AN INFORMATIONAL APPROACH OF INFORMATICA 1 /92 BEING-THERE AS UNDERSTANDING \* 
Keywords: Heideggerian Being-there, Information, Anton P. Železnikar informational formulas, philosophy, text formalization, Volaričeva ulica 8 understanding 61111 Ljubljana 
This essay is a study of possibilities pertaining to philosophical text formalization; it is a trial formalizing the most complicated and semantically intervveaved concepts of Heidegger's Being-there as understanding. »What kind of formal informational system understanding in the context of Being-there could be?« is another, yet unansvvered question. However, this essay is a beginning in formalizing the question of understanding in the contextofBeing (Dasein, Being-in, Being-in-the-world, Being-possible, Being-there, disciosure, existing, explaimng, knowing, seeing, etc) . It is an approach tovvards the so-called informa­tional understanding machine tlirough the arising formalism (informational language). 
The first part of the essay deals with introductory commentaries conceming the way of author's motivation to undertake such particular seeing of the problem. In the next section of the essay a formal informational interpretation of Being-there as understanding is presented in both Heidegger's and informationally formal way, in projecting and constructing formula systems which pertain to the original philosophical sentences. In this manner, in this part of the essay, fifteen paragraphs of Sectioh 31 of Heidegger's Bemg and Time are interpreted in the informationaIly formal way. Several subscripted Greek and Fraktur letter operand and special operator symbols are introduced to make formulas readable and symbolically distinguishable. 
In the continuation of the essay four further paragraphs of Heidegger's text will be formalized and an integrative formal interpretation of the examined paragraphs will be given. Two dictionaries of formal symbols together with explanation in English, German, and Slovene will be attached. 
Informacijski pristop k biti-tu kot razumevanju I* 
Ta spis je raziskava možnosti, ki se tičejo formalizacije filozofskih besedil; je poskus formaliziranja najbolj zapletenih in semantično prepletenih konceptov Heideggrove biti-tu kot razumevanja. Drugo, doslej neodgovorjeno vprašanje je , »Kaj je lahko razumevanje kot način formalnega informacijskega sistema v kontekstu biti (tubiti, biti-v, biti-v-svetu, biti-mogoče, biti-tu, razprtja, eksistiranja, pojasnjevanja, vedenja, videnja in temu podobnega). Gre za poskus približevanja t.i. informacijskemu stroju razumevanja z uporabo nastajajočega formalizma (informacijskega jezika). 
V prvem delu spisa najdemo uvodne komentarje, ki zadevajo napotovanje avtorjeve motivacije v tako posebno gledanje na problem. V naslednjem poglavju spisa je predstavljena formalna informacijska interpretacija biti-tu kot razumevanja, in sicer v Heideggrovi in informacijsko formalni obliki, v pro­jektiranju in konstruiranju formulskih sistemov, ki zadevajo izvirne filozofske stavke. Tako je v tem delu spisa interpretiranih petnajst odstavkov 31. poglavja Heideggrovega dela Bit in čas v informacijsko formalni obliki. Vpeljani so različni operandni in operatorski simboli v obliki indeksiranih grških in gotskih črk, ki zagotavljajo bralnost.in simbolno razločljivost formul. 
V nadaljevanju spisa bodo formalizirani še štirje odstavki Heideggrovega besedila, dana pa bo tudi 
integralna formalna interpretacija obravnavanih odstavkov. Dva slovarja formalnih simbolov s pojasnili 
v angleščini, nemščini in slovenščini bosta dodana na koncu. 
*This essay is a private author's work and no part of it may be used, reproduced or translated in any manner whatsoever without written permission e.xcept in the čase of brief quotations embodided in critical artides and reviews. 
One can see in Heidegger's concem for humble things a continuation ofhis interesi in the heritoge ofmarginal practices. He now sees them aspossi­bilities that have saving power precisely because they have never been taken seriously by the meta­phjsical tradition. Such practices, which have not been singled out as important and so technolo­gized, provide a basisfor resisting the technologi­cal understanding of being. 
—Hubert L. Dreyfus and Jane Rubin [BIW] 338-339 
This essay is a preliminary study of the possibilities of a philosophical text formalization. It pertains to the phenomena of understanding within the frame­work of philosophy of Being or, precisely, within the Heidegger's Being-there [SZ, § 31]. As a first approximationof informational investigation, for­mulas correspondin g to sentences of the Heideggerian text can be joined in a perplexed way, decomposed and composed, universalized and again particularized. In this mode the concept of Being-there as understanding can be depicted and developed formally obtaining some particular conceptualizations for possible later construction, design, and technology of an understanding sys­tem, that is, informational machine. So to say, we are stepping into the realm to make philosophical sentences informational in a symbolic (mathemat­ical) way. One of the basic questions remains, does the possibility of an informational machine for philosophizing in accord to Being-there as under­standing (and vice versa) already exist and what would the necessary approach to come closer to the realization of such concept be at ali? The carefully reader will possibly find hints, kinks, and his own disclosedness of the problem of understanding within the philosophy of Being in general and within the Being-there in particular. Informational formalization of philosophy in question will cer­tainly brighten the domain of understanding. 
1. INTRODUCTION 
To get a right approach to understanding it is essential at the outset not to think of understanding as a cognitive phenomenon. ... For Heidegger primordial understanding is know-how. ... uruler­
standing a hanvner at its most primordial means knovving how to hammer. -Huber t L. Dreyfus [BIW] 184 
The phenomenality of understanding belongs to the main stream of the postmodemistic philosophic, scientific, and technological movement. Irrespec­tive of the philosophic doubt to disclose ever the phenomenality of understanding and make it a scientific and technological tool, the study of intel­ligence in living organisms remains the most dis­mrbing and irritating view of the ftiture research. The phenomenality of understanding opens a suf­ficiently broad and unexplored realm of cognition, intelligence, reason, and mind. 
The question we put into consideration is, how do philosophers comprehend the phenomena of understanding and which concepts (knowledge, beliefs, world views, rarely notions) do they use in the disputes conceming understanding, interpreta­tion, explanation, and so forth. In this sense, our challenge is to examine some parts of the con­cemed philosophic disputes in an informational way. In experiments like these, we can study, luckily, some paragraphs of the text written by Marti n Heidegger , who , as it seems , has determined understanding not only in the most lucid and complex way till now, but, maybe un­consciousiy, aiso in an appropriate informational way. Our attempt will be to prove this assertion in a consequent and formal way. 
The basic question of the present investiga­tion will be how does the system of understanding, which Heidegger hamessed together in the realm of the philosophy of Being and time, inform as an informational entity, that is, as a literary symbolic, operand-operator, open informational system. This investigation can offer several hints for the top-down (or, according to K. Popper, from the view of the third world) cognition and construction of comprehensive, intelligent, and imderstanding systems. To remind the reader, Popper [OK] says that the word world or universe must not be com­prehended too seriously and, in this manner, three worlds or universes can be distinguished: (1) the world of physical objects or states; (2) the world of conscious or mental states, or maybe of ability to act; and (3) the world of objective contents of thought, especially scientific and poetic thought and art works (acts). In the third world there are, for instance, theoretical systems, problems and problem situations, critical arguments, states of discourse and, certainly, the contents of newspa­pers, books, and libraries. 

