Temporal finitism is the doctrine that
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
is
finite
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marked ...
in the
past
The past is the set of all events that occurred before a given point in time. The past is contrasted with and defined by the present and the future. The concept of the past is derived from the linear fashion in which human observers experience t ...
. The philosophy of
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
, expressed in such works as his ''
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
'', 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,
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
, and
Christian philosophers
Christians () are people who follow or adhere to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus Christ. The words ''Christ'' and ''Christian'' derive from the Koine Greek title ''Christós'' (Χρι ...
who, primarily
creationist
Creationism is the religious belief that nature, and aspects such as the universe, Earth, life, and humans, originated with supernatural acts of divine creation. Gunn 2004, p. 9, "The ''Concise Oxford Dictionary'' says that creationism is 'th ...
, were unable to reconcile the
Aristotelian conception of the eternal with the
Genesis creation narrative
The Genesis creation narrative is the creation myth of both Judaism and Christianity. The narrative is made up of two stories, roughly equivalent to the first two chapters of the Book of Genesis. In the first, Elohim (the Hebrew generic word ...
.
Medieval background
In contrast to
ancient
Ancient history is a time period from the History of writing, beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian language, Sumerian c ...
Greek philosophers
Ancient Greek philosophy arose in the 6th century BC, marking the end of the Greek Dark Ages. Greek philosophy continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empire ...
who believed that the universe had an
infinite
Infinite may refer to:
Mathematics
*Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
* Infinite (group), a South Korean boy band
*''Infinite'' (EP), debut EP of American m ...
past with no beginning,
medieval philosophers and
theologians
Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the s ...
developed the concept of the universe having a finite past with a beginning. This view was inspired by the
creation myth
A creation myth (or cosmogonic myth) is a symbolic narrative of how the world began and how people first came to inhabit it., "Creation myths are symbolic stories describing how the universe and its inhabitants came to be. Creation myths develop ...
shared by the three
Abrahamic religions
The Abrahamic religions are a group of religions centered around worship of the God of Abraham. Abraham, a Hebrew patriarch, is extensively mentioned throughout Abrahamic religious scriptures such as the Bible and the Quran.
Jewish tradition ...
:
Judaism
Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
,
Christianity
Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. It is the world's largest and most widespread religion with roughly 2.38 billion followers representing one-third of the global pop ...
and
Islam
Islam (; ar, ۘالِإسلَام, , ) is an Abrahamic religions, Abrahamic Monotheism#Islam, monotheistic religion centred primarily around the Quran, a religious text considered by Muslims to be the direct word of God in Islam, God (or ...
.
Prior to
Maimonides
Musa ibn Maimon (1138–1204), commonly known as Maimonides (); la, Moses Maimonides and also referred to by the acronym Rambam ( he, רמב״ם), was a Sephardic Jewish philosopher who became one of the most prolific and influential Torah ...
, it was held that it was possible to prove, philosophically, creation theory. The
Kalam cosmological argument
The Kalam cosmological argument is a modern formulation of the cosmological argument for the existence of God. It is named after the ''Kalam'' (medieval Islamic scholasticism) from which its key ideas originated. William Lane Craig was principally ...
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, OP (; it, Tommaso d'Aquino, lit=Thomas of Aquino; 1225 – 7 March 1274) was an Italian Dominican friar and priest who was an influential philosopher, theologian and jurist in the tradition of scholasticism; he is known wi ...
was influenced by this belief, and held in his
Summa Theologica
The ''Summa Theologiae'' or ''Summa Theologica'' (), often referred to simply as the ''Summa'', is the best-known work of Thomas Aquinas (1225–1274), a scholasticism, scholastic theologian and Doctor of the Church. It is a compendium of all ...
that neither hypothesis was demonstrable. Some of Maimonides' Jewish successors, including
Gersonides
Levi ben Gershon (1288 – 20 April 1344), better known by his Graecized name as Gersonides, or by his Latinized name Magister Leo Hebraeus, or in Hebrew by the abbreviation of first letters as ''RaLBaG'', was a medieval French Jewish philosoph ...
and
Crescas Crescas (, he, קרשקש) is a Judaeo-Catalan family name, prominent in the former Crown of Aragon. Crescas is a common name among Jews of southern France and Catalonia. There have been a number of scholars and rabbis sharing that surname, incl ...
