For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. (...) It is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

Since string theory has not been able to explain phenomena to date, it may seem that this confirms Feyerabend's view that there is no "method" of science. And yet, string theory is still the most active research program for quantum gravity. But, compared to other non-falsifiable theories, this has something extra, especially mathematical language, with a clear logic of deductions. Up to a point it can reproduce classical gauge theories and general relativity. And there is (...) hope that in the not too distant future experiments can be developed to test the theory. DOI: 10.13140/RG.2.2.28892.33920. (shrink)

In quantum field theory, the main obstacle is the occurrence of the untreatable infinities in the interactions of the particles due to the possibility of arbitrary distances between the point particles. Strings, as extended objects, provide a better framework, which allows finite calculations. String theory is part of a research program in which point particles in particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through space and interact with one another. (...) The purpose of string theory was to replace elementary particles with one-dimensional strings in order to unify quantum physics and gravity. DOI: 10.13140/RG.2.2.18894.82240. (shrink)

In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical (...) methods of theory assessment given the technological inability to directly test the theory. The appropriate response, according to Dawid, is to acknowledge this development and widen the canons of acceptable scientific methods. As I’ll argue, however, the current situation in fundamental physics does not require either of these responses. Rather, as I’ll suggest, much of the controversy stems from a failure to properly distinguish the “context of justification” from the “context of pursuit”. Both those who accuse string theorists of betraying the scientific method and those who advocate an enlarged conception of scientific methodology objectionably conflate epistemic justification with judgements of pursuit-worthiness. Once we get clear about this distinction and about the different norms governing the two contexts, the current situation in fundamental physics becomes much less puzzling. After defending this diagnosis of the controversy, I’ll show how the argument patterns that have been posited by Dawid as constituting an emergent methodological revolution in science are better off if reworked as arguments belonging to the context of pursuit. (shrink)

Eternalism, the view that what we regard locally as being located in the past, the present and the future equally exists, is the best ontological account of temporal existence in line with special and general relativity. However, special and general relativity are not fundamental theories and several research programs aim at finding a more fundamental theory of quantum gravity weaving together all we know from relativistic physics and quantum physics. Interestingly, some of these approaches assert that time is not (...) fundamental. If time is not fundamental, what does it entail for eternalism and the standard debate over existence in time? First, I will argue that the non-fundamentality of time to be found in string theory entails standard eternalism. Second, I will argue that the non-fundamentality of time to be found in loop quantum gravity entails atemporal eternalism, namely a novel position in the spirit of standard eternalism. (shrink)

ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...) but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. -/- This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the like—thereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R -/- 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78. MR0351765 (50 #4253). (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated (...) by Herbrand’s Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

This article had its start with another article, concerned with measuring the speed of gravitational waves - "The Measurement of the Light Deflection from Jupiter: Experimental Results" by Ed Fomalont and Sergei Kopeikin (2003) - The Astrophysical Journal 598 (1): 704–711. This starting-point led to many other topics that required explanation or naturally seemed to follow on – Unification of gravity with electromagnetism and the 2 nuclear forces, Speed of electromagnetic waves, Energy of cosmic rays and UHECRs, Digital string (...) theory, Dark energy+gravity+binary digits, Cosmic strings and wormholes from Figure-8 Klein bottles, Massless and massive photons and gravitons, Inverse square+quantum entanglement = God+evolution, Binary digits projected to make Prof. Greene’s cosmic holographic movie, Renormalization of infinity, Colliding subuniverses, Unifying cosmic inflation, TOE (emphasizing “EVERYthing”) = Bose-Einstein renormalized. The text also addresses (in a nonmathematical way) the wavelength of electromagnetic waves, the frequency of gravitational waves, gravitational and electromagnetic waves having identical speed, the gamma-ray burst designated GRB 090510, the smoothness of space, and includes these words – “Gravity produces electromagnetism. Retrocausally (by means of humans travelling into the past of this subuniverse with their electronics); this “Cosmic EM Background” produces base-2 mathematics, which produces gravity. EM interacts with gravity to produce particles, mass – gravity/EM could be termed “the Higgs field” - and the nuclear forces associated with those particles. It makes gravity using BITS that copy the principle of magnetism attracting and repelling, before pasting it into what we call the strong force and dark energy.” . (shrink)