When I began to write my first essay on informational phenomenality, in spring 1987 [OWI], I was silently hopping that one day I will be able to put the Heideggerian Being-there (Da­sein) as understanding [SZ, §31] into a form of the arising formal interpretation. Now, as this possi­bility dawned, my task is to prove the potentiality and appropriateness of the so-called formal infor­mational language. A formalistic effortconceming understanding was already invested in the essay Understanding as Information II [UAI2], where some Heideggerian views of the loseableness and loosing of understanding have been shown by means of a formal system of informational formu­las. 
In this essay I will use the technique of formal informational interpretation of sentences belong­ing to the Heideggerian text. Each paragraph of the chosen text [BT, §31] will be interpreted by a kemel (in some way background) informational system of formulas as an informationally arising entity. Around such a system additional formulas will occur detailing (and perplexing) the interpre­tation of the system. If a sentence will not be taken into the interpretative consideration (parenthetical or informationally suppressed matter), it will be (temporarily) enclosed into brackets. The reader will come into the position to experience how formal informational interpretations can back­wardly influence the human understanding of the original text, to enrich it informationally in a po­tentially understanding sense. This possibility will arise because of the general and imaginatively unbounded nature of informational operator \= representing the entirety of an informational back­grotmd. 
At the end of the essay, the reader will fmd two dictionaries ordered by the informational sym­bols (occurring operands and operators), corre­sponding English terms, and their translation into German and Slovene. Thus, the oppormnity will be given to make fiirther comparisons of meaning and understanding of formulas interpreting the text in English, German, and Slovene. 
2.	 A FORMAL INFORMATIONAL INTERPRETATION OF BEING­-THERE AS UNDERSTANDING 
Rather, modem natural science, modem mathe­matics, and modem metaphysics sprangfrom the same root ofthe mathematical in the wider sense. Because metaphysics, ofthesethree, reaches farth­est—to what is, in totality—and because at the same tirne it also reaches deepest toward the being ofwhat is as such, therefore it is precisely meta­physics which must dig dovm to the bedrock ofits mathematical base and ground. 
—Martin Heidegger [WIT] 97-98 

2.0.	 THE SEGMENTATION AND STUDYOF THE CHOSEN TEXT 
In this chapter we deal with the verbal and symbolic interpretation of the text belonging to section §31 (Being-there as Understanding) in Heidegger's Sein und Zeit [SZ, 142-148; BT, 182-188; BV, 162-168]. The textof section §31 [BT] includes 18 paragraphs which will be analyzed and formally developed in a sentence by sentence fashion. We shall number the sentences of each paragraph by bracketed markers [paragraph_number,sen­tence_number] and to each sentence corresponding formula by parenthesized marker s (para­graph_number.sentence_number) . The 
Heideggerian terms of Being will be used conse­quently as particular informational entities (head­words, passwords); the reader can find an index of German and English expressions (headvvords) in­cluding short notes in [BT]. On the basis of this index, the reader can study the concepts of partic­ular terms and see how complex the most of them are conceptualized. Each term is an informational system of formulas and terms are mutually per­plexed in various informational ways. By these initial comments, we can proceed by the procedure of study and text formalization in a subsequent and systematic way. 

2.1.	 THE FIRST PARA GRAPH OF ^31 [BT] 
[1.1] State-of-mind is one ofthe existential struc­mres in which the Being of the"there' maintains itself. 

The operands are: Smind marks state-of­mind; Ogjist marks existential structures; ^there marks the Being-there (the Being of the 'there'). The formal interpretation of the sentence is 
(1.1)
 Sn^d G -'exist> (®there \= c?exist) \= ®th ere 

The explanation of operators: L marks the opera­tion is one of. The part of the sentence (meaningly unmodified) ... the Being of the 'there' [^therel maintains itself... within the existential strucmres aexist is formalized in the second line of (1.1) by the so-called metaphysical (circular) form for op­erand OSthere-D 
[1.2] Equiprimordial with it in constituting this Being is understanding. 
The exact meaning of this sentence is the following: Equiprimordial with state of mind in constituting the Being-there is understanding. 
The new operand is U which marks under­standing. The formal interpretation of the sentence is 
(1.2)	 (Smind' ^ Fconst ®there) Fequi_p 
This formula explains the fact that entities B^^^ and U constitute (operator ^=const) entity OSt^gre in an openly equiprimordial way. To be equiprimord­ial (gleichurspunglich) means to inform in an equiprimordial way (operator [=equi_p)- The comma between two informational operands has the meaning of 'the one and the other operand' (parallelism). D 
[1.3] A state-of-mind always has its understand­ing, even if it merely keeps it suppressed. 
The meaning of this sentence is, that a state­of-mind always contains its understanding (in this čase U) and informs this fact in a suppressed man­ner. 
The formal interpretation of the last sentence could be 
\.y.j)	 (U ^always ^mind) Fsupp 
Operator Caivvays is a particular time operator and means 'always has' or 'always contains'. The sup­pressed informing of this containment remains open. D 
[1.4] Understanding always has its mood. 
If iK marks the mood, the formula for this sentence is 
(1.4)	 ?m(ll)Caiways^l 
No further comment on this formula is necessary. 
D 
[1.5] If we Interpret understanding as a fundamen­tal existentiale, this indicates that this phenomenon is conceived as a basic mode of Dasein's Being. 
Let us expand the meaning of this sentence in the following way. The first part of the sentence says that we interpret (understand) understanding as a fundamental existentiale. And if so, then this indicates that this phenomenon (our understanding of understanding) is conceived (understood) as a basic mode of Dasein's Being. The sentence as a whole is implicative. Certainly, the we in this sentence can ha ve the function of Dasein's Being and need not be treated as a separate operand. Evidently, Dasein's Being, marked by SSj) (or, also, Being of Dasein, 93(2))), is a component of Dasein S) and there exist the so-called basic modes t^basic of Dasein's Being. Further, a fundamental existentiale Sfunj is the coming out or meaning produced by understanding. In whole, there is 
(1.5)	 % C S); Ubasic G %); ((53®Nint U) N Sfund) =^ (l^basic ^ %)) 
Operator [=in, has the meaning of interpretative informing and operator => marks the informational implication. Formula (1.5) can be refined (in­formationally completed, supplemented) in sev­eral ways. D 
[1.6] On the other hand, 'understanding' in the sense of one possible kind of cognizing among others (as distinguished, for instance, from 'explaining'), must, likeexplaining, be Interpreted as an existential derivative of that primary under­standing which is one of the constituents of the Being of the "there" in general. 
The meaning of the 'on the other hand' is 'in parallel'. Formulas, separated by a semicolon, are 

understood always to exist in parallel. Understand­ing U as an entity is only one possible kind of cognizing ^cogn among other kinds of understand­ing or there exist always other kinds of understand­ing . But understanding is interpreted as an existential derivative Sg^ist of the very primary understanding Uprin, which constitutes (roots in) (operator C or C^onst can be chosen) the Being of "there". Thus, Being of "there" itself can be con­ceived as the producer of this sort of primary understanding. Furthermore, understanding U is distinguished (operator ^t) from explaining ®expl-Within this view, we can put dOwn the formal system 
(1.6)	 (01 L l?cogn) Nint 5exist) ^ Uprim; ^er e \= (^prim ^ ^B^here)' 11?^®expl 
The last system of formulas ends the formal ization procedure of the sentences of the first paragraph in chapter §31 [BT]. It is to stress that the listed formulas phenomenalizing the sentences of the first paragraph are in no way complete informa­tional systems and can be supplemented in a developmentally and explanatory open way, so at some later state, diey can even informationally exceed the contents of the particular original sen­tences. D 

2.2. THE SECOND PARAGRAPH OF §57 fBTJ 
[2.1] [We have, after ali, already come up against this primordial understanding in our previous in­vestigations, though we did not allow it to be included explicitly in the theme under discussion.] 
This sentence is a kind of comment which concems the previous text. D 
[2.2] To say that in existing, Dasein is its "there", is equivalent to saying that the world is "there"; its Being-there is Being-in. 
We take the follo.wing informational inter­pretation: in informing, Dasein S) is the there Tf^ere of Dasein 2), marked by T(S)there)' this is in­formationally equivalent to the formula that the world SB^orld informs as the there T,i,ere- The world's Being-there 93there(^world) informs as Being-in OSjn. Informing of Dasein can be symbol­ized explicitly by the Dasein formula system (S) |=; t= 3)). Thus, 
(2.2)	 ((®|=;|=®)i=Tthere(2») <=^ (3Bworld N T^there); ®there(^world) N ®in 
The last formula system is rather generalized than reduced in comparison to the second sentence of the second paragraph of §31 [BT]. D 
[2.3] And the later is likewise 'there', as that for the sake of which Dasein is. 
The later in the last sentence concems the Being-in, that is, operand 53in. Further, the ,'is likewise' corresponds to an informational operator and, if we take the most general čase, \=, this operator can always be particularized in an ade­quate way. The sequence 'for the sake of which' points to a causal simation, that is, implication =^, and by the 'Dasein is' the existential (in our lan­guage, informational) namre of Dasein is stressed, which,canbe symbolized explicitly by (® [=; ^ S)). The formula for this sentence becojnes 
(2.3) (%|=Tthere)=»(®NI=S ) 
This completes the symbolic interpretation of the sentence. D 
[2.4] In the "for-the-sake-of-which", existing Being-in-the-world is disclosed as such, and this disclosedness, we have called "understanding". 
This sentence represents a definition of un­derstanding which is the disclosedness conceming formula (2.3) as well as formula (2.2). These formulas build up the informational cycle of Da­sein in which the there, world, Being-there, and Being-in are constitutive components. The dis­closedness of understanding is a kind of informing of Being-in-the-world vvithin this cycle. Let us mark the "for-the-sake-of-which" by <Psake- Thus, the last sentence induces the formal system as a consequence of the previous,two sentences, that is, 
(2.4)	 ((93in-the-world Ndiscl ^ ) ^ ^sakeJ *Psake ^ ^ ((((®^;[=:®)l=:Tthere(®))< ^ 
(5BworldN'^there)); . (®there(®^world) N ®in)' 
((«inNTthere)^(S)|=;NS))) ) 

