I want to comment, in a different way, on the problem described here, namely that of the possible referrent of a name as a description, or of the question as how it should apply to reality. Because, i believe there are really quite many things confused in this description, that is attributed here by Kripke to Frege and Russel, and against he himself wants to argue later. As, at this point in the text, not taking into account his own position on the matter, I rather want to focus on the problem itself, and one of its most peculiar qualities: how it treats names and that, what in names refers, i.e. the designator, as one and the same, when they are not. So, in Order:
What does actually happen when I use a name to refer to a thing? I think, there are actually at least three things in play: the thing, the name and the act of naming. The act of naming is a necessary aspect, because, without it, there would be no sense of connection between the name and what it is naming. The proper name cannot refer to the thing it names in itself, for it is itself a sound or written word, and truely does not have any kind of "meaning" or "sense". But that is true too for every word, and so we must distinguish in the name the specifically referring quality from that, what is its significatory quality, by the means of being a word. In what sense now can we distinguish them - or, in other words, how could there be words which aren't names?
The problem of divising names as being descriptions is most pulpable at this point, since descriptions include words, semantic references, and if all those are fundamentally based on names, there is no chance for a founding of names in semantics. [I exclude grammatical fragments like "and" in this description for now; since they are obviously not names; but non-grammatical words, like house or tree or country names etc. fall under the given problem] However, I think that we must distinguish, in all this endeavour, before we even want to undertake it, the distinction of action of what we are doing when we talk about "founding", "explanation" or "analysis" - namely, that all these words themselves have a double meaning, and that we have at least a twicefold construction of names, according to which we can maybe make more plausible, how both a theory, that takes names to be elementary, and one which thinks of itself in needs to explain them, can both be plausible at the same time; namely, when their sense of "explanation" itself is not quite the same.
Think about it this way: what is fundamentally the object of the analysis of language - or, which are its fundamental elements - are they _immediate_ or _mediated_? We can have here two quite different methods. One, that takes the whole complexity of life - or that, which I call the _immediate mediation_, the non-constructed complexity of things - and tries to analyze, to find the specific content of an expression. However, this also is not quite a direct endeavour; because any attempt first tries to analyze it as a whole, and either stops at wrong intermediate goals (where a complete picture of the life and the "self" seem possible, despite their internally utterly contradictory self-descriptive behaviour), or, when finding this contradiction, understands it already to be everything (as I also did, and as I see the main problem to be in post-structuralism, where the absense of a structure is wrongly taken as the absense of the structural elements within it, at least in the more naive interpretations; the death of the subject is precisely the presence of the problems of "subjectification", how these acts of thought can be thought of without any idea of a centralizing substance); or that tries, after understanding this internal contradiction, to take the whole contradictory material of the self as itself an object of analysis, which would be the immediate object of analysis or reconstruction. The latter is the problem of analytic philosophy, which too often thinks that the description / accidental finding of a transcendental category within the descriptive construction of thought is "analysis"; when really it is the absence of a descriptive framework of such analysis. Now, to be more concrete:
If we try to take too directly all elements and problems of life and try to "analyze" them, we encounter in them countless objects and things, and also descriptions. Those appear to be at the same level of reality, that reality being that of life, after we understood that "life as a whole" cannot be brought into a totalizing idea (the idea of "the self as such" being no less but an internal substitute for the "absolute idea of truth" for the external world). However, this "life" is my life, and "I" is here nothing but a description from my own self-distance; it is a way I miss me. Insofar I miss me, even if always not far from me, that through this near-miss of a self-description (through my way of understanding my actions, thoughts and experiences through ideas and perceptions) I also embue other things with this self-missing quality. And with this, there now is a significant difference between two elements, that I can see within the experience of my life, and of that self-experience within that life:
Lets say I refer to my table, that I am currently writing on. In a certain way I refer to something external; it is part of my life, of my "being" (in that, without me being here, the table wouldn't appear to me; it is not part of my self, but of my to-be, of being as an action). However, it is not merely a significant, it is itself part of thought. On the other hand, I am not refering to something external, I merely refer to an appearance/experience; to the "tabling" of the table, its being-there, not anything else. Most of the time, this is mixed; this is why "appearance" has a double meaning: the act of appearance, i.e. how an _external_ thing _appears to be_; and the thing "appearance", i.e. how this _internal_ experience _really is_.
To which appearance is the logic of analysis now appealing, if it talks about analyzing the meaning of the appearance of things in language etc.? And how can this double nature of appearance be applied to language itself?
There are really two very different approaches here, the realist and the transcendental approach, which lead to quite distinct types of analysis and ontology, and I therefore want to present them separately; and then explain, how they relate to the question of the reality and descriptive quality of the name.
What I would call the realist approach, is to understand this question quite apart from the task to understand the mind; to instead, create a conception of "existence", which is seperate from the self, a being-in-itself. This means: instead of asking, what the table is to me, to then analyze its connections within my linguistic understanding etc, I try to understand what it is in itself, and what it maybe has to do with "language in itself", i.e. not in me, but in a greater context, in society etc. The important fact here is, that, because we ignored the constitutive part coming from self-understanding, this understanding of the table _cannot_ be objective, because objectivity is a kind of pooled subjectivity, of the common agreements of subjects etc; rather, it is manifest of the "reality of its own idea", aka. something primordial to its understanding. The conceptual view of a "realistic analysis" is that of a network of in[de]finite "things in themselves", in Kantian terms, i.e. of things actually existing, viewed as though without context (i.e. in themselves as = without a constitutive part from the viewer, the audience, by an act of apprehension / contextualization), and then stiched together artificially, by terms of "connection of things", i.e. external predicates.
