Logos and True Distinctions in the Logoi💬
Theological considerations
A man who talks to cats and a man who builds robots. These are private reflections of such a man, not Church documents or official theological positions. They are put online for discussions and will be regulary updated. If you take them serious, that is on you, however, if you do so, you’ll see that we can have a lot of fun! This is the greatest invention of them all, communication, using the best biological tool, reflection.
A short article on traditional Christian theology.
Introduction:
St. Maximus the Confessor, the great theologian and philosopher of the Byzantine Christian tradition, articulated the concept of Logos (Greek for “word,” “reason,” or “principle”) and logoi (plural of Logos) as a central aspect of his philosophical and theological framework.
Logos:
Accoding to St. Maximus, the Logos (λόγος) refers to the divine principle or rationality that underlies the entire cosmos. It is the divine ordering principle that gives structure and coherence to all of creation. In Christian theology, this concept is closely linked to the “Word of God” as expressed in the Gospel of John, Christ being the incarnation of the divine principle Logos itself.
logoi:
The logoi are the multiple principles or reasons contained within the divine Logos, I called them “proto-ideas” before. They are the divine ideas or archetypes that pre-exist in the mind of God and serve as the patterns or blueprints for the created order. Universals are the basic “points of existence” that things have in common, or the repeatable resp. recurrent entities that can be instantiated, exemplified or individualised by many particular things. They are created from the blueprints of the logoi. Each created thing, according to St. Maximus, participates in these logoi, which determine its nature, purpose, and position within the cosmos. In the Logos are all logoi, even those who would serve as the proto-ideas of universals of worlds that didn't came to be1.
logoi2 include mixed perfections3, that is, perfections that contain potency4 or some other limitation in their notion or meaning. They are archetypes or proto-ideas of things, and themselves wholly positive. Only when actualized the things depicted will be what is depicted, including act and potency, positivity and negativity5.
logos:
The term “logos,” when written with a lower-case letter, denotes the proto-idea of a composite thing as a single entity. Thus, the logos of man (as a species) is indeed a logoi, but it belongs to the class of logoi that represents several other logoi, it is a logos. Thus, the many logoi of a logos are the properties of that notion. One can express the composition of a logos—its properties—in thee categories: its existence, its origin, and its telos (τέλος): “end,” “goal,” or “purpose”. The logos of a kind, species or type of thing is also called the essence of that thing, that what defines it.
— It should also be noted that “essence” generally refers to an answer to the question, “What is a thing?” However, this question can be answered across various categories, such as “What is a thing substantially or factually?” But here, I refer to what a thing is as idea, without considering whether it is or is not actualized beyong being [an] idea. —
The entire notion of us is therefore already completely expressed through our individual logos, with beginning and telos, and the particular composition of a thing, of us, and thus the answer to the question “how can multiple things be one?”, is by the hierarchy of logoi in the Logos.
The mind quickly comes upon three questions when looking at this truth with due care:
To what extent are we then still free creatures? I will address this question in Free Will I.
Is our downfall as human beings also reflected in the archetypes of God, and if not, where then? I will address this question in a moment.
If the complete notion of us, including our experiences, impulses, thoughts, feelings, already lies within us as the actualization of our individual logos, to what extent can one still assume a practical, actual interaction between different things, if they would add nothing more? After all, everything that an actual interaction would add is already expressed in my own notion, the movement of my actualization of logos. I will address this question in Do we truly interact with each other?
logoi as good archetypes:
Does God also represent injustices within the Logos? At first glance, one might say “No,” for injustice stands in opposition to God. However, does this imply that God has no idea or understanding of the injustices in the world? The answer here is again “No.” Injustice merely does not manifest an archetype in the ontological6 sense. This means that God's knowledge of injustice does not fall within the scope of the aforementioned conception of the Logos, which encompasses order and archetypes, but pertains to a different kind of knowledge. A possible conception of this other knowledge I described with the Word-machine7.
Our participation in the Logos via nous8 provides us with phenomenal categories, the a priori conditions of human experience. These are the necessary structures that the mind imposes on sensory data to produce coherent experiences. Thus, even though one may say sense perceptions are necessary for thoughts (every idea represents sensible notions by picturing them in the end, as some say), they would not be sufficient without phenomenal categories, through which they can form a coherent picture.
