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Temporal finitism

Temporal finitism

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Temporal finitism is the idea that time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

 is finite. The context of the idea is the pre-modern era, before mathematicians had understood the concept of infinity
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...

 and before physical cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

.

The philosophy of Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

, expressed in such works as his physics
Physics (Aristotle)
The Physics of Aristotle is one of the foundational books of Western science and philosophy...

, held that although space was finite, with only void existing beyond the outermost sphere of the heavens, time was infinite. This caused problems for mediaeval Islamic
Early Islamic philosophy
Early Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar and lasting until the 6th century AH...

, Jewish
Jewish philosophy
Jewish philosophy , includes all philosophy carried out by Jews, or, in relation to the religion of Judaism. Jewish philosophy, until modern Enlightenment and Emancipation, was pre-occupied with attempts to reconcile coherent new ideas into the tradition of Rabbinic Judaism; thus organizing...

 and Christian philosophers
Christian philosophy
Christian philosophy may refer to any development in philosophy that is characterised by coming from a Christian tradition.- Origins of Christian philosophy :...

, who were unable to reconcile the Aristotelian
Aristotelianism
Aristotelianism is a tradition of philosophy that takes its defining inspiration from the work of Aristotle. 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...

 conception of the eternal with the Abrahamic
Abrahamic religions
Abrahamic religions are the monotheistic faiths emphasizing and tracing their common origin to Abraham or recognizing a spiritual tradition identified with him...

 view of Creation.

Medieval philosophy


In contrast to ancient
Ancient philosophy
This page lists some links to ancient philosophy. In Western philosophy, the spread of Christianity through the Roman Empire marked the ending of Hellenistic philosophy and ushered in the beginnings of Medieval philosophy, whereas in Eastern philosophy, the spread of Islam through the Arab Empire...

 Greek philosophers
Greek philosophy
Ancient Greek philosophy arose in the 6th century BCE and continued through the Hellenistic period, at which point Ancient Greece was incorporated in the Roman Empire...

 who believed that the universe had an infinite past with no beginning, medieval philosophers
Medieval philosophy
Medieval philosophy is the philosophy in the era now known as medieval or the Middle Ages, the period roughly extending from the fall of the Western Roman Empire in the fifth century AD to the Renaissance in the sixteenth century...

 and theologians
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...

 developed the concept of the universe having a finite past with a beginning. This view was inspired by the creation doctrine shared by the three Abrahamic religions
Abrahamic religions
Abrahamic religions are the monotheistic faiths emphasizing and tracing their common origin to Abraham or recognizing a spiritual tradition identified with him...

: Judaism
Judaism
Judaism ) is the "religion, philosophy, and way of life" of the Jewish people...

, Christianity
Christianity
Christianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...

 and Islam
Islam
Islam . The most common are and .   : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...

.

Prior to Maimonides
Maimonides
Moses ben-Maimon, called Maimonides and also known as Mūsā ibn Maymūn in Arabic, or Rambam , was a preeminent medieval Jewish philosopher and one of the greatest Torah scholars and physicians of the Middle Ages...

, it was held that it was possible to prove, philosophically, creation theory. The Kalam cosmological argument
Kalam cosmological argument
The Kalām cosmological argument is a variation of the cosmological argument that argues for the existence of a First Cause for the universe. Its origins can be traced to medieval Jewish, Christian and Muslim thinkers, but most directly to Islamic theologians of the Kalām tradition. Its historic...

 held that creation was provable, for example. Maimonides himself held that neither creation nor Aristotle's infinite time were provable, or at least that no proof was available. (According to scholars of his work, he didn't make a formal distinction between unprovability and the simple absence of proof.) Thomas Aquinas
Thomas Aquinas
Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...

 was influenced by this belief, and held in his Summa Theologica
Summa Theologica
The Summa Theologiæ is the best-known work of Thomas Aquinas , and although unfinished, "one of the classics of the history of philosophy and one of the most influential works of Western literature." It is intended as a manual for beginners in theology and a compendium of all of the main...

 that neither hypothesis was demonstrable. Some of Maimonides' Jewish successors, including Gersonides
Gersonides
Levi ben Gershon, better known by his Latinised name as Gersonides or the abbreviation of first letters as RaLBaG , philosopher, Talmudist, mathematician, astronomer/astrologer. He was born at Bagnols in Languedoc, France...

 and Crescas
Crescas
Crescas is a Jewish family name. There have been a number of scholars and rabbis sharing that surname, including:* Abiathar Crescas, a 15th-century Jewish physician and astrologer, doctor to King John II of Aragon * Astruc Don Crescas...