To say that something is disclosed means that something informs (the disclosedness) (operator Ndiscl)-^ further interweavement of formulas simulating particular sentences will be discussed in a later section. D 
[2.5] In the understanding of the "for-the-sake-of­which", the significance which is grounded therein, is disclosed along with it. 
This operand marks a joined system of for­mulas (2.2) and (2.3). Understanding U under­stands ^sakc that is, as U(<Psake)- Within this understanding, understanding U is informed by the "for-the-sake-of-which" ^i^ake, that is, (psak& N ^^ The significance of understanding is marked by a generalized operand ^sign- Under these circum­stances, there is, 
(2.5)	 (^sign C U((psake)) Ndiscl 
This formula includes formulas (2.2) and (2.3) through the operand, marked by ^sa^g-^ 
[2.6] The disclosedness of understanding [U Ndiscl]' ^ [^asl the disclosedness of the "for-the­sake-of-which" [U(<Psake) Ndiscll ^ ^ of signifi­cance [^signl equiprimordially, pertains [-^equi_p] to the entirety of Being-in-the-world [83in-the­
worldl' 
In the last sentence we introduced the brack­eted expressions right within the text of the sen­tence to achieve a direct correspondence betvveen the word notions and symbols. Thus, we put im­mediately, 
(2.6)	 ((U|=disci)l=as 
(^(9sake NdiscI^ ^sign Ndiscl)) ~^eqiii_p ^8in-the-world '-^ 
[2.7] Significance [^sigJ is that on the basis of 
which the world [^B^orid is disclosed as such. This sentence yields 
(2.7)	 3Bworld(^sign) Ndiscl ®world ^ 
[2.8] To say that the "for-the-sake-of-which" [^sakJ < ^ significance [^signl ^ ^ both disclosed in Dasein [cpsake. ^sign Qsc l ^1 . tneans [<=»] that 
Dasein [©] is that entity [S) \=; \= ®] vvhich, as Being-in-the-world [93in-the-world] > is an issue for itself[©|=S)]. 
One can put 
(2.8)	 (<Psake' ^sign Qiscl 2)) <=> ((S)Ks«in-the-world)l=®) 
This formula can be additionally interpreted by the corresponding German sentence: Worumwillen und Bedeutdsamkeit sind im Dasein erschlossen, besagt: Dasein is Seiendes [S [=; |= S] , dem es als In-der-Welt-sein um es selbst geht. D 

2.3. THE THIRD PARA GRAPH OF § 31 fBTJ 
[3.1] When we are talking ontically we sometimes use [[=ont,some] the expression 'understanding something' [ll(a)] vvith the significance [meaning Usigi,] of 'being able to manage something' [Nable_itian «1. 'being a match for it' [|=niatch «1« 'being competent to do something' [|=comp °^]­
Formula for this sentence is 
(3,1) t=ont,some("-v^) F (^^sign(^=able_nlan °^)' l^signCNmatch a) , ^AgignCNcomp «))) 
This formula is open as the 'we' or an informa­tional entity (operand) is not considered explicitly on the left side of operator |=ont,some-^ 
[3.2] In [C] understanding [U], as an existentiale [Sexist]' that vvhich we have such competence over [something, that is, |=comp ^ o*"' ^ the form of a process, ®knownl is not [[7^] a ''what'' [3Bwhat]' but [symbol';' or, more definite, operator f=but] Being 
[93] as existing [that is, 031=; ^ 95 or, explicitly. 
®, 
exist ] . 
Evidently, the last part of the sentence is an informational inclusion in regard to the first part. So, 
(3.2)	 (2Bwhat Mcomp «; » Nas (® ^\ N «)) <= (*1 Pas ^exist) 
Another interpretation of this sentence could be, for instance, 
(3.2') (((Sexist N ®known) C U) ^ 3Bwhat) Nbut (® Nas ®exist) 
O Nprim 5Bpossible) ^ 

To these formulas a different formula can be con­
structed from the sentence in German: Das im Verstehen als Existenzial. Gekonnte [®known] ist kein Was, sondem [[=but] das Sein als Existieren. For this sentence the following formula could be, in principle, adequate: 
(3.2")	 ((s 
exist 

Nbut(®Nas(«N;N«) ) The most straightforward formalizing approach of the German sentence would be 
(3.2^) 	(®known F ; as Sexist )CU ; ®known N^ ®what; ®known \= (® Nas exist) 

These examples show-the difficulties which may occur at the translation of sentences from one language into another or, speaking information-ally, differences which may originate at or depend on the plače of observation. D 
[3.3] The kind [R] of Being [93] which Dasein [S)] has [C], as potentiality-for-Being [\=^ ^for-Being]­lies existentially in [Cexist] understanding [U]. 
Formula of this sentence is 
(3.3)	 i(Rm C ®) ^a s ^for-Being) Cexist ^ 
The German sentence is: Im Verstehen liegt ex­istenzial die Seinsart des Daseins als Sein-konnen. This sentence delivers, for instance, the formula 
(3.3' )	 (f?Bemg(®) Nas ^for-Being) Qxist ^ 
where 'die Seinsart des Daseins' is marked by %emg(®)- As we see, the English translation 'the kind of being which Dasein has' gives a different symbolic expression. D 
[3.4] Dasein [S)] is not something present-at-hand [N o^present-at-handl which possesses its competence [Qomp] for something [a] by way of an extra [Nextra]; it [®] is primarily [Npriml Being-possible '-•^possibleJ-
This sentence is a system of two formulas: 
(3.4)	 (a extra''-comp ON "-"^present- at-hand)) N 
[3.5] Dasein [S)] is in every čase what it can be [S) j=; 1=: S)], and in the way in which it is [\=] its possibility [TT]. 
When we say that something is in every čase what it can be, we use a kind of determination, for instance, the defining equivalence [<=^Df] or sim­ply the sign of informing [1=]. So, let it be 
(3.5)	 (S) ^= (S) ^ ; 1= S))) ^ 7t(S)) 
or 
(3.5')	 (S) <^Df (S) N ; N S))) N ^(®) o 
[3.6] The Being-possible [58possible] which is essen­tial for [Nessenjorl Dasein [S)], pertains [Npertains] to the ways of its solicimde [TTsoiicitudeC®)] ^^^ Others [o] and of its [S] concem [Nconceml with the 'world' [3Bworid]' as we have characterized [Hchar] them; and in ali these, and always [^always]' i^ pertains tO Dasein's potentiality-for-Being [7rfor-Being(®)] towards itself, for the sake of itself. 
Let us write down the formal approximation of the last sentence as the following: 
(3.6)	 ((® Npertain ^for-Being) Npertain ^l) (v^^^ssible Nessen_for ^) Npertain 
(((^solicitude(®) Nfor")'' (7r(S)) Nconcem 2Bworld)) Hchar)) 
The corresponding German sentence can deliver another illumination of the sentence understand­ing. It is: Das wesenhafte Moglich-sein des Da­seins betrifft die charakterisierten Weisen des Besorgens der »Welt«, der Fiirsorge fur die an­deren und im aH dem und immer schon das Seinkonnen zu ihm selbst, umwillen seiner. Here, the explaining from the end of the sentence con­firms to major extent the sense of formula (3.6). 
The problem of translation from one to an­other language (English, German, informational) becomes also evident on the formal (or informa­tional) le vel. D 
[3.7] The Being-possible [^Bp^jsiblel which Dasein [L)] is existentially in every čase [Nexist]' is to be  sharply distinguished [9^sharply] ^oth from empty 

