logical reasoning presentation

LOGICAL REASONING PRESENTATION

History of Logical reasoning

est. 2021

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CIVIL BRANCH

CIVIL BRANCH

CONTENT

01.

INTRODUCTION

02.

TYPES OF LOGIC

03.

HISTORY

04.

CONCEPTS

05.

CONTROVERSIES

06.

CONCLUSION

Logic....

Logic possessed of reason, intellectual, dialectical, argumentative is the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition on the basis of a set of other propositions . More broadly, logic is the analysis and appraisal of argument.Philosophy of logic is the area of philosophy devoted to examining the scope and nature of logic. Logic uses such terms as true, false, inconsistent, valid, and self-contradictory. A Necessary truth is one that is true no matter what the state of the world or, as it is sometimes put, all possible words. Logic truth are those necessary truths that are necessarily true owing to the meaning of their logical constants only.

Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence, but not full assurance, of the truth of the conclusion. It is also described as a method where one's experiences and observations, including what are learned from others, are synthesized to come up with a general truth. Many dictionaries define inductive reasoning as the derivation of general principles from specific observations, although there are many inductive arguments that do not have that form.

" In logic and mathematics, a formal proof or derivation is a finite sequence of sentences each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically checkable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof."

In philosophy and mathematics, logical form of a syntatic expression is a precisely- specified sematic version of that expression in a formal system. Informally, the logical form attempts to formalize a possibly ambigous statement into a statement. infirmally, the logical form attempts to formalize a possibly ambigous statement into a statement with a precise, unambigous logical intrepretationwith respect to a formal language. The logical form of an argument is called argument form if the argument.Deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion neverthless to be false. Valid argument must be clearly expressed by means of sentences called well-formed formulas. In deductive reasoning , an argument is sound if it is both valid in form and its premises are true. In logical systems are sound if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.

Syntax is the set of rules, principles, and processes that govern the structure of sentences in a given language, usually including word order. The term syntax is also used to refer to the study of such principles and processes. The goal of many syntacticians is to discover the syntactic rules common to all languages.One basic description of a language's syntax is the sequence in which the subject (S), verb (V), and object (O) usually appear in sentences. Over 85% of languages usually place the subject first, either in the sequence SVO or the sequence SOV.

Semantics is the study of meaning, reference, or truth. The term can be used to refer to subfields of several distinct disciplines including linguistics, philosophy, and computer science.

Logical Linguistics

In linguistics, semantics is the subfield that studies meaning. Semantics can address meaning at the levels of words, phrases, sentences, or larger units of discourse. One of the crucial questions which unites different approaches to linguistic semantics is that of the relationship between form and meaning

TYPES OF LOGIC...

FORMAL LOGIC

PHILOSHOPHICAL LOGIC

MATHEMATICALLOGIC

INFORMAL LOGIC

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PHILOSOPHICAL LOGIC

Philosophical logic refers to those areas of philosophy in which recognized methods of logic have traditionally been used to solve or advance the discussion of philosophical problems. Among these, Sybil Wolfram highlights the study of argument, meaning, and truth, while Colin McGinn presents identity, existence, predication, necessity and truth as the main topics of his book on the subject.Philosophical logic also addresses extensions and alternatives to traditional, "classical" logic known as "non-classical" logics. These receive more attention in texts such as John P. Burgess's Philosophical Logic the Blackwell Companion to Philosophical Logic,or the multi-volume Handbook of Philosophical Logic edited by Dov M. Gabbay and Franz Guenthner.

MATHEMATICAL LOGIC

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science.[1] The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those.

INFORMAL LOGIC

Informal logic encompasses the principles of logic and logical thought outside of a formal setting. However, perhaps because of the "informal" in the title, the precise definition of "informal logic" is a matter of some dispute. Ralph H. Johnson and J. Anthony Blair define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation. This definition reflects what had been implicit in their practice and what others were doing in their informal logic texts. Informal logic is associated with (informal) fallacies, critical thinking, the thinking skills movement and the interdisciplinary inquiry known as argumentation theory. Frans H. van Eemeren writes that the label "informal logic" covers a "collection of normative approaches to the study of reasoning in ordinary language that remain closer to the practice of argumentation than formal logic.

