- Temporal finitism
Temporal finitism is the idea that
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.cite journal|title=Gersonides' Proofs for the Creation of the Universe|author=Seymour Feldman|journal=Proceedings of the American Academy for Jewish Research|volume=35|date=1967|pages=113–137|doi=10.2307/3622478]
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, Christianityand Islam.
Maimonides, it was held that it was possible to prove, philosophically, creation theory. The Kalam cosmological argumentheld 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 Aquinaswas influenced by this belief, and held in his Summa Theologicathat neither hypothesis was demonstrable. Some of Maimonides' Jewish successors, including Gersonidesand Crescas, conversely held that the question was decidable, philosophically. John Philoponuswas probably the first to use the argumentthat infinite time is impossible, establishing temporal finitism. He was followed by many others including Al-Kindi, Saadia Gaon, Al-Ghazali, St. Bonaventureand Immanuel Kant(in his First Antinomy). The argument was revisited once again by William Lane Craigin light of the idea of transfinite numbers in modern mathematics.cite book|title=Charles Hartshorne and the Existence of God|chapter=The Cosmological Argument|author=Donald Wayne Viney|pages=65–68|date=1985|publisher=SUNY Press|ibsn=0873959078]
Philoponus' arguments for temporal finitism were severalfold. "Contra Aristotlem" has been lost, and is chiefly known through the citations used by
Simplicius of Ciliciain 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. [cite journal|title=John Philoponus as a Source of Medieval Islamic and Jewish Proofs of Creation|author=Herbert A. Davidson|journal=Journal of the American Oriental Society|volume=89|issue=2|date=April–June 1969|pages=357–391|doi=10.2307/596519]
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. [cite news|title=What's New in Ancient Philosophy|work=Philosopny Now|author=Mark Daniels|url=http://philosophynow.org./archive/articles/20daniels.htm|date=2007]
The most sophisticated medieval arguments against an infinite past were later developed by the early Muslim philosopher,
Al-Kindi(Alkindus); the Jewish philosopher, Saadia Gaon(Saadia ben Joseph); and the Muslim theologian, Al-Ghazali(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:citation|title=Whitrow and Popper on the Impossibility of an Infinite Past|first=William Lane|last=Craig|journal=The British Journal for the Philosophy of Science|volume=30|issue=2|date=June 1979|pages=165-170 [165-6] ]
:"An actual infinite cannot exist.":"An infinite temporal regress of events is an actual infinite.":"Unicode|∴ 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.":"Unicode|∴ 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 Kantin his thesis of the first antimony concerning time.
Immanuel Kant's argument for temporal finitism, at least in one direction, from his First Antinomy, runs as follows: [cite web|title=Kant's First Antinomy, of Space and Time|work=Critique of Pure Reason|pages=A 426–429|coauthors=Norman Kemp Smith (tr.)|author=Immanual Kant|url=http://meta-religion.com./Philosophy/Biography/Immanuel_Kant/First_antinomy.htm]
Viney 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, pointing 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:
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 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.
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