Mytho-logos . . . (obscure, esoteric, and fanciful answer)
Mythos is a story. Logos is language, and it core is the internal constraints that are necessary for language to make sense. This is the physus of the logos.
One of the things that we need to understand is that truth is an aspect of Being. And Being has meta-levels, and so truth has meta-levels along with the other aspects which are Reality, Identity and Presence.
Another point is that we live in the metaphysical era after Thales. Prior to that was the mythopoietic era (cf Hatab). What happened when we fell into the metaphysical era was that there was a symmetry breaking in time, such that we lost a moment of time, the mythic moment. So when we look back at mythology there is a certain nostalgia for this missing moment of time. Time was originally four dimensional with past, future, present, and mythic (original). The mythic is genealogical time. It is the time in which the ancestors still live and influence our lives directly. It is the time of the generation of the immortals and their interaction with humans.
Past and Future are really the same. Together in Old English (Anglo-Saxon) was called Peterite, i.e. Complete. While the Present is incomplete. The mythic moment is the dual of the Present. It is the origin.
The meta-system has four parts (arena, source-sink, boundary, originary template outside the arena, like the object template in object oriented programming prior to instantiation). The mythic is the originary moment, past and future are like source and sink, the present is what appears inside the horizon of the world within the arena. So the difference between present and mythic is what is inside or outside the horizonal boundary. The source is where the system enters the meta-system (is instantiated within the arena) always already lost in the past. The sink is where the system exists the arena always already lost in the future. But these are the two endpoints that confer completion on the worldline of the human as being-in-the-would (dasein). These two endpoints that signify completion collapse together as the peterite and this is understood via fate (wyrd). On the other hand there is what upwells within the world horizon and that which is beyond the world horizon. What was beyond the horizon was the universal genealogy, the always already lost origin of the community. What is within the horizon is the mitsein and the story, the mythos is the talk (rede) that is always there as a background, always referred to, always invoked. The befindlichkeit (discoveredness) is what is found within the world horizon, we find ourselves as part of a community within the arena of the world. And then the third existentiel is verstehan (understanding). Being is intelligibility. Thinking and Being are the Same as has been said by Parmenides.
Parmenides said there are three ways, two of which should not be taken. There is the Way of Non-Being which is Existence. There is the way of Appearance which is the appearing of what appears, i.e. what is present. And then there is the Way of Being, which is static and unchanging as the substance and substructure of all things that exist simultaneously. As has been said elsewhere in answer to another question we can see that existence is what is found, and thus the basis of discoveredness (befindlichkeit). Appearance is also opinion as DOXA, and that is related to the rede or talk of the mitsein. That talk can be chatter, or it can be the always present stories that are the coin of wisdom and reference as the mythic. Thus we can see that Being is verstehen, i.e. intelligibility of things. So the Existentiels are there in the ways of Parmenides. For him intelligibility is the only way, the only way that is not impossible, because it is the only thing that lasts, like geometrical proofs of Euclid. Parmenides is taken up to the gate in the heavens and this is revealed to him by the mysterious goddess.
Once we understand that both existence and Being share the aspects, and that appearance is defined by three anti-aspects (difference, fiction, illusion) together with presence. So there is a symmetry breaking here. So lets think about the other symmetry breakings of the same kind:
presence [present, phenomenal]:: fiction [mythic, genealogy], illusion [past, memory], difference [future, change] => appearance (phenomena always already there seen serially by individual, befindlichkeit) (missing: grounds, reasons)
identity [future, unchanging]:: absence [present, noumenal], fiction [mythic, not genealogical], illusion [past, no memory] => ideos (apperception always already glossed, simultaneity seen by community, verstehen mutual intelligibility) (missing: order)
truth [mythic, not genealogical]:: difference [future, unchanging], absence [present, noumenal], illusion [past, not memory] => mythos (same stories always already told, mitsein rede) (missing: uncovering)
reality [past, remembered]:: difference [future, change], fiction [mythic, genealogy], absence [present, noumenal] => opinion (ungrounded chatter, useless talk, nihilism always already lost, individual rede) (missing: light)
absence [not present, noumenal]:: identity, truth, reality => noematic nucleus, category theory (shadow: groundless abyss, oblivion)
difference [not future, change]:: truth, reality, presence => essence, set theory (shadow: chaos, entropy, clearing)
fiction [not mythic, geneological]:: reality, presence, identity => arche, model theory (shadow: covering, opening)
illusion [not past, not remembered]:: presence, identity, truth => noesis, symbolic logic as formal system disconnected from reality (shadow: darkness, forgetfulness)
Each aspect stands against the other anti-aspects in a symmetry breaking, and vice versa. The asymmetries in time follow the same pattern.