logical possibility [Trjog t=enipty] ^ d from the con­tingency [Tcontl of something present-at-hand [apresent-at-hand]' so far as [<^so-far-as] with the present-at-hand this or that can 'come to pass' [a 
P '^present-at-handJ • Accordingly to this sentence one can piit 
(3.7)	 (((S) C 58possible) l=exist) ^sharply CC^log Fempty)' Tcontv^^present-at-hand))) ^so-far-as (<^ F '^present-at-hand) 
This formula is an informational implication of the type 'so-far-as'. Considering the original German sentence which in its first part says Das Moglich­sein, das je das Dasein existenzial ist, ..., could deliver (OBpossibie Nexist ®) instead of ((S) C Spos^j. ble) Kxist) ifl formula (3.7). D 
[3.8] As [=\2^] a modal category [Tmodail of P^es­ence-at-hand [Ttjt.ij^d]' possibility [TT] signifies [Nsignl what [a] is not yet acmal [fT^acil ^' ^ ^^^^ is not at any tirne necessary [ ^ Vat_any_time]­
The informational formula for this sentence can be the following: 
(3 • 8) (TmodalC^t^at-hand)) Has (^Nsign ((»N^act)' (« M Vat_any_time))) ^ 
[3.9] It [TT] characterizes [|=char] the merely possi­
ble [OJuierely_possJ* In short, there is, 
(3.9)	 ^ Fchar <^merely_poss'—' 
[3.10] Ontologically [^=ont] it [^1 is on a lower level [Xiower] than [t=than] acmality [agctl and ne­cessity [v]. 
A direct translation of this sentence into in­formational language is 
(3.10)	 (TT t=ont ^lower) Nthan («act' ^) ^ 
[3.11] On the other hand [||=], possibility [K] as an existentiale [Sg^istl is the most primordial and ulti­mate positive way [Uway] in which Dasein [©] is characterized [|=char] ontologically [fronti-
For this sentence one can set 
(3.11)	 (7t|=asS)|^ U 
way' ((Nchar ®) '^ ^way) Nont ^ 
[3.12] As with existentiality in general [®exist N ' N ®exist]' w^ can, in the first instance, only prepare for the problem of possibility [T:]. 
The simplest way to interpret this sentence is formula 
(3.12)	 7t|=as(®existN;N®exist) 
In German, this sentence is: ... zunachst kanu sie [TT] wie Existenzialitat uberhaupt lediglich als Problem vorbereitet werden. The existentiality as a problem of possibility can be understood within the informing of the system <Sexist N ' N ®exist-^ 
[3.13] The phenomenal basiš [(Pbasisl for seeing it [7t] at ali is provided [f^provl hy the understanding 
[U] as a disclosive potentiality-for-Being [Trfor-BeingJ • 
The adequate, universalized formula to this sentence is, for instance, 
(3.13)	 (U |=as ^for-Being) Nprov ((9basis 1= ^ ) N %asis) 
The phrase 'for seeing it at ali' remains hidden in the process ((pbasis N ^) N 9basis-^ 

2.4.	 THE FOURTH PARAGRAPH OF . ^31[BT] 
[4.1] Possibility [u], as an existentiale [Sexist]. does not signiiy [^T^signl ^ free-floating potential-ity-for- Being [TTfor-Being N^ N ^Tfor-Bcingl in the sense [agense] of the 'liberty of indifference' [^^liberCi-indiff] Qibertas indijferentiae). 
The formula is 
(4.1)	 (TT |=as Sexist) l^sign 
((^for-Being N ' N ^for-Being) N c^senseC^liberC^-indiff))) ^ 
[4.2] In every čase Dasein [L)], as essentially hav­ing [Cgssen] a state-of-mind [Smjnd]> has already got [[=already] itself into definite possibilities 
[Ttdef]­The rough formula for this sentence is 
(4.2)	 (Smind Qssen 2») Nalready (® ^ ^def) where we did not consider the entity ' in every čase' which could be expressed, for instance, by opera­tor V at the end of formula (4.2). It is to mention that the German sentence: Das Dasein ist als wesenhaft befindliches ... gives also a 'direct' formula S) has_essen ©mind-• 

[4.3] As the potentiality-for-Being [Ttfor-Beingl which is is [Trfor-Being \=' N ^for-Beingl. it [S)] has let such possibilities [7t(7Tfor-Being)] pass by [l=pass_by]; it is constantly waiving [|=waive] the possibilities of its Being [7r(93(Li))], or else [in parallel] it seizes [t^seizel upon them [7r(S3(S)))] and makes [\=] mistakes [limistakel-
For this sentence we get a system of formu­las, that is, 
(4.3)	 (S) |=as (^for-Being N i N ^for-Being)) 
Fpass_by ^'^for- Being)! ® Nwaive ^(«(®)) ; (®Nseize^(«0)))N(^mistake n 

[4.4] But this [formula (4.3) marked by q)(4.3)] means [<=>] that Dasein is Being-possible [S) \= ®possibie] wliich has been delivered [j^deliver] o^^i" to itself ['^]—thrown possibility [Ttthrovvn] through and through [^=through]­
Thus, the resulting formula is 

(4.4)	 9(4.3) < ^ ((( O 1= 95possible) Ndeliver S)) F ^thrown)) Fthrough 
This formula is nothing else than an explanation of formula (4.3), marked by 9(4.3). The original Ger­man sentence, forcomparison, is: Das besagt aber: das Dasein ist ihm selbst uberantwortete s Moglichsein , durch und durch geworfene Moglichkeit. D 
The formula for diis sentence is 
(4.6)	 (?8possible(S)) Ntrans S ) N «poss _ways '—' 

2.5. THE FIFTH PARA GRAPH OF § 31 fBTJ 
[5.1] Understanding [U] is the Being [93] of such potentiality-for-Being [Ttfor-Being]' which is never [^] something stili outstanding [otstilLoutl ^^ not yet [Nas_not^et] present-at-hand [7Tat_hand]' but which. [in parallel] as something [a] which is es­sentially never [[T^essenl present-at-hand, 'is' with [j=^i,j,] the Being of Dasein [93(2))], in the sense of 
existence [aexist]­The frame system of foi^mulas for this sen­tence is 
(5.1)	 Ol\=m-Kfor.Bdng))^ (o^still-out Fas_not_yet '^aLhand)' ((^(•n^for-Being) Nas °^) Messen ^at_haiid) 
tzz^ith(«(S))Caexist) n 
[5.2] Dasein is such that in every čase [V] it has understood [\=]x] (oraltematively, [in parallel] not understood [^u]) that it is to be thus or thus [S |=; 
NS)]­
Let the first approximation of this sentence be 
(5.2)	 O V O \=^; S \^y)) ]= O \=; \= S) 
Several objections can be made to the last formula. First operator V could be particularized into (=ai. ways or even into |=such_t_e_c ^ith the meaning 'is_such_that_in_every_case'. Furtherv'?o be thus or thus pertaining to Dasein S) and understanding U could be formally interpreted as 

[4.5] Dasein [S)] is the possibility [TT] of Being-free [Sfi-eJ/or its ownmost potentiality-for-Being [7:^^. Bemg(®)]­
The formula for the last sentence is 
(4.5)	 (S) \= 7r(58free)) Nfor ^tfor-BcingCS)) • 

[4.6] Its [L)] Being-possible [53possibie(®)] is trans­parent [[^transi tO itself [S] in different possible ways and degrees [aposs_ways]­
(5.2') (S)VO^u;S)[7^u))l = (((i)^U)^S) ; 
(S)H(U=|®)); 
(S)7^(U7^S)))) 
Certainly, other interpretations of the sentence are possible. D 
[5.3] As such understanding [U] it [L)] 'knows' [[=1^^^^] what it [L)] is capable [f=cap]~that is. 
what its potentiality-for-Being [Ttfor.Being(2))] is capable of. One of possible formal interpretations of this sentence is the following: 
(5.3)	 (®NasU)Nknow((S)Kap). ^for-Being(S)) Ncap) 
As we see, the 'what' [aB^haJ ^^ ^^ capabihty of informing of S) is ignored, however, it can be exphcitly considered within the structure of the previous formula, closing it to some extent in the following way: 
(5.3') (S)NasU)Nknow((S)Ncap®what)< ^for-Being(2)) Ncap ®what) ^ 
[5.4] This 'knowing' [^iaiow(S)) = <P(5.3)] does not first arise [^firstl from an immanent self-percep­tion [^irninC®)]. but [in parallel] belongs [C] to the Being of the "there" [^(r^i^^j^], which is essenti­ally [Nessential] understanding [U]. 
This sentence sounds understandingly and can be immediately formalized as 
(5.4)	 fiknow(3)) Mfirst ^imm(®); ^know(2>) C (93(Tthere) Nessential ^ ) 
Operand i?know(®) is a occurrence of formula 9(5 3) in which S) as understanding informs capa­bly'. D 
[5.5] And only because Dasein, m understanding [(S) ^ U) 1= ©], is its "there" [TthereC®)]' can it go astray [^=astray] and fail to recogniz e l-FfaiLto.recognizeJ itseli. 
The symbolic interpretation of this sentence is 
(5.5)	 (((S) 1= U) 1= 3 ) f= TthereCS))) => Nastray» ® Nfail_to_recognize 
®)n 