The notion of consciousness has been studied in many ways out of which, there could be a scientific approach of studying it using string theory which enjoys the mathematical coherence. The paper aims to study consciousness using string theory in which the role of graviton will be discussed. The notion of parallel universes given by string theory would be tackled to understand consciousness and make an attempt to clarify the notion of other world or (...) universe and parallel universes, the problems of time travel, soul and death in the universe or universes of strings which gets twisted and compactified. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. This chapter analyses the nature and derivation of spacetime topology and geometry according to string theory.

In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in (...) expressing the psychophysical (phenomenological) action pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature’s fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory entails the dialectical interplay of symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper closes by considering the role of the analyst per se in the further evolution of the cosmos. (shrink)

This paper examines the evolution of Husserl’s philosophy of nonintuitive intentions. The analysis has two stages. First, I expose a mistake in Husserl’s account of non-intuitive acts from his 1901 Logical Investigations. I demonstrate that Husserl employs the term “signitive” too broadly, as he concludes that all non-intuitive acts are signitive. He states that not only meaning acts, but also the contiguity intentions of perception are signitive acts. Second, I show how Husserl, in his 1913/14 Revisions to the Sixth Logical (...) Investigation, amends his 1901 theory of non-intuitive acts, which he now calls “empty” intentions. He there accurately distinguishes empty meaning acts from the empty intentions of perception. In the conclusion, I reveal how Husserl’s alterations to his theory of non-intuitive intentions can inform our understanding of a larger shift in his philosophy. (shrink)

Without directly addressing the Demarcation Problem for logic—the problem of distinguishing logical vocabulary from others—we focus on distinctive aspects of logical vocabulary in pursuit of a second goal in the philosophy of logic, namely, proposing criteria for the justification of logical rules. Our preferred approach has three components. Two of these are effectively Belnap’s, but with a twist. We agree with Belnap’s response to Prior’s challenge to inferentialist characterisations of the meanings of logical constants. Belnap argued that for (...) a logical constant to exist, its rules must be conservative over a previously given consequence relation and guarantee the uniqueness of the constant. The twist is that we require logical vocabulary to be provably conservative, not over a previously given formal consequence relation, but over a previously given meaningful vocabulary of a language. Uniqueness is also a feature defined in terms of provability: if two syntactically distinguished expressions are governed by the same rules, then formulas with them as main operators are interderivable. Belnap’s criteria are not only those for the existence of a logical constant, but more: they are what distinguishes logical vocabulary from all other expressions. It is the defining mark of a logical constant that it is provably conservative over the fragment of the language which excludes it and that its rules guarantee its uniqueness. The third component is the topic neutrality of logic. The provable conservativeness of logic over a previously given vocabulary of a language is motivated, in part, by appeal to molecularism in the theory of meaning. Molecularity is a feature endorsed by the theory of meaning as a whole, so it does not distinguish logical constants from other expressions. The same is true for conservativeness. We argue that molecularity, and hence conservativeness, are implicit presuppositions of speakers’ use of language: the addition of new vocabulary to a language is presupposed to be conservative. But this presupposition is one that we should be able reflectively to endorse (such as when attempting a rational reconstruction of the use of the vocabulary). Thus, where conservativeness is found to fail, this defect should be remedied and the use of the vocabulary corrected (as in classical negation) or excised altogether (as in pejoratives). We go on to characterise a notion of topic neutrality, which we argue applies to logical vocabulary. We then note that reflective endorsement of the conservativeness of a topic neutral vocabulary requires a proof that the vocabulary is conservative relative to any base vocabulary. Thus we require that logical vocabulary be demonstrably conservative. Allying this requirement, distinctive of logic, to a general consideration about the commitments of assertion yields a mode of justification for logical constants akin to some conceptions of Harmony, i.e., to the idea that the consequences of assertion of a logical complex need to be warranted by the grounds and ought to be the strongest consequences warranted by the grounds. Intuitionistic logic acquires a somewhat familiar justification but emanating from a new motivation. (shrink)

