You obviously didn't read my posts, otherwise you'd know that I don't assert that a finite entity can create itself -- there's no actual rule saying one way or the other, it's just that we've never seen it happen so we like to assume they can't.
Anyway, my point was, if the universe, as you say, being infinite, always existed (you'd be in pretty staunch disagreement with... well, every scientist anywhere) then the same cane be said about God. Let's say God always existed, just like you propose the universe did. Then he could have existed long enough to create the universe, thereby making it less than infinite, thereby toppling your entire stance.
You don't know that the universe is infinite. It is, at the very best, a good guess.
If God has always existed, he is all that has existed. What has always existed has no beginning, which also means it has no end. Therefore this entity cannot create, because everything that could possibly exist, already exists, thus nothing new can be concocted. Such a metaphysical scheme is incompatible with conventional Christian theology because Christian theology insists that God and the universe are 2 seperate entities. God is one thing, and hte universe is another. If God does not exist separably from the universe, he lacks the personhood, omnipotence, and many other qualities which are essential to the concept of God in standard Christian theology.
Your reading comprehension requires much improvement. None of what you said was relevant to the opening post. The catch was that God cannot exist SEPARABLY from the universe.
Bottom line is, we do know that the universe in itself is boundless or infinite. The alternatives to these we have is that it came from nothing, (absurd) and that it was created by another limited or a finite entity. We would regress ad infinitum seeking the original entity. Eventually, there will have to be a finite entity that came out of nowhere, this is absurd.
Hence, the universe has always existed, because it could not have been any otherwise.
But obviously the world we live in is finite, it could not have always existed. Indeed, it is an extension of the infinite realm. It is an emanation
Influence of Arabic and Islamic Philosophy on the Latin West (Stanford Encyclopedia of Philosophy).
As in Kantian-Schopenhauerian philosophy, we encounter a notion that the finite world or the phenomenal world of experience is an unconscious representation of the noumenal world, or that aforementioned infinite world.
Unlike in creationism, the infinite and the finite are not different things. The former is a distorted perception of the latter. In other words, the infinite realm is all that there is, which we know nothing about, what we know is the world we regard as real, as real as it could be. The world of our finite, unconscious representation.
As stated earlier in the OP.
"Consequently, there is no pure knowledge outside of the world based on our senses, and no objectivity of knowledge possible without being founded on subjectivity. The way we perceive the world seems to consist simply in receiving outside information, and yet, according to Kant, it is a rather complicated relation of first giving and then taking, and consequently any epistemic relation we have to another implies a relation also to ourselves. Kant is not thereby advocating a subjectivism; he invites us to reconsider the nature of objectivity as dependent on our subjectivity. Thinghood or causality, for instance, which Hume sceptically claimed to be merely subjective constructs (subjective in the bad sense of representing something that in reality does not exist), are acknowledged by Kant as indeed subjective concepts, but subjective to a degree that all objectivity of our knowledge depends on them. They are so fundamental, so deeply rooted in our subjectivity, that without them no empirical world remains for us to know." Introduction to the Critique of Pure Reason.
Now, nocap, lets stop talking non-sense shall we?
Ti-Si mode for this thread. Which means, you read the text carefully (Si), make sure you have sensed or seen all the written words and that you remember what was said (without being distorted by your imagination), and then you proceed to analyze each statement you read one by one. Ti, not Ne. Which means statement A only at this point. Not, A,B,C and D simultaneously. When you are done with statement A, you can go to B, and then B only, not A and B simultaneously.
For example, there are infinitely many odd integers, infinitely many even integers, and (hence) infinitely many integers overall. !).
The origin of this equivocation of the word 'infinite' begins to make more sense now.
In Learning To Reason, An Introduction To Logic, Sets and Relations, we have 2 sections. (Nancy Rodgers) 3.5-On Finite Sets, and 3.6 On Infinite sets.
In the very introduction we find this collection of statements. " The term "infinite" is often used in the media to indicate a very large set, but this is not what it means in mathematics. The set of atoms in our universe is one of the largest physical sets that one could imagine; however, this set has less than 10 (80th power) elements, so it is a finite set. To understand the meaning of infinite, we must first understand the meaning of finite". P.271
Here it appears that Rodgers is suggesting that likely a finite set is a countable set, and an infinite set is uncountable. As if we could use the conventional definition of finite as synonymous with countable, and the conventional definition of infinite as non-countable, or uncountable.
