The naïve attitude to the world, after which the words and the things are not distinguished from each other, was restored by Husserl’s phenomenology and Heidegger’s fundamental ontology. The “phenomenon” can be naturally interpreted linguistically, semiotically, and logically as those words, which are the "things themselves", or as the true signs, after which the signifier and the signified are not connected quite loosely and conventionally, but are linked to each other necessarily and thus the three, sign, signifier, and signified coincide with each other, therefore meaning the same from three different viewpoints. Furthermore, 'phenomenon' can be also understood as the unit of the language of "zero-level" and its corresponding logic.
Logic involves the concept of the "order" of a certain given logic according to whether its symbols may refer only to external things ("first-order logic"), to symbols of external things as well("second-order logic") , to the symbols of symbols of external things ("third-order logic"), etc.
One natural generalization of that logical conception is the introduction of "zero-order logic" as well as the corresponding "zero-level language". The symbols do not refer to external things, but they coincide by themselves with those external things. Thus the naive attitude to the world, after which the things and the words coincide by themselves, is transformed into a rigorous and logical notion, that of "zero-level language".
Then, the concept of ontology admits one exact logical definition as any zero-level language or as all zero-level languages. The properties of the zero-order logic and zero-level language can be naturally transferred and thus interpreted as formal and logical properties of ontology allowing of the axiomatic definition of "formal ontology" as the category of a certain mathematical object.
That fundamental approach is widely applied in the research of software formal and artificial languages created by humans for computers for all of them are logically rigorous and grounded on logic. After that conception of formal ontology, the consideration of any programing language to itself rather than to an external supposed "hardware" or to an external reality supposedly modelled generates a formal ontology. On the other hand, meaning a certain hardware or reality for being modelled as granted, a formal software language only repeating them would be their corresponding formal ontology.
Furthermore, ontology implies a special conception of truth, which is not that of correspondence: the correspondence of words and things, for the words coincide with the things by themselves. Ontology is necessarily true in the sense of correspondence in definition and thus that conception of truth as adequacy is useless and meaningless being always valid. Heidegger tried to replace “adæquatio” by ἀλήθεια (unhiddenness) as that kind of truth relevant to ontology. Its sense is the ontology itself as truth or as the special kind of philosophical truth. It means one to move to ontology from any kind of non-ontology. Any non-ontology is mediated by some language conventional to the signified and therefore the former “hides” the latter. If however one manages to see ontology, Hussrel’s “things themselves”, or “phenomena”, which “show themselves in themselves by themselves” in Heidegger, the “veil vanishes” and truth appears by itself right as “unhiddennes”, ἀλήθεια. Thus, ontology is the state of being in truth as well as what is seen in that seen for the state and the seen coincide in definition of ontology.
Problem:
What does the formal interpretation of ontology as the zero-level language imply about Heidegger’s ἀλήθεια (unhiddenness)?
Formulating the thesis as an answer of the above problem:
Heidegger’s concept of truth as ἀλήθεια (unhiddenness) postulates the ontology itself as truth. The concept of truth as adequacy applied to ontology as the zero-level language implies the same. Heidegger’s ἀλήθεια (unhiddenness) can be considered as a meta-conception of truth referring to the question “What is truth?” rather than to that “What (which) is true?” Anyway, that approach implies an implicit answer of the former question: anything of what truth is (ontology) is true, and vice versa: nothing out of ontology is true. Then, one can restore the concept of truth as adequacy even as to ἀλήθεια (unhiddenness), but on a meta-level. One should choose the element of zero-level language (“phenomenon”) to any element of any nonzero level language. This means a certain interpretation of the formal structure of an elementary choice such as a bit of information. However, the same formal structure is shared by truth as adequacy at all.
