Hello Philosophim,

Wonderful points as usual! Let me try to respond adequately.

I don't think we can say an "unbounded infinite of negations". That's really, a "bounded infinite of negations"

By “negation”, to be more precise, I mean a “complete negation”; that is, that the entirety of what is negated is completely obliterated (so to speak). Therefore, I do not mean a “partial negation”. Consequently, I am in agreement with you that “not X” necessarily entails that X is bounded (which is what I noted as “being conceived in toto”) because to negate it I must implicitly treat it as completely not (as opposed to “partially not”).

However, as far as I am understanding you, you seem to be asserting that an “unbounded infinite of negations” (which, we are in agreement, is an “unbounded infinite of nots of bounded concepts”) is somehow entailed to be equivalent to “a bounded infinite of nots of bounded concepts”. In other words, it seems as though, from my point of view, you are rightly identifying the bounded nature of the contents of the unbounded infinity and, in virtue of that, extending it (or maybe misassigning it) to its form.

I can see an unbounded infinite negated, because an unbounded infinite is the base from which all bounded infinites are formed.

Categorically, I think it would be a contradiction in terms to posit the negation of an unbounded infinite: that is actually a bounded infinite. Let me try to explain:

But if we say that all possible bounded infinites are negated, isn't that the same as stating an unbounded infinite is negated?

I don’t think these are the same concepts that you just described and I think it is the root of our dispute. Firstly, it is important to note that I am not, at this point, attempting to prove that there is an unbounded infinite but, rather, I am merely trying to prove there is a valid concept of such that is at your disposal—for, as of now, it seems as though your contention lies in the denial of an “unbounded infinite” as a valid concept (i.e., it is really a “bounded infinite” assigned a new name).

To simplify it down for all intents and purposed for now, it seems as though, to me, you are essentially stating: an unbounded infinite of nots = not an unbounded infinite.

I would describe it as a difference between conceiving in toto and in total. Bundling up all those negations found within the unbounded infinite into a “complete concept” is to necessarily contradict the very concept (that is, attempt some operation which necessitates it to be conceived in toto). By “concepts” I am not entailing that it have a bounded form, which is what I suspect you are at least partially committing yourself to.

You are conceptually performing a different task to completely negate an unbounded infinite. What you seem to have done is analyzed the content of an unbounded infinite in terms of the sum of its parts to derive what it approaches (i.e., in total) and, thereafter, conflated that with in toto--thereby considering “not an unbounded infinite” valid; However, nothing about the sum of the parts of a concept entails that it can be conceived as a whole (that is, nothing about being conceivable in total entails that it is conceivable in toto).

This is the exact issue that required of me to explicate that, in the essay, a sine qua non is “without which, not” not “without which, none”; that is, the natural and swift leap from the sum of the parts of the content of a concept cannot entail its form in any way whatsoever (and nothingness is a great example of that). The unbounded infinite of nots does not necessitate nor prove a complete concept of nothingness (i.e., in the essay: “none”). The essay itself, consequently, does not even attempt to prove that “without the principle of regulation, there is nothingness”, because the PoR is also valid of the statement “without PoR, not nothingness” and “without PoR, not everythingness” (and so on): there is nothing which “escapes” it, so to speak.

The issue you may be having conceptualizing it is quite understandable, as with everything else we tend to swiftly conceive of finites and bounded infinites in toto based off of in total: but I have separated the two modes of thinking. For example, if one were to postulate what an infinite of empty sets would exist as in space, then they are more than likely going to quickly derive the summation of the parts to conclude that it would be nothing. This, however, in the sense of separating the two modes of thinking, is only valid by positing the form of the infinite as bounded. Therefore, I am noting the two different modes of thinking involved in the assessment:

First, the individual determined in total the infinite of empty sets, which is 0. This mode of thinking requires simply the ability to conceive what a sequence approaches (e.g., I cannot actually perform 0 + 0 forever, but I can nevertheless reasonably conclude it results in 0).

