Between Truth and Relativism: the Choice of Psychoanalysis

My aim in this paper is to draw attention to the position of psychoanalysis regarding the opposition between the quest for truth and relativism. It is a conventional opposition of contemporary thought. On one hand, the quest for truth, and on the other, relativism, as the fundament of our intellectual and political life. I do this by means of Lacanian teachings. My objective is to take on the theoretical tools of psychoanalysis and the consequences of clinical facts, in order to enable a critical reflection on this topic. Before proceeding to the precise argument, I briefly introduce the historical ground correlated to modern subjectivity, characterized by the vanishing of the guarantee of both truth and knowledge. Then I then go into the topic by means of a survey of Lacan’s reading of the path of modern logic. Lacan interprets the whole history of logic as a bungled action, “every bungled action is a successful discourse.” In fact, it points to the cardinal place of lack, which is the topic of psychoanalysis. It opens towards a deeper understanding of the role of the signifier of signification – the Bedeutung des Phallus. Lacan’s interpretation of the whole history of logic transforms the achievements of modern logical thought into the writings of a point de capiton for collective rationality. The key here is to focus on the capital role of what I call in conclusion “an inaccessible point” for both individual and collective life. This is the issue I address in the last point. The article is divided into five points: 1. the relativistic drift; 2. the guarantee of knowledge; 3. the guarantee of truth; 4. logic and point de capiton; and 5. the signification (Bedeutung) of the Phallus

METAFISIKA SUBSTANSI ILMU LOGIKA

remains necessary to guide to think and to have valid conclusion in daily life. Good and wise deed could be created from a process of thinking and concluding that are simply right and true. To comprehend Logic as a science from the perspective of substantial metaphysics, it is essential to recognize the focus of the problems as framework. The focus of the problems are 1) is Logic a substance? 2) Which one is the aspect of relation-autonomy in Logic? 3)  Which one is the aspect of renewable-permanence in Logic? 4) Which one is the aspect of transedence-imanence in Logic? 5) What is the essence of Logic in term of normative-ontological-transcendent? This is a library research that collected the whole data from library data. The researcher, as the main instrument, highly determines the data that must be firstly gathered. The early data give direction about aspects that must be studied from the library resources hence it is able to clarify the research map in accordance with formal object and research materials. The result indicates that firstly, Logic that is on the basis of metaphysic-substance perspective is a substance containing the aspects of autonomy relation, permanence-renewable, and immanence-transcendence. Secondly, the aspect of logic autonomy, it is a direct and indirect conclusion drawing as truth form. The relation aspect of logic is the epistemology as material truth. Thirdly, the aspect of permanence of logic, it is the basic principles of thought that are divided into four fundamental principles. The renewable aspect of logic has been the history of logic development. Fourthly, the immanence aspect of logic is proposition. The transience aspect of logic is term of comprehension and existence. Fifthly, the development of logic that relies on the analysis of logic essence on the way of normative-ontology-transcendental must produce a syllabus of Logic that focus on containing the aspects of autonomy relation, permanence-renewable, and immanence-transcendence. Those aspects are the consequences of Logic from the perspective of substance metaphysics

Automatic Proving of Fuzzy Formulae with Fuzzy Logic Programming and SMT

In this paper we deal with propositional fuzzy formulae containing severalpropositional symbols linked with connectives defined in a lattice of truth degrees more complex than Bool. We firstly recall an SMT (Satisfiability Modulo Theories) based method for automatically proving theorems in relevant infinitely valued (including Łukasiewicz and G¨odel) logics. Next, instead of focusing on satisfiability (i.e., proving the existence of at least one model) or unsatisfiability, our interest moves to the problem of finding the whole set of models (with a finite domain) for a given fuzzy formula. We propose an alternative method based on fuzzy logic programming where the formula is conceived as a goal whose derivation tree contains on its leaves all the models of the original formula, by exhaustively interpreting each propositional symbol in all the possible forms according the whole setof values collected on the underlying lattice of truth-degrees

