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.[3]
John Philoponus was probably the first to use the argument that infinite time is impossible in order to establish temporal finitism. He was followed by many others including St. Bonaventure.
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.[4]
A full exposition of Philoponus' several arguments, as reported by Simplicius, can be found in Sorabji.[5]
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 (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:[6]
"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:[2]
"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 in his thesis of the first antinomy concerning time.[2]
Modern revival
Immanuel Kant's argument for temporal finitism from his First Antinomy, runs as follows:[7][8]
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 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 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 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), and the actual infinite, which Cantor called the "true infinite." His notion of transfinite arithmetic became the standard system for working with infinity within set theory. David Hilbert 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."[9] Philosopher William Lane Craig argues that if the past were infinitely long, it would entail the existence of actual infinites in reality.[10]
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 number n, n+1 equals a finite number. An actual infinity has no immediate predecessor.[11]
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.[12] From another perspective, Shandy would only get farther and farther behind, and given a past eternity, would be infinitely far behind.[13]
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.[14]
Input from physicists
In 1984 physicist Paul Davies 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. 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."[15]
More recently though physicists have proposed various ideas for how the universe could have existed for an infinite time, such as eternal inflation. But in 2012, Alexander Vilenkin and Audrey Mithani of Tufts University wrote a paper claiming that in any such scenario past time could not have been infinite.[16] It could however have been "before any nameable time", according to Leonard Susskind.[17] There are also very exotic but consistent physical scenarios under which the Universe has existed in eternity.[18]
Critical reception
Kant's argument for finitism has been widely discussed, for instance Jonathan Bennett[19] 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:
"A temporal process both completed and infinite in duration appears to be impossible only on the assumption that it has a beginning. If ... it is urged that we cannot conceive of a process of surveying which does not have a beginning, then we must inquire with what relevance and by what right the notion of surveying is introduced into the discussion at all."
Some of the criticism of William Lane Craig's argument for temporal finitism has been discussed and expanded on by Stephen Puryear.[20][21]
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 out 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[22] 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[23] expands on this last point by showing that the Tristram Shandy paradox is internally consistent and fully compatible with an infinite universe.
Graham Oppy[24] 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.
A cosmological argument, in natural theology, is an argument which claims that the existence of God can be inferred from facts concerning causation, explanation, change, motion, contingency, dependency, or finitude with respect to the universe or some totality of objects. A cosmological argument can also sometimes be referred to as an argument from universal causation, an argument from first cause, the causal argument, or prime mover argument. Whichever term is employed, there are two basic variants of the argument, each with subtle yet important distinctions: in esse (essentiality), and in fieri (becoming).
The teleological argument is an argument for the existence of God or, more generally, that complex functionality in the natural world which looks designed is evidence of an intelligent creator.
Zeno's paradoxes are a set of philosophical problems devised by the Eleatic Greek philosopher Zeno of Elea.
In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance of infinite entities as given, actual and completed objects. These might include the set of natural numbers, extended real numbers, transfinite numbers, or even an infinite sequence of rational numbers. Actual infinity is to be contrasted with potential infinity, in which a non-terminating process produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps. As a result, potential infinity is often formalized using the concept of a limit.
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 the empire. He wrote extensively on the works of Aristotle. Although his writings are all commentaries on Aristotle and other authors, rather than original compositions, his intelligent and prodigious learning makes him the last great philosopher of pagan antiquity. His works have preserved much information about earlier philosophers which would have otherwise been lost.
Zeno of Elea was a pre-Socratic Greek philosopher. He was a student of Parmenides and one of the Eleatics. Born in Elea, Zeno defended his instructor's belief in monism, the idea that only one single entity exists that makes up all of reality. He rejected the existence of space, time, and motion. To disprove these concepts, he developed a series of paradoxes to demonstrate why these are impossible. Though his original writings are lost, subsequent descriptions by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia have allowed study of his ideas.
Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects are accepted as legitimate.
Eternity, in common parlance, is an infinite amount of time that never ends or the quality, condition or fact of being everlasting or eternal. Classical philosophy, however, defines eternity as what is timeless or exists outside time, whereas sempiternity corresponds to infinite duration.
In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations becomes uncountably infinite. A hypertask that includes one task for each ordinal number is called an ultratask. The term "supertask" was coined by the philosopher James F. Thomson, who devised Thomson's lamp. The term "hypertask" derives from Clark and Read in their paper of that name.
Melissus of Samos was the third and last member of the ancient school of Eleatic philosophy, whose other members included Zeno and Parmenides. Little is known about his life, except that he was the commander of the Samian fleet in the Samian War. Melissus’ contribution to philosophy was a treatise of systematic arguments supporting Eleatic philosophy. Like Parmenides, he argued that reality is ungenerated, indestructible, indivisible, changeless, and motionless. In addition, he sought to show that reality is wholly unlimited, and infinitely extended in all directions; and since existence is unlimited, it must also be one.
Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology and epistemology of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic philosophy. The subject focuses on a number of basic issues, including whether time and space exist independently of the mind, whether they exist independently of one another, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the nature of identity.
The Kalam cosmological argument is a modern formulation of the cosmological argument for the existence of God. It is named after the Kalam, from which its key ideas originated. William Lane Craig was principally responsible for giving new life to the argument in the 20th century, due to his book The Kalām Cosmological Argument (1979), among other writings.
John Philoponus, 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 treatises and theological works. He was born in Alexandria. A rigorous, sometimes polemical writer and an original thinker who was controversial in his own time, John Philoponus broke from the Aristotelian–Neoplatonic tradition, questioning methodology and eventually leading to empiricism in the natural sciences. He was one of the first to propose a "theory of impetus" similar to the modern concept of inertia over Aristotelian dynamics.
The history of the Big Bang theory began with the Big Bang's development from observations and theoretical considerations. Much of the theoretical work in cosmology now involves extensions and refinements to the basic Big Bang model. The theory itself was originally formalised by Father Georges Lemaître in 1927. Hubble's Law of the expansion of the universe provided foundational support for the theory.
Islamic cosmology is the cosmology of Islamic societies. It is mainly derived from the Qur'an, Hadith, Sunnah, and current Islamic as well as other pre-Islamic sources. The Qur'an itself mentions seven heavens.
In philosophy and theology, infinity is explored in articles under headings such as the Absolute, God, and Zeno's paradoxes.
Infinity is something which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
The eternity of the world is the question of whether the world has a beginning in time or has existed for eternity. It was a concern for ancient philosophers as well as theologians and philosophers of the 13th century, and is also of interest to modern philosophers and scientists. The problem became a focus of a dispute in the 13th century, when some of the works of Aristotle, who believed in the eternity of the world, were rediscovered in the Latin West. This view conflicted with the view of the Catholic Church that the world had a beginning in time. The Aristotelian view was prohibited in the Condemnations of 1210–1277.
The Kalām Cosmological Argument is a 1979 book by the philosopher William Lane Craig, in which the author offers a contemporary defense of the Kalām cosmological argument and argues for the existence of God, with an emphasis on the alleged metaphysical impossibility of an infinite regress of past events. First, Craig argues that the universe began to exist, using two philosophical and two scientific arguments. Second, Craig argues that whatever begins to exist has a cause that caused it to begin to exist. Finally, Craig argues that this cause is a personal creator who changelessly and independently willed the beginning of the universe.
"Why is there anything at all?" or "why is there something rather than nothing?" is a question about the reason for basic existence which has been raised or commented on by a range of philosophers and physicists, including Gottfried Wilhelm Leibniz, Ludwig Wittgenstein, and Martin Heidegger, who called it "the fundamental question of metaphysics".
References
Benacerraf, Paul; Putnam, Hilary (1991). Philosophy of Mathematics: Selected Readings (2nded.). Cambridge University Press.
Craig, W. L. (1979). "Whitrow and Popper on the Impossibility of an Infinite Past". The British Journal for the Philosophy of Science. 30 (2): 165–70. doi:10.1093/bjps/30.2.165.
Craig, W. L.; Sinclair, J. D. (2009). "The kalam cosmological argument". In Craig, W. L.; Moreland, J. P. (eds.). The Blackwell Companion to Natural Theology. Wiley-Backwell. pp.101–201.
Davidson, H. A. (1969). "John Philoponus as a Source of Medieval Islamic and Jewish Proofs of Creation". Journal of the American Oriental Society. 89 (2): 357–91. doi:10.2307/596519. JSTOR596519.
Davies, Paul (1984). God and the New Physics. Simon & Schuster.
Eells, Ellery (1988). "Quentin Smith on Infinity and the past". Philosophy of Science. 55 (3): 453–55. doi:10.1086/289451. S2CID170752843.
Feldman, Seymour (1967). "Gersonides' Proofs for the Creation of the Universe". Proceedings of the American Academy for Jewish Research. 35: 113–37. doi:10.2307/3622478. JSTOR3622478.
Sorabji, Richard (2005). "Did the Universe have a Beginning?". The Philosophy of the Commentators, 200–600 AD. Cornell University Press. pp.175–88.
Viney, D. W. (1985). "The Cosmological Argument". Charles Hartshorne and the Existence of God. SUNY Press. pp.59–76.
Further reading
Bunn, Robert (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.
Craig, W. L. (2000). The Kalām Cosmological Argument. Wipf and Stock Publishers.
Draper, Paul (2007). "A Critique of the Kalām Cosmological Argument". In Pojman, Louis P.; Rea, Michael (eds.). Philosophy of Religion: An Anthology (5thed.). Cengage Learning. pp.45–51.
Moore, A. W. (2001). "Medieval and Renaissance Thought". The Infinite. Routledge. pp.46–49.
Sorabji, Richard (2006). Time, Creation and the Continuum (Paperbacked.). University of Chicago Press.
White, M. J. (1992). "Aristotle on Time and Locomotion". The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective. Oxford University Press.
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