[5.6] And in so far as understanding is accompa-nieJ/ry [|=accomp_by] state-of-mind [Smindl and as such is existentially surrendered [t=exist_surr] ^o throwness [Ttiirown]» Dasein has in every čase al­ready [Vaiready] gone astray [t=astray] and failed to recognize [|=fail_to_recognize] itself. 
One of the adequate formulas to this sentence could be 
(5.6)	 ((U pacconip_by '^niind) Pexist_surr '^thrown) ^ 
(S) ^already .to_recognize ©)) • 
[5.7] In its [S)] potentiality-for-Being [Kfor.Beingl 't is therefore delivered [}=deliver] o^^^ to the possi­bility of first finding [f=first_find] itself again in its possibilities [7t(S))]. 
Thus, the last sentence of the 5' paragraph becomes formal ly 
(5.7)	 (S) C TTfor-BeingC®)) Ndeliver (^(®Nfirst_fmdS))C7rO)) 
Thus, we ha ve, in a framing manner, formalized the sentences of the fifth paragraph. D 

2.6. THE SDCTHPARAGRAPH OF § 31 [BT] 
[6.1] Understanding [U] is [|=] the existential Being [53exist] of Dasein 's own potentiality-for-Being [(S) (= 7tfor-Bemg(®)) N ®]." and it [U] is so in such a way that this Being disdoses [^discJ '" itself [53exist] ^^t [SC^haJ '^-^ Being is capable of [pcapJ-
This sentence leaves open various possibili­ties. One of them, as an initial situation, is, for instance, 
(6.1) 	((li h «exist((^ N ^for-BeingC®)) N ®)) Pdiscl ™exist) Pca p •^what(^exist/ 
It is not for the first time that vve use the operand form ^(rj) instead of the explicit operator form ^ ^of ^n- This convention comes probably from the mathematical way of thinking. Hovvever, vve nqust be aware that in ^(T]), entity TI can take the form of an informational formula, arbitrarily complex, open, circular, etc. And this happens in čase of 
®exist((® N 7rfor-Being(2))) N ©)), where 53exist is in positionof ^ , etc. D • 
[6.2] [We must grasp die structure of this ex­istentiale more precisely.] 
This sentence is a comment on that what has to follow in the next paragraphs. D 

2.7. THE SEVENTH PARAGRAPH OF § 31 [BTJ 
Po f ^interconnv''^to-hand) '—' 
[7.1] As [[=as] a disclosure [©disci]. understanding 
[U] always pertains to [^penukJ ^he whole basic State [2Bbasic_state] »f Being-in-the-world [93in-the­worldJ • 
A formula for this sentence is 
(7.1)	 (Uhas^discl ) ^pertain ®basic_state(®in-the worl(l) '—' 
[7.2] As [|=as] a potentiality-for-Being [iifor. Being]. any Being-in [OSiJ is a potentiality-for­Being-in-the-world [7rfor(Q3in.the-world)] • 
(7.2)	 (93in ^=as ^for(^in-the-world) 1^ 
[7.3] Not only is the world [3Bworld]' ^"^ world, disclosed [^disci] as possible significance [^sign_poss]. but [^bu, or in parallel] when that [a] which is within-the-world [a C ?Bworld3 is [=>] itself freed [a. |=free °f]' this entity is freed for its own possibilities [7r(a)]. 
In this sentence two implicative operators appear, where the first one has the meaning of 'when ..., then ...' and the second one of 'if ..., then...' . So, 
(/.3 ) ((-i"world Pa s -"*world) F^discl Ssign_poss/ Nbut (((a C SB^orld) =^ (a Nfree « » => (7t(a) |=free «)) D 
[7.4] That [a] which is ready-to-hand [9?to-hand] is discovered as [|=discover_as] such in its strviceabil­ity [SlservicJ' its usability [^usJ« ^^^ its detrimenta//0' [Sidetriment]­
The appropriate formula is, for instance, 
(7.4)	 (a |=as 2tservice(a); « Nas ^luseC«); 
•^ Nas -^detrimentW) Ndiscover_as (a \= SRto-hand) 1^ 
[7.5] The totality of involvements [ttotalCi-involve)] is revealed as [Nreveal_as] the categorial whole [^categorial] ^f a possible interconnection [^interconn] of the ready-to-hand [5Rto-hand] • 
The corresponding formula is, for example, 
(/.5)	 (5Scategorial Nreveal_as ''^total(''mvolve)) [7.6] But even the 'unity' [u^nitv] of the manifold [l^manifold] present-at-hand [TTat-handJ. of Nature [9]], can be discovered [Ndiscover] ^^^V ^f&possi­bility of it [7r(u^iiijty)] has been disclosed [NdiscJ-
An open formula for this sentence is 
(7.6)	 (Ndiscl ^(^inity))) => 
(Nd iscover	 (^unity(t^inanifold('^at-hand))' U^inity(^))) • 
[7.7] Is it [Nquest] accidental [Naccid] that the question [dg^estion] about [Nabout] the Being of Nature [58(5n)] aims at [Naim_at] tbe 'conditions of itspossibility' [Tcond(^(53(9^)))]? 
This question informs accidentally, that is, 
(7.7)	 ((^question Nabout (®(^) t=aim_at Tcond(^(«(3^))))) Naccid) Nquest • 
[7.8] On what [SB^hatl is such an inquiry [9(7.7)] 
based [Nquest]? The formal information of this sentence is 
(7.8)	 9(7.7) Nquest ^ha t D 
[7.9] When confronted [f=confront] ^it^i this in­quiry [9(7.7)], we can not leave aside the question: why are [|=why] entities'[a] vvhich are not of the character of Dasein [TcharC^*)] understood [[=^3 iu their Being [53(a)], if [<=] they are disclosed [Ndiscl] ^ accordance with the conditions [Tcond] of their possibility [7t(a)]? 
The formula for this sentence can become rather complicated, however, one of its formal approximations could be 
(7.9)	 (Nconfront (9(7.7) Nquest °^)) = ^ 
((((a Nrchar(®))N u	 «(«))< = (Tcond(^(a)) Ndiscl «)) Nwhy) ^ 
[7.10] [Kant presupposes something of the sort, perhaps rightly.] 
This sentence is taken as an insignificant comment. D 
[7.11] [But this presupposition itself is something that cannot be left without demonstrating how it is justified.] 
In the next paragraphs this presupposition will be demonstrated. D 