This is because the connectedness between things is precisely their appearance. The ultimate name of that connection is "life"; so, if we want to see things apart from our life, they must appear apart from meaningful connection, and must gather meaning from their interior, themselves accumulating the qualities previous stored for them into the central focus point of the subject - namely, that now, instead of an interpretation, or an external act of mind, the intentionality living in their appearance, is, by a slight of hand, transferred into those things; and thus these "objects" become "referents","designators" etc, instead of the referring or designating subject that they have replaced. (A similarity between the post-structural and analytic approach; both seem to try to conceptualize this spread-out notion of language/reference/significance in things, rather than in minds, and come to similar problems, for that reason, when talking about the process of signification/naming, where they must find some sort of inherent/necessary connection of signifier and significant, of designator and referent etc. - but without an "I" that refers one to the other)
Also, this approach does not understand that, in a strange way, it itself is positioned within the subject, as a kind of subjective construction of this "external world". By not taking the perspective of the constructor into account, this "objectification" or "death of the subject", of which the authors and successors of the Vienna circle and of literary deconstructions hoped to gain a new perspective, reproduces, from the same perspective, an idea of "unperspective reality", that is, the "subjectless world" is the ultimate expression of the subject. The concepts of "referent" used here, are always prelimary, as the question where there referential quality comes from, is not, as they say, primordial (as if it lies in the act of the use of language itself, as for example proposed by Wittgenstein); because it comes from this _understanding_ from them as being part of the "world", a.k.a. the "life world" of my life, that is, that their understanding is ultimately referring back to me, who I still am nothing but my me-missing-myself - and therefore referring to their own inadequacy to signifiy the meaning of the reality they claim to encode. This inner inadequacy is the deeper reason, why it matters to understand the external description too in relation to the subject, because it shows them not just inadequate in relation to external, but also internal justification, for which reason the description of transcendental categories (although sometimes deminuated as mere "biases") has taken hold over this area of analysis also. Let us thus describe this difference of construction, or what it means to take the transcendental category of self-missing into this question of analysis; or in which way then, we more concretely miss the very construction of language _by enacting it_.
What reproduce we then, when we change the focus of analysis? I think that this really cuts to the core of the question of what we are even analyzing. If the analysis is of actual problems of life, we have the problem of referring to these two very different things: the objects in question, and that what refers to them linguisticly; and if we don't have a mediating subject, we have the unending question of how these designators have gotten their referents. By adding the subject back into it, this becomes quite clear: they gotten their referent by being themselves only tools, by which the subject referred to the object. So then, what becomes of analysis? Obviously, the realistic approach means _something_, right?
Obviously. But much less than usually understood. Because what is this external "referent" really? We too often ask this, and then answer with another designator. We ask: what is the tree?; and answer with a description from the biological lexicon, which _itself only designates things in nature it wants to describe_. That is, we substitute names with other names or descriptions. That is actually not _realistic_, although it claims to be, because it confuses the other with the signification of the other. How can that be, in any way, called realistic?
I think that we therefore must distinguish this: that there _is_ a signification of the other, but that this is different from the internal signification of thoughts; and that we therefore have to distinguish the two. By what criterion? Now, here I go back to the other concept, that the self is, in a certain way, _too much for itself_. I can't think outside of me, because that would still be within me. I can't contain me; for then I would. (This does not mean that I can't concieve of me; this conception must just always be limited, and, once I've thought about it, once I'm aware of this limitation, I must be able to find within it (and any other such conception) a trace of something left out, which can't be left out if the picture would [have] already contain[ed] me, in the way that the idea of a table can contain the table.) This quality is also, in a sense, part of my other thoughts; they have a qualitative element, the how-it-is-to-think-them. This is not part of an external referent, because this referent is precisely understood not to be a designator, i.e. not itself to be part of the conception of thought - lest it already was; in which case it is not external, and couldn't have come into our consideration as an _external designator_. (This includes also things we wouldn't normally call external; for example, my feeling of pain can externally designate a brain state, or a biological function, or even a certain, objectified, "mind state"; the important thing is, that those aren't concepts, that they are not "designators" in the same way that the designation of it is; that the "reference" of a physical pain state to the wound is not an "intentional reference", but a physical one.) And here we can see that when we ask what we analyze, we must really split this discipline in two (or at least in two): on the one hand an analysis of the relation to externality/alterity in this extreme sense, which doesn't allow for a substition of the external referent by a linguistic form; and on the other hand a description of the internal substitution of referents, which are also designators, by each other. Because these referents/designators can stand for each other, and are not just known to us by one side (and it is also quite obviously that it must be that side; for there might be designators, pointing to our thoughts as referents, i.e. intentionality directed at the "internal referents"; however, because the designator is external, so is the act of designation, and thus the whole connection we can only refer to as an external referent - leaving to us only the status where the designator is internal, may the referent be internal or external. (this is more obvious in the case where both referent and designator are external, as per the naming of things by other people, and one can see the similarity to other peoples attempts to "refer" at our thoughts, only being able to grasp their most cruel objectifications)). The first is not strictly speaking part of the understanding of the self, and rather of the relation between the self and the other, and sits at the boundary between the kind of philosophy of self I endure myself in, and other disciplines, whereas the description of internal designation lies squarely within it. I will therefore dedicate the rest of the desciption of this text to this other one; the one we might call, as opposed to the drastically reduced realist framework, the "transcendental" (taking this word in a broader sense). The more interesting thing about this framework/method however, is the way it must constitutionally miss itself, at least at the beginning; and how it can only construct this "method", or the description of inner designation through a reconstruction of language, after a second, and more fundamental, recourse to that language, that already has been its reference to, and limitation to the boundaries of, the mechanism of internal designation of referencing of thoughts and ideas (i.e. _designation_ in the broad sense), and then only after a quite arduous descriptive account of phenomena, followed by two quite different forms of externalization of the inner structure of that account: first for the self, and then to the other. The eventual construction of this "framework" will however give us a certain way of "practical analysis", quite similar to the typical analytical framework, but distinct in understanding, that it is not about life, but about a very specific practice, which is only a limiting case and part of a general understanding of the subject, and bound to in its movement from intuition to aspiration, as the noetical realization of desire.
