Rational logic, symbolic logic and marginal logics

What is logic?
Logic is the form in which a group of words is embedded. It does assure the intelligibility (possibility of being understood) and further, eventually, the possibility of attaching the character of ‘truth’ to a certain number of sentences or statements.

Logic is inherent to grammatical structures and does thus derive from language. It is thus possible to establish a formal logic (symbolic), which does abstract the main forms determining intelligibility by forming a ‘system’.

It is though impossible to talk of intelligibility outside of a more general context of language, or of the more subjective context of the individual as understanding in a given social or national context.

(The question whether it is possible to talk of intelligibility in itself is in fact a fake question. A word, the only entity which is intelligible, although it is possible to talk about virtually intelligible for everything we may think we can eventually name, is not but in a general context, and although we may detect phenomena whose name is yet not –which does explain on the other hand why nations do have words of their own-, the lack is given as a general lack, and not as a subjective inspiration: in the latter case the appearance of a new word may quickly seem as absurd or irrelevant.)

It is a fact that a kantian logic does presuppose that there is some universal form embedded somewhere and ruling on rationality, but it is easy to see, that a form is nothing but an abstraction from a whole, through probable criteria of time and space. Which is to say, that the human has the faculty, shared with no animal, to separate in his mind an empirical impression or perception in what belongs to space (not moving) or to time (moving), so that he abstracts the moving element (matter) from the non moving element (form), through the before mentioned criteria. Which confirms Kant’s thesis that ‘time and space are the forms of sensitivity’. Doing the same effort on language and not anymore on objects (separating the ‘cube’ as form from the ‘wood’ as matter), we discover quickly that there are stable elements called ‘formal’ that are easily to be distinguished from those which can be substituted inside of a certain range of possible variables without disturbing the notion of intelligibility.

It can be thus said, that the determination of forms governing the whole functioning of language, is suspended of the principle of intelligibility, which, on the hand, seems to depend on the principle of identity in its three variants. Intelligibility can though have two meanings which may alter subsequently the extension of application of the principle. Intelligible means nothing but to be understood. A human being may understand even the most irrational statements, depending on his general structuring of reality. Intelligible and rational are thus two very different things.

(Even if it possible to refuse the before mentioned principle, in the case that other definitions are given to fundamental concepts, it becomes quickly visible that this perspective does cover all possibilities even in contradictory definition, thus allowing to further an explanation for the widest range of phenomena possible, which is the principle of rationality we submit to, without though imposing it.)

What means rational?
This strange concept deriving from the Latin word ‘ratio’, touching semantic fields going from rate, parts or share (Spanish ración), measure, reason, is somehow related to the Greek ‘nous’, and is though almost an opposite. The Greek ‘nous’ is a faculty of intelligence that does allow the intuitive apprehension of meaning, of the relationship between word and circumstance, of the implication of an idea, while the Latin ‘ratio’ is the weighing of reality in a given body of law, whether it is formal or social is indifferent. The Greek, following a more intuitive ordering of reality, which finds its most purest expression in the concept of ‘kairos’ developed by early Plato (Socrates), as the ‘being at the right moment at the right place following a spirit or demon’, does understand the human as submitted to moving forces (Gods that are the essence of different passions and orders), and does thus understand the same as moving freely, on the one hand, and subjected to different needs, on the other. For the Greek, the thought that everyone should be given the same amount of food (Latin ratio), is absurd, except in latter Plato, who does thus go to
Italy with his theory …

The concept of reason, shifting heavily from one notion to the other for hundreds of years, does have serious problems to find a proper definition. It seems though essentially to be linked to the notion of order as determined by some faculty of higher apprehension, whether it is an intuitive order or an order as submitted to a given body of law.

The consideration of the changes of the concept through hundreds of years does allow to attempt a definition which may include most of variables: in a general frame that separates the human from the animal through the faculty of determination of notions in concepts, it may be said, that reason is nothing but the absolute submission of the notion to the prior reference as existing, which is to say: instinct. Is instinct the fundamental reference, it is possible to maintain the referential subjective reference (feeling) in the development of concepts that do take birth in the very faculty of conceiving, and which can not be attached to instinct in itself anymore. It means that the concept of survival does enlarge itself until it becomes the concept of life, concept that does imply the possibility of the organization of existence through thought, principle and law, in the determination of the self as such and related to others.

