Ethics in the context of Mathematical rigor

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.

Socrates (/ˈsɒkrətiːz/; Ancient Greek: Σωκράτης, romanized: Sōkrátēs; c. 470 – 399 BC) was an ancient Greek philosopher from Classical Athens, perhaps the first Western moral philosopher, and a major inspiration on his student Plato, who largely founded the tradition of Western philosophy. An enigmatic figure, Socrates authored no texts and is known mainly through the posthumous accounts of classical writers, particularly his students Plato and Xenophon. These accounts are written as dialogues, in which Socrates and his interlocutors examine a subject in the style of question and answer; they gave rise to the Socratic dialogue literary genre. Contradictory accounts of Socrates make a reconstruction of his philosophy nearly impossible, a situation known as the Socratic problem. Socrates was a polarizing figure in Athenian society. In 399 BC, he was accused of impiety and corrupting the youth. After a trial that lasted a day, he was sentenced to death. As related by Plato, he was put to death by administration of poison after refusing offers from allies to help him escape.

Plato's dialogues are among the most comprehensive accounts of Socrates to survive from antiquity. They demonstrate the Socratic approach to areas of philosophy including epistemology and ethics. The Platonic Socrates lends his name to the concept of the Socratic method, and also to Socratic irony. The Socratic method of questioning, or elenchus, takes shape in dialogue using short questions and answers, epitomized by those Platonic texts in which Socrates and his interlocutors examine various aspects of an issue or an abstract meaning, usually relating to one of the virtues, and find themselves at an impasse, unable to define what they thought they understood. Socrates frequently proclaims his ignorance, saying that he is only sure that he does not know.

Ontology is the philosophical study of being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of reality and every entity within it. To articulate the basic structure of being, ontology examines the commonalities among all things and investigates their classification into basic types, such as the categories of particulars and universals. Particulars are unique, non-repeatable entities, such as the person Socrates, whereas universals are general, repeatable entities, like the color green. Another distinction exists between concrete objects existing in space and time, such as a tree, and abstract objects existing outside space and time, like the number 7. Systems of categories aim to provide a comprehensive inventory of reality by employing categories such as substance, property, relation, state of affairs, and event.

Ontologists disagree regarding which entities exist at the most basic level. Platonic realism asserts that universals have objective existence, while conceptualism maintains that universals exist only in the mind, and nominalism denies their existence altogether. Similar disputes pertain to mathematical objects, unobservable objects assumed by scientific theories, and moral facts. Materialism posits that fundamentally only matter exists, whereas dualism asserts that mind and matter are independent principles. According to some ontologists, objective answers to ontological questions do not exist, with perspectives shaped by differing linguistic practices.

In ethics and social sciences, value denotes the degree of importance of some thing or action, with the aim of determining which actions are best to do or what way is best to live (normative ethics), or to describe the significance of different actions. Value systems are proscriptive and prescriptive beliefs; they affect the ethical behavior of a person or are the basis of their intentional activities. Often primary values are strong and secondary values are suitable for changes. What makes an action valuable may in turn depend on the ethical values of the objects it increases, decreases, or alters. An object with "ethic value" may be termed an "ethic or philosophic good" (noun sense).

Values can be defined as broad preferences concerning appropriate courses of actions or outcomes. As such, values reflect a person's sense of right and wrong or what "ought" to be. "Equal rights for all", "Excellence deserves admiration", and "People should be treated with respect and dignity" are representatives of values. Values tend to influence attitudes and behavior and these types include moral values, doctrinal or ideological values, social values, and aesthetic values. It is debated whether some values that are not clearly physiologically determined, such as altruism, are intrinsic, and whether some, such as acquisitiveness, should be classified as vices or virtues.

Rights are legal, social, or ethical principles of freedom or entitlement; that is, rights are the fundamental normative rules about what is allowed of people or owed to people according to some legal system, social convention, or ethical theory. Rights are an important concept in law and ethics, especially theories of justice and deontology.