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FORMAL LOGIC

Formal logic is the study of inference with purely formal content. An inference possesses a purely formal and explicit content such as, a rule that is not about any particular thing or property. In many definitions of logic, logical consequence and inference with purely formal content are the same. Examples of formal logic include traditional syllogistic logic and modern symbolic Logic: Syllogistic logic can be found in the works of Aristotle, making it the earliest known formal study and studies types of syllogism. Modern formal logic follows and expands on Aristotle.Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference, often divided into two main branches: propositional logic and predicate logic.

HISTORY

The history of logic deals with the study of the development of the science of valid inference . Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic. Christian and Islamic philosophers such as Boethius (died 524), Ibn Sina (Avicenna, died 1037) and William of Ockham (died 1347) further developed Aristotle's logic in the Middle Ages, reaching a high point in the mid-fourteenth century, with Jean Buridan. The period between the fourteenth century and the beginning of the nineteenth century saw largely decline and neglect, and at least one historian of logic regards this time as barren. Empirical methods ruled the day, as evidenced by Sir Francis Bacon's Novum Organon of 1620.

Philosophy encompassed all bodies of knowledge and a practitioner was known as a philosopher. From the time of Ancient Greek philosopher Aristotle to the 19th century, "natural philosophy" encompassed astronomy, medicine, and physics. In the 19th century, the growth of modern research universities led academic philosophy and other disciplines to professionalize and specialize. Since then, various areas of investigation that were traditionally part of philosophy have become separate academic disciplines, such as psychology, sociology, linguistics, and economics.

Natural philosophy was the study of the constitution and processes of transformation in the physical world. Moral philosophy was the study of goodness, right and wrong, justice and virtue.

Mathematics includes the study of such topics as quantity structure, space and change. It has no generally accepted definition. Mathematicians seek and use pattern to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects

Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof.

The term "cognitive science" is used for "any kind of mental operation or structure that can be studied in precise terms" . This conceptualization is very broad, and should not be confused with how "cognitive" is used in some traditions of analytic philosophy, where "cognitive" has to do only with formal rules and truth conditional semantics.

Computer science is the study of algorithmic processes, computational machines and computation itself. As a discipline, computer science spans a range of topics from theoretical studies of algorithms, computation and information to the practical issues of implementing computational systems in hardware and software

Linguistics is the scientific study of language. It involves analysis of language form, language meaning, and language in context, as well as an analysis of the social, cultural, historical, and political factors that influence language. Linguists traditionally analyse human language by observing the relationship between sound and meaning

Psychology is the science of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, as well as feeling and thought. It is an academic discipline of immense scope. Psychologists seek an understanding of the emergent properties of brains, and all the variety of phenomena linked to those emergent properties, joining this way the broader neuro-scientific group of researchers

HISTORY..

COMPUTER SCIENCE

PHILOSOPHY

LINGUISTICS

MATHEMATICS

PHYSIOLOGY

COGINITIVE SCIENCE

Controversies

"Is Logic Empirical?"

Case for abandoning certain familiar principles of classical logic: if we want to be realists about the physical phenomena described by quantum theory, then we should abandon the principle of distributivity, substituting for classical logic the quantum logic proposed by Garrett Birkhoff and John von Neumann

Tolerating the impossible

Relevance logic and paraconsistent logic are the most important approaches here, though the concerns are different: a key consequence of classical logic and some of its rivals, such as intuitionistic logic, is that they respect the principle of explosion, which means that the logic collapses if it is capable of deriving a contradiction. Graham Priest, the main proponent of dialetheism, has argued for paraconsistency on the grounds that there are in fact, true contradictions.

Implication: strict or material

The first class of paradoxes involves counterfactuals, such as If the moon is made of green cheese, then 2+2=5, which are puzzling because natural language does not support the principle of explosion. Eliminating this class of paradoxes was the reason for C. I. Lewis's formula.

CONCLUSION

LOGICAL TRUTH

AIM OFLOGIC

IMPORTANCE

HISTORICALPATH

Logic influences every decision we make in our lives. Logical thinking allows us to learn and make decisions that will affect our lifestyle.

In logical truth function is a function that accepts truth values as input and produces a unique truth value as output.

The history of logic deals with the study of the development of the science of valid logic. Formal logics developed in ancient times in India, China, and Greece

The aim of logic is the elaboration of a coherent system that allows us to investigate, classify, and evaluate good and bad forms of reasoning.

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