Furthermore, one should complement the formal feature specific to Heidegger’s ἀλήθεια (unhiddenness). It consists in the existing of the area of being, right the fundamental ontology as a whole. Thus, the choice between an element of the zero-level language and any element of any nonzero language should be postulated as possible always. The formal generalization of that condition is the axiom of choice equivalent to the well-ordering principle. It makes sense only to infinity and infinite ensembles or classes for the choice is always possible as to finite ones without it. Thus, one can conclude that Heidegger’s ἀλήθεια (unhiddenness) can be interpreted formally as that generalization of the standard conception of truth as adequacy, which is able to include infinity consistently.
In other words, Heidegger’s ἀλήθεια (unhiddenness) involves the choice of an element among an infinite set of alternatives unlike the usual understanding of truth as adequacy meaning only a finite set of alternatives. Thus, the formal structure of the latter is that of bits of information, unlike the former: a qubit respectively of quantum information.
Thesis:A qubit of quantum information is the formal structure of Heidegger’s ἀλήθεια (unhiddenness).
A few other arguments in favor of the thesis:
1. A qubit is defined in quantum mechanics and information as the normed superposition of two orthogonal (i.e. disjunctive) subspaces of the separable complex Hilbert space. This definition is equivalent to the utilized above one as the generalization of a bit of information to an infinite set of alternatives and thus to quantum information.
2. Quantum mechanics admits an exhausted representation and interpretation in terms of quantum information. Its base is quite simple and obvious: any element of the separable complex Hilbert space, which quantum mechanics interprets as a wave function, i.e. as a certain state of a certain quantum system, can be equivalently represented as a series of qubits. Thus, the separable complex Hilbert space turns out to be the “free variable” of quantum information, and any wave function a value of quantum information.
Then, if quantum mechanics can be represented as that zero-level language of ontology demonstrating that it possesses a few essential properties of it, the qubit as the formal structure of Heidegger’s ἀλήθεια (unhiddenness) would be supported in an independent way because his conception of truth refers right to ontology.
The formalism of quantum mechanics, the separable complex Hilbert space implies the theorems about the absence of hidden variables in it (Neumann 1932; Kochen and Specker 1968). Two from the fundamental features of the zero-level language, namely the coincidence of model and reality as well as completeness are direct corollaries of that theorem. Indeed, any variable within the complement of the model to reality can be interpreted as a “hidden” one. After the theorem excludes it, that complement is an empty set, and this means that model and reality coincide necessarily.
Furthermore, the alleged or supposed incompleteness of quantum mechanics implies Einstein, Podolsky, and Rosen’s argument (1935). It admits an experimental test (Bell 1964; Clauser, Horne, Shimony, and Holt 1969). That experiment was realized (Clauser and Horne 1974; Aspect, Grangier, Roger 1981; 1982) and repeated many and many times after that. All results refute Einstein, Pododlsky and Rosen’s hypothesis and therefore confirm the completeness of quantum mechanics experimentally quite according to the hypothesis that quantum mechanics is the zero-level language “of nature”.
Indeed, the zero-level language should be complete for anything is also a word of that language. So, It is complete in definition. Furthermore, its completeness should admit an experimental test rather than only a mathematical proof of completeness such as the theorems about the absence of hidden variables in quantum mechanics for the things themselves should confirmed the completeness in virtue of the coincidence of things and words in the zero-level language.
Conclusion: Heidegger’s conception about the properly philosophical and fundamentally ontological truth as ἀλήθεια (unhiddenness) though Heidegger’s criticism versus “truth as adequacy” can be in interpreted in the latter way under the additional condition the area of being (“Sein”) to be postulated in advance. This means that Heidegger’s ἀλήθεια (unhiddenness) can be interpreted as a meta-conception of truth as adequacy. If the formal structure corresponding to truth as adequacy is granted as that of a choice among a finite set of alternatives and thus the quantity of information, the formal structure of ἀλήθεια (unhiddenness) is the choice among an infinite set of alternatives and thus quantum information. An independent argument in favor of that are proof for quantum mechanics as the zero-level language of nature and thus relevant to Heidegger’s ontology.
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