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Genesis of mainstream implication

Disproof of the fallacious proposition

and Correction, leading to a healthy logic,

respecting the time

First edition: 2016-08-01;


2016-09-02: Annexes

2016-09-06: I do not know why, but I previously ommited the central pupose of my paper, for one month - a purpose which was in my french paper. For this reason, I beg the english-speaking reader's pardon.


When I say: " It is false that Pier acts. ", that does not allow me at all to deduct that Pier exists, because "It is false that Pier acts" has no juridical worth to affirm the existence of Pier. Zeno, him,

find it cool to let understand that Pier exists; it is that idiocy which he will tell us in 3rd proposition. But Zeno was not that silly; instead of using an abstract example as for the two first propositions, he

used the "earth" as a subject, letting us understand that it mattered, and this way, letting him to hide what should be false in his proposition.

"Vies et doctrines des philosophes illustres" - restituted texts by Diogenes Laerce, (I cannot find this book in official english translation (!)) but its title may be translated in:

"Lives and doctrines of philosophy idols"

editions: Le Livre de Poche, (collection: La Pochotheque)

- Book VII, Zeno (translated by Marie-Odile Goulet-Cazé), translated then in english here, by Alexandre Courvoisier.

"Truth conditions for a proposition:

From the true follows the true, depending on the Stoics, as from the proposition "It is sunny", the proposition "There is light"."

-Here, these stoics auto-creditbilize themselves, making follow from "From the true follows the true" with "depending on the Stoics" ; that is not the true leading to true which I distrust,

but the situation of "depending on the Stoics". To be conform, "depending on the Stoics" shall precedes the informative content.


"From the false follows the false, as from "It is the night", if it is false, follows "there is obscurity"."

-Here, these stoics begin to take you for idiots: as they previously took the example of sunny weather for true, all what they are doing is to let you admit that the night is false.

But you cannot integrate, you cannot assimilate the false - it is its

definition. Something is false when it does not correspond to reality.

A right sentance would constitute in taking a situation on the Earth on a certain datum where it was sunny, so that we could state that the night was false, as "if" let us do.

But if the night was false, then it leads to no consequence - so that I cannot state about this not existent consequence.

When I say "false", I mean the contrary of "true". A true thing, is a thing which happens; if this thing becomes "false", that does not mean that it changed "its nature" regarding the

previous moment; that means that the considered thing only does not occur, or does not occur anymore.

That written, a thing which do not occur, does not lead - let us hope this! - to any consequence, and this is not in contradiction with what I mentionned above.

"false" is an adjective which is respective to a subject.

When I say "This thing is false", false is respective to the subject through the verb: to be.

How does the verb [to be] operates; is it at least commutative? -This ask seems curious.

When I say: "Philip is a tall and good man", I mean that Philip has two qualities, which I introduced in a man, which last one instanciates in Philip. (With this sense: ⇐).

If I say, in a less common manner: "A tall and good man is Philip", then "is" does not have the same sense (⇐), because if the sentance was read with this sense between brakets, "A tall and good man

is Philip" wouln't mean anything. The sense remains oriented to the most particular instance; such: ⇒. So, the verb "to be" is, in general, not commutative. But I will come back on this consideration


-The negation:

The negation is a language abuse to mean that the operation done on the subject renders this last as being not occuring in the considered place.

Thus is there no such thing as a negation in the mathamatical meaning.

When I say "not proper" or "improper", the expression beginning with the prefix "im-" only does an emphasis, in the second expression.

So is it for the privative "a-", by definition, and for

the prefix "anti-".

"Anti-" underlines a rebellion against a (political, religious) institution, a rebellion against a dominant shifting, but cannot mean the "contrary" of such an establishment.

-Corollary - The "contrary" of "false":

"A thing is false" actually means that this thing does not happen, as nobody can introduce an "anti" concept in a thing, (an "anti-nature").

The contrary of a not happening thing, may be that this thing happens, but may also that another thing be - or don't be! WHAT DOES NOT MEAN FOR SO THAT A FALSE LEAD TO TRUE!