How can the Logos be individible while the logoi are truly distinct?
i) In order to give a better answer, I would first like to explain what I identify with universals essentially, which I think is useful for they represent a [direct] analog to the genera9 or the “lowest” level of the logoi; simple ideas from which all complex ideas can be constructed.
ii) If we consider an arbitrary definition, denoted as D, we can decompose it into smaller components. These components work in unison to form D through what might be termed “direct construction,” i.e. in a single step of combination.
iii) This can now be continued with the components of D, let us call them {D2}, and so forth. However, to prevent circularity, this makes it clear that you get into an infinite chain of specification. In such a scenario, one must swiftly devise new terms to combine them into old ones on a higher level in the ledder.10
iv) This chain is supported by infinitdesimals11 (entities infinite small yet not zero/nothing), the universals through which meaning can be obtained. These may be never reached in our line of thinking, since it is possible that we can never fully walk all the steps. Nevertheless, they remain indispensable for imparting meaning to concepts. I identify the ability to bundle these universals, which underpin every instance of meaning, and therefore to gain an understanding of a thing, with [mathematical] intuition.
v) This last level is analogous to the lowest level of the logoi. Yet, there must also be higher levels in the logoi, for God not only has an idea of the smallest particles, but also of the things that are composed of these particles. A tree, for instance, is known to Him in its entirety, as well as all its constituent parts, whether real or conceptual. These are logos with lower-case “l”.
Question: If these universals and compositions actually presuppose different ideas in God (or proto-ideas e.g. genera or logoi), how is the Logos not indivisible?
vi) Even if one were to admit that there are an infinite number of strands that will extend from the penultimate (pre-last) level into the last, and therefore an infinite number of genera are given (this is what I call the lowest level of logoi), which is an extreme I do not hold anymore as necessary, even then this is not to say that these must also be different in terms of quality.
vii) For this self-existent level (bundled in knowledge of a priori material), which cannot be further reduced, can be infinite in quantity without also being so in quality.
viii) Consider, for example, the binary code. Each complex idea may have an infinite number of strands into the binary plane, which here is just a stand-in for the level of genera, comparable to infinite digits, but each digit is only set to either “1” or “0”, even though there are in fact only two self-existent things that are not composed (universals/genera), since all others are qualitatively identical to “1” or “0”.12 In this case, all complex ideas do not arise from an infinite number of different qualities.
ix) There is another aspect that must be considered at the level of genera. When proposing 1 and 0, and to depict a greater infinity by introducing previously unknown basic conceptions of meaning, which I will designate here only as "& X", a logical connection between 1, 0 & X is necessary to prevent them from being arbitrary and, ultimately, conceptually divisible, since there would be no conceptual thread of connection.
Complex ideas would need to arise from an Arte Combinatoria (1), in order to be non-arbitrarily connected with each other and with the genera, and genera would require a conceptual thread of connection (2).
x) The Arte Combinatoria is a “characteristica universalis”, a natural universal language, capable of generating any conceptual possibility, i.e., complex idea, by combining a finite set of characters or self-existent ideas, without ever allowing a fallacy to occur in the production.13 God, as we know, does all that He can do and is all that He can be.14 If He is not something, or does not do something, it is because it is not the best, and therefore does not mark a perfection which He is moved to actualize. If we now combine the two, activity and combinatorics, we see that from every idea, if we would to master the Arte Combinatoria [which might be impossible except for God], every other idea can be derived, since the division into the genera and every combination of them is evident at the same time. And just as the idea “activity” and the idea “combinatorics” exist, these are not equal to the activities or aspects themselves, but are one of the many productions.
xi) The decomposition and derivation of each logoi ensures that the particularization of each individual logoi does not constitute a completely isolated notion, but it does ensure that the complete identity of a logoi is comparable to a reflective geometric image that is individuated by a unique center - that is, distinguished from another geometric image. A logoi is thus a fractal. All other logoi are built around a particular center in that imagine and that is what completes that notion. With the universals we only see the top of the mountain, the geometric center. The complete view God has about a particular notion contains all the other logoi in the image around.
And this is also why I think that, provided one is aware of the rules of the world and able to think far enough, one can deduce from each thing that one recognizes as a single thing the principles with which one can arrive at all other possible things, if so accessible to our minds. Therefore each individual logoi - even a genus - is [ontologically] indivisible from all the others.
