Derivation: How language relates to logic
John Bjarne Grover
Derivation: How language relates to logic
The fundamental theorem of linguistics: Two different metaphysical items m1 and m2 that belong to two different metaphysical realities are recognized by the human spirit (of 'sinners') as one and the same, and then the 2 reduce to 1 piece of substance s1 to which a linguistic unit l1 is attached in semantic assignment on basis of the original difference between m1 and m2, thereby serving to retain the original difference and hence language serves to preserve knowledge of the original paradise.
The fundamental theorem of logic: Step I: Human logic presupposes equiprobability in distribution if a symbol is supposed to be susceptible to semantic assignment. Step II: Logic is recognized as isomorphic with or equivalent to language in determining the relation between equiprobability and free distribution.
This creates the chinese sign SI = RADICAL 28 = 厶.
The graphic aspects of this derivation should then - by the concordance table at the end of the article on Horace and the chinese radicals - be present in Horace Satire I.iv.34-50, the semantic aspects in Satire II.vii.62,7-68,1.
Satire II.vii.62,7-68,1 - the semantic aspects of the derivation:
Illa tamen se
non habitu mutatve loco, peccatve superne,
cum te formidet mulier neque credat amanti. 65
ibis sub furcam prudens, dominoque furenti
committes rem omnem et vitam et cum corpore famam.
Evasti, credo metues doctusque cavebis;
quaeres
Satire I.iv.34-50 - for the graphic aspects:
["foenum habet in cornu; longe fuge! dummodo risum]
excutiat sibi, non hic cuiquam parcet amico; 35
et quodcumque semel chartis illeverit, omnes
gestiet a furno redeuntes scire lacuque
et pueros et anus.” Agedum, pauca accipe contra.
primum ego me illorum, dederim quibus esse poetas,
excerpam numero: neque enim concludere versum 40
dixeris esse satis; neque, si qui scribat uti nos
sermoni propiora, putes hunc esse poetam.
ingenium cui sit, cui mens divinior atque os
magna sonaturum, des nominis huius honorem.
idcirco quidam Comoedia necne poema 45
esset quaesivere, quod acer spiritus ac vis
nec verbis nec rebus inest, nisi quod pede certo
differt sermoni, sermo merus. "at pater ardens
saevit, quod meretrice nepos insanus amica
filius uxorem grandi cum dote recuset, 50
This constitutes a proof of the relevance of this analysis of the relation between language and logic. It is noticed, once again, that some rather essential albeit human aspect of the semantics (in the second mirror half of the concordance) - here the practical-world affairs of selfishness and privacy contained in the normal meaning of this radical sign - seems to be jolted over onto the graphic part (in the first half). It can be noticed with interest.
For step II - "Logic is recognized as isomorphic with or equivalent to language in determining the relation between equiprobability and free distribution" - it can be noticed that what resides between 'equiprobability and free distribution' probably can be identified as the principle of formal grammars over infinite languages by Chomsky in the 1950's. It is likely that this is the contents of RADICAL 29 = 又. The assignment of fragments to this in Horace can be looked up in the concordance table at the end of the article on Horace and the chinese radicals - and the step of ordinality between radical 28 and 29 likewise.
The news tell that 'Trostianets has fallen'. Could be Horatius as well?
These relations are probably also the theoretic basis for Hermann Grassmann's 'Ausdehnungslehre' of 1844.
Added 8 march 2022:
Radicals 28-31
These form a unit with an internal logical structure like the four elements under #28 and hence account for 'recursion'.
#28 = 厶 leaves a gap open between equiprobability and free distribution - this is where the formal grammars of 29 can be found.
#29 = 又 = 'right hand' by Satire II.vii.57,3-62,7 tells of the essential elements of formal grammars (including the special role of right-hand contexts):
|
uri virgis / auctoratus ferroque necari eas an turpi clausus in arca quo te demisit peccati conscia herilis contractum genibus tangas caput? estne marito matronae peccantis in ambo justa potestas? In corruptorem vel justior? |
phrase segment righthand context pushdown memory model recursive reading head, cp. #28 stack order |
This produces a pushdown automaton - which can be turned into a phrase structure grammar by lifting the stack (or 'box') one level up - which here means to the 'boxes' of #30 (small box) and #31 (big box).
#30 = 口 = 'mouth' = the small box = means really opening, mouth, hole, port, speech, talk - the oral cavity - while it is
#31 = 囗 = 'enclosure' = the big box which means the enclosure proper.