, conversely held that the question was decidable, philosophically.

John Philoponus
John Philoponus
John Philoponus , also known as John the Grammarian or John of Alexandria, was a Christian and Aristotelian commentator and the author of a considerable number of philosophical treatises and theological works...

 was probably the first to use the argument
Argument
In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...

 that infinite time is impossible, establishing temporal finitism. He was followed by many others including Al-Kindi
Al-Kindi
' , known as "the Philosopher of the Arabs", was a Muslim Arab philosopher, mathematician, physician, and musician. Al-Kindi was the first of the Muslim peripatetic philosophers, and is unanimously hailed as the "father of Islamic or Arabic philosophy" for his synthesis, adaptation and promotion...

, Saadia Gaon
Saadia Gaon
Saʻadiah ben Yosef Gaon was a prominent rabbi, Jewish philosopher, and exegete of the Geonic period.The first important rabbinic figure to write extensively in Arabic, he is considered the founder of Judeo-Arabic literature...

, Al-Ghazali
Al-Ghazali
Abu Hāmed Mohammad ibn Mohammad al-Ghazzālī , known as Algazel to the western medieval world, born and died in Tus, in the Khorasan province of Persia was a Persian Muslim theologian, jurist, philosopher, and mystic....

, St. Bonaventure
Bonaventure
Saint Bonaventure, O.F.M., , born John of Fidanza , was an Italian medieval scholastic theologian and philosopher. The seventh Minister General of the Order of Friars Minor, he was also a Cardinal Bishop of Albano. He was canonized on 14 April 1482 by Pope Sixtus IV and declared a Doctor of the...

 and Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....

 (in his First Antinomy). The argument was revisited once again by William Lane Craig
William Lane Craig
William Lane Craig is an American analytic philosopher, philosophical theologian, and Christian apologist. He is known for his work on the philosophy of time and the philosophy of religion, specifically the existence of God and the defense of Christian theism...

 in light of the idea of transfinite number
Transfinite number
Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these...

s in modern mathematics.

Philoponus' arguments for temporal finitism were severalfold. Contra Aristotlem has been lost, and is chiefly known through the citations used by Simplicius of Cilicia
Simplicius of Cilicia
Simplicius of Cilicia, was a disciple of Ammonius Hermiae and Damascius, and was one of the last of the Neoplatonists. He was among the pagan philosophers persecuted by Justinian in the early 6th century, and was forced for a time to seek refuge in the Persian court, before being allowed back into...

 in his commentaries on Aristotle's Physics and De Caelo. Philoponus' refutation of Aristotle extended to six books, the first five addressing De Caelo and the sixth addressing Physics, and from comments on Philoponus made by Simplicius can be deduced to have been quite lengthy.

A full exposition of Philoponus' several arguments, as reported by Simplicius, can be found in Sorabji, listed in Further reading. One such argument was based upon Aristotle's own theorem that there were not multiple infinities, and ran as follows: If time were infinite, then as the universe continued in existence for another hour, the infinity of its age since creation at the end of that hour must be one hour greater than the infinity of its age since creation at the start of that hour. But since Aristotle holds that such treatments of infinity are impossible and ridiculous, the world cannot have existed for infinite time.

Philoponus' works were adopted by many, most notably; early Muslim philosopher
Early Islamic philosophy
Early Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar and lasting until the 6th century AH...

, Al-Kindi
Al-Kindi
' , known as "the Philosopher of the Arabs", was a Muslim Arab philosopher, mathematician, physician, and musician. Al-Kindi was the first of the Muslim peripatetic philosophers, and is unanimously hailed as the "father of Islamic or Arabic philosophy" for his synthesis, adaptation and promotion...