, conversely held that the question was decidable, philosophically.
John Philoponus
John Philoponus (Greek: ; ; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Byzantine Greek philologist, Aristotelian commentator, Christian theologian and an author of a considerable number of philosophical tre ...
was probably the first to use the
argument
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectic ...
that infinite time is impossible in order to establish temporal finitism. He was followed by many others including St.
Bonaventure
Bonaventure ( ; it, Bonaventura ; la, Bonaventura de Balneoregio; 1221 – 15 July 1274), born Giovanni di Fidanza, was an Italian Catholic Franciscan, bishop, cardinal, scholastic theologian and philosopher.
The seventh Minister G ...
.
Philoponus
John Philoponus (Greek: ; ; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Byzantine Greek philologist, Aristotelian commentator, Christian theologian and an author of a considerable number of philosophical tr ...
' arguments for temporal finitism were severalfold. ''Contra Aristotlem'' has been
lost
Lost may refer to getting lost, or to:
Geography
*Lost, Aberdeenshire, a hamlet in Scotland
* Lake Okeechobee Scenic Trail, or LOST, a hiking and cycling trail in Florida, US
History
*Abbreviation of lost work, any work which is known to have bee ...
, and is chiefly known through the citations used by
Simplicius of Cilicia
Simplicius of Cilicia (; el, Σιμπλίκιος ὁ Κίλιξ; c. 490 – c. 560 AD) 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 i ...
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.
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.
The most sophisticated medieval arguments against an infinite past were later developed by the
early Muslim philosopher,
Al-Kindi
Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, physician ...
(Alkindus); the
Jewish philosopher
Jewish philosophy () includes all philosophy carried out by Jews, or in relation to the religion of Judaism. Until modern ''Haskalah'' (Jewish Enlightenment) and Jewish emancipation, Jewish philosophy was preoccupied with attempts to reconcile ...
,
Saadia Gaon
Saʻadiah ben Yosef Gaon ( ar, سعيد بن يوسف الفيومي ''Saʻīd bin Yūsuf al-Fayyūmi''; he, סַעֲדְיָה בֶּן יוֹסֵף אַלְפַיּוּמִי גָּאוֹן ''Saʿăḏyāh ben Yōsēf al-Fayyūmī Gāʾōn''; ...
(Saadia ben Joseph); and the
Muslim theologian,
Al-Ghazali
Al-Ghazali ( – 19 December 1111; ), full name (), and known in Persian-speaking countries as Imam Muhammad-i Ghazali (Persian: امام محمد غزالی) or in Medieval Europe by the Latinized as Algazelus or Algazel, was a Persian polymat ...
(Algazel). They developed 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."
:"Thus an infinite temporal regress of events cannot exist."
This argument depends on the (unproved) assertion that an actual infinite cannot exist; and that an infinite past implies an infinite succession of "events", a word not clearly defined. 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."
:"Thus the temporal series of past events cannot be an actual infinite."
The first statement states, correctly, that a finite (number) cannot be made into an infinite one by the finite addition of more finite numbers. The second skirts around this; the analogous idea in mathematics, that the (infinite) sequence of negative integers "..-3, -2, -1" may be extended by appending zero, then one, and so forth; is perfectly valid.
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 (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
in his thesis of the first
antinomy
Antinomy (Greek ἀντί, ''antí'', "against, in opposition to", and νόμος, ''nómos'', "law") refers to a real or apparent mutual incompatibility of two laws. It is a term used in logic and epistemology, particularly in the philosophy of I ...
concerning time.
Modern revival
Immanuel Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
's argument for temporal finitism, at least in one direction, from his First Antinomy, runs as follows:
Modern mathematics generally incorporates infinity. For most purposes it is simply used as convenient; when considered more carefully it is incorporated, or not, according to whether the
axiom of infinity
In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the ...
is included. This is the mathematical concept of infinity; while this may provide useful analogies or ways of thinking about the physical world, it says nothing directly about the physical world.