A hierarchy of languages, logics, and mathematical theories

We present mathematics from a foundational perspective as a hierarchy in which each tier consists of a language, a logic, and a mathematical theory. Each tier in the hierarchy subsumes all preceding tiers in the sense that its language, logic, and mathematical theory generalize all preceding languages, logics, and mathematical theories. Starting from the root tier, the mathematical theories in this hierarchy are: combinatory logic restricted to the identity I, combinatory logic, ZFC set theory, constructive type theory, and category theory. The languages of the first four tiers correspond to the languages of the Chomsky hierarchy: in combinatory logic Ix = x gives rise to a regular language; the language generated by S, K in combinatory logic is context-free; first-order logic is context-sensitive; and the typed lambda calculus of type theory is recursively enumerable. The logic of each tier can be characterized in terms of the cardinality of the set of its truth values: combinatory logic restricted to I has 0 truth values, while combinatory logic has 1, first-order logic 2, constructive type theory 3, and categeory theory omega_0. We conjecture that the cardinality of objects whose existence can be established in each tier is bounded; for example, combinatory logic is bounded in this sense by omega_0 and ZFC set theory by the least inaccessible cardinal. We also show that classical recursion theory presents a framework for generating the above hierarchy in terms of the initial functions zero, projection, and successor followed by composition and m-recursion, starting with the zero function I in combinatory logic This paper begins with a theory of glossogenesis, i.e. a theory of the origin of language, since this theory shows that natural language has deep connections to category theory and since it was through these connections that the last tier and ultimately the whole hierarchy were discovered. The discussion covers implications of the hierarchy for mathematics, physics, cosmology, theology, linguistics, extraterrestrial communication, and artificial intelligence

Iteration and Truth: A Fifth "Orientation of Thought"

This article offers a novel interpretation of Jacques Derrida's deconstructive thought in terms of model theory. Taking its cue from Paul Livingston's Politics of Logic, which interprets Derrida as a thinker of inconsistent totalities, the article argues that Livingston's description of Derrida is unable to accommodate certain consistency-driven aspects of Derrida's work. These aspects pertain to Derrida's notion of ”iterability”. The article demonstrates that the context-bound nature of iteration – the altering repetition of any discrete unit of meaning – and Derrida's possibilist view of context – that a context need not be part of the actual world to merit consideration – lead to the possibility of articulating iteration with the model-theoretical notion of truth. In model theory, truth is a relation between a sentence and the class of models in which the sentence is true. Arguing that the same holds for Derrida's iterations and contexts, the article, in presenting the first rigorous truth-definition internal to deconstructive thought, outlines a ”fifth orientation of thought” alongside the four orientations listed in Livingston's book: if, according to Livingston, one can relate the whole of being to the whole of thought in one of four different ways, the aspects of Derrida's work that do not fall within this schema call out for another possible orientation

Buddhist Thought on Emptiness and Category Theory

Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim that four truth values, along with contradiction, are admissible in reasoning. Indra's Net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions which are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of Sunyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of Catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's Net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics

An application for solving truth functions

Nowadays, many technical devices are controlled by logic circuits. These circuits evaluate the situation based on the proposed truth functions, which they then use to perform one of the defined actions. In line with the increasing complexity of individual technical devices, the logic circuits and truth functions are also increasingly complex. For this reason, it makes sense to minimise these functions since they can thereby achieve a simpler technological process and the higher reliability of whole logic systems. This paper describes the Karnaugh Studio application, which resolves the minimisation of these truth functions - and was developed at our faculty (FAI, TBU in Zlín). The minimisation is performed using the Karnaugh Map Method - with support for up to eight variables on input. The application is based on the C++ programming language and the Dear ImGui and Magick++ libraries. Its functionality has been verified on a number of examples. This proved its applicability and ability to be used in the solution of logic circuits in industrial practice. © 2020, Springer Nature Switzerland AG

Language and Logic in Wittgenstein's Tractatus Logico-Philosophicus

This thesis discusses some central aspects of Wittgenstein’s conception of language and logic in his Tractatus Logico-Philosophicus and brings them into relation with the philosophies of Frege and Russell. The main contention is that a fruitful way of understanding the Tractatus is to see it as responding to tensions in Frege’s conception of logic and Russell’s theory of judgement. In the thesis the philosophy of the Tractatus is presented as developing from these two strands of criticism and thus as the culmination of the philosophy of logic and language developed in the early analytic period. Part one examines relevant features of Frege’s philosophy of logic. Besides shedding light on Frege’s philosophy in its own right, it aims at preparing the ground for a discussion of those aspects of the Tractatus’ conception of logic which derive from Wittgenstein’s critical response to Frege. Part two first presents Russell’s early view on truth and judgement, before considering several variants of the multiple relation theory of judgement, devised in opposition to it. Part three discusses the development of Wittgenstein’s conception of language and logic, beginning with Wittgenstein’s criticism of the multiple relation theory and his early theory of sense, seen as containing the seeds of the picture theory of propositions presented in the Tractatus. I then consider the relation between Wittgenstein’s pictorial conception of language and his conception of logic, arguing that Wittgenstein’s understanding of sense in terms of bipolarity grounds his view of logical complexity and of the essence of logic as a whole. This view, I show, is free from the internal tensions that affect Frege’s understanding of the nature of logic