Namely, let us think of the following attempt of giving an account of it (which I also, a number of years ago, have undertaken in a deeper form, and might translate when I have the time and energy to), which leads to the realization of its necessity, and is simulatneously, in a different reading of the same description/text, the act of its first externalization, and by that too then part of the second (It is for this thricefold quality that I want to translate this attempt, if I can, with a more descriptive commentary; as its German version is now to some extent readable, but very misleading about the kinds of things actually provable by such a kind of investigation) I will present a shorter form of this description, and one more talking about things than within them (i.e. with less explicit reconstruction, and more indirect descriptions of the acts, that such an understanding might need to take to perform them):
Lets start, conceptually, with the inner "things of thought", or of those elements of things themselves as pure appearances or phenomena. How might we designate them, or even take any of them as a referent? After all, we mean to reference one thing by another, but they are and remain to be different elements of thought.
I think that the fundamental idea here is, that naming is not something inherent, not a difference pre-exsting in these elements. Because, again, these elements are inner elements of thought; they don't directly _refer_ to something outside of thought; because that would be, as an external reference, a reference outside the self, and something, in a certain way, not describable in that aspect. (To be very clear: this does not mean that we, for example, could not have knowledge of things in space, as we clearly do; it means that the whole of space-time, as we imagine it, is an _inner reference_, a designation of a concept we have. Its only external reference is the idea, that this concept is true; that, as is said to define truth here, the concept agrees with the thing. However, that we cannot know internally, as is describes a "reality" outside of understanding. So I will continue to state that all we have here are ideas, or elements of thought conferring back to the self as the not-knowing-myself; but that is because the other elements of the totality that was missed, were not elements of our consideration at all; they either were assumptions about their existence - a quality, that I, unlike _being_ in a semantic sense, can't describe (because "being" here refers to not _that_, but _how_ something exists, or as what; an essential, not an existential operator) - or they were things-in-themselves, and thus completely external to our understanding, as it refers to things _outside of any explanative contexts_. This is the reason we think here of appearances as elements of thoughts; but also of other elements of thoughts (as these thoughts are of course different from their own appearance, or act thereof, as previously differentiated). In short: We limit the description to the selfs content, but not only to its understanding of itself, but also of thoughts which, while not appearing in their acts as thoughts, but as appearances of other things, still are thoughts (i.e. external _designators_ are part of this internal representation, when they are thought about _without their referent_, i.e. as formal elements of thoughts).) If, however, they don't refer naturally, how can a kind of _reference_ be brought into them; how can one thing be made to mean another?
I think that there we must separate two things: how the _act_ of naming can happen; and how the _legitimacy_ of names, or their truth, can be understood. The truth of a name is quite simple to understand, if we separate it from the act itself: once the name is given, it is true because it was established. So how then can the act of it happen? And how is that connected to it being "established"? How can this be separated from the existence of the thing to be named in particular - how can the name as an answer be separated from the name as a problem?
The key is the simple fact that _the name is not the thing_. What is meant by that, is quite simple; for example, that a house does not have five letters, but "house" has (except when there are five letters on the side of a house maybe, but then too is the kind of "having" quite distinct). Naming is here an act of signification, that holds its truth in its _inadequacy for analogy_. Its the non-symbolicness of names, that means their truth.
In this way, they separate themselves from the thing being named. The connection between elements of thought is arbitrary, but not quite: the thing can't signify itself. And mostly, the names are taken from a subset of elements, like sounds or written symbols, to signify all but themselves. However, still, this only explains the act of "establishing", as in, if a given such symbol exists/is used, it is legitimate by not being the thing symbolized by it. The act is, however, different from it.
It is important to see this difference, because I will not explicitly mention this at every stage later. Because the answer here is quite simple: _The act cannot in some meaningful way explained, it simply already happend_. One can describe it in various ways: as an expression of reflection, or of pain, or of connection of things; but that cannot derive this, since there also is no logic here to derive with. But we can see, that simply from elements, by their difference, we can have "names": pairs of elements/intuitions, by which one is called a "name", and is given a truth-value towards one other, and not others, based on _not_ being that thing (in an arbitrary manner for this logic; but it needs not posing that the act of naming is arbitrary, merely that it must be treated _as if it was_ by those re-naming the things with the same names when using the names or words). In this way, we have "reference"; not by internal quality, but by an external act on internal referencing ideas (because the elemental qualities are already referencial, and we now create a new naming-reference structure on top of that).
From here, we can move through the other stages of the construction of more abstract concepts:
In a second step, we can construct what I call the "name-thing", that is the construct of all elements/internal designators, which are named by a certain name. In other words: we can ask for a name always these two sides: what names does this thing have; and what things does this name have?