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor ( , ; – January 6, 1918) was a German mathematician. He played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of ...
recognized two different kinds of infinity. The first, used in calculus, he called the variable finite, or potential infinite, represented by the
sign (known as the
lemniscate
In algebraic geometry, a lemniscate is any of several figure-eight or -shaped curves. The word comes from the Latin "''lēmniscātus''" meaning "decorated with ribbons", from the Greek λημνίσκος meaning "ribbons",. or which alternativel ...
), and the
actual infinite
In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities as given, actual and completed objects. These might include the set of natural numbers, ext ...
, which Cantor called the "true infinite." His notion of
transfinite arithmetic
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an e ...
became the standard system for working with
infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions amo ...
within
set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
.
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
thought that the role of the actual infinite was relegated only to the abstract realm of mathematics. "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought... The role that remain for the infinite to play is solely that of an idea." Philosopher
William Lane Craig
William Lane Craig (born August 23, 1949) is an American analytic philosopher, Christian apologist, author and Wesleyan theologian who upholds the view of Molinism and neo-Apollinarianism. He is Professor of Philosophy at Houston Baptist Univ ...
argues that if the past were infinitely long, it would entail the existence of actual infinites in reality.
Craig and Sinclair also argue that an actual infinite cannot be formed by successive addition. Quite independent of the absurdities arising from an actual infinite number of past events, the formation of an actual infinite has its own problems. For any
finite
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marked ...
number n, n+1 equals a finite number. An actual infinity has no immediate predecessor.
The Tristram Shandy paradox is an attempt to illustrate the absurdity of an infinite past. Imagine Tristram Shandy, an immortal man who writes his biography so slowly that for every day that he lives, it takes him a year to record that day. Suppose that Shandy had always existed. Since there is a one-to-one correspondence between the number of past days and the number of past years on an infinite past, one could reason that Shandy could write his entire autobiography. From another perspective, Shandy would only get farther and farther behind, and given a past eternity, would be infinitely far behind.
Craig asks us to suppose that we met a man who claims to have been counting down from infinity and is now just finishing. We could ask why he did not finish counting yesterday or the day before, since eternity would have been over by then. In fact for any day in the past, if the man would have finished his countdown by day n, he would have finished his countdown by n-1. It follows that the man could not have finished his countdown at any point in the finite past, since he would have already been done.
Input from physicists
In 1984 physicist
Paul Davies
Paul Charles William Davies (born 22 April 1946) is an English physicist, writer and broadcaster, a professor in Arizona State University and Director of BEYOND: Center for Fundamental Concepts in Science. He is affiliated with the Institute ...
deduced a finite-time origin of the universe in a quite different way, from physical grounds: "the universe will eventually die, wallowing, as it were, in its own
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
. This is known among physicists as the 'heat death' of the universe... The universe cannot have existed for ever, otherwise it would have reached its equilibrium end state an infinite time ago. Conclusion: the universe did not always exist."
More recently though physicists have proposed various ideas for how the universe could have existed for an infinite time, such as
eternal inflation
Eternal inflation is a hypothetical inflationary universe model, which is itself an outgrowth or extension of the Big Bang theory.
According to eternal inflation, the inflationary phase of the universe's expansion lasts forever throughout most of ...
. But in 2012,
Alexander Vilenkin
Alexander Vilenkin (russian: Алекса́ндр Виле́нкин; uk, Олександр Віленкін; born 13 May 1949) is the Leonard Jane Holmes Bernstein Professor of Evolutionary Science and Director of the Institute of Cosmology a ...
and
Audrey Mithani of
Tufts University
Tufts University is a private research university on the border of Medford and Somerville, Massachusetts. It was founded in 1852 as Tufts College by Christian universalists who sought to provide a nonsectarian institution of higher learning. ...
wrote a paper claiming that in any such scenario past time could not have been infinite.
It could however have been "before any nameable time", according to
Leonard Susskind
Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicis ...
.
