Logic, science and mathematics

Western philosophy

Western philosophy dates to the Greek philosophers, who were active in Ancient Greece beginning in the 6th century BC. Pythagoras distinguished himself from other "wise ones" by calling himself a mere lover of wisdom, suggesting that he was not wise. Socrates used this title and insisted that he possessed no wisdom but was a pursuer of wisdom. Socrates' student Plato is often credited as the founder of Western philosophy. The philosopher Alfred North Whitehead said of Plato: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. I do not mean the systematic scheme of thought which scholars have doubtfully extracted from his writings. I allude to the wealth of general ideas scattered through them." Eastern philosophy is a term that encompasses the many philosophical currents originating outside Europe, including China, India, Japan, Persia and other regions. They have their own timelines, regions and philosophers. Major traditions include:

• African philosophy and Ethiopian philosophy
• Ancient Egyptian philosophy and Babylonian literature
• Indian philosophy, Jain philosophy and Hindu philosophy
• Iranian philosophy
• East Asian Neo-Confucianism and Buddhist philosophy, Japanese philosophy and Korean philosophy
• Persian Zoroastrianism
• Middle Eastern Islamic philosophy
• European Jewish philosophy and Christian philosophy
• Mesoamerican Aztec philosophy

Knowledge

Traditionally, the term "philosophy" referred to any body of knowledge. In this sense, philosophy is closely related to religion, mathematics, natural science, education and politics. Newton's 1687 "Mathematical Principles of Natural Philosophy" is classified in the 2000s as a book of physics; he used the term "natural philosophy" because it used to encompass disciplines that later became associated with sciences such as astronomy, medicine and physics. Philosophy was traditionally divided into three major branches:

• Natural philosophy ("physics") was the study of the physical world (physis, lit: nature);
• Moral philosophy ("ethics") was the study of goodness, right and wrong, beauty, justice and virtue (ethos, lit: custom);
• Metaphysical philosophy ("logos") was the study of existence, causation, God, logic, forms and other abstract objects ("meta-physika" lit: "what comes after physics").

This division is not obsolete but has changed. Natural philosophy has split into the various natural sciences, especially astronomy, physics, chemistry, biology and cosmology. Moral philosophy has birthed the social sciences, but still includes value theory (including aesthetics, ethics, political philosophy, etc.). Metaphysical philosophy has birthed formal sciences such as logic, mathematics and philosophy of science, but still includes epistemology, cosmology and others.

Philosophical progress

Many philosophical debates that began in ancient times are still debated today. Colin McGinn and others claim that no philosophical progress has occurred during that interval. Chalmers and others, by contrast, see progress in philosophy similar to that in science, while Talbot Brewer argued that "progress" is the wrong standard by which to judge philosophical activity.

Categories

Philosopher questions can be grouped into categories. These groupings allow philosophers to focus on a set of similar topics and interact with other thinkers who are interested in the same questions. The groupings also make philosophy easier for students to approach. Students can learn the basic principles involved in one aspect of the field without being overwhelmed with the entire set of philosophical theories.Various sources present different categorical schemes. The categories adopted in this article aim for breadth and simplicity.

These five major branches can be separated into sub-branches and each sub-branch contains many specific fields of study.

• Metaphysics and epistemology
• Value theory
• Science, logic and mathematics
• History of Western philosophy
• Philosophical traditions

These divisions are neither exhaustive, nor mutually exclusive. (A philosopher might specialize in Kantian epistemology, or Platonic aesthetics, or modern political philosophy.) Furthermore, these philosophical inquiries sometimes overlap with each other and with other inquiries such as science, religion or mathematics.

Metaphysics

Metaphysics is the study of the most general features of reality, such as existence, time, objects and their properties, wholes and their parts, events, processes and causation and the relationship between mind and body. Metaphysics includes cosmology, the study of the world in its entirety and ontology, the study of being. A major point of debate revolves between realism, which holds that there are entities that exist independently of their mental perception and idealism, which holds that reality is mentally constructed or otherwise immaterial. Metaphysics deals with the topic of identity. Essence is the set of attributes that make an object what it fundamentally is and without which it loses its identity while accident is a property that the object has, without which the object can still retain its identity. Particulars are objects that are said to exist in space and time, as opposed to abstract objects, such as numbers, and universals, which are properties held by multiple particulars, such as redness or a gender. The type of existence, if any, of universals and abstract objects is an issue of debate.

Epistemology

Epistemology is the study of knowledge (Greek episteme). Epistemologists study the putative sources of knowledge, including intuition, a priori reason, memory, perceptual knowledge, self-knowledge and testimony. They also ask: What is truth? Is knowledge justified true belief? Are any beliefs justified? Putative knowledge includes propositional knowledge (knowledge that something is the case), know-how (knowledge of how to do something) and acquaintance (familiarity with someone or something). Epistemologists examine these and ask whether knowledge is really possible.

Skepticism is the position which doubts claims to knowledge. The regress argument, a fundamental problem in epistemology, occurs when, in order to completely prove any statement, its justification itself needs to be supported by another justification. This chain can go on forever, called infinitism, it can eventually rely on basic beliefs that are left unproven, called foundationalism, or it can go in a circle so that a statement is included in its own chain of justification, called coherentism. Rationalism is the emphasis on reasoning as a source of knowledge. It is associated with a priori knowledge, which is independent of experience, such as math and logical deduction. Empiricism is the emphasis on observational evidence via sensory experience as the source of knowledge.