I believe however, that it should indeed be so, and the term 'infinite' should be reserved strictly to the uncountable. Or entities so great that could not be countable. That is indeed what Rodgers appears to be saying in the opening paragraph, yet surprisingly, this begins to change as the chapter progresses. From the standpoint of descriptive linguistics (how language is used), this is very interesting, as here we discover how mathematicians have been using the term 'infinite', though from the standpoint of prescriptive, their use of the term encounters problems. The most prominent of which are most closely related to the confusion or even an equivocation with how a word infinite is to be used.
Later in the chapter (3.6), it turns out that there are two kinds of infinite sets, countable and uncountable. The only reason why an entity is uncountable is if it is too large to be counted, and this Rodgers refers to as the 'higher levels of infinity'. Yet, the countable 'infinite' sets are indeed merely very large sets. This is exactly what Rodgers in the opening paragraph stated that 'infinite' does not mean.
In summary, from the standpoint of descriptive linguistics, infinite, by most mathematicians is regarded as a very large set, which appears to be never ending.
From the standpoint of prescriptive linguistics, the set which has an end is to be regarded as finite. The opposite of having an end, is not having an end, therefore is to be regarded as infinite, or the opposite of finite. There is no reason to call a set which has an end, but only appears not to have an end, infinite. That is exactly like calling the race car driver who only has appeared to have won the race but has actually finished second, (completing his course only a 1/1000 of a second after his opponent), a winner.
Lets investigate the writings of Rodgers further in order to shed light onto the descriptive and prescriptive approaches to the use of the word 'infinite'.
Thus, clearly, as stated in the opening paragraph, a finite set is one that has one to one relations with natural numbers. Basically, one that could be expressed in terms of basic numbers, like 4,5,6,7, and so on. No question here, these numbers as entities in themselves are finite, and perhaps the entire collection of such numbers will be as well.
However, an interesting point occurs to us. What if we tried to list all of the natural numbers? 4,5,6,7,8,9 and and forever. Would we ever stop? We certainly would run out of paper in our notebook, or millions of notebooks even, but the numbers would continue forever. For this reason, it is often stated in mathematical books that a set of natural numbers is infinite. Or 'at the higher levels' of infinity, where an entity is so large that it cannot be counted.
Yet, what have we here. A quote from Cantor.
"My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things." Georg Cantor 1845-1918
"Since antiquity, the great nemesis of logic was the vast concept of infinity, which produced disturbing paradoxes. Like the Sumerian clay pots which could never contain an infinite number of pebbles, it was widely believed that a set could not contain an infinite number of elements." P. 275
"Georg Cantor, though, considered a set as "a collection of definite, distinguishable objects of perception or thought conceived as a whole, " and he saw no reason not to conceive of the collection of all natural numbers as a single entity labeled as a set. As he probed and explored the logical ramifications of his idea, he developed an intriguing theory of sets that included both infinite sets and infinite numbers."
"In our culture, most people use "infinity" in the same sense , as the size of a set whose size is beyond comprehension; however, as we will see in the next section, the well-reasoned mind can distinguish between different sizes of infinity."
Thus, here we have a 'higher level' of infinity, which is too big to be counted. Which indeed is the size beyond comprehension, and 'infinite' sets which are only very large, yet not large enough to be beyond comprehension.
"The following method for creating the natural numbers may seem excessively laborious, but great precision is needed to logically escape the finiteness of mortal existence. After all, no human can count all the natural numbers. Even the days of existence for the sun that fuels our solar system is a finite numbers. The belief in an infinite set of natural numbers requires logical articles of faith, which can be boiled down to the following axioms. These axioms were the intellectual product of Georg Cantor's journey in following to its roots 'the first infallible cause of all things." P.276
'The first infallible cause of all things' is indeed the matter that this thread is intensely interested in.
"The first axiom of a set theory postulates the existence of the empty set. Like the Big Bang, this axiom gives us all the material that we need to start building the universe. In the beginning was the empty set, and from this set we will build all our sets and numbers." P.277
I am not exactly sure how to interpret this passage. Though the clear-cut inference is that we have an axiom that nothing comes from nothing. An axiom is a truism, a proposition that does not require to be supported with reasoning.
