Wonderful analysis as always Philosophim: let me try to adequately respond. — Bob Ross
Likewise Bob! Despite my points against your essay, I am always impressed by your creativity, open mind, and thought process. Lets dive in again.
I would like to clarify that neither “in toto” nor “in total” are concepts that directly entail an infinite: the former is a conception which is conceived (i.e., defined) as holistic, whereas “in total” is the conception of the summation of its parts (i.e., in content). — Bob Ross
For me, the confusion about toto came because your previous paragraph talks about infinity. You then mention toto is a concept without bounds, which implies infinity. But if I'm understanding correctly, we're really talking about form, vs what makes up that form. So for example, a tree is a form. All the indeterminate encompassing (possibilities?) which can make up the form of a tree are toto, where as if we could know all the possibilities, we could summate those in total.
But then there seems to be a contradiction here:
For example, I can manifest a conception of a set of integers {1, 2, 3} and determine that the summation of the parts as 6: the former is a conception in toto, and the latter is a conception of that conception in total. — Bob Ross
If a set of integers is 1,2, and 3, aren't the total number of integers 3? If we're listing the set, then we can say the collection is made up of 1,2, and 3, and we don't need the word toto.
for an absolute minimum at y = 2 indicates that f(x) is never negative ys and the limit from the right being infinity tells me that even if the limit to the left is a finite number that the summation of the ys will be infinity.
Again, I would say the concept is finite (that is, bounded), but technically I could be in a state of ignorance or confusion, thusly determining it as indefinite. — Bob Ross
Here is where I also think there is a conflation of words. Bounded does not mean finite. You can have an infinity for example that is bounded by whole integers. All meaningful infinities are bounded. An unbounded infinity, is everything without any defined concept. In the past I've called it "the sea of existence".
Bounded can also refer to the finite. So I could have a set of integers bounded between 1 and 4. Those integers would be 2 and 3. My point in the earlier post was to note that when we speak of meaningful infinity, it is always bounded. It may be bounded by the idea of, "All integers". So that would be an infinite set of numbers that precluded any fractions. This is the same as stating, "All integers less than y=2".
Thus if the following is true:
An infinite content can be determined in total. — Bob Ross
then all meaningful infinities can be determined in total. This again leaves me wondering where toto falls. Again, the overall feeling I get from your essay is more that toto describes the indefinite, or the unknown. The toto number of trees a person can conceive of is an indefinite concept, but one we can conceive of with some type of limit. It is not infinite due to a person's limited life span, but one cannot actually count the number of possibilities.
We can also imagine the idea of an infinite amount of possibilities one person could potentially imagine, even though in reality there are only a limited amount they actually imagine. I could see this as the infinite version of toto that expresses indefinite form. The problem is provability, which of course one can never do with the indefinite.
But again, I'm still not sure we have a clearly defined and applied term of "toto". I think it loses its use in your paper because I believe there is a misunderstanding of infinity and the term bounded. With the idea that all meaningful infinities are bounded, and that we can also bind finite sets, how can toto be used clearly without any ambiguity?
Infinite form and infinite content
This is the realm of sine qua nons (and, in virtue, the principle of regulation): a concept which is repetitive affirmation of negations would be an example of it. This kind of form entails, I must add, only one of its kind as a conception (and not just merely in existence). — Bob Ross
So back to this then, infinite form and content would be all possible forms one could give within all of infinity. This again is the unbounded infinite, or all of existence that one person could form. If you remember our conversation, a form as I'm seeing it would be a "discrete experience". I have largely avoided referencing the terms in my previous paper, as I do not want to distract from yours. But I feel this accurately communicates my intentions easiest, so I will do so here. This is the form within the infinite. So all possible forms would be all possible discrete experiences.
So within all possible forms, you propose a concept that if this concept does not exist, neither can any other concept. Without this discrete experience, no other discrete experience can exist for example. While I am ok with the idea of this, I still am having difficulties seeing how the principle of regulation is this sqn.
Only repeating myself once, you still have the problem of a thinking thing that does not derive. I've mentioned before that you would have to analyze other thinking things besides humans to show that all thinking things derive. At best, you can claim that all humans of a certain intellect derive. I have no problem with this.
At a conceptual level beyond all of this, I would still assert that one must come up with a concept first before one can derive from the concept. The sqn to me would be that one must be able to conceive some form within the unbounded infinite. Without this, no other form can exist within the infinite. From there you could derive the principle of regulation, but I do not see it as a sqn itself. So if you are to assert that the PoR is a sqn, how do you deal with the above concept? Is it not true that the real fundamental is the ability to first conceive of a concept, before one can derive from that concept?
Great work again Bob, I look forward to hearing from you!