The Russell's paradox concerns the foundations of naive set theory. This short short paper is about how it can be interpreted in other contexts and has significance in the world of commands. Understanding the paper assumes that the reader is broadly familiar with the foundations of set theory and its history. The text contains many formulas and therefore the reader should be comfortable in the world of logical formulas. My example is somewhat similar to the barber paradox. There, (...) too, we are puzzled by the feasibility of a task. In the case of the barber paradox there is a solution: the barber is a woman, in my example there is no such escape. (shrink)

CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .

The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical (...) sciences without seemingly begging the question. Appeals to rational intuition and analyticity in order to account for logical knowledge are symptomatic of these commitments to the apriority and basicness of logical evidence. This chapter argues that these historically prevalent accounts of logical evidence are mistaken, and that if we take logical practice seriously we fi nd that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas. (shrink)

A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.

Traditionally, consistency is the only criterion for the quality of a theory in logic-based approaches to reasoning about actions. This work goes beyond that and contributes to the meta-theory of actions by investigating what other properties a good domain de- scription should satisfy. Having Propositional Dynamic Logic (PDL) as background, we state some meta-theoretical postulates concerning this sore spot. When all pos- tulates are satisfied, we call the action theory modular. We point out the problems (...) that arise when the postulates about modularity are violated, and propose algorith- mic checks that can help the designer of an action theory to overcome them. Besides being easier to understand and more elaboration tolerant in McCarthy’s sense, mod- ular theories have interesting computational properties. Moreover, we also propose a framework for updating domain descriptions and show the importance modularity has in action theory change. (shrink)

Contemporary research offers a more compelling account on the complex emotion of envy than the traditional view of envy as simply something bad. This essay explains how Logic-Based Therapy can use this account to coach individuals struggling with negative species of envy. Given that jealousy and envy are often equated, the essay differentiates the two; explains the conditions that make the four species of envy possible; identifies cardinal fallacies associated with negative species of envy; proposes counteractive virtues, and describes (...) ways to help people struggling with negative species of envy acquire these virtues. (shrink)

In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated - informal logic, argumentation theory, evidence law and legal reasoning – but also more recent work in applying and developing it in computer science and artificial intelligence. Beginning with a simple example of an everyday argument, we present an analysis of it visualised as an argument diagram constructed using a software tool. In the (...) context of a brief history of the development of diagramming, it is then shown how argument diagrams have been used to analyze and work with argumentation in law, philosophy and artificial intelligence. (shrink)

An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G (...) class='Hi'>theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic. (shrink)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...) of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

Neutrosophy considers a proposition, theory, event, concept, or entity, "A" in relation to its opposite, "Anti A" and that which is not A, "Non-A", and that which is neither "A" nor "Anti-A", denoted by "Neut-A". Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics.

Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at (...) Buffalo, Buffalo, NY 14260-4150 E-mail: [email protected] The four-letter written-English expression ‘word’, which plays important roles in applications and expositions of logic and philosophy of logic, is ambiguous (multisense, or polysemic) in that it has multiple normal meanings (senses, or definitions). Several of its meanings are vague (imprecise, or indefinite) in that they admit of borderline (marginal, or fringe) cases. This paper juxtaposes, distinguishes, and analyses several senses of ‘word’ focusing on a constellation of senses analogous to constellations of senses of other expression words such as ‘expression’, ‘symbol’, ‘character’, ‘letter’, ‘term’, ‘phrase’, ‘formula’, ‘sentence’, ‘derivation’, ‘paragraph’, and ‘discourse’. Consider, e.g., the word ‘letter’. In one sense there are exactly twenty-six letters (letter-types or ideal letters) in the English alphabet and there are exactly four letters in the word ‘letter’. In another sense, there are exactly six letters (letter-repetitions or letter-occurrences) in the word-type ‘letter’. In yet another sense, every new inscription (act of writing or printing) of ‘letter’ brings into existence six new letters (letter-tokens or ink-letters) and one new word that had not previously existed. The number of letter-occurrences (occurrences of a letter-type) in a given word-type is the same as the number of letter-tokens (tokens of a letter-type) in a single token of the given word. Many logicians fail to distinguish “token” from “occurrence” and a few actually confuse the two concepts. Epistemological and ontological problems concerning word-types, word-occurrences, and word-tokens are described in philosophically neutral terms. This paper presents a theoretical framework of concepts and principles concerning logicography, including use of English in logic. The framework is applied to analytical exposition and critical evaluation of classic passages in the works of philosophers and logicians including Boole, Peirce, Frege, Russell, Tarski, Church and Quine. This paper is intended as a philosophical sequel to Corcoran et al. “String Theory”, Journal of Symbolic Logic 39(1974) 625-637. https://www.academia.edu/s/cdfa6c854e?source=link -/- . (shrink)

