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First Principle
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians. In mathematics and formal logic, first principles are referred to as axioms or postulates. In physics and other sciences, theoretical work is said to be from first principles, or '' ab initio'', if it starts directly at the level of established science and does not make assumptions such as empirical model and parameter fitting. "First principles thinking" consists of decomposing things down to the fundamental axioms in the given arena, before reasoning up by asking which ones are relevant to the question at hand, then cross referencing conclusions based on chosen axioms and making sure conclusions do not violate any fundamental laws. Physicists include counter ...
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Philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy. However, they are considered separate academic disciplines in the modern sense of the term. Influential traditions in the history of philosophy include Western philosophy, Western, Islamic philosophy, Arabic–Persian, Indian philosophy, Indian, and Chinese philosophy. Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the Spirituality, spiritual problem of how to reach Enlightenment in Buddhism, enlighten ...
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Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an ''axiom'' may be a " logical axiom" or a " non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example ''a'' + 0 = ''a'' in integer arithmetic. N ...
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Pre-Socratic Philosophy
Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of these early philosophers spanned the workings of the natural world as well as human society, ethics, and religion. They sought explanations based on natural law rather than the actions of gods. Their work and writing has been almost entirely lost. Knowledge of their views comes from ''testimonia'', i.e. later authors' discussions of the work of pre-Socratics. Philosophy found fertile ground in the ancient Greek world because of the close ties with neighboring civilizations and the rise of autonomous civil entities, '' poleis''. Pre-Socratic philosophy began in the 6th century BC with the three Milesians: Thales, Anaximander, and Anaximenes. They all attributed the '' arche'' (a word that could take the meaning of "origin", "substance" or ...
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Orphism (religion)
Orphism is the name given to a set of religious beliefs and practices originating in the ancient Greek and Hellenistic world, associated with literature ascribed to the mythical poet Orpheus, who descended into the Greek underworld and returned. Orphism has been described as a reform of the earlier Dionysian religion, involving a re-interpretation or re-reading of the myth of Dionysus and a re-ordering of Hesiod's ''Theogony'', based in part on pre-Socratic philosophy. The suffering and death of the god Dionysus at the hands of the Titans has been considered the central myth of Orphism. According to this myth, the infant Dionysus is killed, torn apart, and consumed by the Titans. In retribution, Zeus strikes the Titans with a thunderbolt, turning them to ash. From these ashes, humanity is born. In Orphic belief, this myth describes humanity as having a dual nature: body (), inherited from the Titans, and a divine spark or soul (), inherited from Dionysus. In order to achieve ...
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Hesiod
Hesiod ( or ; ''Hēsíodos''; ) was an ancient Greece, Greek poet generally thought to have been active between 750 and 650 BC, around the same time as Homer.M. L. West, ''Hesiod: Theogony'', Oxford University Press (1966), p. 40.Jasper Griffin, "Greek Myth and Hesiod", J.Boardman, J.Griffin and O. Murray (eds.), ''The Oxford History of the Classical World'', Oxford University Press (1986), p. 88. Several of Hesiod's works have survived in their entirety. Among these are ''Theogony'', which tells the origins of the gods, their lineages, and the events that led to Zeus's rise to power, and ''Works and Days'', a poem that describes the five Ages of Man, offers advice and wisdom, and includes myths such as Pandora's box. Hesiod is generally regarded by Western authors as 'the first written poet in the Western tradition to regard himself as an individual persona with an active role to play in his subject.' Ancient authors credited Hesiod and Homer with establishing Greek relig ...
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Cosmogonies
Cosmogony is any model concerning the origin of the cosmos or the universe. Overview Scientific theories In astronomy, cosmogony is the study of the origin of particular astrophysical objects or systems, and is most commonly used in reference to the origin of the universe, the Solar System, or the Earth–Moon system. The prevalent cosmological model of the early development of the universe is the Big Bang theory. Sean M. Carroll, who specializes in theoretical cosmology and field theory, explains two competing explanations for the origins of the singularity, which is the center of a space in which a characteristic is limitless (one example is the singularity of a black hole, where gravity is the characteristic that becomes infinite). It is generally accepted that the universe began at a point of singularity. When the universe started to expand, the Big Bang occurred, which evidently began the universe. The other explanation, held by proponents such as Stephen Hawk ...
