Essays on the Logical

Already in ancient philosophy, there was a transition from the implicit and hidden action of the Logical ( lógos) in nature ( phýsis) to the scientific and explicit expression of the logical structures of thought, action, the world and language. Heraclitus' heno-logic with Logos as hidden implicit principle of homologization of opposites ( tà enantía) in nature differs from Parmenides' paraconsistent logic developed in a hypothetical hemidyalectics given in the formula ''All is One'' ( hén pánta eînai). Plato's concept of dia-logic (dialektikè téchne ) with a new concept of Logos as the one genus of beings ( hén tí génon toôn ontoôn) in which the word not-Being (negation) got its place enabled production of dyadic logical structure by the granulation of genera into opposite species and sub-species that it contains. Aristotle's concept of triadic-logic as syl-logistics ( syllogismós) and demonstrative science (epistéme apodeiktikê ) give a new approach by new granulation of the concept of Logos into triadic logical structure: (1) the structure of being (substratum-attributes relation), (2) the structure of thought (substance-second substances relation), and (3) the structure of propositions (subject-predicate relation). Plato's dialectic and Aristotle's syllogistic both deconstructed the implicit ontological unity of the world (pan, kosmos, sphairos ) given through the concept of Logos in Pre-Socratic philosophy in order to make that unity in explicit form given by the logical and semantical structures of the propositions about the world, about the thought and about the language. The hidden implicit of the nature, which had to be known intuitively, was transformed into unhidden explicit inferential logical structures given in the semantics and pragmatics of scientific demonstration

Ancient Logic and its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972

Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic

Oral Performance and the Veil of Text:Detextification, Paul's Letters, and the Testcase of Galatians 2-3

It is now common opinion that the biblical documents functioned in an oral context dominated by the spoken word. The present study centres on the letters of Paul, especially Galatians, and addresses the complex relation between this functioning in the original oral setting and the daily praxis of current biblical scholarship in which these documents function as autonomous texts, detached from the context of its original oral delivery. It will be argued that in addition to the difference in media (oral performance there-and-then versus reading the text here-and-now) it is crucial to differentiate the mindsets involved. A highly literate reader in the present structures thought differently from someone in the past who is formed by oral-aural communication. The leading question of this investigation is: How can a biblical scholar here-and-now relate to the text of the letters of Paul (in a printed or digital version) in such a way that he or she can understand (in the typically accompanying highly literate mindset) how the apostle envisioned his original addressees to understand (in their rather unfamiliar oral mindset) the documented words in the event of delivery? It is argued that by textualizing history and historicizing text a detextification of our understanding of these ancient documents is possible. Two testcases of detextification are provided, viz. Gal 3.10–12, in which the presence of a self-evident and simple enthymematic (syllogistic) reasoning is put to the test, and Gal 2.18–20, in which it is argued that Paul counters the call to circumcision by his opponents by a recalling of the baptism of the Galatian converts

Logika, forma a argument

The goal of this thesis is to defend and explain the claim that traditional logical analysis is not the best tool for studying natural language argumentation. The most common critique directed at employment of logical formalisms as tools for analysis of the natural language is usually based on pointing out of differences between structure and semantics of natural languages and languages of logical formalisms. This is not the main issue, I believe. According to my findings the most fundamental problem of the traditional analysis is that it is based on many problematic epistemological assumptions, which are inherited from empiricist-positivist tradition. Namely the positivist version of the classical model of rationality as deductive reasoning from some basis of immediately verifiable and therefore unquestionable knowledge. The doctrine that every reasonable argumentation is reducible on deductions of such kinds is supposed to justify the traditional analysis of argumentation. My original contribution is mainly in showing that without abandoning those presuppositions, we cannot hope to arrive at better understanding of natural language argumentation by developing new and more precise logical formalisms. Logical formalisms are mere tools, which we have to use for the right purpose in the first place....Cílem mé disertace je obhájit a vysvětlit tezi, že tradiční logická analýza není vhodným nástrojem ke zkoumání argumentace v přirozeném jazyce. Nejčastější kritika formální logiky jako nástroje pro analýzu přirozeného jazyka je obvykle založena na poukázování na podstatné rozdíly mezi strukturou a sémantikou jazyků přirozených a jazyků logických formalismů. V tom však nevidím hlavní zdroj problémů. Podle mého úsudku je daleko zásadnějším problémem, že tradiční logická analýza často vychází z problematických epistemologických předpokladů, které analytická filosife zdědila z empiristicko- positivistické tradice. Jedná se především o pozitivistickou verzi klasického modelu racionality, jako deduktivního usuzování z nějaké báze bezprostředně ověřitelných a nepochybných poznatků. Přesvědčení, že každou rozumnou argumentaci lze redukovat na dedukci takového druhu je tím, co má ospravedlnit tradiční logickou analýzu. Můj přínos spočívá především v prokázání toho, že nezměníme-li zásadně tato východiska, pak nám pranic nepomůže, budeme-li zkoušet argumentaci v přirozeném jazyce analyzovat pomocí nových a přesnějších logických formaismů. Problém tedy není ani tak v samotném nástroji, jako spíše ve způsobu jeho užití. Pokud dostatečně zreflektujeme roli demonstrativního usuzování pro argumentaci jako...Department of LogicKatedra logikyFilozofická fakultaFaculty of Art