So, the contrary of "God is false" may be that "God is true", may be that "the devil is false" ; indeed, the quest to a contrary has no sense.


All this being written, I completely admit that from the false follows the false; it is sufficient for this, that a thing be false in a moment on a place, and that it remains false on the next moment on the same place.


»From the false follows the true, as from »The earth flies” follows »The earth exists”.”

It is the fallacious proposition, which mislead humans for millenia. This proposition exposes that »the earth flies” includes »the earth exists”, (what is correct in such), but...


This sentance commit two errors:

  1. It suggest that the action of the earth in flying, implies its existence, what is absurd;

  2. As it is not anymore explained, it ommit to tell us that »the earth flies” is false!

Remember what I mentionned previoulsy:

To search a contrary to a false thing (assuming that it was their attempt or their wish here) does not mean that this thing exists.

Indeed, we canNOT deduct the existence from an absent action. The absent action of a thing, means that we do not see this action, what does not mean at all that the subject, of the absent action, exists.

In few words: You cannot extract a truth, even elementary, from a false thing! Where the false thing - i. e.: which does not occur - stand for elementary (about the subject) - or for a proposition, because (for the emphasis, even if I already mentionned this), if I say »Pier acts is false”, then

I can absolutely not deduct that »Pier exists”.


"But from the true, false cannot come."

Notice that Zeno has changed the verb "follow", which is linear, with a verb which has the opposite sense (come).

The linear sentance, similar to the other cases, gives this:

"From the true, does not follow the false". The sentance is stupefying of pretention, and overall: it is not the everyday experiment !

All the other sentances were clearly presented - even if the previous was inept.

That written, the last sentance try to let you get the pill in believing that there is a definitive truth - with an introduction "But", which let wait for a surprise, adding to what I just mentioned.

Zeno tries to justify his pretention in separating the example.

When the other examples were very linearly presented, with "as", translated Zeno introduce his example with "Because", which suggest that he knew something that he has not yet mentioned to you, in a way

he would make you feel inferior to him, and making an emphasis in "informing" you that "the Earth exists" is a proposition.

Not enough happy with this state of affairs, Zeno seems to re-take his previous example, instead of taking a new one. Thus, with this loop, he re-directs you on something that you thought to have understood, what let

him conclude the affair easily.

Here is the next and the end; the example:

"Because from the proposition "The earth exists", it does not

follow that "the earth is flying"."

But the example is badly presented; as we just saw this, multiple ambushes to natural understanding were posed.

What I am mentionning here, is that:

  1. "True leads to true" is valid; for this, something occurs on a given moment, and then, this thing shall occur the following moment.

  2. "True leads to false" is valid, too. I'll write an annex for this. But to be brief: the brain, the center for reasoning, is a system, with its own inexactitude - with respect to the reality - that is why we shall integrate "True leads to false" to the logic. (But I will describe a formal example, in the future annex).

The right sentance seems obvious, but I have no reason to re-take the example of the Earth, which let admit that it flies with all the lattitude given to the verb "to fly".

The right example:

"From Jean, it follows: Jean acts."

Addendum: What is necessary, and what is sufficient ?

A cause is necessary, by definition. If you are searching a result, deleting systematically the previous step you won't understand anything; without memory and intelligence, as both of

these notions are the same, according to a definition of intelligence, (paper to come).

The effect is not necessary, as I show it in this present paper.

May a cause be sufficient? -If the cause was not sufficient, we were not here having thoughts about it. A cause is necessary but not sufficient, if it does

not generate an effect; (by example, a man who has a genital device without getting pleasure or children from it, has an insufficient cause).

Regarding the cause, the effect may be sufficient, but that does not really make sense to ask this question. If the effect were sufficient, we might wait that it fully replace the cause, but here again, we have no reason to

wait for the cause deletion - because that would mean the loss of our memory as well as of our intelligence.

The cause is always necessary, and the effect may be sufficient.