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in (...) a dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. (shrink)

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic (...) and semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

The aim of this study is to discuss in what sense one can speak about universal character of logic. The authors argue that the role of logic stands mainly in the generality of its language and its unrestricted applications to any field of knowledge and normal human life. The authors try to precise that universality of logic tends in: (a) general character of inference rules and the possibility of using those rules as a tool of justification of (...) theorems of every science, (b) principles of correct formulating of thoughts and using language, and (c) general deductive method of reasoning, i.e in the study of language syntax and semantics. The authors present two theories of language syntax and semantics as exemplifications based on the Tarski’s famous results in metalogic: (1) a formalization of universal syntax system by Andrzej Grzegorczyk based on a new primitive notion of quotation-marks operator, and (2) an enlarged system of axiomatic theory of syntax of any categorial language of Urszula Wybraniec-Skardowska’s in which the main role plays the relation of concatenation understood as a set-theoretical function. The study concludes in arguing that the importance of the result (2) lies not only in solving some philosophical problems but also in different fields of knowledge and spheres of human life as ex. in discussion and education as well. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...) exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

In this paper I sketch some arguments that underlie Hegel's chapter on judgment, and I attempt to place them within a broad tradition in the history of logic. Focusing on his analysis of simple predicative assertions or ‘positive judgments’, I first argue that Hegel supplies an instructive alternative to the classical technique of existential quantification. The main advantage of his theory lies in his treatment of the ontological implications of judgments, implications that are inadequately captured by quantification. The (...) second concern of this paper is the manner in which Hegel makes logic not only dependent on ontology generally, but also variant in regard to domains of objects. In other words, he offers a domain-specific logical theory, according to which the form of judgment or inference is specific to the subject of judgment. My third concern lies with the metaphilosophical consequences of this theory, and this includes some more familiar Hegelian themes. It is well known that Hegel frequently questioned the adequacy of the sentential form for expressing higher order truths. My reading of his theory of predication explains and contextualizes this tendency by demystifying notions like the so-called speculative proposition. (shrink)

Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working with (...) semantic generalizations – are addressed. Finally, I’ll introduce the case studies that I’ll be dealing with in part II. Chapter 2 is concerned with the origins and development of Jaśkowski’s discussive logic. The main idea of this chapter is to systematize the various stages of the development of discussive logic related researches from two different angles, i.e., its connections to modal logics and its proof theory, by highlighting virtues and vices. Chapter 3 focuses on the Gentzen-style proof theory of discussive logic, by providing a characterization of it in terms of labelled sequent calculi. Chapter 4 deals with the Gentzen-style proof theory of relevant logics, again by employing the methodology of labelled sequent calculi. This time, instead of working with a single logic, I’ll deal with a whole family of them. More precisely, I’ll study in terms of proof systems those relevant logics that can be characterised, at the semantic level, by reduced Routley-Meyer models, i.e., relational structures with a ternary relation between states and a unique base element. Chapter 5 investigates the proof theory of a modal expansion of intuitionistic propositional logic obtained by adding an ‘actuality’ operator to the connectives. This logic was introduced also using Gentzen sequents. Unfortunately, the original proof system is not cut-free. This chapter shows how to solve this problem by moving to hypersequents. Chapter 6 concludes the investigations and discusses the future of the research presented throughout the dissertation. (shrink)

This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘_p_ is a reason for _q_’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most extant accounts (...) of conditionals. (shrink)

Editors van Ditmarsch, Hendriks and Verbrugge of this special issue of topiCS on lying describe some recent trends in research on lying from a multidisciplinary perspective, including logic, philosophy, linguistics, psychology, cognitive science, behavioral economics, and artificial intelligence. Furthermore, they outline the seven contributions to this special issue.

The strings of physics’ string theory are the binary digits of 1 and 0 used in computers and electronics. The digits are constantly switching between their representations of the “on” and “off” states. This switching is usually referred to as a flow or current. Currents in the two 2-dimensional programs called Mobius loops are connected into a four-dimensional figure-8 Klein bottle by the infinitely-long irrational and transcendental numbers. Such an infinite connection translates - via bosons being ultimately composed (...) of 1’s and 0’s depicting pi, e, √2 etc.; and fermions being given mass by bosons interacting in matter particles’ “wave packets” – into an infinite number of 8-Kleins. Each Klein 1) is one of the universe’s subuniverses (our own is 13.7 billion years old), 2) is made flexible through its binary digits which seamlessly, or almost seamlessly, join it to surrounding subuniverses and eliminate its central hole, and 3) possesses warped time and space because its foundation is the programmed curves in its mathematical Mobius loops (along with the twists they generate [p.7]). The universe functions according to the rules of fractal geometry. So the Mobius does not exist only at the cosmic level. It also manifests at the quantum scale, giving us photons and protons etc. Space and time are no longer separate, but are an indivisible space-time. So if space and the universe are infinite, how can time not be eternal? The past and the future must both extend forever (the idea of time being finite arises from confusion of our subuniverse with the one infinite universe). -/- BITS (Binary digiTS) only suggest existence of the divine if time is linear. Although a non-supernatural God is proposed via the inverse-square law coupled with eternal quantum entanglement, Einstein taught us that time is warped. Warped time is nonlinear, making it at least possible that the BITS composing space-time and all particles originate from the computer science of humans. -/- I suspect many readers will be content with reading this abstract. While there are more details, and mathematics, in the content; my natural style of writing is to avoid jargon and maths. I also tend to get philosophical. While I personally feel that there’s a lot of precious information in the content, I realize it won’t all be to everyone’s liking. Other subjects dealt with in this article are - the “Pioneer anomaly”, refinement of gravitational physics, dark energy and dark matter, quantum phenomena like mass and electric charge and quantum spin, Kepler’s laws of planetary motion, deflection of starlight by the sun, tides, falling bodies, Earth’s orbit, ancient Greek philosophers, Newton, Kepler, Galileo, Aristotle, Parmenides, Zeno of Elea, time travel into the past as well as the future, the elimination of distances in space, humanity’s construction of this universe we live in, The Law of Conservation of Matter-Energy, and support for the science-fiction-like idea of the electronic binary digits of 1 and 0 being the building blocks of our universe. (shrink)

