Symbolic Logic

Medium density fiberboard (MDF) is an engineered wood product that has density and specific gravity similar to solid wood, ranging from 600 to 800 kg/m3 of density and 0.6 to 0.8 of specific gravity. This makes MDF suitable to partially replace solid wood, particularly for interior application. Approximately over than 100 million m3 of MDF are produced in 2020, resulting in a large amount of waste MDF will be generated in the next 20 years. MDF is produced using urea-formaldehyde (UF) resins adhesive. UF resins adhesive is a poly-condensation product of urea and formaldehyde via an alkaline acid two-step reaction. Sustainable MDF production is required as the world is facing climate change and deforestation. Recycling is a way to support sustainable production in the engineered wood products manufacturing. Many attempts have been done to find ways to recycle waste MDF. The main problem is UF resins, which bond the MDF panel fibers. In order to re-manufacture the waste MDF into new r...

Пропонований навчальний посібник є спробою доступного викладу вихідних понять й припущень, концепцій та теорій сучасної символічної логіки. При підготовці лекцій до друку було враховано результати, отримані шляхом розробки актуальних проблем сучасного логічного знання. Навчальний посібник знайомить читача із базовими розділами сучасної символічної логіки – класичними логіками (логікою висловлювань і логікою предикатів) та некласичними логіками (модальною, алетичною, темпоральною, епістемічною, деонтичною логіками). Для студентів та аспірантів філософських спеціальностей, а також усіх, хто цікавиться здобутками сучасної символічної логіки.

The author contends that a number of steps should
be taken if we want to honestly upgrade the thinking
instruments of a person, in particular of the Filipino.
Since logical reasoning is contextually rooted in
everyday discourse, it is argued that we replace the
logical term proposition with the term constative.
Secondly, if we intend to train ourselves to think
abstractly, then the Polish notation, rather than the
Hilbert-Ackermann notation, can better do this
function. At any rate, the Polish notation can serve as
an alternative just as perfectly as the Hilbert-Ackermann
notation. Thirdly, it is suggested⎯especially for
Filipino seminaries⎯to go symbolic since it is
economical and convenient, while at the same time
cleansing our modes of thinking of emotive barriers.
Lastly, for one to be completely logical, one needs to
understand that a three-unit course in modern logic,
while in the right direction, is insufficient.

Пропонований навчальний посібник призначений для практичного освоєння логічної теорії. За допомогою перспективної методики у ньому розглядаються головні теми і ключові проблеми логіки як теоретичної та навчальної дисципліни, а також наводяться логічні завдання і методики їх розв’язання, що забезпечує набуття логічного досвіду, підвищення рівня логічної культури мислення. Для студентів, аспірантів, викладачів та усіх, хто вивчає логіку самостійно, вдосконалює мислення й розвиває інтелект.

The aim of the paper is show that that W. V. O. Quine's animadversions against modal logic did not get the same attention that is considered to be the case nowadays. The community of logicians focused solely on the technical aspects of C. I. Lewis' systems and did not take Quine's arguments and remarks seriously – or at least seriously enough to respond. In order to assess Quine's place in the history, however, his relation to Carnap is considered since their notorious break was about the status of extensionality and modal logic (and analyticity was much more of a second issue). Since much of the works about the history of analytic philosophy is centered on the relationship of Quine and Carnap, their break about modality deserves much more attention – it also sheds some light on why should anyone wonder about Quine's early arguments against modal logic. The paper ends with some further considerations regarding the early formation of modal logic and hitherto unconsidered problematic issues.

Brouwer's views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional calculus and its extensions. The theory of these systems has become an independent branch of logic with connections to lattice theory, topology, modal logic and other areas. This paper aims to present a modern account of semantics for intuitionistic propositional systems. The guiding idea is that of a hierarchy of semantics, organized by increasing generality: from the least general Kripke semantics on through Beth semantics, topological semantics, Dragalin semantics, and finally to the most general algebraic semantics. While the Kripke, topological, and algebraic semantics have been extensively studied, the Beth and Dragalin semantics have received less attention. We bring Beth and Dragalin semantics to the fore, relating them to the concept of a nucleus from pointfree topology, which provides a unifying perspective on the semantic hierarchy.

The paper addresses the abundance of imperfections in Nature and Society, i.e., Reality. Imperfections are encountered in all Sciences and the Arts, models of what this author refers to as Virtual Realities. They are specifically recorded in systems of Logic, and cover Linguistics, Mathematics, and all Natural, Biological and Social Sciences, Humanities, and the Professions. Photographs are included from different fields, that highlight topics in Astronomy, Painting, Sculpture and Architecture, vividly capturing certain aspects of these imperfections. Ways towards managing imperfections are put forward, consistent with what this author refers to as a New Epistemology, a field using methods from the fields of Nonlinear Dynamics, Fuzzy Sets Theory, Quantum Mechanics, and Modern Metrology. In this third paper of a triptych, the mathematical Theory of Optimization is added to the mix, as more attention is focused on Symbolic Logic. The effort is directed towards deriving a Quantum Reasoning approach to Logic and Computing. Subjects involved in purposeful individual behavior are used, as the material to structure a General Theory of Action, where the critical role that an observer, operating within a space-time scale, plays is emphasized.  There is an Addendum to this paper here: https://www.academia.edu/49456134/%CE%9F%CE%9D_IMPERFECTIONS_Addendum_I