There is nothing such as a "logical equivalence", since the cause and the effect cannot interchange.

A cause may lead to an effect, which itself leads to another effect - so the

first effect is the cause of the second effect.


Mainstream implications:

false leads to false,

false leads to true,

true does not lead to false,

true leads to true;

are summarized in the expression:

"notA or B"

(not the cause or the effect).

But it happens to be a logic which don't have respect for the time, because of the particular case where the "Or" is an "And", and which is exactly the line where false were leading to true, and which is

the line which I am denunciating.

That is why the syllogism, appearantly redundant (on the cause), has been needed, and that it yields only to undemonstrables.

It is an undemonstrable tautology, what constitute an antinomy which we shall be mefiant about.

The only mean to distinguish true from false in an operational manner, was, for Zeno, a false which may lead to true, without possibility for true to lead to false. It could let him to stick, on his shoulder, the label of

"the definitive truth". But there is no such thing as a "definitive truth". Depending on the mainstream, in the particular problematic case, I am allowed to write:


(result: C).

But we just stroke the intermediate results - but there is no understanding in a result.

Logic is not about "The born of the universe from the vacuum" it goes on the human reasoning itself.

Understanding is in the logical way, that's why the causes cannot be deleted.

Not a single false may logically lead to true. If, by coinscidence, an absence were about to lead to an existence, so it is necessarily because there was a lack in some parameters; (as an action of God, which is to say that there was pre-existent from always).

Any science based on logic such as defined by Zeno, what means: which re-takes its implication, as the parts I am criticizing here - especially the fallacious sentance trying to extirpate the true from the false, are impacted

and shall re-define their boolean - called classical - implication, such:

[The false imply the true] is invalid;

[The true imply the false] is valid;

[The true imply the true] is valid;

[The false imply the false] is valid.

A cause is always necessary, an effect may be sufficient.

Balance sheet

If the current understanding of the implication were satisfying, it were sufficient to make false hypothesis, and to write on an enough number of pages, until the false were turning magically into true.

As you see, not a single guy on this planet dare to do this. We have an implication (or a series of-), and no one want to use its third line (except linear algebra or geometry).

The best the reasoning could do about false, were to confirm it (inert operation), or turn it magically as I wrote two lines before.

But we don't want the reasoning to be inert or magical; we want the reasoning to be a construction.

If the "true lead to true only", answers were guaranted for ages, and there were no merit in studies works; moreover, with this state of affairs, if "false may lead to true" (without reciprocal), it were a crual malediction that something was false, still, nowadays.

"Not the cause or the effect" shall be replaced with:

The cause or no consequence, with these components:

[false imply true] is invalid;

[true imply false] is valid;

[true imply true] is valid;

[false imply false] is valid.

Concretely: We see a pulsar from which we receive a radio signal.

The next moment, we don't receive the signal anymore. I may not have an exact mecanism to propose for the radio cast - as it is most probably the case, but when I do not receive this one anymore,

that does not mean that the pulsar disappeared;

we have to wait a moment until new reception of the

radio signal. (For the ones who think that the re-iteration (belief) is a metaphysical consideration, I answer it does not matter: metaphysics

an logic are the same; as the Emerald Table exposes: What is above is as what is under. Anyway, it may occur that we have a mechanism representation for the pulsar rotation - so that the reiteration is not anymore a belief).

-A science based on nowadays logic, as physics, leads only to universe destructions, on long term, beacuse this science want a result. But remember: There is no understanding in a result; there is understanding in the logical way.

-Linear algebra is almost relegated to the rank of an artistical invention by my article, as far as it does a misuse of the implication, the one of the mainstream, as I remember.

-Even could it be validated that the equality be a differently noted implication, (if I write m/V = d, I have no mean - in a rigorous consideration - to write d = m/V in this sense, because it would mean to add informations).

Analysis, as far as it operates a reduction of the informations (for computational purpose), (as analysis in chemistry or in philosophy) - instead of inventing such informations - is

the only legal math.

A cause is always necessary, an effect may be sufficient.

