I have seen many stories telling of the divide between Science and Philosophy, more specifically Physics and Philosophy. The main crux of the argument seems to be on whether or not abstract ideas actually exist in some fashion. i find it compellingly odd and funny that people are using 2 different languages to settle an argument about abstract concepts being real… in languages. Let’s first think about that. A language is a set of given symbols, spoken, or written, or even body language, grouped, to represent other concepts/things in the real world. so they are using an abstract thing to argue about whether or not abstract things are real in some way. Seems self-evident to me. And kind of silly, but maybe that is just me. A lot of bluster to get back to one basic fact: the things you see on the screen, or pages, or hear people say, or watch them do and you interpret to be representative of something is indeed a carefully constructed, over generatins of use and success/failure cycles, set of symbols, used and taught from birth to represent the physical world around us. Even science has this limitation, albeit with a more powerful language, Mathematics.
I will, in the course of this writing, attempt to reconcile this philosohical difference with a simple proof. In this preface however, this is my blog, and I will jest, I will make nuanced innuendos at lesser sciences, and laugh barbarically at the frantic attempts to equate their languages to mathematics, or better. I will acknowledge one caveat: Mathematics is the most powerful written language. other languages evolved as spoken first, ten written, and as such, have a greater dimensionality to them than Mathematics. you can write I am one, or 1=1 or one equals one, or even point at your self and say “am” after it, wor write it down, and get basically the same message out. but writing 1=1 is referencing a vary particular set of axioms and definitions that make math a powerful language. I’m defining language here to mean any set of given symbols used to convey information between given consciousnesses. I will later be using a mixmash of languages to describe my proof, i preemptively ask for your fogiveness, my education does not permit me the luxury of a formal proof, and I wholeheartedly welcome any attacks on my reasononing as a learning opportunity. I mean that. Personal attacks or any other arguments other than the above will be deleted or ignored,or possibly both. An irony I hope is evident later.
Before I get to rigor, let me say these things. I love science and math. I am biased. I believe them to be part of the crown jewels of human thought. I yearn for a fluency in all their lovliness. I also hate the way most people are taught them. I always thought that it was wrong when my teachers would tell me that moving a rock from one area to another was “addition”, when it obviously left behind and empty spot. It wasnt until much later that I was told it is also really the addition of a negative, that I realized it was more correct. I understand the reasoning now, but I felt quite betrayed in my indignant youth. I also was fortunate enough to have a set of wonderfully amazing teachers and chance encounters in my life, and I feel quite blessed to have been taught by them. One taught our class the rules of basic logic and had us play games. Using logical statements, the Converse, Inverse, and Contrapositive, we would evaluate if statements were true (logically consistent) or not. I found it to be the most wonderful tool I have ever learned, and I will always be grateful for it. I also have had a lot of time to reflect on the precepts that must create such a tool, and I think there is a bit of a law. I feel there is a flaw in several axioms of classic logical reasoning, but only in certain situations. I believe mathematics actually holds the key, and may very well be a window to the soul of the universe. Let’s think about what math really means, or any language for that matter, and we will start from there. I believe in the observational and experiential Universe, I also believe there is more, or we need to define universe better. With that, I will also say, this is not an ontological proof, I will be using mathematical terms, only in concept and as support or naming convention, as I lack a more formal knowledge of how to write it, so I will try to derive all my terms within, and relative to the work as much as possible, so it will not result in external arguments being used and a term or vocabulary issue being a determinant. The only thing I have is language, so understand, writing this is not the same as me waving my hands in the air and pantomiming it while speaking, nor is it a repalcement for a full mathematical proof, but I believe it to be self-consistent, and subject to logical rigor of some sort.
I also want to mention some arrogance, on the part of others, and my own. There may be others who say this proves their ideas and such by trying to transmogrify their beliefs to mine, and calling theirs right. I have not found an exact duplicate anywhere, only in some vague religious references, and some long-held conventions that are not understood. I believe this to be the conceptualities that all religions seek to convey in some terms, and I say that with great humility. And with great arrogance I say, if you think my reasoning is your religion’s, then why didn’t they say it like me before? and as far as I know, most of them have one key difference I will illustrate later, but they do not. And as I said above, I welcome valid corrections, or at least well thought refutations that I can at least respect enough to warrant thinking about. I am not a religious person, except that I thought of a version of this sometime when I was about 12, and as I have learned better vocabularies, my understanding and belief in its elegance and truth has only grown. I believe this to be something that must be true to some extent, if not complete. It is too elegant and beautiful not to be. and it fits the logic test… for as long as that test is valid.
