Temporal finitism

Write the text of your article herTemporal finitism is the idea that time is finite. The context of the idea is the pre-modern era, before mathematicians had understood the concept of infinity and before physical cosmology. 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.

Medieval philosophy
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. 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.

Modern philosophy
Immanuel Kant's argument for temporal finitism, at least in one direction, from his First Antinomy, runs as follows: "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

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 Harshorne

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 Harshorne

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.