The third step is the combination of these two about a particular element. This means now, that I look at a particular element of thought, and ask back and forth: what is this named; what is named such; etc. So I can assotiate a thing with its qualities, and then with other things that have this qualities etc. In this way I can create what I call the "phenomenon" (Important: this flipping of name and object does not actually move the intuition away! This was one aspect I descibed this originally quite poorely, as one could just say "X is", then take "being" as the predicate and move to any "Y" that is. the "name-thing" is related to a specific naming, i.e. to the way a specific quality gets a name in a particular instance, that is, "being" is not a general quality here, because it does refer to something, if that something is not specifically understood to "be a being"; so that the main focus here is to describe various "names" of the same thing, which however must be connected by that very thing, as the names don't name each other, but the thing named, hence moving between the name and the "name-thing"; for example, in the case of the black wooden table, I move from the table, to "wooden", to the table, to "black", etc, and then also to other things with such qualities, but these other things are things like "what appears within it", i.e. the specific forms/shapes within the wood, which are not the table, but part of the "phenomenon", since they are a thing also referred to, by a quality we understood to be said about another thing occuring in this constituitive thing-name-chain of the phenomenon)
However, this only creates assertive qualities, not negative. This is because the connection is still that of naming, i.e. of connection, not of distance. To create a connection of distance, the following concept is employed: first, I create a relation, by which I can relate one element to another; namely, I say an element A fits to / into element B, if A appears somewhere in the "pheonomenon" of B, as described before, and as a specific thing. Then we can say, that "B is A", if A fits B, and "B is not A", if A doesn't fit B. It's important to understand the limited quality of this statement: it doesn't mean that I have a real description of an object with a predicative structure towards other things as predicates; it only means, that when looking at / thinking about a certain element of thought, I can't think how to connect it to the other. And in this way, we can say "B is not A", not because we've seen the non-A-ness of B (which would be impossible), but because we tried to see the A-ness of B and failed; or rather, we tried to see how A could fit B, and failed. The important change is the move towards the predicate as the "subjective position", or we could also say as the active, the predicative position. We say: A doesn't fit B; because we look at A, looking for B. Because if we would look at B, A wouldn't appear; but then we would not know why to even look for it. The conundrum of non-existence does not need to be touched; non-A-ness can be explained in purely eleatic terms, (that is, without negating existence of anything, even as a predicate) as a limited expression of my lack of imagination, of finding a proporty, when starting with the property, in a chain of appearances/name-things; we do not need to then have to worry about how this B then could be non-being A, for it only is, positively, a thing, which is one, so that another, A, does not fit to it; but this non-fitting actually _appears_, as a lack of imagination, and is not a non-being, or an inexistance. An _object_ is now a particular element, assotiated with all of its appearances as fitting or unfitting in other elements, as represented as _properties_ on it.
After this, we can go on to _compare_ to such objects in relation to any specific element, if it fits both or either or only one, but not the other. In this way, we might find if two objects share properties, or differ in them.
Now however we go beyond that, and compare comparisons. How should be do that? Well, I can think comparisons as _acts_; such understood, intependent of their causal description, merely as a combination of two objects, directed towards a particular element, we can try to understand comparisons themselves as elments, and we get a) a name of them ("comparison of X and Y towards Z"); b) a "name-thing", consisting in other things called the comparison, or being their condition, such as the pheenomena X and Y, an aspect/element Z, the fact that their is a fittingness of Z in X and Y in positive or negative quality, that this fittingness is itself connected to, and then that it is thought in X and Y; c) the phenomenon are then all equivalent comparisons (between the same things in the same way, but maybe happening at different times etc., and thus not being the same intentional act); d) the comparson as an object contains the various things phenomenaly assotiated to it as properties, be it some times only as its abstraction (i.e. the _object of the comparison_ includes X and Y, but only the phenomenon of Z, not Z itself (which is an element, not a phenomenon), the positve/negative quality of fittingness (but not the specific "fittingness" itself, as that is tied to Z, not the phenomenon of Z), and thus too the _relations of fittingness_ and their corresponding properties in X and Y, which are, as general _results_ of comparisons, more likely tied to the phenomon of Z than to Z itself); so that now we can have e) a comparison of two such comparisons, in all those qualities: we can compare the objects X,Y, X',Y'; the aspects Z and Z' in their phenomena; the positive/negative affirmation (as a quadrifold comparison of logical positve/negative qualities); then the specific kind of "fittingness", or rather their phenomena; and finally the qualities of fittingness in objects themselves, i.e. the comparison of their properties. Through this idea of "fittingness" we can now serially compare multiple objects by the smae "quality" or "property", without having stipulated this as an abstract idea beforehand; rather, it is an result of the gradual comparison of comparisons in this way of abstraction.
From this comparison of comparisons it is not difficult to get what I call empirical abstraction: lets say I have here a red object, and there a red object; all those are mere elements of thought. Now I can compare them, and see, that regarding the aspect of the color (which is merely an element, and _becomes_, in the act of comparison, a property shared between them), they are equal in their fittingness, that the color has to them. From this, the _empirical abstraction_ of red, are all properties, which are shared between all objects, which compare equally to this object with this aspect, and this in some sense is the definition of "red" as an abstract idea, independent of a specific intuition of red (and similarly, all the properties, which are shared between all objects, which compare differently to this quality, can define an idea of "non-red"; however, this could also be confused with the aspect of "red" which includes negative properties - which are part of "red", not "non-red" (as in: "red" is not X; in opposition to "non-red" is X); a reason I won't use this abbreviation). And similarly, once we have the ideas "red", "green" etc, we can abstract the idea "color" from it.