Question: Can the genera, in the example they were 1 and 0, each be separate, whereby the logos would be indivisible in terms of logoi, but divisible in terms of activities or aspects that lead to the logoi?
xii) The genera would be divisble if there were no necessary connection between them and no connection to something third. This means that a real subset15 of what it means to be divisble is to have no common participation. This logical connection to each other or a third, which is what I mean by participation, must not exist via combinatorics, for combinatorics already build on genera.
What I have found as a solution is (first) “necessity of the other qua opposition” and (second) the “necessary existence of everything that is the opposite of something else” as genus.
Thus: Each opposition in every possible combination is the set of all logoi. The Logos is indivisible even in the genera and divine operations or principles they partake in because activity (pure act) (1), opposition (2) and combination (3) are together one and that is what the Logos is, activity in combinations of oppositions, expressing infinite proto-ideas.
Concerns with Dualities
The above is sufficient to map out number theory, vector spaces, set theory, Boolean algebra, group theory, and topological dualities; resp. that what can be expressed thereby. An example of what cannot be expressed by oppositions at least easily would be abstract algebra.
Dualities are pairs of concept linked most fundamentally16 and revealing underlying symmetries and correspondences, often providing a means of transforming one into the other. Examples are:
Algebraic duality (e.g., vector spaces and their duals)
Geometric duality (e.g., points and lines in projective geometry)
Topological duality (e.g., dual complexes)
Logical duality (e.g., De Morgan's laws)
But along came Gödel and showed us mainly two things: [1] In any consistent formal system that is rich enough to express arithmetic, there exist true statements that cannot be proven within that system. [2] No such system can demonstrate its own consistency. That implies limitations in any formal mathematical system, which challenges the notion of reducing all mathematics to dualities, as there are truths and structures that elude complete formalization. Thus, the above program is generating only those logoi which can be expressed based on dualities.
This article I wrote thanks to Energeiologian, who asked the question: “To all of you who affirm real multiplicity and mutual distinction of the logoi: how do you solve the apparent conflict with the indivisibility of the Logos?”
I welcome every comment and am eager to respond!
With sincere thanks,
~ Justus.
Provided one does not believe that God created a vast multiverse that exhausts all His (positive) ideas, or logoi, which is contrary to at least traditional conceptions. In my theory of the “word-machine” I argue that God did not have to create all possible worlds, and that modal possibility must not be identical to factual possibility.
I always write it lower-cased even at the beginning of a sentence to show that it is a plural of lower-cased logos, and never the one Logos.
As Quasi noted in a conversation with me.
Act (or actuality) and potency (or potentiality) play a crucial role in explaining change, causality, and the nature of being in Aristotelian and Thomistic metaphysics. In short: Actuality: What is really existing right now; Potentiality: That which has the potential to exist, but which must first be acted upon in order to do so. For example, a cold coffee has the potential to be heated, but the actuality of heat (or movement of what we observe to be particles) needs to get to it for that potential to be actualised. Whether that is a real or imaginable distinction depends on the model of metaphysics in use.
Positivity refers to “what is”, the presence of some entity, quality, or attribute. Negativity refers to “what is not”, the absence or lack of some entity, quality, or attribute. Traditionally understood, light is positive and shadow or darkness negative: the lack of light.
Concerning the nature of being, existence, or reality.
A concept I developed to show how God could create a particular of all possible worlds without change in Himself due to His own movement, instead of all possible worlds, even assuming that there is more than just one [modal] possible world.
As described at the end of the article.
A universal, simple notion or “point of meaning” which is predicated of several specifically distinct subjects and which incompletely expresses their essence.
Nowadays, I say the steps to the genera are not necessarily infinite.
Nowadays, I say the number of the genera is not necessarily infinite.
Of course, one may argue the genera in God must be more than just 1 and 0, since this way you cannot represent every infinity and therefore not the fullness of every idea.
I wrote a short introduction to that in I: Philosophy and God, an overview on concepts.
Actus purus in an extreme understanding. Here too, the manifestations of God do not necessarily have to be all-encompassing, since what God can do, or how He shows Himself in creation, also depends on creation. Actus Purus traditionally negates merely “passive potency”. Active potency refers to the inherent ability or capacity of an entity to bring about change or to act. It is the potential to perform actions or produce effects. Passive potency refers to the inherent ability or capacity of an entity to undergo change or to be acted upon. It is the potential to receive actions or effects from external sources.
A set s that contains elements only from another set S while not containing all elements of S.
Here, most fundamentally means that they are considered only in a framework including them being in opposition to the other.