René Descartes in the context of "Real part"

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.

In philosophy, rationalism is the epistemological view that "regards reason as the chief source and test of knowledge" or "the position that reason has precedence over other ways of acquiring knowledge", often in contrast to other possible sources of knowledge such as faith, tradition, or sensory experience. More formally, rationalism is defined as a methodology or a theory "in which the criterion of truth is not sensory but intellectual and deductive".

In a major philosophical debate during the Enlightenment, rationalism (sometimes here equated with innatism) was opposed to empiricism. On the one hand, rationalists like René Descartes emphasized that knowledge is primarily innate and the intellect, the inner faculty of the human mind, can therefore directly grasp or derive logical truths; on the other hand, empiricists like John Locke emphasized that knowledge is not primarily innate and is best gained by careful observation of the physical world outside the mind, namely through sensory experiences. Rationalists asserted that certain principles exist in logic, mathematics, ethics, and metaphysics that are so fundamentally true that denying them causes one to fall into contradiction. The rationalists had such a high confidence in reason that empirical proof and physical evidence were regarded as unnecessary to ascertain certain truths – in other words, "there are significant ways in which our concepts and knowledge are gained independently of sense experience".

Foundationalism concerns philosophical theories of knowledge resting upon non-inferential justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises. The main rival of the foundationalist theory of justification is the coherence theory of justification, whereby a body of knowledge, not requiring a secure foundation, can be established by the interlocking strength of its components, like a puzzle solved without prior certainty that each small region was solved correctly.

Identifying the alternatives as either circular reasoning or infinite regress, and thus exhibiting the regress problem, Aristotle made foundationalism his own clear choice, positing basic beliefs underpinning others. Descartes, the most famed foundationalist, discovered a foundation in the fact of his own existence and in the "clear and distinct" ideas of reason, whereas Locke found a foundation in experience. Differing foundations may reflect differing epistemological emphases—empiricists emphasizing experience, rationalists emphasizing reason—but may blend both.

The mind–body problem is a philosophical problem concerning the relationship between thought and consciousness in the human mind and body. It addresses the nature of consciousness, mental states, and their relation to the physical brain and nervous system. The problem centers on understanding how immaterial thoughts and feelings can interact with the material world, or whether they are ultimately physical phenomena.

This problem has been a central issue in philosophy of mind since the 17th century, particularly following René Descartes' formulation of dualism, which proposes that mind and body are fundamentally distinct substances. Other major philosophical positions include monism, which encompasses physicalism (everything is ultimately physical) and idealism (everything is ultimately mental). More recent approaches include functionalism, property dualism, and various non-reductive theories.

In the philosophy of mind, mind–body dualism denotes either that mental phenomena are non-physical, or that the mind and body are distinct and separable. Thus, it encompasses a set of views about the relationship between mind and matter, as well as between subject and object, and is contrasted with other positions, such as physicalism and enactivism, in the mind–body problem.

Aristotle shared Plato's view of multiple souls and further elaborated a hierarchical arrangement, corresponding to the distinctive functions of plants, animals, and humans: a nutritive soul of growth and metabolism that all three share; a perceptive soul of pain, pleasure, and desire that only humans and other animals share; and the faculty of reason that is unique to humans only. In this view, a soul is the hylomorphic form of a viable organism, wherein each level of the hierarchy formally supervenes upon the substance of the preceding level. For Aristotle, the first two souls, based on the body, perish when the living organism dies, whereas there remains an immortal and perpetual intellective part of mind. For Plato, however, the soul was not dependent on the physical body; he believed in metempsychosis, the migration of the soul to a new physical body. It has been considered a form of reductionism by some philosophers, since it enables the tendency to ignore very big groups of variables by its assumed association with the mind or the body, and not for its real value when it comes to explaining or predicting a studied phenomenon.

Baruch (de) Spinoza (24 November 1632 – 21 February 1677), also known under his Latinized pen name Benedictus de Spinoza, was a philosopher of Portuguese-Jewish origin, who was born in the Dutch Republic. A forerunner of the Age of Enlightenment, Spinoza significantly influenced modern biblical criticism, 17th-century rationalism, and Dutch intellectual culture, establishing himself as one of the most important and radical philosophers of the early modern period. Influenced by Stoicism, Thomas Hobbes, René Descartes, Ibn Tufayl, and heterodox Christians, Spinoza was a leading philosopher of the Dutch Golden Age.

Spinoza was born in Amsterdam to a Marrano family that fled Portugal for the more tolerant Dutch Republic. He received a traditional Jewish education, learning Hebrew and studying sacred texts within the Portuguese Jewish community, where his father was a prominent merchant. As a young man, Spinoza challenged rabbinic authority and questioned Jewish doctrines, leading to his permanent expulsion from his Jewish community in 1656. Following that expulsion, he distanced himself from all religious affiliations and devoted himself to philosophical inquiry and lens grinding. Spinoza attracted a dedicated circle of followers who gathered to discuss his writings and joined him in the intellectual pursuit of truth.

Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences (French: Discours de la Méthode pour bien conduire sa raison, et chercher la vérité dans les sciences) is a philosophical and autobiographical treatise published by René Descartes in 1637. It is best known as the source of the famous quotation "Je pense, donc je suis" ("I think, therefore I am", or "I am thinking, therefore I exist"), which occurs in Part IV of the work. A similar argument without this precise wording is found in Meditations on First Philosophy (1641), and a Latin version of the same statement, "Cogito, ergo sum", is found in Principles of Philosophy (1644).

Discourse on the Method is one of the most influential works in the history of modern philosophy, and important to the development of natural sciences. In this work, Descartes tackles the problem of skepticism, which had previously been studied by other philosophers. While addressing some of his predecessors and contemporaries, Descartes modified their approach to account for a truth he found to be incontrovertible; he started his line of reasoning by doubting everything, so as to assess the world from a fresh perspective, clear of any preconceived notions.

The Latin cogito, ergo sum, usually translated into English as "I think, therefore I am", is the "first principle" of René Descartes' philosophy. He originally published it in French as je pense, donc je suis in his 1637 Discourse on the Method, so as to reach a wider audience than Latin would have allowed. It later appeared in Latin in his Principles of Philosophy, and a similar phrase (Ego sum, ego existo, 'I am, I exist') also featured prominently in his Meditations on First Philosophy. The dictum is also sometimes referred to as the cogito. As Descartes explained in a margin note, "we cannot doubt of our existence while we doubt." In the posthumously published The Search for Truth by Natural Light, he expressed this insight as dubito, ergo sum, vel, quod idem est, cogito, ergo sum ("I doubt, therefore I am—or what is the same—I think, therefore I am."). Antoine Léonard Thomas, in a 1765 essay in honor of Descartes, presented it as dubito, ergo cogito, ergo sum ("I doubt, therefore I think, therefore I am.").

Descartes's statement became a fundamental element of Western philosophy, as it purported to provide a certain foundation for knowledge in the face of radical doubt. While other knowledge could be a figment of imagination, deception, or mistake, Descartes asserted that the very act of doubting one's own existence served—at minimum—as proof of the reality of one's own mind; there must be a thinking entity—in this case the self—for there to be a thought.

Reductionism is any of several related philosophical ideas regarding the associations between phenomena which can be described in terms of simpler or more fundamental phenomena. It is also described as an intellectual and philosophical position that interprets a complex system as the sum of its parts, contrary to holism. Reductionism tends to focus on the small, predictable details of a system and is often associated with various philosophies like emergence, materialism, and determinism.