Revista Cunoașterea Științifică este o publicație trimestrială din domeniile științei și filosofiei, și domenii conexe de studiu și practică. -/- Cuprins: -/- EDITORIALE / EDITORIALS -/- Dan D. FARCAȘ Limite ale cunoașterii în cuvânt, logică, matematică și teorii Limits of knowledge in words, logic, mathematics and theories Nicolae SFETCU Cunoașterea științifică – Metodologii Scientific knowledge – Methodologies Nicolae SFETCU Știința schimbărilor climatice The science of climate change Nicolae SFETCU Știință sau pseudoștiință? Science or Pseudoscience? -/- ȘTIINȚE NATURALE / NATURAL (...) SCIENCE -/- Nicolae SFETCU Epistemologia gravitației cuantice Epistemology of Quantum Gravity Nicolae SFETCU Fabrica de apă grea Drobeta Turnu Severin: Construcția Drobeta Turnu Severin Heavy Water Plant: Construction Nicolae SFETCU Fabrica de apă grea Drobeta Turnu Severin: Funcționarea și oprirea Drobeta Turnu Severin Heavy Water Plant: Functioning and Shutting Down Albert TORMA PandemiA: Femei și polițiste Pandemia: Women and Policewomen Adrian KLEIN, Robert Neil BOYD Interacțiuni între creier, biocâmpuri și lumea fizică Interactions between the brain, the biofields, and the physical Adrian KLEIN Conectivitatea psiho-neuronală The Psycho-Neural Connectivity Nicolae SFETCU Probleme cu teoria corzilor din gravitația cuantică Problems with String Theory in Quantum Gravity -/- ȘTIINȚE SOCIALE / SOCIAL SCIENCE -/- Miriam MIRCEA Manipularea ca fenomen corelativ al puterii politice – o sinteză Manipulation as a correlative phenomenon of political power – a synthesis Daniela Georgiana GOLES, Oana Ștefania COȘA Repetabilitatea istorica a problemelor de securitate manageriale și noile cerințe in contextul economic actual The historical repeatability of managerial security issues and the new requirements in the current economic context Ionuț IORDACHE Reglementări internaționale privind falimentul International bankruptcy regulations Vlad BARBU, Ionuț IORDACHE, Adrian-Călin CUCULIS, Naciu Costin MERGEANE Rolul statului în relațiile de muncă The Role of the State in Labour Relations Tiberiu TĂNASE 24 Ianuarie, o zi cu dublă semnificație națională January 24, a day with double national significance Stan PETRESCU Iuliu Maniu – Lumini și umbre: O viață închinată Marii Uniri și propășirii României Mari Iuliu Maniu – Lights and shadows: A life devoted to the Great Union and the prosperity of Greater Romania Dumitru MAZILU Parohia în textul sfintelor canoane și în practică bisericească The parish in the text of the holy canons and in church practice Dumitru MAZILU Despre calitatea de paroh-administrator în funcționarea unei unități parohiale moderne About the quality of parish administrator in the operation of a modern parish unit Alexandra MOCANU Cultura anime în România Anime culture in Romania Alexandra MOCANU Abandonul școlar în România School dropout rate in Romania Emilian M. DOBRESCU Importanța pământurilor rare pentru economia mondială The Importance of the Rare Earths for the World Economy Nicolae SFETCU Modele ale inteligenței emoționale în cercetare și educație Models of Emotional Intelligence in Research and Education Nicolae SFETCU Aventurile lui Pinocchio – Educația The Adventures of Pinocchio – Education Dan D. FARCAȘ Câteva opinii privind etnogeneza românilor (1) Some opinions regarding the ethnogenesis of the Romanians (1) Denisa Oana PĂTRAȘCU Sancțiunile internaționale, măsură suprastatală de coerciție International sanctions, supra-state measure of coercion Tiberiu TĂNASE Puncte de vedere asupra proiectului de democratizare a Orientului Mijlociu Extins Viewpoints on the project of democratization of Middle East Extended -/- ȘTIINȚE FORMALE / FORMAL SCIENCE -/- Alida Monica Doriana BARBU Aplicații ale AI, machine learning, deep learning și big data în domeniul militar Applications of AI, machine learning, deep learning and big data in the military field Nicolae SFETCU Identitatea și inteligența artificială în Aventurile lui Pinocchio Identity and Artificial Intelligence in The Adventures of Pinocchio Sebastian BIDAȘCĂ Etica în inteligența artificială: provocări și perspective Ethics in Artificial Intelligence: Challenges and Prospects Nicolae SFETCU Măsurarea formei populației pentru înțelegerea tendințelor demografice Measuring population shape to understand demographic trends -/- FILOSOFIE / PHILOSOPHY -/- Adrian KLEIN Legea karmică – O abordare sinoptică Karmic Law – A Synoptic Approach Adrian KLEIN, Robert Neil BOYD Principiile subcuantice ale vieții și conștiinței Subquantum Principles of Life and Consciousness Silviu PETRE Pentru un realism al secolului XXI For a 21st century realism Dan D. FARCAȘ Câteva reflecții privind contactele extrasenzoriale Some reflections on extrasensory contacts Nicolae SFETCU Teorii cauzale ale referinței Causal theories of reference Nicolae SFETCU Filosofia inteligenței emoționale Philosophy of Emotional Intelligence -/- RECENZII CĂRȚI / BOOK REVIEWS -/- Traian OSTAHIE Nicolae Mavrocordat – disimulare și prudență la început de secol XVIII - Răgazurile lui Filotheu Nicolae Mavrocordat - concealment and prudence at the beginning of the 18th century - Răgazurile lui Filotheu Nicolae SFETCU Reconstrucția rațională a științei prin programe de cercetare The rational reconstruction of science through research programs Nicolae SFETCU Umanism, devenire și demiurgul în Aventurile lui Pinocchio Humanism, Becoming and the Demiurge in The Adventures of Pinocchio -/- ISSN 2971 – 9070 ISSN-L 2821 – 8086, DOI: 10.58679/CS49741. (shrink)