Because nothing comes from nothing, the infallible cause of all created things could not be nothingness. It must be something. This something must have always existed. It did not derive from anything. Thus, we have not contravened the axiom concerning the impossibility of something coming from nothing. This something must cover all things, because if it covers only some things, the things that it does not cover must have come from nothing.
This is not possible.
Thus, a universal set, or everything, is to be preferred over the empty set, which is nothing. However, upon a superficial survey, it is difficult to tell the difference between an empty set and a universal set, as everything is as difficult to define as 'nothing'. When we define an entity, we assign one particular trait to it, or a combination of traits. Yet, we cannot define an entity that is everything because our combination would have to include all things that exist. This is not possible because this elevates to the 'higher levels of infinity' the levels beyond comprehension.
For this reason, Rodgers was likely justified in regarding this infallible cause of all created things' as an empty set, as mathematically, we cannot provide a clear-cut value for either of the two.
You bring up a very interesting point, an idea similar to which, Rodgers takes a very careful note of.
Now, we start section 3.6, on the Infinite Sets.
"It seemed as though the infinite were beyond the grasp of logical inquiry. What was missing was the language that would give a precise description of this very massive concept. Thanks to Georg Cantor and the other mathematical pioneers who developed axiomatic foundations for set theory, we can now work with infinite sets in a logical manner and even construct infinite numbers that make as much sense as finite numbers." P.284
This obviously requires much further thorough explanation. I myself do not find the idea of how there are 'many levels of infinity' some countable, and some not so, to be plausible, as the two concepts could simply be demarcated as countable and not countable. Countable is finite, and non-countable is infinite. Cantor made discoveries with regard to how we ought to manipulate very large mathematical figures and how to express them, but he did not figure out how to deal with the non-countable, or non-expressive, of course that would be non-sense to say that he did. This of course is not a matter of purely mathematical concepts, but words we ought to use to convey them.
I argue that infinite ought to be reserved strictly for the large beyond our understanding, the non-countable, as otherwise confusion is incurred, as we have witnessed above.
In any case, lets continue with the exegesis of Rodgers.
"A proper subset of an infinite set can have the same size as the original set." P.288
"A set is infinite if and only if it has a proper subset of the same size."
"A set S that has the same size as the set N of natural numbers is called countably infinite. We use the term countable to cover both finite sets and countably infinite sets. The set (5,8,7) is a countable set that is finite, whereas the set (3,6,9) is a countable set that is infinite. A set that is not countable is called uncountable. The term uncountable represents a higher level of infinity, a level beyond the size of the natural numbers." P.289
It is not clear to me what pattern is represented by the symbol (5,8,7) or the 3,6,9, yet the suggestion here appears to be that the latter being infinite and the former being finite is that the latter leads to higher numbers than the former. Yet, apparently, not high enough to be considered uncountable. It is still puzzling to me why it is regarded as infinite, and EXACTLY how high must a value be in order to be considered infinite. This is not clearly explained.
Thus, your point is very interesting and deserving mention.
[(You had said "an entity that is unbounded (which is infinite by definition) will occupy all things, simply because there is nothing to prevent it from doing so.", yet here we see two infinite sets coexisting right next to each other, and they do not "occupy" each other!).
Under this definition of infinite, we simply have to very large sets. Yet, if we had the infinite of the 'higher levels' of infinity, such a thing would not be countable. Precisely because it occupies all possible things.
Thus, what we have in the end is that the universe has always existed, as I have explained to nocapszy in this post, and this represents the uncountable, the infinite, or as Rodgers says, the 'higher levels of infinity' and the 'infallible cause of all created things'.
Certainly the phraseology of 'created things' is inexact. The thing that is all things necessarily contains all created things. What is 'created', has been concocted from the material provided by the entity that is all things. For example, if the clay is our whole world, I could create an entity which resembles a human body made of clay and a car. But these entities are not separable from clay itself.
Thus, this is not creation, as creation implies an innovation of a wholly new entity. What we have here is a concoction of an entity, the material for which has already inhered within the original set. This is precisely the explanation for the existence of our known world. It was not a creation, it did not come afresh, it is a rearrangement of materials that have always existed.
How? If that is so, you could give us "the last number"; the end of the set, then.