Annexe 1/4 - Example of true which leads to false:

A man see two buildings basis, until a certain hight, equal, for the two buildings; but he see, also, that the one on the right has a bigger basis (100m x 100m), when the first seems to have a smaller basis (of only 50m x 50m).

The reason to see these buildings in part only, is that there is smog, rather uniform in altitude.

All the buildings the man has seen before (i. e.: in this thinking experiment), were built by architects who had elementary knowledges in physics: these architects gave a bigger basis to their buildings when this basis should support a bigger hight.

The man deducts that the building with a bigger basis, the one on the right, is the taller of the two buildings.

Later, he calls the architect, telling him what he has seen, and what he has deducted.

But the architect invalids his deduction: “I wanted to give to these buildings sort of an artistical signature of my own. Also, the building on the right is a garrage, which needs a bigger surface,

but which requires also few hight - when the first building is a simple cheap house, which shall give the opportunity to accept a lot of people over fewer surface.”

-The man, completely devasted by this infirmation, goes on place the morrow. On this day, the weather is sunny, and the man makes the constatation that the architect told true to him, so that the essential deduction he made, on a true basis, is false.

Nota Bene:

One may reproach to me that the infirmation required external informations - the one of the architect, so that the true cannot yield to false in a simple way (in analysis).

But this is incorrect; in the thinking experiment, the call to the architect is wholly optional.

The man invalided indeed his own deduction, in comparing it with his reality. And it could not be else. Remember: a thing is false, is a thing which does not occur somewhere.

In order to make such statement, we shall go on the considered place, and make the constatation that this thing is not.

And this is ultimately what makes - fortunately! - the logic as being not (or not only) speaking about itself. The values "false" constitute a confrontation to the reality which was invalidated.

Thus, the false has no possibility to yield to true in a logical construction, and that - on the other hand - during the measures, incertitudes of them cumulates to the others, a thing classified as being true, may yield to false.

Annexe 2/4 - Correspondance with a mathematician:

(In brief, as I had several correspondances with him, I ask him how does he do, and then, expose - in brief - which arguments I have found against current implication).


“The implication (x=1 -> x>0) is always true.

Particularly for x=2.

x = 1 is false,

x > 0 is true,

what give: false imply true”.


“You only made an update of your given, with the insertion of “Particularly...”, moreover: an anti-dated update. If you provide anti-dated documents to an administration, you risk highly; nevertheless, that is what you make everyday, in mathematics.”

Effectively, why were I about to understand that “for x = 2” should replace the x = 1 of the beginning given, “without really replacing it”?

All the Art of a high Science, as of any other profession, is to avoid to the other the act in re-inventing the wheel in the considered domain.

Even if I cooperate in understanding “x = 1 -> x > 0, particularly for x = 2”, that I do a correspondance between the pairs presenting an equality, then I only obtain:

“x = 2 --> x > 0”. But even in this case, something is going wrong: We are using this implication, estimated as being true, and which is a whole thing!, in order to explain that a false might yield to true... The problem is taken upside-down!

Why should I go from a set to explain its parts?

That is not all; in the worst case, I can say that “for x = 2” is not mentioned as being true, so - by precaution - I consider it as being not known or true, what means it is false, so that x “remains” equal to 1.

And I can even pretend that the text arrangement is sufficient to itself, in pretending that it is x positive, which imply “particularly” that x = 2, where “particularly” means well that this is a possibility among other positive numbers.

But this optic were a probabilist or modal view of the implication, which I do not envisage very seriously to this day.

Annexe 3/4 - Extract of a nice logic book:

“Introduction to standard logic” (in french) - by Denis VERNANT.

-I decided to buy this book before to do the publication of my critic; I did not want to do this publication on the only basis of my knowledge of 10 years ago; so that I were in the ability to operate a kind of update.

This book seems to adopt a new fashion in modesty: It entitles itself as an “Introduction” although it is 400 pages long.

(This is not the sole book such entitled; also physics books. So, we see in the author's repository, and there is not a single book following the “introduction”.

