Al-Kindi in the context of "Mathematician"

Early Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar (early 9th century CE) and lasting until the 6th century AH (late 12th century CE). The period is known as the Islamic Golden Age, and the achievements of this period had a crucial influence in the development of modern philosophy and science. For Renaissance Europe, "Muslim maritime, agricultural, and technological innovations, as well as much East Asian technology via the Muslim world, made their way to western Europe in one of the largest technology transfers in world history." This period starts with al-Kindi in the 9th century and ends with Averroes (Ibn Rushd) at the end of 12th century. The death of Averroes effectively marks the end of a particular discipline of Islamic philosophy usually called the Peripatetic Arabic School, and philosophical activity declined significantly in Western Islamic countries, namely in Islamic Spain and North Africa, though it persisted for much longer in the Eastern countries, in particular Persia and India where several schools of philosophy continued to flourish: Avicennism, Illuminationist philosophy, Mystical philosophy, and Transcendent theosophy.

Intellectual innovations, achievements, and advancements of this period included, within jurisprudence, the development of ijtihad, a method or methodological approach to legal reasoning, interpretation, and argument based on independent inquiry and analogical deduction; within science and the philosophy of science, the development of empirical research methods emphasizing controlled experimentation, observational evidence, and reproducibility, as well as early formulations of empiricist epistemologies; commentaries and developments in Aristotelian logic, as well as innovations in non-Aristotelian temporal modal logic and inductive logic; and developments in research practice and methodology, including, within medicine, the first documented peer review process and within jurisprudence and theology, a strict science of citation, the isnad or "backing".

Islamic philosophy is philosophy that emerges from the Islamic tradition. Two terms traditionally used in the Islamic world are sometimes translated as philosophy—falsafa (lit. 'philosophy'), which refers to philosophy as well as logic, mathematics, and physics; and kalam (lit. 'speech'), which refers to a rationalist form of Scholastic Islamic theology which includes the schools of Ash'arism, Maturidism and Mu'tazilism.

Early Islamic philosophy began with al-Kindi in the 2nd century of the Islamic calendar (early 9th century CE) and declined with Ibn Rushd (Averroes) in the 6th century AH (late 12th century CE), broadly coinciding with the period known as the Islamic Golden Age. The death of Ibn Rushd effectively marked the end of a specific discipline of Islamic philosophy usually called the Islamic peripatetic school, and philosophical activity declined significantly in the west of the Islamic world, including al-Andalus and the Maghreb.

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.

The Hindu–Arabic numeral system (also known as the Indo-Arabic numeral system, Hindu numeral system, and Arabic numeral system) is a positional base-ten numeral system for representing integers; its extension to non-integers is the decimal numeral system, which is presently the most common numeral system.

The system was invented between the 1st and 4th centuries by Indian mathematicians. By the 9th century, the system was adopted by Arabic mathematicians who extended it to include fractions. It became more widely known through the writings in Arabic of the Persian mathematician Al-Khwārizmī (On the Calculation with Hindu Numerals, c. 825) and Arab mathematician Al-Kindi (On the Use of the Hindu Numerals, c. 830). The system had spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century Liber Abaci; until the evolution of the printing press in the 15th century, use of the system in Europe was mainly confined to Northern Italy.

The existence of God is a subject of debate in the philosophy of religion and theology. A wide variety of arguments for and against the existence of God (with the same or similar arguments also generally being used when talking about the existence of multiple deities) can be categorized as logical, empirical, metaphysical, subjective, or scientific. In philosophical terms, the question of the existence of God involves the disciplines of epistemology (the nature and scope of knowledge) and ontology (study of the nature of being or existence) and the theory of value (since some definitions of God include perfection).

