Pardalos, Athanasios Migdalas, Rainer E. Williams - Studies in logic and the foundations of mathematics, vol. Partition Relations for Cardinals: Studies in Logic and the Foundations of Mathematics Series:
Craig argues that various paradoxical consequences follow from these examples, which shows that the idea of an actually infinite collection of things is metaphysically suspect.
But a universe without beginning would entail an actually infinitely large collection — of days, years, or whatever other unit of time you care to take.
Hence the argument concludes the notion of a universe without a beginning is also metaphysically suspect. My objection noted that Craig is as I am an adherent of presentism, i. Given presentism, I argued, it is incorrect to say that a universe without beginning entails an actually infinite collection in the relevant sense.
For past things and events including past days, years, etc. The only things and events that exist are present things and events, and they are not infinite in number. The only day that exists is the current day, and a single day is obviously not an infinite number of days. Something similar could obviously be said of weeks, months, years, etc.
As far as I can tell, Craig makes three points that might be thought to be relevant to my objection. By the same token so the argument seems to continue, if I understand it correctly if the universe had no beginning, that would entail that there is an actually infinite collection of years.
For example, Snow White knew seven dwarfs, and we can go through them, by name, and count them. First, Grumpy; second, Sleepy; etc. The number of moments that have actually existed is infinite. The number of moments that actually exist is infinite. A beginningless universe would entail 1, but it would not entail 2, certainly not if presentism is true.
Precisely because all the past years, days, etc. Craig would not deny that it is legitimate for mathematicians to talk about infinite series in various ways, e. The reason this is okay is that numbers unlike hotel guests, hotel rooms, etc. But is a collection of units of time minutes, days, years, etc.
But in fact, this seems false. It seems instead to be more like the latter.
Aug 06, · Sub: lambda calculus application to program optimization (algorithmic optimization) I have a very brief knowledge of lambda grupobittia.com somebody please tell me whether lambda calculus can be used for optimization of a program. Whether some work has already been done in this regard. Specifically I am interested in an artificial intelligence. The proposed computation is based on an OBDD-rewriting of the notion of Ackermann encoding of hereditarily finite sets into natural numbers." if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. Note: Publisher: American Assoc. Artificial Intelligence, USA. News Archives June , North American Summer School in Logic, Language and Information (NASSLLI ), Bloomington IN, U.S.A. July , 5th International School on Rewriting (ISR ), Utrecht; 28 June - 23 July , Asian Initiative for Infinity (AII) Graduate Summer School in Logic, Singapore.
This is especially plausible if, like Aristotle and Aquinas, we deny that time exists apart from change and the concrete objects that undergo change. To speak of time apart from change is a bit like speaking of a universal like redness apart from actual red things—it is to engage in abstraction from the concrete conditions under which the thing in question redness, or time can actually exist.
Craig may be more inclined to think of units of time as relevantly analogous to concrete objects like hotel guests, etc. This brings me to a second remark Craig makes that might be thought relevant to my objection.
For example, if the number of past events is infinite, he says, then the number of odd-numbered events is no smaller than the number of total events, since the series of odd numbers is of course infinite.
He also rehearses other points along these lines. But the problem with this should be obvious from what has already been said. Again, Craig does not have a problem with mathematicians talking about infinite series of natural numbers, despite the fact that the series of odd numbers is no smaller than the series of all natural numbers.
The collection of hammers would constitute an actual infinite. Now, Craig says that it would constitute an actual infinite even if the hammers did not still exist, and he cites the example only to illustrate his claim that past things need not continue to exist in order to constitute an actual infinite.
But it seems to me that what he should say, in order to try to make of this example a response to the objection from presentism that I have put forward, is this: Suppose such a blacksmith has been working for an infinite number of years, has used a new hammer each year, and has preserved each of these hammers.
Perhaps this could be developed into a promising reply, but as it stands it too seems to me to fail.In this paper, we combine term graph rewriting and infinitary term rewriting thereby addressing both components of lazy evaluation: non-strictness and sharing.
Moreover, we show how our theoretical underpinnings, based on a metric space and a complete semilattice, provides a unified framework for both term rewriting and term graph rewriting. Learning robots and agents. Jean Piaget, Das Erwachen der Intelligenz beim Kinde.
Klett, [Ahonen/a] Helena The American Statistician, Vol. 52 (2), [Harabagiu/a] S.M. Harabagiu, WordNet-Based Inference of Textual Cohesion and Coherence. FLAIRS Proceedings of the 11th International FLAIRS Conference, AAAI Press, Join GitHub today.
GitHub is home to over 28 million developers working together to host and review code, manage projects, and build software together.
The entire wikipedia with video and photo galleries for each article. Find something interesting to watch in seconds. Sep 08, · Yeah, but is it actually actually it's worth pointing out that science doesn't advance by rewriting current knowledge--it does so by building on itself and taking established theory to deeper layers of explanation.
& Keating, R. E. (, July).
Around the world atomic clocks: predicted relativistic time gains. American. Papers md Papers md Home. Keying Hash Functions for Message Authentication Handle-Rewriting Hypergraph Grammars Examples include first-order logic, equational logic, Horn-clause logic, higher-order logic, infinitary logic, dynamic logic, intuitionistic logic, order-sorted logic, and temporal logic; moreover, there is.