Logically we can say that there are many things we say, which do attack life, survival, notions and concept as such, are thus intelligible, but to a certain extent, irrational. (It is always difficult to evaluate the irrationality of something, as what seems ‘shocking’ to a superficial view, can be in fact ordering internal structures, thus maintaining reason in a more general approach.)

From this point of view, it is possible to say, that word, or all virtually intelligible, does keep the principle of rationality in given forms. We may also affirm that the fact of not respecting these forms, may have as consequence the destruction of vital functions of intelligence, the loss of apprehension of reality as a whole, and consequently death, subjective, or a more general disaster.

Forms though are not enough. The statement as given may be ‘formally correct’, but needs of a subjective disposition in order to be ‘true’. As much you give to the Romans (formally correct), you will have to give to the Greek: a statement has to be appropriate to situation in order to disserve the title of ‘truth’, so that it becomes of need to say the truth ‘subjective’, and this only, when submitted to the formal criteria as given.

It appears clearly that a statement does first have to have a certain number of formal characters, and then, to be rationally embedded in a certain context. The first is of reason, the second of wisdom. To differentiate the one from the other you may use the distinction in language offered by the differentiation of rational and reasonable.

The formalization of logical structures
Probably the most difficult of human activities, the formalization of logical structures does appear very lately in history and does progress very slowly.
Starting with Socrate’s use of dichotomy (to cut in two) as tool of demonstration, it arrives with Aristotle’s theory of definition and demonstration to a stuck for more than two thousand years.
Dichotomy is a technique that does allow proving a certain type of statements through the confrontation with the contradiction in essence or through the similarity in essence. Used by Socrates only to establish the essential identity between just/good/beauty/truth and the essential difference between those and other concepts as interest, pleasure, etc. which is to say, between a realm determined by ideas and one determined by the submission to physical impulses, it does though hardly allow to establish scientific statements. Aristotle does develop the theory of definition in categories (the essence is not thus ‘what must be in common with itself in order to allow it to be named that way’ as in Plato, but ‘the belonging to a larger concept to which it is absolutely submitted’, a tiger to the category of animal, eg), and further through syllogisms the possibility of general statements concerning mainly the empirical areas. Taken this way, you may not say that Plato and Aristotle are contradictory, just complementary. It is obvious that Aristotle makes fun on Plato when he pushes the theory of ideas (only applicable to abstract notions) so far as to want to apply it on empirical concepts (argument of the third man). Plato does never counterattack by revealing the inconsistency of Aristotle’s abstract concepts, but he could have done so.
Syllogism is an archaic way of ordering demonstration through essence. It consists in the differentiation of ‘All’, ‘Some’, and ‘One’ (one of Kant’s categories of understanding), and the submission of the one to all through the essence. The most known example: “All men are mortal. Peter is a man. Peter is mortal.” In modern symbolic logic it would be formalized as follows: a & b > c. Or said otherwise: The group of men has as an essential character to be mortal. Peter belongs to this group, and consequently (logical proof) the essence is his, too: he is mortal.
What seems very simple, is though extremely complex, as Aristotle does formalize the possibility of attaching a particular (Peter) under a general concept (man) through an essence in a determined group. In a certain way, it does give the formal steps of what is the function of what Kant calls the ‘faculty of judgement’: the possibility of attaching an abstract concept to a particular case, situation or object.
For hundreds of years, if not for thousands, rationality will be suspended of these three formal mechanisms.
In simple words we may say that reason does base itself at that time on 1. non contradiction (dichotomy as way of demonstration) 2. definition through essence and accident 3. grouping of objects in categories having something in common and allowing to order empirical impressions in the different groups through the category or through the essence.
Aristotle is the first to observe that the grammatical structures have main formal structures, conveying intelligibility, but does still not formalize these structures.
We will have to wait until the end of the XIXth Century until a progress is made in the formalization of proper logical structures. Attempt is made in order to substitute the heavy grammatical interactions by symbols. Together with Wittgenstein, it is finally the
English
School that does the main work of formalization (Russel, aso).
The result is that for the first time in history, we can see the formal bones transmitting intelligibility in very simple structures and in a so called rational frame (depending on principles, laws and definitions). And becomes thus &, a statement is an ‘a’, v means ‘or’, etc. The statements (a, b, c) are linked one to another through a restricted number of connectors (or, and, thus, equal to, not, only if), and their validity is determined by the function: if ‘a’ is false and ‘b’ is true and you say ‘a & b’, you must say = f (false), aso.
Some thought to have produced a machine in order to make eternal truths prop out of nothingness, forgetting that you have to fill in the variables in order to produce intelligibility, and that the very filling in of the variables did generate more problems than to offer solutions. In fact, though a monstrous effort of abstraction and a universal step forward in the attempt of simply understanding the extremely complex mechanisms of human understanding, symbolic logic does quickly show an extreme weakness.
It does intelligently reduce the grammatical functions to three or four logical ones, instead of getting lost in little nuances of ‘but, instead,’ etc, but it does not make on the first hand the consequent differentiation of functions, which are all connectors, and it does forget, on the other hand, Aristotle’s essences when the time comes to fill the variables. It does further forget to introduce the notion of hypothesis as differentiating statements of different types of reality.