order, light, ground, uncovering are the characteristics of the positive fourfold, otherwise known as the fourfold of heaven, earth, mortals and immortals that we learn from reversing the negative fourfold from the Birds of Aristophanes.
From this we see that the “strangely truthful logic of myth” comes out of the asymmetries of time and the aspects of Being and existence. Traditionally Plato defined myth as lies, perhaps cunning lies, perhaps based on metis. But fiction and truth are two sides of the same aspect. Mythos comes when truth confronts the other anti-aspects. the strangeness of this mythos comes from the meta-levels of Being. In other words there are different meta-levels of truth.
The first meta-level of truth beyond facticity is verification. Notice verification is a relation between truth and reality. Validation is a relation between presence and reality. Coherence is a relation between identity and reality. Meaning comes into model theory via the advent of reality to the formal system which only has presence, truth and identity as aspects. This is the kind of truth that we see in the Oedipus myth when the person comes to verify that Oedipus was a foundling and not the child of his adopted parents.
The second meta-level of truth beyond verification, is uncovering (Aleithia), that is a dynamic truth, truth as process (as becoming true). This is the meaning of truth Heidegger uncovers from the Greeks that we had forgotten. This is the kind of truth that appears when Oedipus realizes that he killed his father and married his mother just like the oracle had said he would and which he ended up doing by trying to avoid that fate.
This third meta-level of truth is related to Hyper Being, Differance and what Plato called the Third kind of Being beyond stasis (Parmenides) and flow (Heraclitus). It is the truth that the Demiurge creates the world as an insemination, much like the poet in the Mahabharata gives rise to his own main characters, the Pandavas through insemination of one of his own female characters. The poet brings meaning and creates through his own embodiment in his own story. In this there is confusion between the poet as author and the poet as character in his own work. At the level of Hyper Being all the distinctions we might make (differences that make a difference) keep slip sliding away. This is the truth that Oedipus himself is the cause of the plague that he is trying to find the cause of in his search for the truth of the community and its defilement.
The fourth meta-level is related to Wild Being. Wild Truth is where truth and falsehood are mixed up like in the Novel. Sometimes literature is more true than realistic documentaries and non-fiction works. Wild Being is like the Mandelbrot set where each point is iterated on to find its acceleration as a line of flight and on the basis of this the point is given a color and we see the overall pattern by the various colors that are assigned to various points due to their acceleration in iteration, i.e. each point has its own intensity, isolated from all other points. There is mixture but patterning in the mixture of intensities that form a rhizome. (cf Delueze). This is the truth that Oedipus sees when he puts out his own eyes. He wanders blindly and then eventually becomes a sage, and initiates the sons of Theseus. This is the truth that comes from the experience of the limits of the human condition.
Mythology as we know it from the Greeks in general is about exploring those limits of the human condition within the Indo-European worldview. And those limits are seen in the interplay between mortality and immortality between heaven and earth.