Here goes. I will start with a thought experiment. there is me, with a rocks in each hand, different colors, on a riverbank, with lots of other rocks. first, there is such a thing as a rock I can hold in my hand. It has characteristics. I will use the term rock loosely, for illustrative purpose, and not as a tool to prove the details of geology. This setting, and the frame work behind it of our experiential world, i.e., I am not the only human, and other banal assumptions, are assumed also, and only the setting and situation are idealized for the purposes of description. Since science uses the language of mathematics, I will use some references to observational science in here, to support the reasoning, as observation is the key to what I am trying to prove, that the language of math is enough to describe the universe we live in philosophically, and what may be its limitations of description even. As we often want to know the limits of what we can know.
I have one rock in my hand, this is something I can see is separate from my hand, so I call it “1 rock”. I have another rock in my other hand, and this is also separate, and also I can call this “1 rock”. But, i need to know which is different, so I see that there are differences between the two rocks, so I can call them 1 rock grey and 1 rock white now, and the group them together under just “rocks” and I can also now call them 2 rocks, but 1 of each color. This is the structure of language. We teach it from birth. Representation by nomenclature. But, language arose from reality, so we know it to be true experientially, or experimentally, if you like the term better, or at least the words attempt to describe something that is considered to be categorizble. We can repeat those results quite often. This also allows me to use the terms already here to illustrate inherent, or assumed, qualities. There is the 2 rocks, my hands, which are a subgroup of me, and the rocks, are not me. Understand by not me, I group all of them. I am going to use the term set instead of group, as it works better for me, and relates better to the later ideas, but I mean the terms the same, grouping things. In this case, we generate sets of objects with similar characteristics and give those things names, and modifiers. Also, we have overlapping sets, with objects that can belong to more than one group. Now, I will say that it is part of science’s quest to find these true characteristics, and systematically define them so we can see the true defining characteristics at a high level, or small level, depending on your perspective. I will say we can say this about our sets. There exists an inverse relationship between the number of characteristics we use to define these sets, and the number of that sets members. So the set with the least amount of defining characteristics or filters, will contain the most members. This will quickly bring us to something that has always been hard to prove. I will state it here explicitly, according to my intent: The set of All exists.
lets list this for a moment:
1) we can group objects, ideas, and other conceptualities into called sets, and these sets can be grouped, and these groupings are done by using characteristics, and operators, to define them.
2) there exists an inverse relationship between the number of defining characteristics of a set, and the number of the members it contains
3) the universe we know is iterative. Meaning one state is built upon the last.
If we follow both 1 and 2 to their logical conclusion, we come to the set with the least characteristics, and the most members. This will be the set of all sets. We will call this set All. All is self-defined. Meaning, it is the total. All things, the set of impossible things, the set of all things made of atoms, the set of all possible things, all are contained within it. This self-definition means that any new thing found, just increases the size, it does not mean that we create a new set. The very definition of it means that it contains everything. Again, I know I am using mathematical language, and likely not rigorously, and I do not mean it in any mathematical terms specifically as I do not know the specifics. I mean contain in a more colloquial sense, though possibly more strict in its encompassing definition. For the Definition of Not, I will go to experiential 1st principles. If I have a black rock, and I definie it as its summation of quarks and structure that give it all of its physical qualities in time and space, I also immediately implicitly define the not. I then claim that all things that do not fit those criteria are “not” that group. That is the definition of Not at the highest level then: All things that are not (description). The reference being, my foot is not my hand, and neither is the rock, neither are me, but they are a part of me, and not part of the rock, but all are made up of atoms. The set of things made up of atoms encompasses all the others, but there are still both explicitly distinct, and arbitrarily distinct, items within the set.