 (Alkindus); the Jewish philosopher
Jewish philosophy
Jewish philosophy , includes all philosophy carried out by Jews, or, in relation to the religion of Judaism. Jewish philosophy, until modern Enlightenment and Emancipation, was pre-occupied with attempts to reconcile coherent new ideas into the tradition of Rabbinic Judaism; thus organizing...

, Saadia Gaon
Saadia Gaon
Saʻadiah ben Yosef Gaon was a prominent rabbi, Jewish philosopher, and exegete of the Geonic period.The first important rabbinic figure to write extensively in Arabic, he is considered the founder of Judeo-Arabic literature...

 (Saadia ben Joseph); and the Muslim theologian
Kalam
ʿIlm al-Kalām is the Islamic philosophical discipline of seeking theological principles through dialectic. Kalām in Islamic practice relates to the discipline of seeking theological knowledge through debate and argument. A scholar of kalām is referred to as a mutakallim...

, Al-Ghazali
Al-Ghazali
Abu Hāmed Mohammad ibn Mohammad al-Ghazzālī , known as Algazel to the western medieval world, born and died in Tus, in the Khorasan province of Persia was a Persian Muslim theologian, jurist, philosopher, and mystic....

 (Algazel). They used his two logical arguments against an infinite past, the first being the "argument from the impossibility of the existence of an actual infinite", which states:
"An actual infinite cannot exist."
"An infinite temporal regress of events is an actual infinite."
" An infinite temporal regress of events cannot exist."


The second argument, the "argument from the impossibility of completing an actual infinite by successive addition", states:
"An actual infinite cannot be completed by successive addition."
"The temporal series of past events has been completed by successive addition."
" The temporal series of past events cannot be an actual infinite."


Both arguments were adopted by later Christian philosophers and theologians, and the second argument in particular became more famous after it was adopted by Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....

 in his thesis of the first antinomy
Antinomy
Antinomy literally means the mutual incompatibility, real or apparent, of two laws. It is a term used in logic and epistemology....

 concerning time.

Modern philosophy


Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....

's argument for temporal finitism, at least in one direction, from his First Antinomy, runs as follows:
Modern mathematics has no great problems working with infinity, but the concept still troubles some philosophers, such as Viney who argues that it is a mistake to conclude, because philosophers have been unable to answer the problems posed by the idea of an actual infinite, expounded by Kant and others, that one should not believe in an infinite past, asserting out that both metaphysical world views, that time is finite and infinite, incur paradoxes. He invokes Charles Hartshorne
Charles Hartshorne
Charles Hartshorne was a prominent American philosopher who concentrated primarily on the philosophy of religion and metaphysics. He developed the neoclassical idea of God and produced a modal proof of the existence of God that was a development of St. Anselm's Ontological Argument...

's principle of least paradox (As long as the problems in one's own position are fewer than those in the positions of others, there is no justification for capitulating to the arguments of opponents.) and points out several problems with the idea of temporal finitism.

One such problem is given by Hartshorne's argument against the existence of a first moment in time:
Another, subtler, problem is that a first moment would never appear to be a first moment. Pointing to the similar arguments given by the defenders of Creation Science
Creation science
Creation Science or scientific creationism is a branch of creationism that attempts to provide scientific support for the Genesis creation narrative in the Book of Genesis and disprove generally accepted scientific facts, theories and scientific paradigms about the history of the Earth, cosmology...

, and similar arguments made by Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...

, he argues that there is a paradox that infects the view that a first moment of time existed: Because every event appears to have been caused by some previous event, any first event cannot look like a first event, and so the universe must always appear to be older than it actually is. In Hartshorne's words:
A third problem is that the notion of a first moment implies that it is impossible to conceive the idea of the universe being older than it is. Viney's argument, which he notes was also recognized as a problem by St Bonaventure, runs as follows: To claim that the universe could have begun, say, 2 seconds earlier is to imply that there is some measure of time that is outside and independent of the universe. However, since the first moment of time, by definition, marks the beginning of time, there can be no such independent and external measure of time.

Viney thus declares the debate between the finitist position and the infinitist position on time to be a stalemate, since the former is no less paradoxical than the latter.