This strange truth when take to the level of Ultra Being, becomes Beyng (Seyn) (cf Heidegger Contributions to Philosophy: from Ereignis). At the impossible limits we see the strange, unique, onefold of Beyng which is the unstriated dual of Being which is striated by the meta-levels. To see Beyng we must jump over Ontological difference to realize another possibility, one in which we are oblivious to that is encompassing us, and not merely something receding that we have forgotten. This ultra truth is the truth of the Oracle itself. The oracle is a singularity at Delphi where a comet hit the earth, i.e. where heaven and earth come together. As Plato said it was a stone that was not on any boundary from which all the boundary stones were measured. There the fumes came up from the underworld that allot the Pythoness to chant what was revealed from the unseen. Cryptic sayings that had hidden truths for humans to discover for themselves. Orientation toward Beyng in the midst of Being is ereignis: event, happening, appropriation, discerning (http://en.wikipedia.org/wiki/Heideggerian_terminology#Ereignis). All myth is measured from this impossibility at the core of possibility.
Logic is the core of the logos, the physus of the logos, i.e. the internal constraints of language itself that need to be respected for it to remain intelligible. There is also the logos of the physus, i.e. the schemas, i.e. the templates of organizatoin and understanding that we project on the noumena. The inner logic of myth that we find truthful at higher meta-levels of Being as we approach the impossible limits of Beyng is its strange, unique and onefold character that comes from the lost moment of mythic time. We are mortals trapped in our finitude looking at our own limits as archetypal projections of immortals. We are walking between Heaven and Earth standing upright. When we approach the nondual core of our worldview we see order, right, good, fate, source, root as the layers of our worldview and of ourselves. What tells us about the perils of living in a worldview like this, what shows us the nondual core by example, it is myth, the truthful lies or the lies of truth. As Nietzsche says truth is a lie we tell ourselves to maintain our viability and life within the world in which we find ourselves, immersed in nihilistic chatter, and it is what we cling to because of our non-understanding of that world. That limit is DOXA to which we oppose our RATIO in the divided line. The limits of the divided line are Paradox and the Supra-rational. But this boils down to what Kant called serial verses simultaneous time. Objects in the world are simultaneously in community, but we experience them serially based on our freedom to move. Causality is the flip side of freedom. Paradox grows out of contradiction and is mixture of contradictories and when intensified becomes absurdity. The supra-rational is when two opposite things are real, true, identical, present at the same time without interfering with each other. Thus the supra-rational comes from our comprehension of the parallel and simultaneous nature of time in nature, in the physus. But internally we mix up what we see serially and need to strive to keep it separate with logic and schemas. We use the aspects to attempt to situate ourselves within our Indo-European worldview. the aspects apply to both Existence (as emptiness or void) and Being but they are also the way we bring intelligibility to the world through our understanding. We play the aspects off of each other in relation to the other anti-aspects and this is the way we experience the equiprimordiality of time as a symmetry breaking with a lost moment, always already missing in the metaphysical era. We have our nostalgia for the mythopoietic era, and we yearn for the next era of heterochrony, when time becomes symmetrical and parallel again.
In Heterochrony, i.e. when there are separate orthogonal timelines as seen by Dunne originally in the twenties of the last century and which we recover in F-theory, we lose the present as well as the mythic in another symmetry breaking that gives us a new symmetry. This is the worldview where the pluriverse, multiverse, is taken for granted and we realize that they are on multiple orthogonal timelines. Those other universes are absent and never present except as dark matter and dark energy, or what is beyond the big bang or black hole singularities. In a heterchronic worldview era we will be nostalgic for the present as well as mythos. The present was too incomplete and the the mythos too complete as to be fated, and wyrd. The completion of the peterite seen as the past or future will be al we have, as we see in relativity theory where there are four dimensional blocks to which our worldlines are pinned never changing. Future and past are the same, and the difference is meaningless in four dimensional timespace with lightcones. If we lose the assymetry of the present in relation to the peterite, then we lose track of time all together. Symmetrical time is timeless. And it is precisely the timeless that we lost when the symmetry breaking occured that took us from the mythopoietic to the metaphysical era. Again timelessness will appear in a multidimensional time of heterochrony, where both mythos and present are lost moments both nihilistic opposites of incomplete and too complete, and all we are left with is the complete either as past or future which are really the same distanåçce from ourselves in time and thus also nihilistic opposites. What is left according to Heidegger is Ereignis, happenings, appropriations, discernments by dasein as being-in-the-world who is suddenly encompassed by Beyng.