2.8. THE EIGHTH PARAGRAPH OF § 31 fBTJ 
[8.1] Why [IBwhy] does [[=questl the understanding [U]—whatever may be the essential dimension [Sdim] of that which can be disclosed in [|=discl] it—always press fonvard [|=al_press_for] "^to possi­bilities [TT]? 
This sentence can be interpreted by the fol­lowing system of formulas: 
(8.1)	 (((SdimCa Cdisci U) |=alLpress_for ^) N U) l^quest ((a N Sdim) N a) N Sdim(a); (U Oiiscl Sdim(a)) Cldiscl ^ 
This formal system may appear to be stronger than the original sentence, but, it expresses the regular circular power of entities in question. The reader can try to think through this particular situation by himself. D 
[8.2] It is because [=^ (p(8 j)] the understanding has in itself the existential structure [crexist ^ U] we call "projection" [Ttproject]­
A simple formula, modeling this sentence, is, for instance, 
(8.2)	 ((CTexist C U) ^ TTproject) =» 9(8.1) • 
[8.3] With equal primordiality [|=^itij_gq_p] the tmderstanding projects Dasein's Being both upon [[=pj.pj_ypQjj] its "for-the-sake-of-which" [9sake(^)] ^ d upon significance [^signl. as the worldhood [5Bworldhoodl of its current world 
L^ciir_worldJ • One of formal possibilities for these sentence is, for instance, 
(8.3)	 (Uh=with_eq_p®(S)))Nproj. .upon 
(*PsakeC*l) > Ssign Pa s ^orldhood(®cur_world(^)) ^ 
[8.4] The character of understanding [TcharC^)! ^ projection [Trpi-ojectl is constitutive [[^constl ^or Being-in-the-world [^Bjn.the.^orid] with regard to [Nwith_regard] the disclosedness [Sdiscll of its ex­istentially constitutive [t=exist constl state-of-Being 
[Sof-Being] by which the factical potentiality-for-Being [<Pfact(^for-Being)] gets [^get] its leeway [^leeway(TcharW)] [Spielraum]. 
For this sentence, one of possible formaliza­tions is 
(8.4) 	((Tchar(ti) Pa s '"^project) Pconst 
^in_the-world) Pwith_regard ^discKC^of-BeingdcharCU))) Nexist_const)' (TcharC^) t=by 9fact(^for-Being)) Nget '^leeway (Tchar(tl)) 
This formula system can be substantially modified by reading of the rwo equivalent German senien­ces, which are: Der Entwurfcharakter des Ver­stehen s konstituier t das In-der-Welt-sei n hinsichtlich der Erschlossenheit seines Da als Da eines Seinkonnens. Der Entvvurf ist die ex­istenziale Seinsverfassung des Spielraums des faktischen Seinkonnens. The modified system for these German sentences is 
(8.4')	 (Tchar(^project(^)) Nconst ®iD-the-world) 
Pwith_regard 
(^discl('"^there(Tchar(''^project(^)))) Pas 
'^thereV^for-Being))» 
''^project Pexist 
®of-Being(^leeway(<Pfact(^for-Being))) D 
[8.5] And as throvvn [Tthrown]' Dasein is tlirown [|=jj^^Q^^^] into the kind of Being [l?(Q3)] which we call "projecting" [gJprojectl-
The formula is 
(8.5)	 (S) Pa s "^throvm) Pthrown 
[8.6] Projecting [^rojectl ^as nothing to do with [^] comporting [Ecomportl oneself [oioneselfl to­wards a plan [TTpian] that has been thought out [Nthink_out]. and in accordance with [Haccordl which Dasein arranges [[=317] its Being. 
The approximate formula for this sentence can be put as 
(8.6)	 ^roject P (®comport(^oneself) Ptovvards 
((pthink_out ^plan) Haccord(®Narr«(S)))))n 

[8.7] On the contrary [t=contra]' ^ y Dasein has, as Dasein, already projected itself; and as long [NasJong_as] as it is, it is projecting [^rojectl-
The formula system for this sentence is char­acteristically circular, that is, 
(8.7)	 S ^contra ((® Nas ^) Nproject 2»; ( O \=; ^ S)) has_long_as ®) N %roject • 
[8.8] As long as [NasJong_as] it is, Dasein always has understood [Nal_underst] itself and always will understand itself in terms of possibilities. 
Cyclicity of Dasein and its possibilities is characteristic for this sentence which can be for­mally interpreted as 
(8.8)	 (((S) N ; N S)) KsJong_a s S)) N al_underst 
S))|=as7r(S))n 

[8.9] Furthermore, the character of understanding [TcharC^)] as projection [Ttprojectl is such [a] that the understanding does not grasp thematically [Ngrasp.themJ that upon which [a] it projects—that is to say, possibilities [TT]. 
There is, 

(8.9)	 (Tchar(U) \= Kproject) N 0C\ tt Ngrasp_theina ((^(o^) Nproject oc), iz) LJ 
[8.10] Grasping it [®grasp(ll)] ^ such [(p(8.9)] a manner [|=in_nianner] would take away from [ptake_away-l 
what is projected [^roJectC«)] its very character as a possibility ['n('Xchai(^))], and would reduce [[=reduce] it to [\=io\ the given eon-tents which we have in mind [TcontentC^^mind)]; whereas projection [Ttprojectl. ^ throvving [SthroNvl. throws before [Nthrow_before] itself the possibility [TT] as possibility, and lets it be as such. 
This sentence delivers a complex formal in­terpretation, for instance, 
(8.10)	 (®grasp(11) Nm.maimer 9(8.9)) Ntake_away (01 \= ^roject(a) ) Nas ^(Tchar(ll))) i ®grasp(tt) Nreduce ( ^ Nto Tcontent(t^mind))' ((''^project ^ *throw) Nthrow_before 
^project) N 











((7tNas^)N;N(^Nas^))n 
[8.11] As projecting [^rojectl' understanding is the kind of Being of Dasein [5?(S(L)))] in which it is its possibilities [7rCU)],as possibilities. 
Thus, for the last sentence of this paragraph, there is, formally, 
(8.11)	 (u ^ (71(11) Ks^(U)))c : 
((UNasVoject)N^(®(®))) ° 

2.9. THE NINTH PARAGRAPH OF § 31 [BTJ 
[9.1] Because [=>] of the kind of Being [^(93)] which is constituted [Nconstl ^V the existentiale of projection [Lexist(^project)]' Dasein is constantly 'more ' [S) Nconstantly |Jmore(®)] than [Nthanl it factually [Nfactiially] is> supposing [=»] that one [OoneJ might want to make [Nmakel an inventory of it [!.inventory(®)] as [|=as] something-at-hand [»at-haiidi and list [Nlistl the contents of its Being [Tcontent(®(®))]' and supposing that one were able [Nablel to do so. 
The approximate formalization of this sen­tence might be a single implicative formula 
(9.1)	 (OoneNable 
(v^one Nmake (''inventory(^) Nas '^at.hand))' (Oone Nlist Tcontent(®(2)))))) ^ 
((Sexist(^project) Nconst ^(^3)) =^ (ON constantly t^more(®)) Nthan ( ^ Nfactually' Nfactually ®))) ^ 
[9.2] But [4=] Dasein is never more than [Nmore.thanl it factically is [Nfactically]. for tO itS facticity [9fact(^)] its potentiality-for-Being [Tr^f. Being(®)] belongs essentially [Gessenl-
One of the implicative formulas for this sen­tence is 
(9.2)	 O Nmore_than (® Nfactically)) <= (^for-Bemg(2)) ^essen <Pfact(®)) ^ 
[9.3] Vet [|=yet] as Being-possible [Spossiblel > moreover, Dasein is never anything [a] less [Nlessl; that is to say [in parallel], it is existentially [Nexist] that which in its potentiality-for-Beiiig [^for-Being(®)]. it is notyet [^^^i]. 
A formal depiction of this sentence could be, for instance. 

(9.3)	 ( O ^a s ^ossible) Mless «) Nyet S); 
(S) |=exist a) Nin (S) Nyet ^for-Being(S))) 
We can certainly bring up some slightly modified formulas for this sentence through the displace­ment of several operators. D 
[9.4] Only because [Nonly_because] 1^6 Being of the "there" [93(Ttiiej.e)] receives its Constimtion [f constl throug h [[=through] understanding and through the character of understanding [Ychar(^)] as projection [TTproject]' o^V because it is what it becomes (or, altematively, does not become), can it say to itself 'Become what you are', and say this with [t=say_witli] understanding. 
This sentence is rather complicated as it can be seen from the following formal example of it: 
(9.4)	 ((93(Tthere) Nsay »(^there)) Psay_with because 
((58(Tthere) |—receive Tconst(®(i^there))) 
Nthrough \\"-'' TcharW Pas ^project)' 
(®(T^there) N ' \= ®('Cthere)' 
?^«(Tthere);«(^there)?N))) 
The construction of this formula begins from the last part of the sentence, for sentence as a whole expresses an implicative intention [operator Nonly.because]- Several explanations to formula 
(9.4) can be given which can substantially impact the understanding of the original sentence in a circular spontaneous manner and, simultaneously, stressing the way of Being of understanding in question together with the possibilities of its infor­mational formal expression. For instance, the syn­tagma it is what it becomes (or altematively does not become) conceming the Being of the "there", in the last formula is expressed in a completely and not only metaphysically open form, that is 
^("^there) N^ t= ^C^there)­A ^(''^there)' ^C^^there) A 
where even the alternative general operator of non-informing :^ instead of [7^ is used. The reader may imagine some further implications in possibil­ities of using such spontaneous circular mecha­nisms in an informational machine. D 

