Empirical evidence in the context of "Antiquarian"

The Age of Enlightenment (also the Age of Reason) was a period in the history of Europe and Western civilization during which the Enlightenment, an intellectual and cultural movement, flourished, emerging in the late 17th century in Western Europe and reaching its peak in the 18th century, as its ideas spread more widely across Europe and into the European colonies, in the Americas and Oceania. Characterized by an emphasis on reason, empirical evidence, and scientific method, the Enlightenment promoted ideals of individual liberty, religious tolerance, progress, and natural rights. Its thinkers advocated for constitutional government, the separation of church and state, and the application of rational principles to social and political reform.

The Enlightenment emerged from and built upon the Scientific Revolution of the 16th and 17th centuries, which had established new methods of empirical inquiry through the work of figures such as Galileo Galilei, Johannes Kepler, Francis Bacon, Pierre Gassendi, Christiaan Huygens and Isaac Newton. Philosophical foundations were laid by thinkers including René Descartes, Thomas Hobbes, Baruch Spinoza, and John Locke, whose ideas about reason, natural rights, and empirical knowledge became central to Enlightenment thought. The dating of the period of the beginning of the Enlightenment can be attributed to the publication of Descartes' Discourse on the Method in 1637, with his method of systematically disbelieving everything unless there was a well-founded reason for accepting it, and featuring his dictum, Cogito, ergo sum ('I think, therefore I am'). Others cite the publication of Newton's Principia Mathematica (1687) as the culmination of the Scientific Revolution and the beginning of the Enlightenment. European historians traditionally dated its beginning with the death of Louis XIV of France in 1715 and its end with the outbreak of the French Revolution in 1789. Many historians now date the end of the Enlightenment as the start of the 19th century, with the latest proposed year being the death of Immanuel Kant in 1804.

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work.

Proofs employ logic expressed in mathematical symbols, along with natural language that usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures. The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.

Flat Earth is an archaic and scientifically disproven conception of the Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat-Earth cosmography. The model has undergone a recent resurgence as a conspiracy theory in the 21st century.

The idea of a spherical Earth appeared in ancient Greek philosophy with Pythagoras (6th century BC). However, the early Greek cosmological view of a flat Earth persisted among most pre-Socratics (6th–5th century BC). In the early 4th century BC, Plato wrote about a spherical Earth. By about 330 BC, his former student Aristotle had provided strong empirical evidence for a spherical Earth. Knowledge of the Earth's global shape gradually began to spread beyond the Hellenistic world. By the early period of the Christian Church, the spherical view was widely held, with some notable exceptions. In contrast, ancient Chinese scholars consistently describe the Earth as flat, and this perception remained unchanged until their encounters with Jesuit missionaries in the 17th century. Muslim scholars in early Islam maintained that the Earth is flat. However, since the 9th century, Muslim scholars have tended to believe in a spherical Earth.

Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented.

Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, scientific laws do not express absolute certainty, as mathematical laws do. A scientific law may be contradicted, restricted, or extended by future observations.

Natural science or empirical science is a branch of science concerned with the description, understanding, and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and reproducibility of findings are used to try to ensure the validity of scientific advances.

Natural science can be divided into two main branches: life science and physical science. Life science is alternatively known as biology. Physical science is subdivided into physics, astronomy, Earth science, and chemistry. These branches of natural science may be further divided into more specialized branches, also known as fields. As empirical sciences, natural sciences use tools from the formal sciences, such as mathematics and logic, converting information about nature into measurements that can be explained as clear statements of the "laws of nature".

In philosophy, empiricism is an epistemological view which holds that true knowledge or justification comes only or primarily from sensory experience and empirical evidence. It is one of several competing views within epistemology, along with rationalism and skepticism. Empiricists argue that empiricism is a more reliable method of finding the truth than purely using logical reasoning, because humans have cognitive biases and limitations which lead to errors of judgement. Empiricism emphasizes the central role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. Empiricists may argue that traditions (or customs) arise due to relations of previous sensory experiences.

Historically, empiricism was associated with the "blank slate" concept (tabula rasa), according to which the human mind is "blank" at birth and develops its thoughts only through later experience.

Normative ethics is the study of ethical behaviour and is the branch of philosophical ethics that investigates questions regarding how one ought to act, in a moral sense.

Normative ethics is distinct from metaethics in that normative ethics examines standards for the rightness and wrongness of actions, whereas meta-ethics studies the meaning of moral language and the metaphysics of moral facts. Likewise, normative ethics is distinct from applied ethics in that normative ethics is more concerned with "who ought one be" rather than the ethics of a specific issue (e.g. if, or when, abortion is acceptable). Normative ethics is also distinct from descriptive ethics, as descriptive ethics is an empirical investigation of people's moral beliefs. In this context normative ethics is sometimes called prescriptive (as opposed to descriptive) ethics. However, on certain versions of the view of moral realism, moral facts are both descriptive and prescriptive at the same time.

The scientific method is an empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and medieval world. The scientific method involves careful observation coupled with rigorous skepticism, because cognitive assumptions can distort the interpretation of the observation. Scientific inquiry includes creating a testable hypothesis through inductive reasoning, testing it through experiments and statistical analysis, and adjusting or discarding the hypothesis based on the results.

Although procedures vary across fields, the underlying process is often similar. In more detail: the scientific method involves making conjectures (hypothetical explanations), predicting the logical consequences of hypothesis, then carrying out experiments or empirical observations based on those predictions. A hypothesis is a conjecture based on knowledge obtained while seeking answers to the question. Hypotheses can be very specific or broad but must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested.