Mathematics Field of study Mathematics (from Greek: μάθημα, máthēma, 'knowledge, study, learning') includes the study of such topics as quantity (number theory),[1] structure (algebra),[2] space (geometry),[1] and change (analysis).[3][4][5] It has no generally accepted definition.[6][7] Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.[10] Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day. History The Babylonian mathematical tablet Plimpton 322, dated to 1800 BC. Etymology ). from . .
Logicians From Wikipedia, the free encyclopedia Philosophy portal A logician is a person, such as a philosopher or a mathematician, whose topic of scholarly study is logic. See List of logicians for a manually compiled list. For more information, see List of logicians. Subcategories This category has the following 6 subcategories, out of 6 total. Pages in category "Logicians" The following 64 pages are in this category, out of 64 total.
Rhizome (philosophy) "As a model for culture, the rhizome resists the organizational structure of the root-tree system which charts causality along chronological lines and looks for the original source of 'things' and looks towards the pinnacle or conclusion of those 'things.' A rhizome, on the other hand, is characterized by 'ceaselessly established connections between semiotic chains, organizations of power, and circumstances relative to the arts, sciences, and social struggles.' Rather than narrativize history and culture, the rhizome presents history and culture as a map or wide array of attractions and influences with no specific origin or genesis, for a 'rhizome has no beginning or end; it is always in the middle, between things, interbeing, intermezzo.' "In this model, culture spreads like the surface of a body of water, spreading towards available spaces or trickling downwards towards new spaces through fissures and gaps, eroding what is in its way. Deleuze, Gilles and Félix Guattari. 1980.
Philosophy of logic Study of the scope and nature of logic Different types of logic are often distinguished. Logic is usually understood as formal logic and is treated as such for most of this article. Formal logic is only interested in the form of arguments, expressed in a formal language, and focuses on deductive inferences. Informal logic, on the other hand, addresses a much wider range of arguments found also in natural language, which include non-deductive arguments. The philosophy of logic also investigates the nature and philosophical implications of the fundamental concepts of logic. The metaphysics of logic is concerned with the metaphysical status of the laws and objects of logic. The term "logic" is based on the Greek word "logos", which is associated with various different senses, such as reason, discourse, or language. General characteristics [edit] There is wide agreement that logic is a normative discipline. Logical and non-logical formal systems Conceptions based on syntax or semantics " and "
Reasoning Reason is the capacity for consciously making sense of things, applying logic, for establishing and verifying facts, and changing or justifying practices, institutions, and beliefs based on new or existing information. It is closely associated with such characteristically human activities as philosophy, science, language, mathematics, and art, and is normally considered to be a definitive characteristic of human nature. Epistemology Philosophical study of knowledge 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. Separate branches of epistemology focus on knowledge in specific fields, like scientific, mathematical, moral, and religious knowledge. Early reflections on the nature, sources, and scope of knowledge are found in ancient Greek, Indian, and Chinese philosophy. Epistemology explores how people should acquire beliefs. The word epistemology comes from the ancient Greek terms ἐπιστήμη (episteme, meaning knowledge or understanding) and λόγος (logos, meaning study of or reason), literally, the study of knowledge. Knowledge is an awareness, familiarity, understanding, or skill. Knowledge contrasts with ignorance, often simply defined as the absence of knowledge. . Major schools of thought [edit]
Philosophy Study of general and fundamental questions Philosophy (from Greek: φιλοσοφία, philosophia, 'love of wisdom')[1][2] is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language.[3][4][5] Such questions are often posed as problems[6][7] to be studied or resolved. Some sources claim the term was coined by Pythagoras (c. 570 – c. 495 BCE),[8][9] although this theory is disputed by some.[10][11][12] Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation.[13][14][i] Historically, philosophy encompassed all bodies of knowledge and a practitioner was known as a philosopher.[15] From the time of Ancient Greek philosopher Aristotle to the 19th century, "natural philosophy" encompassed astronomy, medicine, and physics. For example, Newton's 1687 Mathematical Principles of Natural Philosophy later became classified as a book of physics. Definitions Western philosophy
Metaphysics Metaphysics is a traditional branch of philosophy concerned with explaining the fundamental nature of being and the world that encompasses it,[1] although the term is not easily defined.[2] Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:[3] Ultimately, what is there?What is it like? Prior to the modern history of science, scientific questions were addressed as a part of metaphysics known as natural philosophy. Originally, the term "science" (Latin scientia) simply meant "knowledge". Etymology[edit] However, once the name was given, the commentators sought to find intrinsic reasons for its appropriateness. There is a widespread use of the term in current popular literature which replicates this understanding, i.e. that the metaphysical equates to the non-physical: thus, "metaphysical healing" means healing by means of remedies that are not physical.[8] Central questions[edit] Cosmology and cosmogony[edit] Determinism and free will[edit] [edit]
Philosophy of mathematics The terms philosophy of mathematics and mathematical philosophy are frequently used interchangeably.[1] The latter, however, may be used to refer to several other areas of study. One refers to a project of formalizing a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labors of scholastic theologians, or the systematic aims of Leibniz and Spinoza. Another refers to the working philosophy of an individual practitioner or a like-minded community of practicing mathematicians. Recurrent themes[edit] Recurrent themes include: What is the role of Mankind in developing mathematics? History[edit] The origin of mathematics is subject to argument. Many thinkers have contributed their ideas concerning the nature of mathematics. Greek philosophy on mathematics was strongly influenced by their study of geometry. 20th century[edit] Major themes[edit] Mathematical realism[edit] Platonism[edit] Some[who?]
Ethics The three major areas of study within ethics are:[1] Meta-ethics, concerning the theoretical meaning and reference of moral propositions, and how their truth values (if any) can be determinedNormative ethics, concerning the practical means of determining a moral course of actionApplied ethics, concerning what a person is obligated (or permitted) to do in a specific situation or a particular domain of action[1] Defining ethics[edit] The word "ethics" in English refers to several things.[6] It can refer to philosophical ethics—a project that attempts to use reason in order to answer various kinds of ethical questions. [edit] Main article: Meta-ethics Meta-ethics asks how we understand, know about, and what we mean when we talk about what is right and what is wrong.[8] An ethical question fixed on some particular practical question—such as, "Should I eat this particular piece of chocolate cake?" Meta-ethics has always accompanied philosophical ethics. Normative ethics[edit] Virtue ethics[edit]
Philosophy of mind Branch of philosophy The philosophy of mind is a branch of philosophy that deals with the nature of the mind and its relation to the body and the external world. The mind–body problem is a paradigmatic issue in philosophy of mind, although a number of other issues are addressed, such as the hard problem of consciousness and the nature of particular mental states.[1][2][3] Aspects of the mind that are studied include mental events, mental functions, mental properties, consciousness and its neural correlates, the ontology of the mind, the nature of cognition and of thought, and the relationship of the mind to the body. The problems of physicalist theories of the mind have led some contemporary philosophers to assert that the traditional view of substance dualism should be defended. A related problem is how someone's propositional attitudes (e.g. beliefs and desires) cause that individual's neurons to fire and muscles to contract. Dualist solutions to the mind–body problem [edit]