For this however, "red" must become a mere element of thought again; it loses its abstractness. In a sense, we will never know if not all intuitions had these kind of abstractness to begin with. In fact, we know they are tied to consciousness itself and the abyss of the absolute, trying to know itself. For this precise reason, this here is not a simple "derivation"; it is only an explanation, how one, starting with them, only knowing them as elements (whatever they really are), can recreate these kind of structures on their own.
This happens over and over again, but there is one limitation: any such idea can only used as a property of the last layer. After all, that's how they were created, and for most things this makes sense: color is a property of red, not of a red thing, etc (it would only be a property of a property of a red thing). However, we can now think about something, at least conceptually, which would close the loop; something, that would be its own abstraction.
This thing is the mathematical variable. X is defined to be that, which is described by its definition, to be X. The pure X = X entails nothing but this X itself. And by that, we fall in a kind of hole; because now, we can't go back to the intuition, compare etc; the mathematical element is not fit for comparison, only for proof, and thus we find, that by this leap, not a gradual process, we can create mathematical abstractions; but not by a leap of faith, but by a limiting step, which itself is also so typical by the method thus described. (I also thought of this step, at the time, to be typical of Hegel; if that is true, of the Hegelian "Dieses" in the first chaper of the phonomenology of spirit, indeed is such, is a different question, but it no doubt shares a number of central qualities, most importantly that it is thought of as its own result; which I tried to complement with it too being its own beginning only still.)
However, this account of the creation of abstract thoughts is itself flawed in may ways; and in the next paragraph I want to explain how so, and how that leads us to the idea of a different kind of "analysis", one that is chiefly tasked with understanding the very notions of "intuitiveness", "naming", "fitting", "comparison" and "abstraction" itself.
Let us reflect on the kind of "comparison" we used to gather a new idea from mere names (a process also generally known under the name "abstraction", and here only restricted to "empirical abstraction" by restricting its inputs, the things we compare, to specific elements of the kind described before, namely from a lower level of abstraction): In what way did we actually compare elements, or thougth them to be similar? Lets take the example of color. We did compare "red", "green", "blue", "yellow" etc, and what is in common between them, undoubtably has something to do with colcor. But: could we have made the comparison without having this idea of "color" before?
I don't think it would be possible, because we never would think then about creating these elements "red", "green", "blue", "yellow", by the comparisons of intuitons of things with the same - color; and would never then think, that for a smiliarity of the kind of comparison that these ideas arose from, they might have something in common. In other words: while the specific element of "red", as pertaining to the expression of self-misunderstanding, as an "intuitive" element, might be derived from such an act of comparison; this act presumes an idea of "color" that preexisted, and that is not an element, but a mode of action, or of intentionality. "comparing in relation to color" is older than the idea "color" itself; in this way, we cannot go back to primitive elements alone, as without their ideas of composition, they would be entirely unintelligble, even for the task of analysing the ways they might be composed.
The same goes generally also for the more abstract elements - elements like "comparison" or "naming" themselves. It is true, that the way it's describe, they're not presumed as elements of language, but arise from natural actions on these elements; but these kinds of actions precisely entail this kind of intentionality, this way-of-understanding.
The important thing to understand here is that the idea of something truly is not composed in intuitions. For example: I cannot understand, what a house is, from what it is made from. I may know everything about building materials, but that doesn't tell me what a living room or bed room is. The "idea of a house" could be described in the definition: "a house is a building where people live", depending on an idea of "living" that can't be found in the house, but in what the house is for - also a kind of intentionality, but one with external designator and referent. Given that our cases operate, as stated, only with internal references, the situation is not entirely the same; but it is similar in that ideas denoting representations/interpretations of such external objects (which, as internal designators of external referents, are still internal in nature and therefor part of the network of internal referentiation), _cannot_ be constructed from other internal referents, that are designators/denoters/interpreters for the parts of the objects the original interpreter/denoter was denoting (as otherwise, going to the external elements, they also could be similarly understood; this is a kind of equivalency, or one could say a _functor_, that could server as an _equivalency of categories_ of external and internal intentionality, insofer it is connected through internal designators of external referents (i.e. of the relevant subcategories, described by either end, image and co-image, of this construction), althought the representation is not suitably formal for this to be fully developed, let alone be proved in terms of clear definitions - but I think that the idea of such a formalization is not just reasonable, but also can move the two disciplines, descibed in their difference, between external and internal referents, above, closer together, describing formal similarities, while still understanding, that they describe fundamentally different categories - in the same way, that in a certain sense, algebra and topology are alike, but that, while topological structures certanly have certain inherent algebraic qualities, when they are formalized (by words on a page), algebraic objects only gain geometry through construction (homology etc), and not by an internal geometry they may have - one could say, in this sense, internel designators referencing an internal referent, can be "isomorphic" to an external reference, but only by the possibility of such a construction, of a "canonic construction of reality from though", only _up to the isomorphy class induced by the specific kind of interpretation of reality_ (that is the kind of reality indistinguishable but such an interpretation)).
