
	Where results make sense

Topic: Actual infinite

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	The Kalam Cosmological Argument
		Infinite series have a certain property that will be important in the discussion that follows: it is impossible for anyone to complete an infinite series.
		According to (a), it is impossible for there to be an infinite number of objects, events, steps in a series, or members of a set; and it is impossible for any object or event to possess a property of infinite magnitude—e.g., infinite density, infinite mass or infinite speed.
		Traversal of an actual infinite is logically impossible (i.e., impossible in the strongest sense of that term).
	www.acsu.buffalo.edu /~jbeebe2/kalam.htm (7120 words)

	INFINITY AND THE PAST
		This argument is based on a fallacy of equivocation with respect to the phrases “actual infinity” and “potential infinity.” Whitrow’s proof that the past if infinite is “actually infinite” is based on a different sense of “actually infinite” than that belonging to his proof that an “actually infinite past” is impossible.
		However, in his proof that an actually infinite past is impossible, Whitrow uses “actually infinite” in the sense of a series of events some of which are separated from E by an infinite number of intermediate events.
		For if the past is an “actual infinity” in the sense of being an infinity of events that have really occurred, it does not follow that it is also an “actual infinity” in the sense that some past events are separated from the present event by an infinite number of intermediate events.
	www.qsmithwmu.com /infinity_and_the_past.htm (5159 words)

	Aristotle's Potential and Actual Infinite and Cantor
		It was actually considered that the for real objects the actual infinite is not possible, that an object could not have something which exceeds all limits.
		According to Aristotle, actual infinities cannot exist, but potential infinities exist in nature and are manifested to us in various ways, for instance the indefinite cycle of the seasons or the indefinite divisibility of a piece of matter.
		It necessarily follows from this that infinite weight, if there is such a thing, being, on the one hand, as great and more than as great as the finite, will move accordingly, but being, on the other hand, compelled to move in a time inversely proportionate to its greatness, cannot move at all.
	www.mlahanas.de /Greeks/Infinite.htm (1632 words)

	PROFESSOR MACKIE AND THE KALAM COSMOLOGICAL ARGUMENT
		He contends that a proper understanding of the principles employed in infinite set theory enables us to see that the alleged absurdities entailed by the existence of an actual infinite (for example, infinities of different sizes), to which the proponent of the kalam argument appeals as evidence for (2.11), in fact involve no real contradiction.
		Mackie admits, however, that many people still harbour doubts about the existence of an actual infinite in the real world and that not all mathematicians or philosophers are ready to accept the actual infinite even in the mathematical realm.
		With regard to (2.2) he is mistaken to call this a prejudice against the actual infinite, for the argument does not deny, as does (2.1) that an actual infinite can exist, but only that it can be formed by successive addition, or to use the medieval idiom, that it can be traversed.
	www.leaderu.com /offices/billcraig/docs/mackie.html (3924 words)

	On Gillespie’s Misapplication of the A-Theory of Time to the Impossibility of an Actual Infinite in the Kalam ...
		When Dr. Craig speaks of the impossibility of an actual infinite being instantiated in the real world he means to suggest that there can be no actual infinite sets that bear any ontological status beyond nominalist or conceptualist restraints.
		The Titanic sinking is an instance of broad actuality while the existence of this article is narrowly actual.
		However, I have shown that the nature of the A-Theory of time does not preclude the problem of an actual infinite number of past events so long as one is able to make the distinction between past events and the past itself or that past events are not replaced but, rather, are accumulated.
	examinedlifejournal.com /archives/vol1ed3/gillespie_response.html (2469 words)

	Infinity and Jesus' Humanity
		The term, actual infinite, is confusing, because the word, actual, makes it seem as if it were actually possible for there to be an actual infinite.
		In other words, it is not possible for there to be an actual infinite set of physical objects or temporal durations in the universe.
		Clearly, it is not appropriate to use a potential or an actual infinite with respect to Deity, because these types of infinites refer to physical or temporal entities, such as sets or as divisible continuums.
	www.muhammadanism.com /Jesus/JesusInfinite.htm (1974 words)