The Western tradition of philosophical discussion of the existence of God began with Plato and Aristotle, who made arguments for the existence of a being responsible for fashioning the universe, referred to as the demiurge or the unmoved mover, that today would be categorized as cosmological arguments. Other arguments for the existence of God have been proposed by St. Anselm, who formulated the first ontological argument; Thomas Aquinas, who presented his own version of the cosmological argument (the first way); René Descartes, who said that the existence of a benevolent God is logically necessary for the evidence of the senses to be meaningful. John Calvin argued for a sensus divinitatis, which gives each human a knowledge of God's existence. Islamic philosophers who developed arguments for the existence of God comprise Averroes, who made arguments influenced by Aristotle's concept of the unmoved mover; Al-Ghazali and Al-Kindi, who presented the Kalam cosmological argument; Avicenna, who presented the Proof of the Truthful; and Al-Farabi, who made Neoplatonic arguments.

Abu Zayd Ahmed ibn Sahl Balkhi (Persian: ابو زید احمد بن سهل بلخی) was a Persian Muslim polymath: a geographer, mathematician, physician, psychologist and scientist. Born in 850 CE in Shamistiyan, in the province of Balkh, Greater Khorasan, he was a disciple of al-Kindi. He also founded the "Balkhī school" of terrestrial mapping in Baghdad. Al-Balkhi is believed to have been one of the earliest to diagnose that mental illness can have psychological and physiological causes and he was the first to typify four types of emotional disorders: fear and anxiety; anger and aggression; sadness and depression; and obsessions.

Muslim philosophers both profess Islam and engage in a style of philosophy situated within the structure of the Arabic language and Islam, though not necessarily concerned with religious issues. The sayings of the companions of Muhammad contained little philosophical discussion. In the eighth century, extensive contact with the Byzantine Empire led to a drive to translate philosophical works of Ancient Greek Philosophy (especially the texts of Aristotle) into Arabic.

The ninth-century Al-Kindi is considered the founder of Islamic peripatetic philosophy (800 CE – 1200 CE). The tenth-century philosopher al-Farabi contributed significantly to the introduction of Greek and Roman philosophical works into Muslim philosophical discourse and established many of the themes that would occupy Islamic philosophy for the next centuries; in his broad-ranging work, his work on logic stands out particularly. In the eleventh century, Ibn Sina, one of the greatest Muslim philosophers ever, developed his own unique school of philosophy known as Avicennism which had strong Aristotelian and Neoplatonist roots. Al-Ghazali, a famous Muslim philosopher and theologian, took the approach to resolving apparent contradictions between reason and revelation. He understood the importance of philosophy and developed a complex response that rejected and condemned some of its teachings, while it also allowed him to accept and apply others. It was al-Ghazali's acceptance of demonstration (apodeixis) that led to a much more refined and precise discourse on epistemology and a flowering of Aristotelian logic and metaphysics in Muslim theological circles. Averroes, the last notable Muslim peripatetic philosopher, defended the use of Aristotelian philosophy against this charge; his extensive works include noteworthy commentaries on Aristotle. In the twelfth century, the philosophy of illumination was founded by Shahab al-Din Suhrawardi. Although philosophy in its traditional Aristotelian form fell out of favor in much of the Arab world after the twelfth century, forms of mystical philosophy became more prominent.

Medieval Islamic philosophy was steeped in both Aristotelianism and Neoplatonism from its ninth-century beginnings with al-Kindi, but the influence of Neoplatonism becomes more clearly visible in the tenth and eleventh centuries with Al-Farabi and Avicenna. Al-Farabi expanded on Plato's concept of an ideal city ruled by philosopher-kings to develop a political philosophy that could accommodate the religious and cultural diversity central to Islamic nations. On the other hand, both al-Ghazali and Ibn Rushd vigorously opposed Neoplatonic views.

The characteristic of Neoplatonic thought in Islamic theology is that of emanation, linking God's transcendence with the corporeal reality of his creation. Islamic Neoplatonism was introduced by Al-Farabi, although Avicenna proved to have the greater influence. Both authors present a complex scheme of emanation.