Among the numerous topics within metaphysics and epistemology, broadly construed are:

• Philosophy of language explores the nature, the origins and the use of language.
• Philosophy of mind explores the nature of the mind and its relationship to the body. It is typified by disputes between dualism and materialism. In recent years this branch has become related to cognitive science.
• Philosophy of religion explores questions that arise in connection with religions, including the soul, the afterlife, God, religious experience, analysis of religious vocabulary and texts and the relationship of religion and science.
• Philosophy of human nature analyzes the unique characteristics of human beings, such as rationality, politics and culture.
• Metaphilosophy explores the aims of philosophy, its boundaries and its methods.

Value theory

Value theory (or axiology) is the major branch of philosophy that addresses topics such as goodness, beauty and justice. Value theory includes ethics, aesthetics, political philosophy, feminist philosophy, philosophy of law and more.

Ethics

Ethics, or "moral philosophy", studies and considers what is good and bad conduct, right and wrong values, and good and evil. Its primary investigations include how to live a good life and identifying standards of morality. It also includes meta-investigations about whether a best way to live or related standards exists. The main branches of ethics are normative ethics, meta-ethics and applied ethics. A major point of debate revolves around consequentialism, where actions are judged by the potential results of the act, such as to maximize happiness, called utilitarianism, and deontology, where actions are judged by how they adhere to principles, irrespective of negative ends.

Aesthetics

Aesthetics is the "critical reflection on art, culture and nature." It addresses the nature of art, beauty and taste, enjoyment, emotional values, perception and with the creation and appreciation of beauty. It is more precisely defined as the study of sensory or sensori-emotional values, sometimes called judgments of sentiment and taste. It divides into art theory, literary theory, film theory and music theory. An example from art theory is to discern the set of principles underlying the work of a particular artist or artistic movement such as the Cubist aesthetic. The philosophy of film analyzes films and filmmakers for their philosophical content and explores film (images, cinema, etc.) as a medium for philosophical reflection and expression.

Political philosophy

Political philosophy is the study of government and the relationship of individuals (or families and clans) to communities including the state. It includes questions about justice, law, property and the rights and obligations of the citizen. Politics and ethics are traditionally linked subjects, as both discuss the question of what how people should live together. Other branches of value theory:

There are a variety of branches of value theory.

• Philosophy of law (often called jurisprudence) explores the varying theories explaining the nature and interpretation of laws.
• Philosophy of education analyzes the definition and content of education, as well as the goals and challenges of educators.
• Feminist philosophy explores questions surrounding gender, sexuality and the body including the nature of feminism itself as a social and philosophical movement.
• Philosophy of sport analyzes sports, games and other forms of play as sociological and uniquely human activities.

Logic, science and mathematics

Many academic disciplines generated philosophical inquiry. The relationship between "X" and the "philosophy of X" is debated. Richard Feynman argued that the philosophy of a topic is irrelevant to its primary study, saying that "philosophy of science is as useful to scientists as ornithology is to birds." Curtis White, by contrast, argued that philosophical tools are essential to humanities, sciences and social sciences.

The topics of philosophy of science are numbers, symbols and the formal methods of reasoning as employed in the social sciences and natural sciences.

Logic

Logic is the study of reasoning and argument. An argument is "a connected series of statements intended to establish a proposition." The connected series of statements are "premises" and the proposition is the conclusion. For example:

1. All humans are mortal. (premise)
2. Socrates is a human. (premise)
3. Therefore, Socrates is mortal. (conclusion)

Deductive reasoning is when, given certain premises, conclusions are unavoidably implied. Rules of inference are used to infer conclusions such as, modus ponens, where given “A” and “If A then B”, then “B” must be concluded.

Because sound reasoning is an essential element of all sciences, social sciences and humanities disciplines, logic became a formal science. Sub-fields include mathematical logic, philosophical logic, Modal logic, computational logic and non-classical logics. A major issue in the philosophy of mathematics revolves around whether mathematical entities are objective and discovered, called mathematical realism, or invented, called mathematical antirealism.

Philosophy of science

This branch explores the foundations, methods, history, implications and purpose of science. Many of its sub-divisions correspond to a specific branch of science. For example, philosophy of biology deals specifically with the metaphysical, epistemological and ethical issues in the biomedical and life sciences. The philosophy of mathematics studies the philosophical assumptions, foundations and implications of mathematics.

History of philosophy

Some philosophers specialize in one or more historical periods. The history of philosophy (study of a specific period, individual or school) is related to but not the same as the philosophy of history (the theoretical aspect of history, which deals with questions such as the nature of historical evidence and the possibility of objectivity).

Hegel's Lectures on the Philosophy of History influenced many philosophers to interpret truth in light of history, a view called historicism.

Philosophical schools

Some philosophers specialize in one or more of the major philosophical schools, such as Continental philosophy, Analytical philosophy, Thomism, Asian philosophy or African philosophy.