The history of social conflicts has often involved attempts to define and redefine rights. According to the Stanford Encyclopedia of Philosophy, "rights structure the form of governments, the content of laws, and the shape of morality as it is currently perceived".

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 "principle") of the world to, respectively, water, apeiron (the unlimited), and air. Another three pre-Socratic philosophers came from nearby Ionian towns: Xenophanes, Heraclitus, and Pythagoras. Xenophanes is known for his critique of the anthropomorphism of gods. Heraclitus, who was notoriously difficult to understand, is known for his maxim on impermanence, ta panta rhei, and for attributing fire to be the arche of the world. Pythagoras created a cult-like following that advocated that the universe was made up of numbers. The Eleatic school (Parmenides, Zeno of Elea, and Melissus) followed in the 5th century BC. Parmenides claimed that only one thing exists and nothing can change. Zeno and Melissus mainly defended Parmenides' opinion. Anaxagoras and Empedocles offered a pluralistic account of how the universe was created. Leucippus and Democritus are known for their atomism, and their views that only void and matter exist. The Sophists advanced philosophical relativism. The Pre-Socratics have had significant impact on several concepts of Western philosophy, such as naturalism and rationalism, and paved the way for scientific methodology.

Courage (also called bravery, valour (British and Commonwealth English), or valor (American English)) is the choice and willingness to confront agony, pain, danger, uncertainty, or intimidation. Valor is courage or bravery, especially in battle.

Physical courage is bravery in the face of physical pain, hardship, even death, or threat of death; while moral courage is the ability to act rightly in the face of popular opposition, shame, scandal, discouragement, or personal loss.

Søren Aabye Kierkegaard (/ˈsɒrən ˈkɪərkəɡɑːrd/ SORR-ən KEER-kə-gard, US also /-ɡɔːr/ -⁠gor; Danish: [ˈsɶːɐn ˈɔˀˌpyˀ ˈkʰiɐ̯kəˌkɒːˀ] ; 5 May 1813 – 11 November 1855) was a Danish theologian, philosopher, poet, social critic, and religious author who is widely considered to be the first existentialist philosopher. He wrote critical texts on organized religion, Christianity, morality, ethics, psychology, love, and the philosophy of religion, displaying a fondness for metaphor, irony, and parables. Much of his philosophical work deals with the issues of how one lives as a "single individual", highlighting the importance of authenticity, personal choice and commitment, and the duty to love. Kierkegaard prioritized concrete human reality over abstract thinking.

Kierkegaard's theological work focuses on Socratic Christian ethics, the institution of the Church, the differences among purely objective proofs of Christianity, the infinite qualitative distinction between man and God, and the individual's subjective relationship to the God-Man Jesus Christ, which came through faith. Much of his work deals with Christian love. He was extremely critical of the doctrine and practice of Christianity as a state-controlled religion (Caesaropapism) like the Church of Denmark. His psychological work explored the emotions and feelings of individuals when faced with life choices. Unlike Jean-Paul Sartre and the atheistic existentialism paradigm, Kierkegaard focused on Christian existentialism.

Eclecticism is a conceptual approach that does not hold rigidly to a single paradigm or set of assumptions, but instead draws upon multiple theories, styles, or ideas to gain complementary insights into a subject, or applies different theories in particular cases. However, this is often without conventions or rules dictating how or which theories were combined.

Eclecticism in ethics, philosophy, politics, and religion is often compared to syncretism, but the two concepts differ in their approach to combining elements from different traditions. While syncretism in religion involves the merging or assimilation of several distinct traditions into a new, unified system, eclecticism adopts elements from various systems without necessarily integrating them into a single cohesive framework. This distinction allows for a broader, more inclusive approach in eclecticism, where the selection is based on individual merit or preference rather than an attempt to create a new unified tradition.

Wisdom, also known as sapience, is the ability to apply knowledge, experience, and good judgment to navigate life's complexities. It is often associated with insight, discernment, and ethics in decision-making. Throughout history, wisdom has been regarded as a key virtue in philosophy, religion, and psychology, representing the ability to understand and respond to reality in a balanced and thoughtful manner. Unlike intelligence, which primarily concerns problem-solving and reasoning, wisdom involves a deeper comprehension of human nature, moral principles, and the long-term consequences of actions.