	Infinite Series
		In general, an infinite series is a series without an ending term, like the series of natural numbers, 1, 2, 3… Mathematician and logician Georg Cantor, defined it more precisely as a series that has the same number of terms as one of its subseries.
		A potential infinite, however, is a series that approaches an infinite number but never reaches that point, as when we try to list all the natural numbers, one by one, or when we divide an object by half, and then by half again, and so on.
		To show that there cannot be an actually infinite collection of things, he refers to the paradoxes noted by Cantor: (1) In an infinite series, the whole is equivalent to some of its parts.
	www.frame-poythress.org /frame_articles/2005Infiniteseries.htm (1422 words)

	RUSSELL, INFINITY, AND THE TRISTRAM SHANDY PARADOX
		Analytic philosopher Bertrand Russell believed that an actual infinite could be achieved as long as the counter possessed an actually infinite number of years to do it.
		In other words, there is no reasons to adhere to an actual infinite by simply pushing back the length of the task to the time of the task.
		It would appear to me that the failure of an actual infinite to succumb to the basic principles of mathematics is why the infinite remains forever untouched by finite beginning points.
	www.sguthrie.net /infinity.htm (1766 words)

	Infinity
		Aristotle argued against the actual infinite and, in its place, he considered the potential infinite.
		The very suggestion that certain objects, infinite in number, are "equal in magnitude" to others implies that not all such objects, infinite in number, are so equal.
		the totality of all numbers is infinite, and that the number of squares is infinite.; neither is the number of squares less than the totality of all numbers, nor the latter greater than the former; and, finally, the attributes "equal", "greater", and "less" are not applicable to the infinite, but only to finite quantities.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Infinity.html (4009 words)

	Infinite loop - Wikipedia, the free encyclopedia
		While most infinite loops can be found by close inspection of the code, there is no general method to determine whether a given program will ever halt or will run forever; this is the undecidability of the halting problem.
		Infinite recursion, a special case of an infinite loop, is an infinite loop caused by recursion.
		When using structural recursion, infinite recursions are usually caused by a missing base case or by a faulty inductive step.
	en.wikipedia.org /wiki/Infinite_loop (1149 words)

	On Dissecting the Cosmological Argument (Site not responding. Last check: 2007-11-01)
		Put simply, kalam arguments try to demonstrate (1) that the existence of an actual infinite (a concept from modern set theory to be discussed shortly) is impossible and (2) that even if it were possible, the universe itself is not actually infinite and hence must have had a beginning.
		In contemporary set theory, an actual infinite is a collection of things with an infinite number of members, for example, a library with an actually infinite set of books or a museum with an actually infinite set of paintings.
		Another way of stating the difference between an actually infinite set and a potentially infinite set is that the latter has identical ordinal and cardinal numbers, but the former has a cardinal number known as the aleph zero or aleph null and an ordinal number which designates the entire series of natural numbers.
	users3.ev1.net /~trinitite/kalam.html (5273 words)

	Questions of whether an actual infinite exists, and in what capacity, have woven their way through the history of ...
		Questions of whether an actual infinite exists, and in what capacity, have woven their way through the history of philosophy and mathematics.
		He states, "[Craig] concedes that infinite set theory is a logically consistent system; consequently, it seems that he concedes that there are logically possible worlds in which various 'infinites' obtain." But it is by no means obvious that this second alleged concession follows from the first.
		If this understanding is correct, then the possibility of an actual infinite being formed by successive addition (or subtraction), whether in ω or ω* or ω+ω* set-types, or even existing at all as completed or whole, is incoherent.
	www.tektonics.org /guest/kalam.htm (6714 words)