In broad overview, dunes are rounded, elliptical, parabolic or crescentic mounds of loose sand, which have been piled up by wind action in the areas of lakes, (lacustrine dunes), rivers, sea coasts and deserts.
    There are 5 or 6 supposed basic dune-types, as well as a few other variations, so herein is an approximate mathematical treatment for the simpler ones, since exactness is a pointless goal with this type of natural phenomenon, that evolves over long periods of time, and can be looked at either as a flowing object or as a stationary one, depending on one's approach.
Dunes are all composite structures, that can be deconstructed mathematically.  Their aerial views/profiles and lateral profiles will be examined as well as the rippled surfaces of some.

The traditional conflict in epistemology has been between rationalism and empiricism. Philosophers have often tried to align themselves in one of these schools even though a close reading of some of their writings may suggest they may often have used both varyingly, one more than the other. This paper demonstrates that both rationalism and empiricism work together and are thus called the rational-empiric model. The paper extends the scope of the rational-empiric model to also evolving cognitive developments and other aspects of reasoning such as computational thought and makes an effort towards summarizing the nature of human reason by explaining the functional intellect and the structural brain since the time of Aristotle to date drawing from theology, philosophy, logic, computer science, and psychology. The paper presents the rational-empiric model in a broader in-depth context with supporting ideas and evidence. Various literature on theology, logic, philosophy, and psychology has been used to elaborate on the concepts.  The paper concludes that the purpose of the rational empiric model is to discover knowledge by finding and understanding ontologies as they exist and function or as they ought to exist and function.

Adapting a term coined by Ian Hacking, this essay analyzes certain of the styles of reasoning that appear in two novels, Fyodor Dostoevsky’s _Zapiski iz podpol’ya_ (Notes from Underground, 1864) and Natsume Sōseki’s _Kokoro_ (1914). The confession of the underground man, the protagonist of Dostoevsky’s novel, includes an argument against the Chernyshevskian doctrine of rational egoism. The underground man’s argument may, as this essay shows, be analyzed in terms of logical truth-tables to demonstrate that, however thorough the underground man’s argument may appear, it does not consider the counterexample of selfless altruism. This omission prepares the way for the underground man’s rejection of Liza at the climax of the second part of the novel. Sōseki’s novel, too, contains a confession, namely Sensei’s testament, in which Sensei relates how he arrived at his belief that humanity is fundamentally selfish. Sensei’s style of reasoning is primarily inductive, in contrast with that of other characters in Sōseki’s novel, and the present essay argues that Sensei’s style of reasoning is a primary cause of his suicide. In each novel, then, there is a sustained consideration of how and to what extent a style of reasoning is bound up with a character’s fate.

(in _Comparative Literature Studies_ vol. 54, no. 3 [2017], pp. 489-517)

В предлагаемой книге предпринята попытка общедоступного изложения современной логики. Содержание работы затрагивает наиболее актуальные вопросы математической, вероятностной и неформальной логики трех доминирующих разделов современного логического знания. Впервые в отечественной литературе логика сопоставляется с критическим мышлением.

The Symbolic Logic Study Guide is designed to be used in conjunction with Language, Proof, and Logic (LPL), by Jon Barwise and John Etchemendy, (CSLI Publications 2003). It is intended to help instructors teach and students learn the text more effectively. The guide helps students navigate the detailed contents and logical symbols covered in LPL. The first part of the guide contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide an easy-to-follow, well-designed roadmap for the understanding of the text as follows: (1) Introduction; (2) Atomic sentences; (3) Conjunctions, Disjunctions, and Negations; (4) Conditionals and Biconditionals; (5) Introduction to Quantification; (6) Formal Proofs involving Quantifiers; (7) Some Specific Uses of Quantifiers. In addition, to help students prepare for the class tests, the second part of the Guide consists of twelve sample quizzes and solutions.

The Symbolic Logic Study Guide is essential for all instructors and students who use LPL in their symbolic logic classes.

PREFACE INTRODUCTORY TO DRAFT 3; EXPLANATORY IMPORTANT NOTICE
This paper contains many interrelated sections, most of which are complete. Those, that are incomplete, are `works-in-progress' and their updated versions are intended for appearance ASAP, hopefully weekly. This premature publication is due to the recent news broadcast of research findings (the black hole Sagittarius A and dark matter) of the Nobel prize winners Roger Penrose, Reinhard Genzel and Andrea Ghez. Their areas of research are also covered in this draft paper, and each reader has the opportunity to make his/her own personal discernment and/or judgement of the conclusions thereof. ────────────────────────────────────

This article looks at Propositional Logic, also called Statement Calculus, from a combinatorial and algebraic point of view, its implementation in software, and its application to digital electronics. An historical section covers the shift in viewpoint from classical logic (based on Aristotle’s syllogism) to modern symbolic logic, with the key papers (1830-1881) that drove this shift shared in the online logic sourcebook section of the references.