2.10. THE TENTH PARAGRAPH OF § 31 [BT] 
[10.1] Projection [iTproject] always pertains to [l=aiways°Npertain] the full disclosednes s [<Pfuii(9disclose)] of Being-in-the-world [Sin-the­world]; as potentiality-for-Being [TTfor-Being]' un­derstanding has itself possibilities which are sketched out beforehand [Nsketch_out_beforehand] within the range [prangel o^ ^hat is essentially disclosable [|=essen°Ndiscl] i° it. 
This sentence can be reasonably decomposed in three consequent formulas: 
(10.1) ^project Falways°Ppertain <Pfull(^disclose(®m-the-world))» 7r(U) C (U t=as ^tfor-Belng)); 7^(^) Nsketch_out_beforehand (^(^) ^ 
((Prange Pessen°Pdiscl ^what) 
Pessen°Pdiscl Prange)) In this system we introduced two composed types of operators between operands, that is, operator 
composition t=always°t=pertain and t=essen°t=discl-This does not mean that in these compositions the left operator pertains merely to the left operand and the right operator merely to the right operand. Such explicit operator composition pertains always to both operands. Operators, possessing transitive function, can be understood as distributed opera­tional units, intenvoven with operands. D 
[10.2] Understanding can devote itself primarily [Ndevotel to [t=prim_to] the disclosedness of the world [Odisciose(2Bworld)]' that is, Dasein can, proximally [[=prox] ^tid for the most par t [Nmost_part]' understand [[=u] itself in terms of its world [OB^orldC®)]­
Using operator composition of the form ^pj.Qjjo|=njQ5t_part, the last sentence can be formal­ized in the following way: 
(10.2)	 (U |=devote ^ ) Nprim.to ^disclose(®world)' (S)K®)Nprox°N most_part 
As one can see, the function of operators |=devote and t=u becomes transitive in regard to operator Nprinuo and to operato r composition 
NproxoNmost_part. respectively. D [10.3] Or else [in parallel] understanding throws [Nthrovvl itself primarily into [[=prim_into] the "for­the-sake-of-which" [<Psake]' ^^^ is, Dasein exists as [Nexist_as] itself. 

With the transitive function of operator Ntlirow ia regard to operator hpnm. formalize this sentence as 
(10.3)	 (U hthrovv U) Nprim. into 9sake' S)Nexist_asS) n 
[10.4] Understanding is either [[^eitherl authentic [Uauthl. arising out of [|=arise_out] oiie's own Self [t^selKoone)] as such, or inauthentic [Uinauthl-
One of possible formulas for this sentence is 

(10.4)	 (U Neither (Uauth N arise_out 
(c^selKOone) Nas c^self))) Nor (U N llinauth) • 

[10.5] The 'in-' [li J of "inauthentic" [f-jnaiuhl does not mean [[T^meanl that Dasein cuts itself off [Ncut_off] from its Self [ageiK?))] and understands 'only' [[zzuo|=bnly] the world. 
There is, fornially, 

(10.5)	 (tjji po f Liuauth) Nmean 
Pcut_off '-inauth Nmean (^ Nu°Nbnly ®world) ^ 
[10.6] The world belongs to [L] Being-one's-Self 
[®one's-self] ^	 Being-in-the-world. A simple formalization of this sentence is 
(10.6)	 (9Q3world Nas ®in-the-world) ^ ®one's-Self ^ 

[10.7] On the other hand [in parallel], authentic understanding [Uauth]» ^^ less than that which is inauthentic [Uinauthl > ^^" t)e either genuine [one can choose Tgenulnd ^^ tiot genuine. 
A further way of formalization of authentic and inauthentic understanding is, according to the last sentence, 
(lU. / ) (Uauth» *linauth Neither Tgenuine) Nor v^auth' ^inauth N Tgenuine) '—' 
[10.8] As potentiality-for-Being [TTfor-Beingl un­derstanding is altogether permeated [^pemieatel with possibility. 
There is 
(10.8)	 7t [=permeate ( ^ Nas ^for-Being) ^ 
[10.9] When one [Oone] is diverted [|=diverti i^to [Sichverlegen in] one of these bašic possibilities [^basic_l] of understanding, the other [7rbasic_2] is not laid aside [Nlay_aside] [i^gt... nicht abj. 
We separately marked the one and the other basic possibility, thus. 
(10.9)	 (Ttbasic, 1 (U) Ndivert Pone). =^ (Nlay_aside ^basic_2(^)) 
This formula is a temporal implication which per­tains to the form when ... then ... of the last sentence. D 
[10.10] Because understanding, in every čase, per­tains rather to [Nalways°Npertain] Dasein's full disclosedness [<Pfuii(9disclose(2'))] as Being-in-the­world, this diversion [^diversionl ofthe understand­ing is an e.ristential [|=exist] niodiflcation of projection [UmodiKT^project)] ^ « ^^ole [aBwhole]­
One possible formal interpretation of this sentence is 
(10.10) ((U [=as S3in-the-world) Nalways"Npertain <Pfull(%sclose(S)))) = ^ 
(("diversion(^) Nas ^^hole ) Nexist t^modifV^project/) 
For the right side of this implication we could put also 
^diversionv^) r^exist (f^modifv^project) Nas ®whole) 
depending of our understanding of the sentence. D 
[10.11] In understanding the world [ll(2Bworid)]» Being-in is always understood [Nalways°Nu] along with it [83in(U(®Jworld))]' ^^ile [in parallel] understanding of existence [ll(Sex)] as such is al­ways an understanding of the world. 
Formalization of this sentence is, for in­stance, 
(10.11) U(2Bworld)Nalways°Nu	 93in(U(iIB^orld)); (U(Sex) Nas.U(Lex)) Nalways li(®world) 
The wliile in die last sentence is interpreted by the parallelism of formulas, however, it could also be expressed explicitly introducing a particular oper­ator. D 

2.11.	 THE ELEVENTH PARAGRAPH OF § 31 [BTJ 
[11.1] As factical Dasein [%act]' ^ V Dasein has already diverted [|=divert] i^s potentiality-for-Being into [^intol a possibility of understanding. 
A straightforward formula for this sentence is 
(11.1)	 (S)Nas%act)Ndivert (^for-Bemg(S>) Ninto ^(^) ) 
In this formula, the diverting (operator |=divert) means 'diverts'as 'has already diverted'. O 

2.12. THE TWELFTHPARAGRAPH OF § 31 [BT] 
[12.1] In [^jn] its projective character [TcharC^proj­ect(U))], understandin g goes to make up [Nmake_up] existentially [t=exist] what we call Dasein's "sight" [asight(S))] [Sicht^. 
We interpret this sentence by formula 
(12.1)	 Tchar(Voject(ll)) Nin (^ l=make_up°l=exist c^sightC®)) 
The 'in' at the beginning of the sentence has the meaning 'inform(s) in' (operator |=iij). D 
[12.2] With the disclosedness of the "there" [Sjis-closeCT^there)]. this sight [asigijt(S))] is existentially [Nexist] [existenzial seiende]; and Dasein is this sight equiprimordially in each of those basic ways [Nequi_p°Nalways] of its Being which we have already noted: as the circumspection [Tcircumsp] [Umsicht] of concem [Tconcem]' ^ the consider­ateness [Tconsiderl [Rucksicht] of solicitude [^solicitude]. and as that sight [asjght] which is directed upon Being as such [93 \=^ 93] [Sicht auf das Sein als solches], for the sake of which [t=sakel any Dasein is as it is [S ^ ; [= S)]. 
We can formally interpret this sentence by a system of two formulas: 
(12.2)	 asightO) Nwith (^disclosev"^there) Pexist)'' ((S) t= asjght(S))) f=equi_p ° Nalways «(®)) Nas 
vTcircunispvTconcern)' TconsiderC^soIicitude^ > <^sight((S Nas 93) Nsake (2) N; N S)))) 
In this čase, the meaning of operator Nexist ^s 'inform(s) existentially'. D 
[12.3] The sight [asight(S))] which is related pri­marily and on the whole to [Nrel_prim_whoIe] exist­ence [Sgj] we call "transparency" [Ttransparl [Durchsichtigkeit]. 
There is 
(12.3)	 (SexNreL .prim_whole "si ght(s») N 4ranspar 
In this formula, operator Nrel_prim_whole is a com­position of operators Nrelatc Npriimrily. and Non_tiie_whole' that is, for instance, 
(Nrelate°Npriinarily)°Non_the_whole '—' 
[12.4] We choose this term [Ttransparl to designate 'knowledge of the Self [i?know(c^self)] ^ a sense which is well understood [crsense(^well)]» ^o as to indicate [in parallel] that here it is not [^] a matter of percepmally tracking down and inspecting a point called the "Self" [^JperceptCc^self)]' ^ut [f=but] rather one of seizing [SseizeJ tipon the full dis­closedness of Being-in-the-world [9fuii(Sdis­close(®in-the-world))] throughout ali 
[f=throughout°Nall] the constitutive items [t,item(T const)] which are essential to it, and doing so with understanding, 
The formula system for this sentence could be 
(12.4)	 tfransparN (°knowC<^self) N ^sense(*^well//' ("^transpar N rperceptC^self) Nbut (®seize(9full(^disclose(®in-the-worId))) 
Nthroughout°Nall 
(''item(Tconst) Nessen (''^transpar' 