The different logical functions
If it is easy to understand that a connector it a symbol that does connect one statement to another in a certain way, it becomes difficult to follow why ‘no’ should be a connector, as it is not connecting anything to anything, but just putting a sign on the character of the statement (positive or negative). Not only, the sign = (is equal to) is not connecting either, it is identifying something to something through a value (true or false in a given logic), thus b & c = c & b, is not connecting but identifying. This differentiation does allow to better understand the = put in front of v or f in the metalanguage of laws. The law is not connected to a v or an f, but identified to them taking into consideration a certain number of criteria as given.
What is then the difference between a character, a connection and an identification?
The character does affect the nature of the statement. (is a or non a)
The connection does put two statements into relationship without saying anything about the nature of any of them. (a & b)
The identification puts two statements into relationship through an essence or value implying the nature of both in a certain logic. (a or b = b or a)
What is then the function of the famous ‘thus’ symbolized by >? Strangely it is the only function symbolic logic does consider in a hypothetical state: if ‘a’ than (or thus) ‘b’, which is not necessary, as you could consider ‘a’ thus ‘b’, as in the example: It is raining, thus I become wet. Why saying in a general ‘natural’ (consider here ‘natural’ as saying not hypothetical) context, that the function > is to be put in a hypothetical dimension? On the other hand, what kind of connection is produced by the use of the function? There are two similar functions: > and the same underlined, which means, only and only if, to differentiate statements of the kind: If it rains I become wet (true), Only if it rains I become wet (false), only if I get in touch with a liquid, I become wet (true).
Apparently, it is more than specifying a character (no), more than connecting (& and v), less than identifying (= or the same with three lines for absolute equivalence). What is this function showing exactly? It is relating a statement to another through an INNER characteristic of both, which is to say, through a semantic characteristic that is not formal: Aristotle’s tool of proof in syllogism or developed syllogism.
As symbolic logic does forget to introduce Aristotle’s theory of essences into the general theoretical frame, all statements depending on > are inconsistent. > is a logical consequence as demonstration that does need of the theory of essence in order to be valid.
The purpose of symbolic logic, wanting to establish a form of ‘truth’ as warrant for all scientific statement without semantic dependence, does empty symbolic logic of the possibility of establishing consequence as proof. Ironically, people working with symbolic logic will finally be obliged to fall down to Aristotelian theory of knowledge in order to validate scientific results: “Most cases observed do show that people who smoke have cancer, consequence: smoking is cause of cancer.” And this although most thinkers do agree on the fact, that it is impossible to obtain a universal statement out of general observation. (Aristotle said, that the notion of the ‘universal’ is born from the recurrent print left by an impression on mind.)