Signs In Time: The Hypothesis Of Social Time For A Cultural Semiotic Analysis

http://www.ester.ee/record=b4482490*es

Automated Validation of State-Based Client-Centric Isolation with TLA ⁺

Clear consistency guarantees on data are paramount for the design and implementation of distributed systems. When implementing distributed applications, developers require approaches to verify the data consistency guarantees of an implementation choice. Crooks et al. define a state-based and client-centric model of database isolation. This paper formalizes this state-based model in, reproduces their examples and shows how to model check runtime traces and algorithms with this formalization. The formalized model in enables semi-automatic model checking for different implementation alternatives for transactional operations and allows checking of conformance to isolation levels. We reproduce examples of the original paper and confirm the isolation guarantees of the combination of the well-known 2-phase locking and 2-phase commit algorithms. Using model checking this formalization can also help finding bugs in incorrect specifications. This improves feasibility of automated checking of isolation guarantees in synthesized synchronization implementations and it provides an environment for experimenting with new designs.</p

Collection and division in Plato’s Dialogues

Plato describes a way of reasoning that comprises two complementary operations, collection and division. Collection unifies many into one while division divides one into many. In other words, while collection brings together many parts into a whole, division divides a whole into many parts. While Plato goes into some detail in his observations on collection and division, several questions remain unanswered. More specifically, the means by which collection and division operate, their product, and their relation to deductive and non-deductive reasoning are uncertain. The purpose of this study is to shed light on collection and division by defending the following thesis: collection and division define logical frameworks that underlie both deductive and non-deductive reasoning. Chapter 1 will introduce collection and division by reviewing recent literature, defining key terms, and discussing illustrations of collection and division in the dialogues. Chapter 2 will explain how collection and division define logical frameworks through three operations: seeing, naming, and placing. These operations will be discussed in terms of their relations to reasoning about wholes and parts. Chapter 3 will present four models for interpreting the logical structures that are produced by collection and division. It will present the argument that collection and division define non-hierarchical structures of overlapping parts. Chapter 4 will present the argument that collection and division define whole-part relations that underlie deductive reasoning on the one hand, and the formulation of definitions in dialogues such as the Sophist and the Statesman on the other. Chapter 5 will explore the relation between collection and division and non-deductive reasoning. It will present the argument that Meno’s definition of virtue and Euthyphro’s definition of piety are formulated using collection and division. Chapter 6 will provide a summary of key points from the preceding chapters and discuss unanswered questions and avenues for future research

Exploring the landscapes of "computing": digital, neuromorphic, unconventional -- and beyond

The acceleration race of digital computing technologies seems to be steering toward impasses -- technological, economical and environmental -- a condition that has spurred research efforts in alternative, "neuromorphic" (brain-like) computing technologies. Furthermore, since decades the idea of exploiting nonlinear physical phenomena "directly" for non-digital computing has been explored under names like "unconventional computing", "natural computing", "physical computing", or "in-materio computing". This has been taking place in niches which are small compared to other sectors of computer science. In this paper I stake out the grounds of how a general concept of "computing" can be developed which comprises digital, neuromorphic, unconventional and possible future "computing" paradigms. The main contribution of this paper is a wide-scope survey of existing formal conceptualizations of "computing". The survey inspects approaches rooted in three different kinds of background mathematics: discrete-symbolic formalisms, probabilistic modeling, and dynamical-systems oriented views. It turns out that different choices of background mathematics lead to decisively different understandings of what "computing" is. Across all of this diversity, a unifying coordinate system for theorizing about "computing" can be distilled. Within these coordinates I locate anchor points for a foundational formal theory of a future computing-engineering discipline that includes, but will reach beyond, digital and neuromorphic computing.Comment: An extended and carefully revised version of this manuscript has now (March 2021) been published as "Toward a generalized theory comprising digital, neuromorphic, and unconventional computing" in the new open-access journal Neuromorphic Computing and Engineerin