The philosophy of Aristotle, expressed in such works as his physics, 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, and Christian philosophers, who were unable to reconcile the Aristotelian conception of the eternal with the Abrahamic view of Creation.
In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians 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: Judaism, Christianity and Islam.
Prior to Maimonides, it was held that it was possible to prove, philosophically, creation theory. The Kalam cosmological argument 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 was influenced by this belief, and held in his Summa Theologica that neither hypothesis was demonstrable. Some of Maimonides' Jewish successors, including Gersonides and Crescas, conversely held that the question was decidable, philosophically.
John Philoponus was probably the first to use the argument that infinite time is impossible, establishing temporal finitism. He was followed by many others including Al-Kindi, Saadia Gaon, Al-Ghazali, St. Bonaventure and Immanuel Kant (in his First Antinomy). The argument was revisited once again by William Lane Craig in light of the idea of transfinite numbers 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 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.[dead link]
Philoponus' works were adopted by many, most notably; early Muslim philosopher, Al-Kindi (Alkindus); the Jewish philosopher, Saadia Gaon (Saadia ben Joseph); and the Muslim theologian, Al-Ghazali (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 in his thesis of the first antinomy concerning time.
If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away in that world an infinite series of successive states of things. 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, and that a beginning of the world is therefore a necessary condition of the world's existence.—Immanuel Kant, First Antinomy, of Space and Time
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'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:
Even a beginning is a change, and all change requires something changing that does not come to exist through that same change. The beginning of the world would have to happen to something other than the world, something which as the subject of happening would be in a time that did not begin with the world.—Charles Hartshorne, Man's Vision of God, p. 233
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, and similar arguments made by Bertrand Russell, 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 first moment of time would be an ontological lie through and through, a joke of existence upon itself.—Charles Hartshorne, Man's Vision of God, p. 234
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.
- Seymour Feldman (1967). "Gersonides' Proofs for the Creation of the Universe". Proceedings of the American Academy for Jewish Research (Proceedings of the American Academy for Jewish Research, Vol. 35) 35: 113–137. doi:10.2307/3622478. JSTOR 3622478.
- Craig, William Lane (June 1979). "Whitrow and Popper on the Impossibility of an Infinite Past". The British Journal for the Philosophy of Science 30 (2): 165–170 [165–6]. doi:10.1093/bjps/30.2.165
- Donald Wayne Viney (1985). "The Cosmological Argument". Charles Hartshorne and the Existence of God. SUNY Press. pp. 65–68. ISBN 0-87395-907-8.
- Herbert A. Davidson (April–June 1969). "John Philoponus as a Source of Medieval Islamic and Jewish Proofs of Creation". Journal of the American Oriental Society (Journal of the American Oriental Society, Vol. 89, No. 2) 89 (2): 357–391. doi:10.2307/596519. JSTOR 596519.
- Mark Daniels (2007). "What's New in Ancient Philosophy". Philosopny Now.
- Immanual Kant; Norman Kemp Smith (tr.). "Kant's First Antinomy, of Space and Time". Critique of Pure Reason. pp. A 426–429.
- Richard Sorabji (2005). "Did the Universe have a Beginning?". The Philosophy of the Commentators, 200–600 AD. Cornell University Press. pp. 175–188. ISBN 0-8014-8988-1.
- Robert Bunn (June 1988). "Review of Time, Creation, and the Continuum: Theories in Antiquity and the Early Middle Ages by Richard Sorabji". Philosophy of Science 55 (2): 304–306. doi:10.1086/289436.
- Maimonides (1956). The Guide To The Perplexed II. translated by M. Friedlander. London: Dover. pp. 15–16,25.
- A. W. Moore (2001). "Mediaval and Renaissance Thought". The Infinite. Routledge. pp. 46–49. ISBN 0-415-25285-7.
- Jaakko Hintikka (April 1966). "Aristotelian Infinity". The Philosophical Review (The Philosophical Review, Vol. 75, No. 2) 75 (2): 197–218. doi:10.2307/2183083. JSTOR 2183083.
- Michael J. White (1992). "Aristotle on Time and Locomotion". The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective. Oxford University Press. ISBN 0-19-823952-1.