The origin of the universal and the confusion with empirical general statement
It can be said in simple words, that the notion of ‘universal’ can only and only be referred to concept or to any statement made through the use in variable logics of the theory of essence. It can never be said that a ‘universal’ can be used in an empirical context of observation. This is so because the word is the product of the human mind in the use of the determining principle of identity, so that he can say ‘for all things falling under the concept of … animal … either they have these characteristics or they are no animals’. It is obvious that it does not depend on observation, but on the ability of the human to form groups of things through essential and accidental characteristics, so that he can say without any shame ‘all’, without being obliged to know them all or to have seen and touched them all. ‘All’ thus, as potentially submitted to the concept in question is timeless and spaceless, but as such, only referred to the concept and never to the object. Consequently, a universal statement is the one that does operate in these particular sphere, where concepts are put in relationship one with another through essence and accident and logical operation, without considering the empirical observation as such, although this must have proceeded at a certain moment. This realm is the so called ‘a priori’ realm of Kant. Strangely it does allow, contrary to what he says, universal statements also on subjects concerning matters linked to the empirical world, as it is possible to determine the governing logics of a process (physics, chemistry, biology, psychology, etc), to define in essence a certain number of concepts and logically to state something in universal terms.
For the problem of cancer and smoking, the logical mistake appears as follows: Most of the people who smoke finish up by having cancer. LACK: which is the characteristic, physical, psychic or other, that does differentiate those who finish having cancer of those who don’t? STATEMENT: People who smoke and … (lacking specification) do have cancer. (A priori statement)
Or: Smoke does contain this and that element. This element has this interaction with the human cells. This interaction may deteriorate a certain function of cells, thus being at the origin of cancer. The possibility this to happen is much higher if the human cells do have these characteristics, or the smoke does contain these and these elements. (empirical statement).
It is obvious that the so called ‘scientific’ statement above does fuse in irrational manner both modes of establishing a statement. It does mix up the a priori sphere with the empirical sphere, and does thus not allow to obtain clear intelligible statements.

The absurd of the f & v > v law
Considered this way, we quickly see how absurd the f & v > v law can be. In no case, a false statement may have inherent an essential characteristics that may allow to link it to a statement that is true. If you can say, ‘elephants are animals, and thus, they reproduce themselves’, how do you say ‘elephants are cucumbers and animals, and thus they reproduce themselves’? The human mind will necessarily conclude that the elephant has to be a cucumber in order to justify reproduction, which is absurd.
On the other hand it seems to suspend logical consequence of a possibility, which is absurd, too. ‘It could be that elephants are cucumbers’, and ‘they reproduce themselves’, is not ‘true’, but ‘could be true’.
It is obvious that for reasons that should be established, the symbolic logic confuses hypothesis as premises of scientific demonstration and established statement, as if it confused the process with the result. It is different to say: “If I make this and this experiment, and the experiment does match in results this and this thesis, it can be said, that the general theoretical frame is valid for this and this phenomena”, than to say “Test have proofed that the substance ‘xcf’ does have as side effect this and that, so that the chemistry has to be forbidden to children under four years”, both valid, if considered separately.
In any case, it is obvious that the only rational law could be v & v > v.

The validity of given logic
It can be said, that symbolic logic does govern most of the structures of main languages as given. It is though certainly observable, that there are languages that do not have enough level of abstraction so as to comprehend main complex abilities involving consequence as proof or definition through essence. To say thus, that it is a ‘universal’ logic is true only if referred to the concept: “for all human using this logic —if corrected as said—it warrants rational statement”, but in no case it could be said, “results deriving of symbolic logic are valid for all human beings.” As there are many human beings incapable of following the demonstrative process, foundation of understanding. On the other hand, there are many deviating logics, too, whose validity is more restricted, but also acceptable. It would be interesting to know how far these deviating logics have not, in fact, avoided a general disaster consisting in the disappearance of fundamental rational functions as a consequence of the so called ‘evidences’ deriving of symbolic logic as given before.