Critical reception
Kant's argument for finitism has been widely discussed, for instance
Jonathan Bennett points out that Kant's argument is not a sound logical proof: His assertion that "Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away", assumes that the universe was created at a beginning and then progressed from there, which seems to assume the conclusion. A universe that simply existed and had not been created, or a universe that was created as an infinite progression, for instance, would still be possible. Bennett quotes Strawson:
Some of the criticism of William Lane Craig's argument for temporal finitism has been discussed and expanded on by Stephen Puryear.
In this, he writes Craig's argument as:
# If the universe did not have a beginning, then the past would consist in an infinite temporal sequence of events.
# An infinite temporal sequence of past events would be actually and not merely potentially infinite.
# It is impossible for a sequence formed by successive addition to be actually infinite.
# The temporal sequence of past events was formed by successive addition.
# Therefore, the universe had a beginning.
Puryear points out that Aristotle and Aquinas had an opposing view to point 2, but that the most contentious is point 3. Puryear says that many philosophers have disagreed with point 3, and adds his own objection:
:"Consider the fact that things move from one point in space to another. In so doing, the moving object passes through an actual infinity of intervening points. Hence, motion involves traversing an actual infinite ... Accordingly, the finitist of this stripe must be mistaken. Similarly, whenever some period of time elapses, an actual infinite has been traversed, namely, the actual infinity of instants that make up that period of time."
Puryear then points that Craig has defended his position by saying that time might or must be naturally divided and so there is not an actual infinity of instants between two times. Puryear then goes on to argue that if Craig is willing to turn an infinity of points into a finite number of divisions, then points 1, 2 and 4 are not true.
An article by Louis J. Swingrover makes a number of points relating to the idea that Craig's "absurdities" are not contradictions in themselves: they are all either mathematically consistent (like Hilbert's hotel or the man counting down to today), or do not lead to inescapable conclusions. He argues that if one makes the assumption that any mathematically coherent model is metaphysically possible, then it can be shown that an infinite temporal chain is metaphysically possible, since one can show that there exist mathematically coherent models of an infinite progression of times. He also says that Craig might be making a cardinality error similar to assuming that because an infinitely extended temporal series would contain an infinite number of times, then it would have to contain the number "infinity".
Quentin Smith attacks "their supposition that an infinite series of past events must contain some events separated from the present event by an infinite number of intermediate events, and consequently that from one of these infinitely distant past events the present could never have been reached".
Smith asserts that Craig and Wiltrow are making a cardinality error by confusing an unending sequence with a sequence whose members must be separated by an infinity: None of the integers is separated from any other integer by an infinite number of integers, so why assert that an infinite series of times must contain a time infinitely far back in the past.
Smith then says that Craig uses false presuppositions when he makes statements about infinite collections (in particular the ones relating to Hilbert's Hotel and infinite sets being equivalent to proper subsets of them), often based on Craig finding things "unbelievable", when they are actually mathematically correct. He also points out that the Tristram Shandy paradox is mathematically coherent, but some of Craig's conclusions about when the biography would be finished are incorrect.
Ellery Eells expands on this last point by showing that the Tristram Shandy paradox is internally consistent and fully compatible with an infinite universe.
Graham Oppy embroiled in debate with Oderberg, points out that the Tristram Shandy story has been used in many versions. For it to be useful to the temporal finitism side, a version must be found that is logically consistent and not compatible with an infinite universe. To see this, note that the argument runs as follows:
# If an infinite past is possible, then the Tristram Shandy story must be possible
# The Tristram Shandy story leads to contradiction.
# Therefore, an infinite past is not possible.
The problem for the finitist is that point 1 is not necessarily true. If a version of the Tristram Shandy story is internally inconsistent, for instance, then the infinitist could just assert that an infinite past is possible, but that particular Tristram Shandy is not because it's not internally consistent. Oppy then lists the different versions of the Tristram Shandy story that have been put forward and shows that they are all either internally inconsistent or they don't lead to contradiction.
Citations
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{{Time in philosophy
Philosophy of time
Philosophy of physics
Philosophy of Aristotle
Infinity
Metaphysical theories