Going back to our problem: We have these kinds of modes of intentionality, that compare things as "in relation to". In a way, we have not solved the problem of relating the elements to each others at all, because we still do not know how these acts work, how they can relate to each other etc. However, we did something else: We started with elements, that did have no organisation or structure at all, simply things appearing in life, and now we have them at different levels of abstraction, up to the mathematical level of "self-reference" - and know we discover, that for all these levels and acts, there is a "mode of intentionality", that we need to study also. The nice thing about this is, that the problem is complexer, and thus has more structure; we can analyze the problem not as a problem of creation of structure, but by the explanation of its inner referential content. And thus, instead of starting with elements, trying to form connections, we start with these strange connecting predicates like "A and B compared in relation to having-the-same-color by a specific intuition X", and try to analyze these predicates _as something that operates on elements of internal referentiality_.
Because one could say, that in a certain way, we are right where we started, at language analysis. But that is not true. Because now, the specific content of the language is internal referents only; however, by demonstrating that these kinds of predicates must have existed, we prove that the _form_ of such a language is still universal, and that there therefore is something to analyze, and that it's not limited to artifical constructs with no general propositionality. (Outside of the kinds of propositions, necessary for these predicates of comparison, however, the language is quite poor; and one could use that to speculate, that speech acts outside of internel/mental predication, may _always_ require external referents to take effect.)
In any way, there are now ways to analyze these structures. And the interesting question is now: what do we find in the analysis? The disappointing answer is: precisely the kind of structure we already created. There was a reason that the construction of "red" looked natural; and that is, that the only actual predicates we can find in "red" are similarities of red things. They are not formed as in the "empirical abstraction", they don't contain all properties true of all things comparing similarly to a certain red-intuition; rather, they are elements which are logically/sementically connected to "red", and describe the similarities of red things, because of which we call them red (i.e. the actual determining factors, if the predicate "A and B compared in relation to having-the-color-red by a specific intuition X" is used v.s. the predicate, where "having-the-color-red" is replaced with something completely independent, a kind of red', which appears to be true for all red things, but is not compared against in the comparison "in relation to" being red and not red').
In this way, there is a process of "analysis", by which we deconstruct ideas, down to intuitions; but this deconstruction is not about genesis, but semantic content. This is the major difference at this step: we already covered the genesis of them, as elements, before: now we want to understand their content, as a general form, describing their various relating modes of intentionality. We go then here, for example, backwards, from "quality" to "color" to "red" to a red thing (like a red apple), and then to a situation, where I might say "here is this red apple", and thus describing the semantic content of the description of an intuition; of the sentence "X appears", "X is".
At this point, one might think the whole thing is over. We have found the ultimate representation of designators of external referents, as endpoints of a second analysis. However, that is not the case. This "X is" is _not_ an external referent. To understand that, is precisely the question for the construction of the idea of the _phenomenon_, or of the explanation of a possibility of analytic phenomenology.
What do we mean, when we say, that something, that appears, "is"? To put it simply - we mean precisely, that it appears. This means, that for an appearing thing, its existence is in a sense implied; it has to _be_ if it _is_ a thing, something-that-is. Here we go against a boundary. Weren't we supposed to stay within internal referents? How can there here be something, that is, in an emphatic sense?
It is strange, indeed, that there should be such a thing within language as an existing thing; and references cannot quite catch it. The existential operator has thus far always been the catching point of analytical philosophy; because ultimately, what does it _signify_? - That something is - But what is this _is_ other than that which it is signifying about? Could it honestly say, that this, which it is referencing, is not? Can there be such a thing as significance of inexistence?
This is the old trap of Parmenides, as reinstated by Quine (his reinstation is specifically about language and significance, and differs in this way, we might say, only in description or linguistic difference). But I do think that this actually here has a significance. It means, that there is something like an inner structure of a designator, even if referring to an inner referent. It holds a) a semantic content, something said to be true about the referent (negation changes this content; one could say, the same content is negated, but there is no need for that, as we could simply posit the negative content: a is not b, and a is non-b, is in this description of designation the same, _because_ it is reduced to semantic content; or to put in other words: both negative and infinite judgements (the two statements provided) are different _modes_ of signification, but have the same content; and the mode is not a difference of signifier, or of signification, but of the kind of use of language in non-propositional, illistic ways); and b) something that refers to the referent, a reference or pointer to it. Those two things are different; and in a way, the parmenidean paradox simply states that a designation of non-existence is only valid for an invalid reference (a kind of ontological null-pointer; that what Plato called the non-being, in a positive way; or we can also refer to the empty space in the post-modern structure, the gap leaving a trace, Badious interpretation of the empty set as the root of ontology etc.). We see though that there must be a connection between them; and I believe, this connection is precisely the _mode_ of assertion. So actually, there are three things: semantic content, reference and mode. (The difference of negative and infinite judgements, as described above, is one such mode; but there are many others, most are described under "illistic" categories, usually.)
From these, the content is just another designator - that what it says about it. To say, this is read, designates the color red positively about "this" (which is another internal referent, say of perception). This was already subject to analysis; and when we think about its end point, we can see that the last statements, the "X appears" etc, have empty semantic content, besides existence itself. In other words: their content _is the reference itself_; they merely state: this thing is this thing; and therefore, it is false, to state, this thing is another, if they're not equal, because then I don't designate the reference about itself (even if the statement might be accidentally right, it is not an identity statement, and therefore not subject to this kind of analysis at this point; it is false as a statement of _existential quality_). This also explains why "X doesn't exist" is precisely true, if the reference to X is invalid; because the semantic content of "isn't" is the broken reference itself, and so any such broken references must be identical.
However, there is second element in this "existence", and that is its mode. And this mode of affirmation is here precisely the linguistic element - saying "X is" is _affirming_ X about itself. The next step, and the last, of this kind of analysis, therfore moves from this X to its reference. But at this point, we are at a loss again.