There is a 'box' that behaves peculiarly in the poetic grammar study - the synchronic part. This box can add reason to the role of the Catalan number - it can be analyzed via TEQ 575 which ends as follows:
[...]
Her action?
Her action was like sweet little box.
My doors...
That gives the nature of my poetry
down Security Lane.
In 50-60 days...
Oui
Assuming that action = the event studies in the poetic grammar study:
| Die Verwandlung (Unter vier Wänden) | 1250 | honey | 574 | - As I walk to the right in Sofie's street, he follows after me in the car. He drives a little too close before he trespasses the street obstacle illegally, and drives into the street. |
| wie Wochen die lebn in dem Mangel. | 574 | box | 1250 | - A black plastic band is lying on the asphalt. |
| 20 Gedichte - in September und Oktober | 1519 | box | 305 | - Also, a man was doing something in Glükstad's gate (kneeling, sitting, or in some other strange position, I cannot recall), and I may have seen him before I transgressed the boundary, but it may also be that I did not really notice him before I had passed this line. |
| über die Macht, | 305 | nose | 1519 | - A car with TELENOR written on its side in the other end of the street. |
one finds that the BOX of #30 behaves in accordance with the Catalan constant:
|
1250 in 50 m y m y Mach |
box 574 60 day5-74 doys oui d t über die |
|
305 nose 1519 → |
9151 eson 503 0, 915 9 6 5 594... |
By Horace Sat.II.vii.53-54 (cp. also the three ear-bones):
|
proiectis insignibus anulo equestri Romanoque habitu |
G =, black plast / badge 0, Macht-nose 1519 ↔ 9151 |
This shows that #30 is about the natural language which the radical sign also means: This is detected in the form of the three aural bones (anulo equestri = stapes, stirrup) with basis in Horace and in the Catalan equivalence to the written forms. Hence this #30 can be called the 'linguistic unit' in the fourfold form of #28 - against the 'substance' of the same contained in the enclosure of #31.
This means that the four elements of the fundamental theorems of linguistics and logic can be recognized also in the four radicals 28-31 via Horace - 28-29 are the two metaphysicals while 31 is the substance and 30 the language.
Hence from #31 it seems that one can take it back to #28 again and the whole derivation can be done on this higher level of 28-31.
This accounts for what recursion is.
It provides also some support to the theory of the Catalan constant.
The ordinality seems to consist in the lifting one level up of one essential element: From 28 to 29 is lifted the structural form of the triangle which also is of 'head between knees' when reading nesting loops, and from 29 to 30 the idea of the little box wherein the righthand contexts of the pushdown in 29 can be stored. It is this lifting which turns the pushdown into a phrase structure grammar. The chinese sign for 'RIGHT-hand' also contains this little box of radical 30.
These were the semantics of the second (mirror) half of the listing at the end of this file. The graphic properties of #31 can be studied from the same fragment of Satire I.iv.81,9-97,9 divided into four parts:
1 = i) NEG[ation] of throat (laughter, fama) = honey, box,
ii) NEG of ear (invent what never saw) = box,
iii) NEG of closed mouth = nose - concluded on
iv) black heart of roman.
2 = 3 * 4 = tellenor (counting north/words) = black heart roman
3 = theft of capital = black heart roman
4 = the fragment interrupted at precisely URBE (city, Rome) = phrase border precision = black heart roman.
Hence there are four 'black heart of roman' in this graphic half of #31 - this constitutes the square spiritual storebox of the formal grammar of #29.
In 'politics', this 'Black Heart Roman' could be seen as a 'Black Sea Loop' along the eastern arm of the european swastika, turning into a 'Black Heart Roman' - here 'black plastic band' - by 'black heart/shirt of the fascies' of the fascists of Rome under Mussolini.
These four parts turn recursively into the four NEG forms under 1 like they turn into the four elements of #28.
This in total constitutes the graphic form of #31 - the big box - and it makes sense of the recursion to #28 - by the way the graphic form of #31 in Satire I.iv.81,9-97,9 comes to provide for a principled explanation to the metaphysical storage needed for turning the pushdown of #29 in Satire II.vii.57,3-62,7 into a context-free phrase structure grammar.
It is important to come to an understanding of this - but it is not necessary to run it on the map and in the politics - with drama and wellbeing and all that.
