The Principia Mathematica is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–1927, it appeared in a second edition with an important Introduction to the Second Edition, an Appendix A that replaced ✱9 and all-new Appendix B and Appendix C. PM was originally conceived as a sequel volume to Russell's 1903 The Principles of Mathematics, but as PM states, this became an unworkable suggestion for practical and philosophical reasons: "The present work was originally intended by us to be comprised in a second volume of Principles of Mathematics... But as we advanced, it became increasingly evident that the subject is a very much larger one than we had supposed; moreover on many fundamental questions which had been left obscure and doubtful in the former work, we have now arrived at what we believe to be satisfactory solutions."
Truth is the property of being in accord with fact or reality. In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.
Saul Aaron Kripke was an American analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Kripke is considered one of the most important philosophers of the latter half of the 20th century. Since the 1960s, he has been a central figure in a number of fields related to mathematical and modal logic, philosophy of language and mathematics, metaphysics, epistemology, and recursion theory.
The history of logic deals with the study of the development of the science of valid inference (logic). 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.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge.
The development of Indian logic dates back to the anviksiki of Medhatithi Gautama ; the Sanskrit grammar rules of Pāṇini ; the Vaisheshika school's analysis of atomism ; the analysis of inference by Gotama, founder of the Nyaya school of Hindu philosophy; and the tetralemma of Nagarjuna.
According to the redundancy theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence "'Snow is white' is true" is equivalent to asserting the sentence "Snow is white". The philosophical redundancy theory of truth is a deflationary theory of truth.
Anekāntavāda is the Jain doctrine about metaphysical truths that emerged in ancient India. It states that the ultimate truth and reality is complex and has multiple aspects.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
The analytic–synthetic distinction is a semantic distinction used primarily in philosophy to distinguish between propositions that are of two types: analytic propositions and synthetic propositions. Analytic propositions are true or not true solely by virtue of their meaning, whereas synthetic propositions' truth, if any, derives from how their meaning relates to the world.
Trivialism is the logical theory that all statements are true and that all contradictions of the form "p and not p" are true. In accordance with this, a trivialist is a person who believes everything is true.
Jain philosophy or Jaina philosophy refers to the ancient Indian philosophical system of the Jain religion. It comprises all the philosophical investigations and systems of inquiry that developed among the early branches of Jainism in ancient India following the parinirvāṇa of Mahāvīra. One of the main features of Jain philosophy is its dualistic metaphysics, which holds that there are two distinct categories of existence: the living, conscious, or sentient beings (jīva) and the non-living or material entities (ajīva).
Jainism emphasises that ratnatraya — the right faith, right knowledge and right conduct — constitutes the path to liberation. These are known as the triple gems of Jainism and hence also known as Ratnatraya
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterization, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
Yashovijaya, a seventeenth-century Jain philosopher-monk, was a notable Indian philosopher and logician. He was a thinker, prolific writer and commentator who had a strong and lasting influence on Jainism. He was a disciple of Muni Nayavijaya in the lineage of Jain monk Hiravijaya who influenced the Mughal Emperor Akbar to give up eating meat. He is also known as Yashovijayji with honorifics like Mahopadhyaya or Upadhyaya or Gani.
Jainism made its own unique contribution to this mainstream development of philosophy by occupying itself with the basic epistemological issues. According to Jains, knowledge is the essence of the soul. This knowledge is masked by the karmic particles. As the soul obtains knowledge through various means, it does not generate anything new. It only shreds off the knowledge-obscuring karmic particles. According to Jainism, consciousness is a primary attribute of Jīva (soul) and this consciousness manifests itself as darsana (perception) and jnana (knowledge).
Logic is the study of correct reasoning, including both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
Ajñāna was one of the nāstika or "heterodox" schools of ancient Indian philosophy, and the ancient school of radical Indian skepticism. It was a Śramaṇa movement and a major rival of early Buddhism, Jainism and the Ājīvika school. They have been recorded in Buddhist and Jain texts. They held that it was impossible to obtain knowledge of metaphysical nature or ascertain the truth value of philosophical propositions; and even if knowledge was possible, it was useless and disadvantageous for final salvation. They were specialized in refutation without propagating any positive doctrine of their own. Sanjaya Belatthiputta was one of the major proponents of this school of thought.