Recently, we have proposed quantum language ( or the linguistic Copenhagen interpretation of quantum mechanics). Quantum languages describe both classical and quantum systems and therefore have great power to solve almost all philosophical problems. Thus, we believe that quantum language can be regarded as the language of science. Therefore, it makes sense to study Wittgenstein's picture theory within the framework of quantum language, since Wittgenstein's language (i.e., the language that he supposed, but didn't define in his book "Tractatus Logico-Philosophicus") (...) may be a particular subclass of quantum language. In this paper, we show that a class of binary projective measurements in classical quantum language has a logical structure. And thus, the proposition that Wittgenstein studied in his book can be regarded as a binary projective measurement in classical quantum language. Therefore, we conclude that Wittgenstein's language is realized as the central part of classical quantum language. If so, we think that his picture theory should be praised not only from a philosophical point of view but also from a scientific point of view. (shrink)

Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, (...) strong modal force, generality, topic neutrality, basicness, and (quasi-)apriority, (v) the veridicality of logic and its applicability to science, (v) the normativity of logic, (vi) error, revision, and expansion in/of logic, and (vii) the relation between logic and mathematics. The high explanatory power of the truth-theoretic approach does not rule out an equal or even higher explanatory power of the proof-theoretic approach. But to the extent that the truth-theoretic approach is shown to be highly explanatory, it sets a standard for other approaches to logic, including the proof-theoretic approach. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory (...) of finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Editors van Ditmarsch, Hendriks and Verbrugge of this special issue of topiCS on lying describe some recent trends in research on lying from a multidisciplinary perspective, including logic, philosophy, linguistics, psychology, cognitive science, behavioral economics, and artificial intelligence. Furthermore, they outline the seven contributions to this special issue.

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact" Mark Twain-Life on the Mississippi -/- This is a lovely book full of fascinating info on the evolution of physics and cosmology. Its main theme is how the idea of higher dimensional geometry created by Riemann, recently extended to 24 dimensions by string theory, has revolutionized our understanding of the universe. Everyone knows that Riemann created multidimensional geometry (...) in 1854 but it is amazing to learn that he also was a physicist who believed that it held the key to explaining the fundamental laws of physics. Maxwell´s equations did not exist then and Riemann´s untimely death at age 39 prevented his pursuit of these ideas. Both he and his British translator Clifford believed that magnetic and electric fields resulted from the bending of space in the 4th dimension-more than 50 years before Einstein! The fourth dimension became a standard subject in the popular media for the next 50 years with several stories by HG Wells using it and even Lenin wrote about it. The American mathematician Hinton had widely publicized his idea that light is a vibration in the 4th spatial dimension. Amazingly, physicists and most mathematicians forgot about it and when Einstein was looking for the math needed to encompass general relativity 60 years later, he had never heard of Riemannian geometry. He spent 3 years trying to find the equations for general relativity and only after a math friend told him about Riemann was he able to complete his work. Riemann´s equations with four dimensional metric tensors describing every point in space were incorporated almost unchanged into relativity. And on and on it goes. Since this review I have written a great deal on the language games of math and science, uncertainty, incompleteness, the limits of computation etc., so those interested should find them useful since this volume like most science frequently wanders across the line into philosophy (scientism). -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