As a practical aid, we implement the grammar of the statement calculus in the Symbolic Logic Simulator (SLS), a program written in 28 lines of Forth, that allows computer-aided verification of any theorem in Propositional Logic (see Appendix 1 for source code). The program makes it straight-forward to explore non-obvious logical identities, and verify any propositional logic theorem or conjecture, in particular see Appendix 2 for key identities in the statement calculus (duality, algebraic, and canonical identities).

The concept of linguistic adequacy is developed iand the NAND Adequacy Theorem is proved showing that NAND can generate all logical operations. A corollary is that any digital logic circuit can be built up entirely using NAND gates, illustrated using the free Digital Works software

Symbolic logic faced great difficulties in its early stage of development in order to acquire recognition of its utility for the needs of science and society. The aim of this paper is to discuss an early attempt by the British logician Lewis Carroll (1832– 1898) to promote symbolic logic as a social good. This examination is achieved in three phases: first, Carroll's belief in the social utility of logic, broadly understood, is demonstrated by his numerous interventions to fight fallacious reasoning in public debates. Then, Carroll's attempts to promote symbolic logic, specifically, are revealed through his work on a treatise that would make the subject accessible to a wide and young audience. Finally, it is argued that Carroll's ideal of logic as a common good influenced the logical methods he invented and allowed him to tackle more efficiently some problems that resisted to early symbolic logicians.

This 8-page long paper addresses the Linguistic implications of two Latin expressions, involving temporal sequencing regarding structures, objects and events, for Set Theory, Topology and Symbolic Logic in view of fuzziness and fluidity, two core characteristics in the field of what this author has called the “New Epistemology”. The two Latin expressions analyzed are: terminus ante quem, together with its modification terminus ante quem non, and terminus post quem.

ÖZ Formel mantık alanında Venn şemalarıyla kıyasların geçerlilik denetlemelerinde bazı güçlükler doğmaktadır. Venn şemalarıyla güçlü geçerli kıyasların anlaşılması ve belirlenmesi gayet kolayken, zayıf geçerli olduğu durumlar ile geçersiz olduğu durumlar arasındaki fark hemen anlaşılmamaktadır. Kategorik bir kıyasın zayıf geçerli olarak kurulması, Aristoteles tarafından doğru kabul edilmesine rağmen Boole tarafından "varoluşsal hata" (existential fallacy) olarak adlandırılır. Çünkü "altık kipli" olarak da adlandırabileceğimiz bu tür kıyaslar iki tümelden tikel bir sonuç çıkararak, aslında varoluşsal yükü olmayan tümel önermelerden varoluşsal yükü olan tikel bir önerme çıkarmış ve varoluşsal bir varsayımda bulunmuştur. Elbette bu konu başka bir çalışmanın ilgi alanını oluşturacaktır, çünkü bu çalışmada daha baştan böylesine varoluşsal varsayımlı kıyasların geçerli olduğu kabul edilmiş ve Venn şemalarıyla denetlerken geçerliliğine ilişkin kuralların varlığı araştırılmıştır. Oldukça teknik sayılabilecek bu çalışma aracılığıyla alana ilgi duyan akademisyen ve eğitimcilere yol göstermek de amaçlanmıştır. Temel problem zayıf veya varoluşsal kipte olan kıyasların geçerliliğine ilişkin kapsayıcı kuralları bulmaktır ve bu tür kıyasların geçersiz olan kipleri de Venn şemaları yoluyla incelenmiştir. Özellikle dördüncü şekil varoluşsal kipte olan kıyaslar fazlasıyla sorunlar içermekte ve bu çalışmanın odak noktasını oluşturmaktadır. İzlenen temel yöntem Venn şemalarıyla denetim ve sonuçlarını yorumlamak şeklindedir. Giriş sayılabilecek bazı bilgilerle mantığa uzak okuyucunun da konuyu ve problemi rahat bir şekilde anlamasını sağlamak amaçlanmıştır. Daha sonra problemin sergilenmesi için kategorik kıyasın dört şekline ait

Contemporary orthodoxy affirms that singular terms cannot be predicates and that, therefore, ‘is’ is ambiguous as between predication and identity. Recent attempts to treat names as predicates do not challenge this orthodoxy. The orthodoxy was built into the structure of modern formal logic by Frege. It is defended by arguments which I show to be unsound. I provide a semantical account of atomic sentences which draws upon Mill’s account of predication, connotation and denotation. I show that singular terms may be predicates, that it is highly implausible that there is an ‘is’ of identity in natural languages, and that modern formal logic is deficient in that it cannot recognise propositions, including singular existentials, in which singular terms are predicates, or inferences which depend upon the logical role rather than the logical category of expressions.