Because what is this reference? The intentional meaning of _something_. Some kind of appaerance. We are back at the appaerance. But remember: we had two options: the appearance as the _act of appaering of something_ (this is what we did so far - external referents _appear_ for the mind) - or as these "appearances" itself, as existing elements of the mind, but not as designators of something else, but as the appearance _in its reality_.
I think this is what this X in the "X is" really is. It is the reality of the appearance, as visible in the intentional quality of the reference in any existential designator. "X is" leads to X, by means of its signification, and by stripping away from it its self-affirmation. (This "stripping-away" is, not for chance, similar to Husserl process of Epoché). But what do we now do with this X? It is something, it is a thing, it "is" also (as a signification). In what way now can we understand, "analyze" them?
There are two obvious comlementary moves here. Once we can just go from one thing to the other; they have no connection, but all _are_. These fragments of existence create a kind of unconnected network, a gigantic discrete graph, on top of which the network of semantic connections is positions (by references to them, and by the "is" as an equally spread out network of loops at the vertices). We simply get a vast array of different "beings", of appearances, of different kinds and origins etc. And indeed one can study them; and this study is that what I would call "phenomenology" of the proper kind, of the more stricter desciption/designation.
However, that is not the only thing we could do. We could also do just that, but we could also want to analyze these phenomena themselves. This leads us to a different process, a very different kind of analysis, that I call the _internal objective construction_.
We start here again with intuitions. However, these are not elements, they are already points in this giant network, with a huge element of semantic form attached to them. However, we can _temporarily suspend_ that networt, and recreate, step by step, it from particularly elementary relations, specifically:
1. First by names between phenomena (by the connection of the phenomenon of the named thing to the phenomenon of the name as sound)
2, Secondly by the connection of multiple things by such connections among each other, as phenomena,
3. By the connection of those to the original elements.
....
It is quite obvious that this is _exactly_ the blueprint of our previous construction from elements! But now it works. Why?
Because we now don't assume that we start just with elements. They are connected; we can always set back the network of semantic connections on top of the intentional network of phenomena. Because of that, we are in no necessity to wander where are relational predicates stem from; they _are_ precisely our elements, as analyzed in this linguistic framework before. And because of that, we don't fail at the same step this time.
I indeed believe that the construction works out here, and gives a kind of sublime object, the ultimate element of this reconstruction - the X = X, or the variable, as the self-abstraction. (Important: it is no self-signification! X _is not_ the Idea of X = X; but it in some way is that statements abstraction, as something, which's only role is, to somehow - be).
This object is then the basis of mathematics. I think that mathematical constructions ideed start from here, from the X = X, that founds first logical statements, then axioms, then set theory and so on. One could go here deeply into mathematical considerations; however, because this is not a math textbook, I will refrain from doing so (despite it easily could fill tons of pages), and instead will move to the next step, namely that element, that is itself missed here, and which will form the next step of our analytical framework.
What mathematics misses, is itself. This is true in many ways of reading the sentence; but the one most important here, is that it misses itself as in: it can't describe its own action. The specific mathematical action of doing mathematics (I.e. proving things, deriving etc, like we are presumed to do with the simple X = X), is a kind of forwards- and back-reference: I want to prove X for something, therefore I construct Y, because I know X is true of Y. For example: we search for a solution of an equation. Therfore, we construct something that is a solution. The start is something completely general: we want _any_ solution; but we get one. After the fact, we use then this Y to prove X. This Y can be many things; it can be a system of axioms for example, by which we can prove a particular theorem for an algebraic structure. This system of axiom however defines this structure. In the end, we get into a self-reference; but beyond the trivial self-reference, found in the reference of a definition to that what is true about it (one which only is there by choice of words); even without all such technical terms, speaking only in reference to the X = X (like was tried and imagined in the Principia Mathematica), there is still the self-reference of desire, that we want a particular result and therefore we invent _something_ for which it is true. And this self-reference is not linguistic, is not intentional; it is, for the first time in this analysis, a relation of will or of desire.
This mode of desire, in a sense, represents the self. It is, I believe, the self in particular way: let's say I ask, what is necessary. If I ask like this, I must be there asking, too must I be able to ask, and also I must be willing to do so. These three things - myself, my imagination/thought, and my desire - and one might add the connection of thought and desire, which might represent the fourth element of logos - are here the only really necessary things. Anything else _truely necessary_ would be empty - tautological - and in that way represented by the form of mathematics.
I think that we therfore can identify the mathematical process with precisely these elements. The tautology is the vast network of proofs; the self is a kind of starting point (the X = X itself, the empty referent, the empty set etc; one might even say the non-being); the imagination is the process of construction; desire is the will to find the solution; and logos is their connection, or this form of thinking itself, of placing the desired goal _before the solution that tries to achieve it, but without informing that solution it is not merely an element of construction/logic_. And I think, that in this way, by analyzing the mathematical process coming from the self, as the empty significant, we can reach the more eminent Self of the subject, as a result of the methodological analysis of mathematical thought, or of its own inner modes of abstractive action.
But where _can_ subjective analysis go from here? I think, that the only point is precisely that of objective analysis. But how could it get there?
When we talk about subjective and objective analysis, it might seem we refer back to the difference of internal and external referents, but we're not. Instead, let us focus on the newly constructed subject iself, from our last step of analysis out of mathematics. What is its inner structure?
