#formal logic

• Analytics — A branch of logic or philosophy dealing with the study of methods of analysis and the decomposition of concepts, propositions, or complex arguments into simple formal elements. Historically, the term refers to Aristotle's fundamental works dedicated to syllogism and logical demonstration (Prior and Posterior Analytics), while in a modern sense, it represents the systematic study of language structures and gnoseological foundations.
• Analyzable — Capable of being analyzed, subjected to analysis, or decomposed into component elements; susceptible to critical or scientific examination. It describes a concept, a statement, a substance, or a system whose internal structures are clear and defined enough to allow the separation, identification, and individual study of its constituent parts.
• Analyzability — The property or characteristic of an object, system, statement, or phenomenon of being analyzable; the structural capacity to be decomposed into its elementary constituent parts for systematic study. In epistemology and computer science, it represents a qualitative metric determining the degree of clarity and modularity of a data structure or logical argument, allowing the precise identification of causal relationships between components.
• Analogism — A school of thought, doctrinal method, or theoretical tendency based on the systematic and exclusive use of analogy as the primary tool for knowing, explaining, and interpreting reality or language structures. In philosophy, it designates the type of reasoning that explains universal phenomena through strict proportional correlations and correspondences between microcosm and macrocosmos, while in ancient linguistics, it represented the doctrine asserting that language is governed by regular, proportional, and logical rules, in opposition to anomalism.
• Analogos — An erudite philosophical and linguistic term, borrowed directly from Ancient Greek, designating an element, principle, or concept that stands in a relationship of analogy, mathematical proportion, or perfect structural symmetry with another entity. It is used in hermeneutic essays or classical logic studies to emphasize the identity of functional relationships between two different systems, acting as an explanatory core within comparative argumentation.
• Anti-logical — Contrary to the laws of formal logic, reason, or common sense; presenting a contradictory structure that eliminates the possibility of coherent deduction. In a philosophical sense, it describes an aberrant reasoning, an absurd paradigm, or a paradoxical system of thought that defies the fundamental principles of identity and non-contradiction.
• Anti-logicality — The property, trait, or state of an utterance, reasoning, or conceptual system of being completely devoid of formal logic, violating the laws of reason, or containing insurmountable internal contradictions. In a structural sense, it represents the absurd or irrational character of an argumentative framework that prevents the establishment of a provable truth.
• Antisymmetric — Possessing the property of antisymmetry; changing its algebraic sign upon the inversion of elements (in mathematics and physics) or involving a binary relation where if one element relates to a second and vice versa, then the two elements are necessarily identical (in logic and set theory). In linear algebra, the term describes square matrices whose transpose equals their negative.
• Antisymmetry — A structural property of certain binary relations, functions, matrices, or physical systems of being antisymmetric. In logic and set theory, it represents the quality of a relation whereby if an element x relates to y and y relates to x, it necessarily follows that x equals y; in algebra and quantum physics, it defines the inversion of the sign of a function or tensor upon the interchanging of components or particles.
• Aristotle — Aristotle of Stagira (384–322 BCE), one of the most significant philosophers and scientists of Ancient Greece, a disciple of Plato and tutor to Alexander the Great. Founder of the Lyceum and the Peripatetic school, his encyclopedic body of work laid the foundations for formal logic, ethics, politics, metaphysics, rhetoric, and biology, exerting a massive influence on medieval Christian, Islamic thought, and the entirety of Western culture.
• Aristotle — An onomastic variant or regional/archaic linguistic form used to denote Aristotle, one of the greatest philosophers of Ancient Greece, a disciple of Plato and mentor to Alexander the Great. A systemic thinker, he founded the Lyceum in Athens and laid the formal foundations of logic, metaphysics, ethics, politics, and biology, with his structural work deeply influencing Western and medieval Islamic culture.
• Aristotelian — Belonging to the Greek philosopher Aristotle or to his philosophy, relating to Aristotelianism; a follower of the Aristotelian philosophical doctrine. In a cultural and academic sense, the term describes a rigorous method of thought, based on formal logic, empirical observation of reality, systematic classification, and the use of fundamental concepts such as act and potency, matter and form, or the four causes.
• Aristotelian — The feminine form of aristotelician; an adjective describing a work, theory, method, or conceptual approach that follows the principles of Aristotle's doctrine; a feminine follower of the peripatetic system. In academic analysis, the term is often applied to qualify logic, physics, or ethics developed historically from the Greek philosopher's writings.
• Aristotelianism — A philosophical movement grounded in the works and doctrines of Aristotle, characterized by rigorous rationalism, the use of formal logic as an analytical tool, and the adoption of an empirical perspective on concrete reality. This conceptual system dominated medieval scholastic thought through Arabic and Christian commentaries, defining the European university structure and shaping the evolution of metaphysics, ethics, and natural sciences for centuries.
• Aristotelianism — A spelling or archaic variant for 'aristotelism' (Aristotelianism); a fundamental philosophical movement based on the writings of Aristotle and continued by the Peripatetic school. This doctrinal system emphasizes the empirical study of nature, syllogistic logic, virtue ethics as a form of balance, and metaphysics based on the concepts of substance, matter, and form. The form with 'z' appears in older Romanian texts or those influenced by Slavic or German transcription.
• Assertoric — Asserting or denying something as a real, certain, and axiomatic fact; relating to a value judgment or a proposition that simply states an existing state of affairs, without presenting it as necessary or purely axiomatic (as opposed to apodictic or problematic). In a structural sense, it describes the logical modality through which the truth of an utterance is linked strictly to observable empirical reality.
• Assertoric — A semantic variant perfectly equivalent to the term 'asertoric'; asserting or denying a state of affairs as being real and empirically unquestionable. Used particularly in classic translations of formal logic treatises to define the contingent truth value of a declarative proposition.
• Asyllogistic — Not conforming to the rules of the syllogism or not based on the classic structure of a syllogism; non-syllogistic. In formal logic and philosophy, it describes a reasoning system or an argumentative utterance that does not use structural deduction based on major premise, minor premise, and conclusion, operating instead with other forms of inference or propositional associations.
• Assumption — A learned and rare variant for assumption; a theoretical hypothesis or premise accepted as true without prior proof, used to build a syllogism or a complex argument. In a structural sense, it represents the intellectual act of considering a statement as an axiomatic starting point in academic research.
• Self-negated — Having been rejected, invalidated, or canceled by itself; a system, concept, statement, or individual that has undergone a process of self-negation, thereby losing its initial validity or former identity. In logic and epistemology, it describes a paradoxical state where the constitutive terms of a theoretical structure mutually cancel each other out by their very utterance.