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Ancient Greek Philosophy
Ancient Greek philosophy arose in the 6th century BC. Philosophy was used to make sense of the world using reason. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics. Greek philosophy continued throughout the Hellenistic period and later evolved into Roman philosophy. Greek philosophy has influenced much of Western culture since its inception, and can be found in many aspects of public education. Alfred North Whitehead once claimed: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato". Clear, unbroken lines of influence lead from ancient Greek and Hellenistic philosophers to Roman philosophy, early Islamic philosophy, medieval scholasticism, the European Renaissance and the Age of Enlightenment. Greek philosophy was influenced to some extent by the older wisdom litera ...
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Axiomatic Reasoning
In mathematics and logic, an axiomatic system is a set of formal statements (i.e. axioms) used to logically derive other statements such as lemmas or theorems. A proof within an axiom system is a sequence of deductive steps that establishes a new statement as a consequence of the axioms. An axiom system is called complete with respect to a property if every formula with the property can be derived using the axioms. The more general term theory is at times used to refer to an axiomatic system and all its derived theorems. In its pure form, an axiom system is effectively a syntactic construct and does not by itself refer to (or depend on) a formal structure, although axioms are often defined for that purpose. The more modern field of model theory refers to mathematical structures. The relationship between an axiom systems and the models that correspond to it is often a major issue of interest. Properties Four typical properties of an axiom system are consistency, relative ...
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A Priori Knowledge
('from the earlier') and ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. knowledge is independent from any experience. Examples include mathematics,Some associationist philosophers have contended that mathematics comes from experience and is not a form of any ''a priori'' knowledge () tautologies and deduction from pure reason. Galen Strawson has stated that an argument is one in which "you can see that it is true just lying on your couch. You don't have to get up off your couch and go outside and examine the way things are in the physical world. You don't have to do any science." () knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge. The terms originate from the analytic methods found in '' Organon'', a collection of works by Aristotle. Prior analytics () is about deductive logic, which comes from d ...
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Metaphysics
Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of human understanding. Some philosophers, including Aristotle, designate metaphysics as first philosophy to suggest that it is more fundamental than other forms of philosophical inquiry. Metaphysics encompasses a wide range of general and abstract topics. It investigates the nature of existence, the features all entities have in common, and their division into categories of being. An influential division is between particulars and universals. Particulars are individual unique entities, like a specific apple. Universals are general features that different particulars have in common, like the color . Modal metaphysics examines what it means for something to be possible or necessary. Metaphysicians also explore the concepts of space, time, ...
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Epistemology
Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowledge in the form of skills, and knowledge by acquaintance as a familiarity through experience. Epistemologists study the concepts of belief, truth, and justification to understand the nature of knowledge. To discover how knowledge arises, they investigate sources of justification, such as perception, introspection, memory, reason, and testimony. The school of skepticism questions the human ability to attain knowledge while fallibilism says that knowledge is never certain. Empiricists hold that all knowledge comes from sense experience, whereas rationalists believe that some knowledge does not depend on it. Coherentists argue that a belief is justified if it coheres with other beliefs. Foundationalists, by contrast, maintain th ...
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A Posteriori
('from the earlier') and ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. knowledge is independent from any experience. Examples include mathematics,Some associationist philosophers have contended that mathematics comes from experience and is not a form of any ''a priori'' knowledge () tautologies and deduction from pure reason. Galen Strawson has stated that an argument is one in which "you can see that it is true just lying on your couch. You don't have to get up off your couch and go outside and examine the way things are in the physical world. You don't have to do any science." () knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge. The terms originate from the analytic methods found in '' Organon'', a collection of works by Aristotle. Prior analytics () is about deductive logic, which comes from d ...
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