of a primitive recursively formulated system of notations for constructive ordinals. A semiformal system closed under a primitive recursively restricted -rule is described and proved equivalent to (...) the transfinite progressions with respect to the prenex sentences. (shrink)

We study a hierarchy of Kalmàr elementary functions on integers based on a classification of LOOP programs of limited complexity, namely those in which the depth of nestings of LOOP commands does not exceed two. It is proved that -place functions in can be enumerated by a single function in , and that the resulting hierarchy of elementary predicates (i.e., functions with 0,1-values) is proper in that there are predicates that are not in . Along the way the rudimentary predicates (...) of Smullyan are classified as. (shrink)

We’re tired of trees. We should stop believing in trees, roots, and radicles. They’ve made us suffer too much [ … ] Nothing is beautiful or loving or political aside from underground stems and aeri...

An elementary theory of concatenation,QT+, is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, quantifier-free part of Kirby’s finitary set theory, and Adjunctive Set Theory, with or without extensionality. The most basic arithmetic and simplest set theory thus turn out to be variants of string theory.

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...) 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

A new method of "minimal" realizability is proposed and applied to show that the definable functions of Heyting arithmetic (HA)--functions f such that HA $\vdash \forall x\exists!yA(x, y)\Rightarrow$ for all m, A(m, f(m)) is true, where A(x, y) may be an arbitrary formula of L(HA) with only x, y free--are precisely the provably recursive functions of the classical Peano arithmetic (PA), i.e., the $ -recursive functions. It is proved that, for prenex sentences provable in HA, Skolem functions may always be (...) chosen to be $ -recursive. The method is extended to intuitionistic finite-type arithmetic, HA ω 0 , and elementary analysis. Generalized forms of Kreisel's characterization of the provably recursive functions of PA and of the no-counterexample-interpretation for PA are consequently derived. (shrink)

A realizability notion that employs only primitive recursive functions is defined, and, relative to it, the soundness of the fragment of Heyting Arithmetic (HA) in which induction is restricted to Σ 0 1 formulae is proved. A dual concept of falsifiability is proposed and an analogous soundness result is established for a further restricted fragment of HA.

A realizability notion that employs only Kalmar elementary functions is defined, and, relative to it, the soundness of EA-(Π₁⁰-IR), a fragment of Heyting Arithmetic (HA) with names and axioms for all elementary functions and induction rule restricted to Π₁⁰ formulae, is proved. As a corollary, it is proved that the provably recursive functions of EA-(Π₁⁰-IR) are precisely the elementary functions. Elementary realizability is proposed as a model of strict arithmetic constructivism, which allows only those constructive procedures for which the amount (...) of computational resources required can be bounded in advance. (shrink)

Kristiansen and Murwanashyaka recently proved that Robinson arithmetic, Q, is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory QT+, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings, and sets. We also introduce a “hybrid” elementary theory of strings and trees, WQT*, and establish its mutual interpretability with Robinson’s weak (...) arithmetic R, the weak theory of trees WT of Kristiansen and Murwanashyaka, and the weak concatenation theory WTCε of Higuchi and Horihata. (shrink)

The thesis critically examines the question of the philosophical coherence of finitism, the view which seeks to interpret mathematics without postulating an actual infinity of mathematical objects. It is argued that a widely accepted characterization of finitism, most recently expounded by Tait, is inadequate, and a new characterization based on the notion of elementary abstraction is proposed. It is further argued that the notion of elementary abstraction better explains the bearing of Godel's incompleteness theorems on the issue of the coherence (...) of finitism. By abstraction is meant a procedure by which one recognizes or establishes that some infinite process exhibits a distinctive uniformity. If the procedure does not require one to conceive of the integers in any other way than as the result of simple iterations, we call such abstraction elementary. Some six different formal models exploring a variety of different ways in which this notion can be made precise are proposed as possible formal characterizations of finitistic truth. It is proved that all these different models are equivalent with respect to finitistically meaningful sentences. This is taken as strong evidence that the notion of elementary abstraction is determinate enough to provide a basis for a coherent philosophical formulation of finitism. (shrink)

Seventeenth-century advancements in physical science are often presented as overthrowing the Aristotelian tradition; perhaps Aristotle's emphasis on formal and final causes left little room for a physical theory grounded in material and efficient causes. In Aristotle's Science of Matter and Motion, Christopher Byrne argues that Aristotle is not to blame, as he indeed possessed a unified theory of matter and motion. In contrast to traditional interpretations, which place an undue explanatory burden on formal and final causes, Byrne argues that Aristotle's (...) theory of the physical world is dependent on the features possessed by perceptible objects, qua perceptible, as well as non-teleological changes in matter.Byrne's... (shrink)

In On Generation and Corruption 1. 10 and 2. 7 Aristotle discusses mixing and mixtures. Recent scholars tend to read the two texts together, thus treating the production of homoeomers in GC 2. 7 as a process of mixing the material elements. I argue that the tendency to treat homoeomers as mixtures of material elements is incorrect: GC 1. 10 explains the mixing of bodies that have already been produced from the elements, whereas GC 2. 7 explains the processes that (...) produce compound bodies from simpler constituents. In GC 2. 7 only the primary contraries mix in the formation of a homoeomer: material elements cannot be constituents of mixtures for theoretical and physical reasons. This makes sense of the production of homoeomers in GC 2. 7 despite worries about mixing the material elements. For Aristotle, the production of homoeomers is simultaneously a process of mixing the primary contraries and generating the homoeomers from the destruction of material elements. (shrink)

according to a certain interpretative tradition, Aristotle is committed to prime matter—an indefinite, indeterminate, and unknowable material substratum that exists as pure potentiality and underlies, among other features, the elements and their mutual transformations.1 This interpretative tradition has come under attack from various sources; among such sources are those who wish to deny Aristotle’s commitment to a material substratum that is ontologically more basic than the elements, and who instead affirm the conclusion that Aristotle’s account of nature and change does (...) not require prime matter.2A different objection to the interpretative tradition is voiced by those who wish to maintain Aristotle’s commitment... (shrink)

A nonlocal equation of motion with damping is derived by means of a Mori-Zwanzig renormalization process. The treatment is analogous to that of Mori in deriving the Langevin equation. For the case of electrodynamics, a local approximation yields the Lorentz equation; a relativistic generalization gives the Lorentz-Dirac equation. No self-acceleration or self-mass difficulties occur in the classical treatment, although runaway solutions are not eliminated. The nonrelativistic quantum case does not exhibit runaways, however, provided one remains within a weak damping approximation. (...) The correspondence limit shows that a classical limit may be taken, again within the same approximation. (shrink)

In The Powers of Aristotle’s Soul, Thomas Kjeller Johansen offers a fresh treatment of Aristotle’s De Anima, showing that Aristotle can successfully explain the cause of life and activities of living things by appealing to a minimal number of definitionally independent capacities, in much the way that a faculty psychologist would. Johansen situates Aristotle’s account of the soul within the framework of his natural philosophy, arguing that the definitional independence of the soul’s capacities does not conflict with the internal unity (...) of the soul. In doing so, he offers explanations of the further abilities and capacities of the soul, including phantasia and locomotion.In the first eight chapters of the book .. (shrink)

This article analyzes the fundamental aesthetic views of two major representatives of European culture, the Croation Juraj Krizanic and the Moldavian Nicolai Spatarul, who worked in Russia in the second half of the 17th century, and who through their works made it possible for Russian culture of the time to adopt the ideas of Western European aesthetics. (edited).