The difference between understanding it and turning it into politics is the mystery of the poetic equivalence of script form and meaning, including the Catalan equivalence to numerality. It is like that 'schimmelbild' of the indian's hand (search 'bovine') as the basis for a script: When the chinese calligrapher runs his brush-stroke over the paper, that is because it would have been there anyhow - if he had not run his brush there it would have run the brush there anyhow. That is a poetic wisdom which should not be turned into the pride of power claiming to be in control of the world.
Tragic politics (über die Macht) tries to make the script meaningful by mixing up the borders of the subject with the borders of the community - but that should not be necessary when one understands the semiotic functionality. It is not necessary to make a european swastika on the map for understanding this 'enclosure' of radical 31 and running the eastern arm or wall of the box up in NEG fashion along Italy. It is likely that the plans of a Black Sea Loop (since the nazis of WWII?) were for reasons of this single aspect of Horace - either for imitating it or for protecting its secrecy and privacy.
Europe should not have to sink into an ocean of selfishness (#28) for understanding this.
Is this the story of a puerile club of nazi 'intelligence' fanatics protecting the secrets of Horace for putting it into history for the new computer age, claiming to be in control of the world? If so, did they know about this structure of Horace - or is it all subconscious interpretation of the semiotic structure of the human psyche that guides the form of thought and understanding?
If this is a known structure of Horace which deliberately albeit secretly is implemented into history, the secrecy should have been considered a crime against humanity and been part of the basis for the Nürnberg processes - and it is time to understand that the damages to the world come from the secrecy on such matters and not the other way round.
It is dogs who bury their best bones, it should not be humans who do it.
Why on earth should this be secret? Only for giving you a chance to be among us privileged ones while that chap over there is an ignorant outsider without a chance - so that we can sit on his back and be 'in control of the world'? But that is to turn the precious bones into conflict and destruction. It is dogs who do that. Human intelligence should be able to do it better. Powerful mind-controlling upperhand tools were permitted strategies when the local societies were threatened by barbaric hordes on horseback - but when the program is a global community with a peaceful equilibrium it is no longer permitted to keep such ideas secret. In particular if it is administered by the intelligences who are financed by normal taxpayers money for keeping the democracy in shape for letting people know what they are voting for.
Those who argue for democracy should claim such secrets - administered by the state intelligences - published.
Horace was obligatory reading in schools up to WWII after which he has been fading out as general education. But he should not be put into history by being faded out and his ideas taken over by people who do not credit the source properly - neither should he be put into history by an implementation of his ideas into political history. It is the new technology which must say thanks to Horace, that is all - and so Europe needs not sink into new tragedies under the pretext of quasi proof that should hold good.
The lefthand column - including the days of the 'Wochen' in my poem - tell of the functionality - including the semiotic mystery of the Catalan constant.
The radical #31 tells of this fourfold functionality which also feedbacks recursively to 4 * 7 = #28 or continues further on to 4 * 8 = #32 = 'territory, opium'.
Ordinality can be outlined from this: The essentials of #30 recur in #31 under the first part, the NEGations, for the earbones. The fourfold mystery of #31 is the box that contains the indexes to the righthand contexts of #29. The head at the knees of #29 is the structural triad of #28.
The discoveries in these studies of Horace are my own, a result of my lonely work with poetry and theoretics to it. I do not know if these structures of Horace have been known earlier or if it only looks so because they are a part of the human semiotic constitution controlling the mind and its understanding of the world. If you want to use these ideas, do not hesitate with crediting me as the source - even if the 'intelligences' come running and say that I am their intelligence project which is supposed to be secret. I am not their intelligence project and I am particularly not secret - but it may be that the 'intelligences' have been abusing my life and work since my childhood and are nervous that it can come to be discovered. Could be this even if the theme of a possible third world war - the hope of keeping the bones hidden and secret - and the war in Ukraine could about preventing just that buildup. If the 'intelligences' claim that the knowledge in these studies is their secret, one should not listen to such talk - what I have published is my own lonely work and I have never had access to any secrets at all.
Sources (in addition to the internet 'wiktionary'):
Chomsky, N.: Syntactic structures. Mouton, The Hague 1957.
Grassmann, H.: Die Ausdehnungslehre 1844. In: Gesammelte Mathematische und Physikalische Werke. Herausgegeben von Friedrich Engel. Teubner, Leipzig 1894.
Horace: Satires, Epistles and Ars Poecitia. With an english translation by H.Rushton Fairclough. Harvard University Press, Cambridge, Massachusetts / London, England 1978.
© John Bjarne Grover
On the web 5 march 2022
Last upated 8 march 2022