Now, as it fits our rules 1 & 2, we say this must exist. its only characteristic is self definition. Self reference is true because I can point at myself and say me at the same time. There is perspective, and some necessary characteristics involved, but it is still true withing some lesser set than that of all. In fact, as the Set of sets, it must include some paradoxes, or so it is thought. I will actually tackle those as mostly defining characteristics of smaller sets within All. First, The set of all things not All. Understand, exclusions principles, and other logical rules do not filter this set. Those filter lesser sets. By definition, this set has only one modifier, and as such, is the true expression of 1. it is the true unity. the Least modified, most broadly definied of sets. the set of things that obey logical laws is a lesser set. Except for one. The set of all things that are Not All. A self referencing definition. That makes only 2 modifiers. And yet, it seems impossible. No, impossible is another characteristic, therefore must be a smaller set. No, the set of all things Not All is actually the same set, just separated. All is an exclusive definition. it is Only All. Any other charateristic lessens it. To separate out the set is to create those things that are not All. We already know from our setting that there are things that are not all contained within it. Rocks, streams, us. Arbitrary definitions, but still hold up. Rocks and my hands are different, but we both belong to the set of all things made up of atoms, of which things animate, and things not animate are 2 sub sets.
This is critical, Not is also All. the tiniest speck, or idea, separated out, creates something that is not all, but is still a part of it. other modifiers can then be applied to create subsets, but they are all contained within All. The set of all things infinite? Yep, as there would also be a set of all things finite, both All and Not apply, so these are both lesser sets. in order to make Not be All, we say something like, All that is Not, in place of all. It makes the modifiers make more sense. We also can determine that Not is a Set just as big as All, but is only from within the Set of all itself. This requires perspective. Perspective is driven by a logical operator, well, two, but they are 2 aspects of one thing.
And. More precisely, And/Or. The difference in our frame of reference is perspective. To include (Add) is to make a larger set, while the Or denotes a smaller set. Other logicals like XOR would then be recognition of multiple sets within a set. This line of reasoning would demand that the more characteristics you need to apply to define a set, the further removed from All your set is. So, in order to apply Not to both, you would need to define it as, all that is not(Not, All). I went into some notation. Basically, not, Not and All. But, it has more definitions, not, Not or All. lets look at these in a couple of different ways. Not AND All. Not OR All. We established earlier that And and Or were the same, just from perspective. The only way to define this logically without perspective is to define it as the set of all things that contain some portion of both. It satisfies all of the prior defining characteristics. The OR part of it makes the end points included, so And and Or are also included. I want to stop and examine where we are. i will try to write this in arithemtic notation so we can see just how weird this is right now.
-(Not,All) = -(Not), -(All), since All=All that is not All, AND would be 1+(-1)=0. The perspective of OR means that for All, Not would be the equivalent of -(All) and All would be the equivalent of -(Not). So, All AND Not would be Nothing, or as I like to say it, No Thing. The Or would then include either, but only as an Exclusive Or.
1=-1, then with perspective, 1+(-1)=0
The exclusive or in (All) means that all lesser sets will see them as separate, but only from outside that larger set will the All, Not and Nothing be seen as the same. We can intuitively know, but the structure of the sets prevents anything in the lesser sets below -(Not,All) to only see the 3 as separate. Anything that was in the AND category would be able to see more, as aspects of both All and Not are contained within. Nothing (no thing) would be exactly that, something that was both one and not one. This would apply to anything that was not wholly All, or not completely All that is Not. So all smaller sets would have some amount of view into the higher sets, as each would contain parts of both, or aspects of both All and Not.
So far I am saying that laws of logic breakdown as you go up the scales of reality, as far as perspective goes, and tacitly acknowledging that there is nonphysical components to reality. I am saying that and confident in it. I am not only confident in it, I am saying that since we exist in a world that is not All, that we should see things come in cycles, as the only way for Not to truly be “All that is Not” is to have relative aspects to the tiniest particles that make up our reality have some sort of influence relative to each other. I believe we call that Time. Geometrically speaking, the root of Not one is a cyclic equation describing things going through imaginary circles, and you iterate them to any point, eventually all points will have been reached, and the sum total of each cycle will be nothing. For anything in the lower sets, all values will seem to emanate from the center of that point, the “nothing”. It does have one benefit of making Zero the combination of 1 and -1, which makes it an even number, as it can be divided into 2 equal sets.
Also, All must contain the set of all things not contained by itself. This is usually where reason breaks down, but the answer is simply, the Null set, or Empty set. The group with no elements or members. it is a thing, or idea, so the idea is included within, but there is an empty list of what is not included (by the self-referencing definition we gave before) so it satisfies the basic necessary paradox of being within, and the elements being without. And it also is one of the main paradoxes to opposition of the set of All.