U))) This formula is an evident čase of formal abstrac­tion and modification (symbolic simplification) of the original sentence. However, it is stili open in many respects, so additional improvements and even universalization of it can be easily performed. The reader can expect some help in understanding the German sentence which is the following: Wir wahlen diesen Terminus zur Bezeichnung der wohlverstandenen »Selbsterkenntnis«, um an­zuzeigen, dal3 es sich bei ihr nicht um das Nvahmehmende Aufspiiren uhd Beschauen eines Selbstpunktes handelt, sondem ein verstehendes Ergreifen der vollen Erschlossenheit des In-der­Welt-sein s durch seine wesenhaften Ver­fassungsmomente hindurch. We agree that this sentence can deliver an informationally entirely different formalization to formula (12.4). D 

[12.5] Inexisting [®exist]. entities [a] sight [hsightl 'themselves' [sichtet "sich" only in so far as [l=so_far] ^e y have become transparent to them­selves [TtransparCa)] with equal [Nwith ° Nequal] primordiality [iTprini] in those items [t-JtenJ which are constimtive for their existence [®exist(<^)]- their Being-alongside the world [S8alongside(®worid)] and their Being-with Others [®with(w)]­
For the last sentence of this paragraph we have the following formalization: 
(12.5)	 (a |=sight ®exist(a)) Nsojar (a p (TtransparCo^) Fwith°Fequal 
•'^primCf^item F ®exist(°^)))» ®exist(°^) 1= %ongside(^orld' ®witli(w)) ^ 

2.13.	 THE THIRTEENTH PARA GRAPH OF %31[BT] 
[13.1] On the other hand [in parallelj, Dasein's opaqueness [Dopaque(®)] [Undurchsichtigkeitj is not rooted [^T^rootl primaril y and solely in [|=prim_sol] 'egocentric' [Sggo] self-deceptions [S Ndecept ®]' i^ is rooted [|=root] J^^t as much in [Njust_as_much] lack of acquaintance [aiacquaint] with the world. 
For the only sentence of this paragraph we 
have 
(13.1)	 Qopaque(25) b^root ° Nprim_sol Sego(® Ndecept ^) ; 
There are certainly other possibilities for the for­malization of Dasein's egocentric self-deceptions. 
D 

2.14.	 THE FOURTEENTH PARAGRAPH OF 
§ 31 [BTj 
[14.1] We [one] must, to be sure [[=sure]' guard against [hguard_against] a misunderstanding [Unus] of the expression 'sight' [Sexpress(^sight)]­
The formula we can propose is 
(14.1)	 (OoneNguard_ .against *^mis'^i (f^sisht))) 
misv"^expressv^sig ^ (Oone Fsure) ^ 
[14.2] It [Sexpress(«^sight)] COrresponds [Korresp] to die "clearedness" [Tciearl [Gelichtetheit] which we took as characterizing [j^charl the disclosedness of the "there" [^disclose(^there)]• 
There is, for mstance, 
(14.2)	 Lexpress(^sight) Fcorresp vTcleared Fchar ^discloseCt^there)) '—' 
[14.3] 'Seeing' [B^Q^ does not mean jus t [Mmeaii°Njust] perceiving [^rceivel with the bod­ily eyes [SeyesObody)]' but [in parallel] neither does it mean pure non-sensory [|=pure°N^sense] awareness of something [SlavvareC'^)! present-at­hand [ofpresent_at_hand] in its presence-at-hand [^aLhaiid(o^)]­
The less or more appropriate formula system for this sentence is 
(14.3)	 Sseeb^ niean°Fjust vHTjerceive Fwith 
^eyes(Pbody))' ^seeFmean (2J^aware(°^) Npure°N^ sense 
((a [= apresent_at_hand) ^ ^at- hand(°^))) D 
[14.4] In giving [o^^^ Ngiv&l an existential signifi­cation [CTsign_exist] to "sight" [asjght], we have merely drawn upon [|=draw_upon°Nmerely] the pe­culiar feature of seeing [fPfeatureC^pecuIiarCSsee))]' that it lets entities [en] which are accessible [t=access] to it be encountered unconcealedl y 

*-'opaque Froot ° Fjust_as_niiich [Nencounter^b^conceal] in themselves. ^lack(^acquaint Nwith ®world) Formulas corresponding to this sentence are 
(14.4)	 (OQXIQ Pgiv e '^exist(^sight)) 
Pclraw_upon ° Pmerely 9feature(^peculiar(^see)) > ^ Pencounter°Pconcea l y^ Paccess 'Pfeanire('^peculiar(®see))) '—' 
[14.5] Ofcourse, every 'sense' [agense! ^oes [[=do] this [9(14.4)1 within that domain of discovery which is genuinel y itS OWn [Odoniain(^discover(Cfsense))]­
A simple formal interpretation of tiiis sen­tence is 
(14.5)	 (CTsense Nd o 9(14.4) ^ '^domainv"disclose('^sense)) ^ 
[14.6] But from the beginning onwards the tradi­tion of philosophy [(SbeginC-^tradCVilo))] ^^^ t)een oriented primarily towards [^orient°(Nprini°Nto­wards)] 'seeing' as a way of access [0Bway(2J^access)] to entities and to Being. 
A formula for this sentence is 
(14.6)	 ^beginCT^tradC^lo)) 
Porient ° (pprim ° Ptowards) (®see Nas (2Bway(2Iaccess) Nto «. ®)) ^ 
[14.7] To keep the connection with [[=coimect] this tradition, we [Conel ^^V formalize [Nformalize] "sight" and "seeing" enough to obtain [[=enough­°Nobtam] therewithauniversal term [Ttenn_imi] ^^^ characterizing any access to entities or to Being, as access in general [©general]­
For the last sentence of this paragraph there is 
(14.7)	 Ttrad \= connect v°one Pformalize ('^sight' ^see Penough°Fobtain (Sterm. .uni Peha r 
(^access Fto (<^' ™ Fas (^access ^ ©general)))))) ^ 

2.15. THE FIFTEENTHPARAGRAPH OF § 31 [BTJ 
[15.1] By showing [f=show] how aH sight is grounded primarily in [Cgroimd^^^prini] under­standing (the circumspection of concem [fcir­cumsp(Tconcem)] is understanding as common sense [ T common(cfsense)] [Verstdndigkeit]), [^ ] wehave deprived [hdeprivel P^^^ intuition [VreCi-intuition)] [Anschauen] of its priority [^priorl' which corrcsponds noetically to [t=corresp­°Nnoe] the priority of the present-at-hand in tradi­tional ontology [-rtrad(Oontology)]­
The implicative formula for this sentence is 
(15.1)	 (Oo„eNshow 
(('^sight ^ground°^pri m ^) ' 
vTcircuinsp(Tconcem) F 
(t i Fa s Tconim^^^sense)))) ^ 
((^one Fdeprive (^pure(''intuition 

'^priorv^pureC ^ intuition)))) Pcorres p ° Fno e 
•"^prior(^at_hand ^ '^trad(Oontology)) '-' 
[15.2] Tnmition' and 'thinking' [S;think] are both derivatives of understanding [^derive.remote]' ^ ^ already rather remote ones. 
A simple formula is 
(15.2) ''intuition' ^think Nalready ^derive_reraote(tt) I—I 
[15.3] Even the phenomenological [tpphenomenal] 'intuitio n o f essences ' [l-intuitionCSessence)] ["Wesenschau"] is grounded in [Cg^undl existen­tial understanding [Uesist]­
An adequate formula for this sentence is 
(15.3)	 'Pphenonienal( ^ intuition(^essence)) ^ground "-esist '—' 
[15.4] We can decide about [f=decide] this kind of seeing [R(Q^^] only if we have obtained explicit conceptions of Being [Tconcept_ex(®)] ^ ^ of the structure of Being [astructure(^)]' such as only phenomena in the phenomenological sense can 
become [Xiogic((Pphenomenal)]­The implicative čase of formalization of this sentence is 
(15.4)	 (Tconcept_ex(®). f^structureC®) Nas 
^logicv^phenomenal)) ^ (Oone Ndecide ^(Ssee(®))) 
The last formula is a formal generalization which pertains to the entire realm of the Heidegger­ian Being. D 
(Will be continued)