Re: Infinity & beyond
What would you say to the idea that the demarkation for ‘actual’ and ‘potential’ infinity is yet another remnant of Aristotle? A hundred years afterwards Archimedes pretty much set up the death of the idea that ‘actual infinity’ does not have actual existence, when he used the idea of actual infinty to find the areas and volumes of curved shapes. Were these ideas overlooked in favour of the Aristotlean view and thus not really dealt with rigorously, until Newton and Leibniz leading Leibniz to exclaim:
“I am so in favour of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.”
The more you know…
Fighting:
Here again, the word
actual actually means
real, that is, can be related to real objects. Therefore,
real, with regard to the meaning of “infinity,” means
potential infinity. Unless it can be delimited, that is determined to be this number rather than that, as
all other species of number can be and are, it must be understood to mean,
potential. (I wish there was a better word.)
Number is
form; it is
species. Only real things that are countable, as well as possessing all their other attributes, are actually actual. The number of stars in the universe is countable (of course, it would not be easy work!). So, that number, whatever it is, represents how many real stars there are one by one… That number, whatever it is, is not a separate entity, or object, or thing that is knowable in the same way that stars are knowable. We know stars because they are that which confronts our senses, or, more precisely, they are that which strikes us (our senses) in that same way a fist might. (Which is the derivation of the word, “object,” from the Latin,
objectum.)
Now,
form, unlike matter, exists - but only in the
potentialities of matter. It is, for all intents and purposes, privative. In other words, it exists as
privation, an exclusion of other determinants that determine other deer to their species. That is why it is called
species. The attributes of a white tailed deer are what separates (speciates) white tailed deer from all other deer and all other herbivores. But, those attributes don’t exist on their own; they only exist within the matter of the deer. And, sufficiently so, so that the deer seem to ‘know’ it. All actual numbers are speciated by the final number of their set, or sequence. One hundred trillion, five hundred billion, two hundred forty million, six hundred thousand, four hundred and thirty-three is a final number in a set or sequence. Though it may not be said of any real things in particular, it may be said of real things. Perhaps the number of atoms constituting a car. As such, it can also represent other numerous things: such as molecules, stars, moons, etc., so it is real only as a determinant, or, delimiter. And, since the same number can be used to refer to various things, it is its own
species. Deer is said of all deer, not merely one of them.
But, there does not exist a determinate or, delimited, number that is represented by the word ‘infinity’. The word cannot describe how many units are in it. It is, by its very definition, unbounded, undelimited, unlimited, undetermined, un-ending, un-stoppable, and so on. There is no final number that anyone can point to as the number
infinity. If there were, we should be able to know whether it was an odd number or an even number. It is, to us, a vague, but, large group of whatever that is supposed to be represented by it. Unlike the large number above, which has determination, a determining end number, ‘infinity’ has none. As such, it is, in its mode of actuality, a
potential infinity. A
potential infinity can exist, because at any point, it can be halted and measured by ‘one.’ An
actual infinity cannot be halted or measured by ‘one,’ as it numerically exists well beyond any possible point at which it may be halted - without
end. There cannot exist an actual linear infinity. If it could, it would continuously fill all of space and all of beyond space so that nothing else could co-exist with it. It would crowd-out all finite beings.
Aristotle was a pretty smart guy! I am amazed that so many others are unable to correctly comprehend the concept. Mathematics has no
matter; it consists of
form only.
God bless,
jd