In this paper I present a formalization of the theory of ideal concepts applied to the concept of God. It is done within a version of the Simplest Quantified Modal Logic (SQML) and attempts to solve three meta-problems related to the concept of God: the unicity of extension problem, the homogeneity/heterogeneity problem and the problem of conceptual unity.

Modern cosmology has two competing theories of the origin of the universe: the "Singularity theory" and the "Superstring theory". Four Dilemmas of the "Super-string theory" are presented: the incompleteness of the eleven space–time dimensions,the inextricable dependence on the “Space–Time Background”, the "Zero-Brane the-ory" admitting stuff smaller than the Planck scale, and the pure mathematical theory that cannot be falsified by experiments. Although the "Singularity theory" is faced with many critiques from the "Superstring theory", (...) from the perspective of Informa-tion Ontology, treating the "Singularity" as "Origin Information" can dissolve these troubles well. For the "Singularity theory", the new philosophical thinking frame-work effectively explains the parameter problems of the universe, and gives satisfied response to the challenges from the "Superstring theory". As a result, the "Singularity theory" has a more competitive advantage on the origin of the universe. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

C.D. Broad’s Reflections stands out as one of the few serious examinations of Moral Sense Theory in twentieth century analytic philosophy. It also constitutes an excellent discussion of the interconnections that allegedly exist between questions concerning what Broad calls the ‘logical analysis’ of moral judgments and questions about their epistemology. In this paper I make three points concerning the interconnectedness of the analytical and epistemological elements of versions of Moral Sense Theory. First, I make a general point about (...) Broad’s association between the Naïve Realist Moral Sense Theory (an epistemological view) and Objectivist Moral Sense Theory (a ‘logical analysis’). Second, I raise doubts about one of Broad’s arguments that Trans-Subjectivist Moral Sense Theory (logical analysis) can account for the apparent synthetic necessity of general moral propositions (epistemological). Third, I briefly discuss a view about logical analysis that should be of interest to contemporary Moral Sense Theorists – Neo-Sentimentalism – and respond to an argument whose conclusion is that this analysis is incompatible with a particular kind of epistemological view. (shrink)

The anti-exceptionalist debate brought into play the problem of what are the relevant data for logical theories and how such data affects the validities accepted by a logical theory. In the present paper, I depart from Laudan's reticulated model of science to analyze one aspect of this problem, namely of the role of logical data within the process of revision of logical theories. For this, I argue that the ubiquitous nature of logical data is responsible for the proliferation of (...) several distinct methodologies for logical theories. The resulting picture is coherent with the Laudanean view that agreement and disagreement between scientific theories take place at different levels. From this perspective, one is able to articulate other kinds of divergence that considers not only the inferential aspects of a given logical theory, but also the epistemic aims and the methodological choices that drive its development. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. (...) The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

Abstract: We propose a dichotomy between object-entities and meaning-entities. The former are entities such as molecules, cells, organisms, organizations, numbers, shapes, and so forth. The latter are entities such as concepts, propositions, and theories belonging to the realm of logic. Frege distinguished analogously between a ‘realm of reference’ and a ‘realm of sense’, which he presented in some passages as mutually exclusive. This however contradicts his assumption elsewhere that every entity is a referent (even Fregean senses can be referred (...) to by means of suitably constructed expressions). We apply the meaning/object dichotomy to mathematical and fictional entities, and develop a view of mathematical and other abstract objects as the results of certain types of demarcation – as for example the North Sea is the result of demarcations built into naval charts. Such demarcations reflect demarcatory acts, which presuppose complex cognitive and social structures enabling the creation of maps, of theories (of mathematics, of natural science), and of novels. (shrink)