Life is not a continuous process, there's some sort of finite number of achievements that defines your life.
Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.
The first rule of economics is that there is an infinite number of desires chasing a finite number of goods, services and resources. The first rule of politics is to ignore the first rule of economics.
Definitions must contain the means of reaching a decision in a finite number off steps, and existence proofs must be conducted so that the quantity in question can be calculated with any degree of accuracy.
To make our position clearer, we may formulate it in another way. Let us call a proposition which records an actual or possible observation an experiential proposition. Then we may say that it is the mark of a genuine factual proposition, not that it should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.
When I was in college, for the games of that era, I was as hard core as anyone was. I wouldn't say I outgrew it, but you always have to have a finite number of addictions.
Internet TV and the move to the digital approach is quite revolutionary. TV has historically has been a broadcast medium with everybody picking from a very finite number of channels.
In any finite region of space, matter can only arrange itself in a finite number of configurations, just as a deck of cards can be arranged in only finitely many different orders. If you shuffle the deck infinitely many times, the card orderings must necessarily repeat.
However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.
In theory, there is nothing the computer can do that the human mind can not do. The computer merely takes a finite amount of data and performs a finite number of operations upon them. The human mind can duplicate the process
The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.
What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.
We each have a finite number of heartbeats, a finite amount of time. But we have enough heartbeats and enough time to do what is important.
The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.