At 400 pages the “introduction”, we expected however a treaty about the essential, of 1000 p. to 4000 p. long).

Indeed, having such a 400 p. introduction, I were about to think that the author were not very competent, not to overtake to introduction after 400 p. But as I wrote, that is a modern fashion, which is not the monopole of this author.

Nevertheless, the reading of it is easy: very well structured. Its table of contents includes until 5 levels in indented hierarchical lists, what is important, when we want to be rigorous in treating such a subject.

Until this day, I made a focalisation on its implication (p. 40), and this, already becomes litigious. The author makes a quotation of Philon de Megare in first place, one which passed through the latin in order to impress people with the form instead of the fundamentals, knowing:

“From what we want, follows the true”; it is in extend noticed, in footnote, that: “The de Megare's definition for the implication, correspond “exactly” to our truth table”, with, between bakets, “IVe-IIIe s.”; it seems to be before J. C.*

-Here, “exactly” means that de Megare renders 2 lines over 3 of our implication truths. But it is nothing astonishing:

When someone makes a “discover”, then thousand explainers come to get an official title of the best understanding of it, and over this thousand, rarely one dares to bring the “discover” under questionning.

*Was P. de M. anterior, or ulterior to Zeno? -To be honnest, I do not care at all of that, since Philon de Megare does a quotation even sillier than Zeno did.

“From what we want, follows the truth” constitute, depending on me, a proposition which does not even merit the analysis whose benefited Zeno, here before.

It were about to mean that all we would like to be possible will be, or: “When we want we can”...

-The only criticism I'll do about it, is that: If you really believe that false may yield to true (for a wish), then you'll be able to eat anything.

Denis Vernant seems to discuss about the counter-intuitive case, “false yields to true”, (case nbr. 3), in writing:

“If we render the conditional (Ndr: the implication) to be false for the case 3, it becomes a bi-conditionnal (ndr: a reciprocal implication)”

- but nobody ever pretended that the line of “true yields to false” should remain invalid.

So why should it be valid that false yields to true, instead of true yields to false? -Denis Vernant prefers not to have to explain this.

-A little farer, in page 41, he explains:

“The terms of antecessor and of consequent are hazardous: the condition is not a relationship of consequence at all, which were linking the two elements of a common domain. A fortiori...”

then, after “A fortiori”, he write almost the same thing, writing that it is not a causality.

Hum... “A fortiori” (i. e.: necessarily) is needed to make the auditorium accept an evidence, or to remember an already explained thing to it... not to make any counter-intuitive claim as being any establishment.

So, if I continue his reasoning, our narrow symbol should be replaced by anything, too. An author about logic, cannot take an ancient philosopher, who includes the time in his quotation, for a beginning reference, and then exclaim himself:

“But warning: there is not really the time in there...”.

Indeed, (on the human scale), we observe determinisms, occasionaly re-doable, we extract from them the most normal way to write reasonings, the logic, then, at this step, we pretend that in the place of the central connector, the implication, any form of causality or temporality vanished?

I beg his pardon, but I cannot believe that. The best it can be, were this an “update” done by some moderns.

If there were no causality in the implication, nor temporality, so the false should yield to NOTHING; overall not to true, and not even to the false (except itself, without what there IS temporality).

-This is the work given as to distinguish OPERATIONNALY the true with regard to the false, which renders the logic, as this logic is explained in all my previous paper, here included the temporality.

Annexe 4/4 - The so-called “temporal logics”:

You'll find several “temporal logics” on Wikipedia. But they re-take the mainstream definition of the implication, which one is a-temporal (or more exactly, which has an anti-temporal component (false yields to true)).

These so-called logics can encapsulate this implication if it looks freaky enough to their authors who may do a clown danse if it makes them happy, these logics would only consist in a muld on a wood leg.

(And go to know if they are not an intox against any industrial spying...)

The logic - as I redefine it - may ONLY BE temporal.


© Alexandre Courvoisier, 1028 Préverenges.

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