	John's Page: My Mind's Dark Depths (Site not responding. Last check: 2007-11-01)
		Actual Infinite - a series that has neither a beginning or an end, but continues "infinitely" in both directions from any given point.
		If Time never had a beginning (was actually infinite), then no matter what day it is, there would still be an infinite number of days left to arrive at today.
		So, if time was actually infinite, we wouldn't exist because enough time could never have passed to arrive at the day of our birth.
	crmstaff.org:16080 /stokes/MyMind/scienceVSfaith/actualInfinity.shtml (446 words)

	Is The Past Really Finite? (Site not responding. Last check: 2007-11-01)
		An actual infinite, by its definition, cannot be added to (for it is the number of all possible numbers).
		The reason that an actual infinite cannot be completed by successive addition is not merely that there is not enough time to complete it, but rather that no amount of time is sufficient to allow an actual infinite to be completed in this fashion.
		Craig still has three gaps in his logic to discuss: why the past, if infinite, must be an actual infinite; why the past must be formed by successive addition; and, if the finitude of the past can be proven, why it follows that the universe must have begun.
	ccwf.cc.utexas.edu /~govind/stories/finitude.html (3433 words)

	Could an Infinite Series of Past Events
		If that were all Craig meant, then an actually infinite temporal series of distinct events would be no more objectionable to him than an actually infinite spatial series of distinct objects, and the truth of premise (2.21) would be wholly dependent on the soundness of Craig’s general argument against the actual infinite.
		He argues that sin ce an infinite series of numbers must be "defined" starting with some number, an actually infinite series could not be "formed" by successive addition.
		In fact, the only way in which we can define the infinite set of negative integers is by beginning with –1, but this does not correspond to the order in which the events that we may wish to associate with them occur in time.
	stripe.colorado.edu /~morristo/infpast.html (6005 words)

	Nicholas of Cusa and the Infinite
		The former is a view from the finite upward toward the unattainable and incomprehensible infinite, while the latter is an incomprehensible view from the infinite downward toward the finite that is identical with the infinite.
		Thus, the actual infinite ultimately had to be explicitly affirmed in mathematics in order to provide a foundation for the numbers used in both analytic geometry and calculus.
		The history of the Infinite thus reveals in both mathematics and philosophy a development of increasingly subtle thought in the form of a dialectical dance around the ineffable and incomprehensible Infinite.
	www.integralscience.org /cusa.html (5490 words)

	God on the Internet: Answers to Real Internet Questions about God and the Meaning of Life: Chapter 1
		Of course, one must actually present the evidence for the existence of God to fully answer this question.
		Actually, Kant did not object to the power of the teleological argument itself but to the idea that the argument shows an infinite God.
		A few of Hume’s objections to the teleological argument were based on the idea the universe is infinite and with an infinite amount of time, anything is possible or the universe is simply a "happy accident." Science and logic show that the universe has not been around for infinite amount of time, as mentioned previously.
	members.cox.net /wwcw/MarkHarptBookCh1.html (2535 words)

	The Cheshire Cat Sneers
		An actual infinite is a collection of things with an infinite number of members.
		There are several things that are logically objectionable about this statement, but the main thing to note is that he is asserting the actuality and some of the characteristics of God before demonstrating his existence, which is supposedly what this little exercise is all about.
		Those who raise this objection are referring to the fact that theists often refer to God as "infinite," so they naturally want to know how this tallies with the assertion that an actual infinite cannot exist.
	ourworld.compuserve.com /homepages/billramey/cheshire.htm (3515 words)

	Religion B3: Moreland - In the Beginning (Site not responding. Last check: 2007-11-01)
		Moreland thinks that the second premise here is false -- because mathematics gives us examples of actual infinites.
		He takes the second premise only to deny that there could be an actual infinite in the real world -- for example, a library with an infinite number of books.
		He admits that there are infinite sets (like infinite sets of numbers) in the abstract world of mathematics.
	www.jcu.edu /philosophy/Gensler/RE/r-b3--0c.htm (248 words)

Try your search on: Qwika (all wikis)