Philosophically, wisdom has been explored by thinkers from Ancient Greece to modern times. Socrates famously equated wisdom with recognizing one's own ignorance, while Aristotle saw it as practical reasoning (phronesis) and deep contemplation (sophia). Eastern traditions, such as Confucianism and Buddhism, emphasize wisdom as a form of enlightened understanding that leads to ethical living and inner peace. Across cultures, wisdom is often linked to virtues like humility, patience, and compassion, suggesting that it is not just about knowing what is right but also acting upon it.

The history of philosophy is the systematic study of the development of philosophical thought. It focuses on philosophy as rational inquiry based on argumentation, but some theorists also include myth, religious traditions, and proverbial lore.

Western philosophy originated with an inquiry into the fundamental nature of the cosmos in Ancient Greece. Subsequent philosophical developments covered a wide range of topics including the nature of reality and the mind, how people should act, and how to arrive at knowledge. The medieval period was focused more on theology. The Renaissance period saw a renewed interest in Ancient Greek philosophy and the emergence of humanism. The modern period was characterized by an increased focus on how philosophical and scientific knowledge is created. Its new ideas were used during the Enlightenment period to challenge traditional authorities. Influential developments in the 19th and 20th centuries included German idealism, pragmatism, positivism, formal logic, linguistic analysis, phenomenology, existentialism, and postmodernism.

Aristotelianism (/ˌærɪstəˈtiːliənɪzəm/ ARR-i-stə-TEE-lee-ə-niz-əm) is a philosophical tradition inspired by the work of Aristotle, usually characterized by deductive logic and an analytic inductive method in the study of natural philosophy and metaphysics. It covers the treatment of the social sciences under a system of natural law. It answers why-questions by a scheme of four causes, including purpose or teleology, and emphasizes virtue ethics. Aristotle and his school wrote tractates on physics, biology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, and government. Any school of thought that takes one of Aristotle's distinctive positions as its starting point can be considered "Aristotelian" in the widest sense. This means that different Aristotelian theories (e.g. in ethics or in ontology) may not have much in common as far as their actual content is concerned besides their shared reference to Aristotle.

In Aristotle's time, philosophy included natural philosophy, which preceded the advent of modern science during the Scientific Revolution. The works of Aristotle were initially defended by the members of the Peripatetic school and later on by the Neoplatonists, who produced many commentaries on Aristotle's writings. In the Islamic Golden Age, Avicenna and Averroes translated the works of Aristotle into Arabic and under them, along with philosophers such as Al-Kindi and Al-Farabi, Aristotelianism became a major part of early Islamic philosophy.

Nicomachus (Ancient Greek: Νικόμαχος; fl. c. 375 BC) was the father of Aristotle. The Suda states that he was a doctor descended from Nicomachus, son of Machaon the son of Asclepius. Greenhill notes he had another son named Arimnestus, and a daughter named Arimneste, by his wife Phaestis, or Phaestias, who was descended from Asclepius as well. He was a native of Stageira, and the friend and physician of Amyntas III, king of Macedonia, 393–369 BC. Nicomachean Ethics, Aristotle's work on Ethics may have been dedicated to his father. Aristotle's son was also called Nicomachus.

In political science, legitimacy is a concept concerning the right of an authority, usually a governing law or a regime, to rule the actions of a society. In political systems where this is not the case, unpopular regimes survive because they are considered legitimate by a small, influential elite. In Chinese political philosophy, since the historical period of the Zhou dynasty (1046–256 BC), the political legitimacy of a ruler and government was derived from the Mandate of Heaven, and unjust rulers who lost said mandate therefore lost the right to rule the people.

In moral philosophy, the term legitimacy is often positively interpreted as the normative status conferred by a governed people upon their governors' institutions, offices, and actions, based upon the belief that their government's actions are appropriate uses of power by a legally constituted government.