Second, the individual implicitly shifts their mode of thinking to in toto to “package” and “bundle” their conclusion into a wholly conceivable concept (e.g., 0 in space is nothing); that is, they assume that their evaluation in total of the infinite of empty sets warrants the ability to substitute the infinite for a bounded counterpart equal it in total (e.g., the total of the infinite is 0, therefore where ever I utilize the infinite I can substitute 0 for it). But, there is a distinction here, I think, in that they are not necessarily equivalent and, thusly, they are not always guaranteed to be valid of substitution: performing substitution of a bounded for an unbounded necessarily means that the form of the concept has been reshaped (by means, I would say, of utilizing a different mode of thinking). This substitution is only valid if the intents have no bearing on the form of the infinite: if the form matters, then 0 cannot be a valid substitution for an infinite of empty sets. Admittedly, a vast vast majority of the time I think the form is dismissable; however, my essay (I would argue) is an example where the distinction is vital.

The best I can think of is that we must be able to make conceptualizations out of/within the unbounded infinite. Because if something could not, then nothing could create any sort of differentiation between bounded, and unbounded. Does this somehow fit within your PoR?

I may be misunderstanding you here, but PoR can be utilized to make distinctions, but the very concept of PoR is also via itself. Therefore, the indifferentiation or differentiation of PoR from other things is via PoR. In that sense, PoR cannot be separated from anything, including nothing.

This again is where I have a hard time. Without a sqn, nothing can be. Which means without a sqn, concepts cannot be either. The way I read the essay and your explanation, it seems to imply without a sqn, the infinite, bounded or unbounded could not be.

Another great point Philosophim! This, I would say, is your other major contention with my work (which is not the same as what was previously mentioned). Let me explain it back to you (to ensure that I am understanding correctly) and then I will attempt to adequately address it. Here’s what I think you are essentially saying:


#1
p1. A sine qua non is “without which, not”
p2. Therefore, by definition of #1p1, a sine qua non contains “without which, not “concepts””

#2
p1. A unbounded infinite is a concept
p2. By substitution property and #1p2, a sine qua non contains “without which, not “unbounded infinite””
p3. By #2p2, it is a contradiction in terms to assert an unbounded infinite as a sine qua non.
p4. Therefore, an unbounded infinite cannot be a sine qua non.

The issue I would have is:

1. #1p2 is only partially true: I am allowing a “concept” to be incomplete in form and, therefore, a sine qua non only contains “without which, not “concepts with a complete form””. The mode of thinking matters to me.

2. Therefore, a sine qua non cannot contain a concept with an incomplete form.

Note: by “incomplete form”, I do not mean a concept merely conceived as incomplete in content (e.g., an incomplete apple) as that is complete in form (e.g., a complete concept of an incomplete apple).

Now, at face value, my response seems to be a contradiction: if a sine qua non is an unbounded infinite of negations, then it seems as though I ought to be able to negate it within itself, otherwise it cannot be deemed true. The answer is that one can subvert a sine qua non through itself; however, that is to necessarily erode its form to that of being bounded (i.e., to shift my mode of thinking to in toto), which is not really a sine qua non: I am thereafter dealing with an imposture so to speak and not the real thing.

Likewise, if only complete forms are allowed, then it seems as though there is something which persists with the negation of a sine qua non: concepts with incomplete forms, which contradicts the idea of it being a sine qua non in the first place. However, again, an incomplete form is an unbounded infinite or a contradiction in terms (e.g., either unbounded with infinite content or a contradiction wherein it is unbounded with finite content). In terms of the latter, it is invalid. In terms of the former, we must contend with it: does an unbounded infinite persist, as a concept with incomplete form, without a sine qua non? The answer is no, because, again, to posit an unbounded infinite as without a concept necessarily shifts the mode of thinking in toto, which contradicts the term itself. If this operation is permitted, then the unbounded infinite simply (1) is not an unbounded infinite and (2) does not persist without a sine qua non because its eroded bounded conception is wholly within the jurisdiction of a sine qua non (“without which, not”). Therefore, I submit to you that an unbounded infinite is not out of nor within wholly and, therefore, it stands not outside (without) a sine qua non and, in turn, it does not pose a threat to the concept thereof.

Again, I think that our dispute first lies in whether an “unbounded infinite” is valid as a concept, which hopefully I have proved herein, and, after that we can then discuss whether there is such a concept. As always, I could merely be wrong about the concept itself.

Bob