The structure of the subject - of its own inner reference, of imagination and desire etc, of the connecting logos - is very complicated, and is, in a way, the framework also containing all of this talk about internal referents. (One might say, that every ontology that wants to be complete, must be necessary fractal, because it needs to cover the category that contains itself; and thus is in no less a bind than the subject, trying and failing to understand itself.) But one important question here is, if it indeed is referring only to itself or also to another subject.
I think it is much easier, but much more complex to: the subject necessarily refers to itself as to another subject; it is, to itself, already something/someone else. How can I explain this adequatly?
The subject is, as explained, a kind of externalization of the mathematical method; it is the position of a goal, and a reposition to how that can be achieved; it is the irreducible illogical element in logic - the method of proof itself. This "subject" (which is not the whole person, but merely a kind of reduction as self-consciousness of this method of thought and action in general, only containing these most general aspects, of being, thinking, wanting, and their connection - present formally in mathematics and materially in life) is already in itself represented as a kind of repetition, as an X = X. This form of equality is the background; but it is also the most incomprehensible.
I could go for longer into this, and indeed, have (the whole PPWC talk is in a way about this inner difference, and its distinction from the difference within plurality). But it actually is not important for these matters, because this kind of inner distance is, as much as it provides the logical space of the self to be itself or something else for itself, not enough to represent any actually distinct subject from itself, but the other abysses/shadows within itself and its desires. So, objectification has to happen, if it can, somewhere else.
How can there be _another subject_ if the subject is in its way formal? Well, only by comparison to the _actions of the subject_. There are particular expressions of subjectivity in this context, most notably the acts of imagination and desire itself, as expressed through action (of any kind, be it linguistic, motoric, plural mind interaction etc.). So we can see certain events in the world and might say, that they belong to another subject, by understanding them as _actions_. This is a purely coincidental interpretation; it is not necessary, and indeed, cannot be proven. Therefore, the kind of understanding that calls itself _objective_ must, in this way, understand itself as a hypothesis, namely of
a) the existence of another subject at all
b) the possibility of interaction / communication (the goal, on which objective knowledge is based)
c) the existence of shared external referents.
The last one is clearly important, as it implies the possibility of something like a shared world. However, this understanding can be reduced, because it is indeed quite a claim, to say anthing at all about external referents, let alone to create something like a relation of "sharedness" or "equality" for external referents, when we only really understand them for internal referents (as "sharedness" here refers, in some sense, to the mind, and the relation of intentionality here is not external, hence also not the referents inducing these modes of "sharedness" or "inclusion" of thought), The reduced thesis might look something like this:
c') the hypothesis of a correspondence of situations, in which subjectively-constructed, empirical terms are demonstrated
This means specifically: If I have a term, of which I have a subjective reconstruction (i.e. a construction which happens after phenomenology, as explained before), and I explain this reconstruction in reference to specific phenomena, which are specific situations (situations which "X is" or "X appears" refers to, as explained above), then I can help reconstruct the other, in their mind, the same construction, thus transferring a kind of correspondence. It is only a correspondence, because they are likely to have the phenomenon interpreted quite differently; but there is a correspondence, in that there is a situation and then, following from it, a kind of construction; but only a reconstruction, as the elements are constitutively necessarily there to constitute the elements of phenomena to begin with.
This now leads us to a specific kind of "analysis": We can judge what a word means, by analyzing it in the way demonstrated before, and originally explained by my old text, and the way in which that failed. However, this form of analysis works applied to phenomena, because it presumed a background of semantic content. However, this semantic content is _not_ shared in the objective analysis. This means:
The objective analysis allows me to analyze, if _I_ can reconstruct a certain construction based on certain shared (or supposedly shared) phenomena; it fails if the construction to me makes no sense.
This is the form of analysis, the particular practical variant, that I wanted to point towards. Why now all of this? Because, we can see directly how certain terms directly fail this test of "objectivity", like a concept of justice or truth, or mathematical ideas in relation to intuition, because they do not in fact refer to phenomena and construction, and much more to predefined semantic content. On the other hand: a construction like "red" is more likely to succeed, based on shared red-intuitions. This allows a separation of abstract and empirical claims, totally independent of the necessity of shared sense date or external referents, instead putting the test on the non-reliance on the background network of semantic content within situational phenomena.
This was quite a tangent (a whole essay long; but the tangent, in fact, does tend to infinity, and also on paper not for graphs), and it might have gotten myself forgetting what I was talking about. I was examining the question, how a _description_ can be a name, and about the difference of designators and names more generally.
I think, that after this long description of the movement from things to names/ideas to constructs of those to phenomena, and then to the self-objective reconstruction, and then further to the external-objective reconstruction, we have seen a lot of different modes both of naming and of analysis, that the following kind of statement should make sense:
Naming, on the level of proper names, seems to be an intuitive act, something irreducible. That is true on the level of naming phenomena, in subjective constructions and reconstructions. At the same time, they seem to be the final result of analysis; that is true both of the necessary pre-analysis of phenomenology, and too of the objective reconstruction, which we recieve as a complex idea, trying to find out if it is indeed based on any correspondence or not.
In this way. I think that the paradox, how names can refer to descriptions, can be closed, by saying, that _pre-phenomenological and objective_ names _are_ descriptions; but _subjective_ names are not, they are acts/actions on phenomena. And as such, not just can they not be named, they are, as the fundamental elements of subjective reconstruction and reflection, elements of thought impossible to reconstruct but by the assumption of action, i.e. by the belief in the foreign mind and spirit.