Logic History Overview...

Logic History Overview...
Quantification Logic...

Monday, July 18, 2016

PHILOSOPHIC COMMENTS ON THE NEW RESULT: "ABSOLUTIVITY" REPLACING RELATIVITY

PHILOSOPHIC COMMENTS ON THE NEW RESULT: 
"ABSOLUTIVITY" REPLACING RELATIVITY 

Science on the large scale, that is science dealing with the fundamentals of reality and the universe, has always had and still has a major effect on the non-scientific - social - general philosophic thinking of that science’s society and its leaders.

The beginning of the scientific method and the work of scientists such as Copernicus and Galileo resulted in the new period of "The Age of Reason" and "The Enlightenment" – rationality and empiricism replacing dogma and faith. 

The new developments that Newton introduced led directly to the concept of the "clockwork universe" and the strong belief in laws, order and regularity. 

And, Einstein’s theory of relativity coupled with the 20th Century’s attribution of actual uncertainty or indeterminism to all physical objects, an extension far beyond the original valid Heisenberg Uncertainty of measurement due to the act of measuring changing the object measured, resulted in our contemporary outlook of a probabilistic reality with no certainty, everything relative with no firm truths, upon which we can lay some of the responsibility for the horrors and tragedies of the 20th Century. 

How is that so ? 

In general, a statement and its contradiction cannot be simultaneously true. Therefore, there are some absolute truths. Thus there is absolute truth, which is the collective body of absolute truths. 

Not all statements are absolute truths. Aside from error, which by definition is not true, there is opinion. For example: 

· Some people state their liking for candy; some their dislike. It is a matter of opinion. 
· But, the statement "Some candy has properties that appeal to some people" is an absolute truth. 

The point of view that the questions, "What is truth ?" and "What is real ?" are meaningless questions without answers is not only incorrect but quite negative and harmful in that it suppresses inquiry and progress that could otherwise take place. 

Truth is that which conforms to and describes reality. Reality is that which is, not only matter and energy in their various forms but also: feelings and emotions, ideas and cultures, languages and arts, and so forth. 

Whether we can know, sense, measure, or understand some aspect of reality or not it still, nevertheless, is.

Its being does not depend on our consent nor our observation nor our understanding of it, nor even our own being. We are not gods. 

The problem is not whether there is absolute truth or not -- there is. The problem is finding out, coming to know, what the absolute truth is, what is true and what is not. Just what is the "real" reality. 

This problem has beset mankind since the earliest stages of the development of our reasoning. It has resulted in a more or less collective decision to grant equal validity to a number of different versions of the truth in spite of their being mutually contradictory. 

Not that individuals, organizations and governments hold the opinion that their own version of the truth is not correct. Rather, they ardently believe in the correctness of their own views. But, their inability to prove their views and their inability to defeat differing or opposing 
views necessitates their getting along in some fashion with those other views and the multiplicity of contradictory views of reality. 


That state of affairs has existed for so many human lifetimes that it has essentially implanted in our collective and individual thinking the incorrect belief that there is no absolute truth, that truth is what we say it is -- especially that truth is what we can enforce it to be. 

We have gone from inability to determine the truth to non-belief in its existence and then to belief that truth, and reality, are whatever we choose to believe them to be and can force on our fellows. 

The most significant characteristic of the 20th Century, other than its explosion of technology, has been its adoption of the attitude that truth is different for each person and each case, that it is what each individual perceives it to be -- that there is no objective reality, only the subjective reality as perceived by each individual -- that all is relative. 

The great damage that such thinking does is the license that it gives. It gives license to create, choose, decide upon one's own "reality" and then act accordingly. Such thinking ultimately gives us war, rapine, holocausts. 

But, if there is an absolute reality, objective truth, then, even if we are not able to completely know and understand it, we are subject to it. We are measured and judged by it; we experience the effects and consequences of it whether we agree and approve or not, and we feel compelled to behave accordingly. 

Thus absolute reality and objective truth, 
which indeed exist, 
also are desirable and beneficial. 
They are, in fact, essential to civilized society.

And, that is the beneficial result of Absolutivity replacing Relativity. 

Friday, December 26, 2014

A Few IFA Proposals - Conventional - Unconventional

Friday, December 05, 2003

A Few IFA Proposals - Conventional - Unconventional

Ah yes, Edward. Quite a problem we seem to be in. Since Edward asked this question, I thought I might stick my head out and see how many chop it off. Somehow, I feel they may not since we are all in such a quandry... "What this means is that the seesaw analogy fails: Europe cannot go up while the US goes down: both need to descend together. So the problem here is architectural (any suggestions Lloyd?):"

As I stated in one of my posts at: MacroMouse and in thorough agreement with you Edward, "We have never been here before." Due to the vast imbalances in global ppp's, wages, debts, trade, wealth, exchange rates, etc., which have evolved since the collapse of the Bretton Woods System in 1971-`73, we face the most serious challenge since,oh who knows when, forever. So what would I do with the international financial architecture? If enough serious minds are willing to admit something needs to be done, then there are definately several answers.

The goal, of course, is to rebalance the entire global system. How? Well, many forms of external exchange clearing have been put forth since Plato first advocated it, though none overly appeal to me or many others, as suggested - they reduce too much autonomy. Therefore, I suggest several different forms of conventional exchange clearing and several unconventional forms of internal exchange clearing - which allow a higher degree of local autonomy. I see no other way to otherwise rebalance the massively out of balance system. If we had originally, in 1971, rebuilt the then broken system by making balanced floating exchange the law of the land, we wouldn't be here, but we didn't. Just for the record, we could have made a 10% maximum balance band law the IMF would have been mandated to follow when nation's ppp's drifted out of balance, that they should have been mandated to rebalance, even though we had abandoned the pegged system. A rebalancing framework could have and should have been set up at that time, even if it meant loaning, or using a standby agreement until hostilities ended, the money needed by the U.S. to finish the war, etc. It would have been smarter than destroying the entire system as has nearly happened. There were many ways to rebuild a workable system at the time, it was just the acrimony over the war that prevented such a wise course. I mention this for background on what now must be done.

I have only recently come across enough information and empirical evolution to possibly offer a few new and different answers. I am no where near ready, but I can set the framework. At the outset, moral hazard must be guarded against most in the workings of any new system. As Alfred Marshall suggested, we could use his units of purchasing power as a solid standard of a new architecture. I suggest a very large basket[20% of GDP] of commodities, production, goods, and services as the new standard for all nations. This large 20% is required because I further suggest using many forms of derivatives contracts and bond contracts as insurance for the new system of clearing - to satisfy the large financial interests. I suggest this be a minimal financial computer controlled international clearing architecture - politics removed after implementation. To implement, all capital markets must be either closed[short term] or laws of gradual rebalance must be written into the architecture implementation and evolution. This way all nations can maintain their sovereignty and autonomy more than other already advocated systems. If the laws and computer programs are properly written, the world can evolve over a given timeframe to a new global balance of all thus mentioned markets. Rebalancing is a simple accounting trick if enough financing is forthcoming, to do so. It will take much new IMF financing, but the rebalancing will recreate so much new credit productivity, it will pay itself back over time just as the massive public financing of global WWII did.

There is also internal exchange clearing, a non-conventional system, that I have written George Monbiot about. There are several of these variations, also, but for now I will enter my e-mail to George:
Earlier today I came across an article of yours about a meeting, to come up with an alternative to capitalism other than the other failed system - totalitarianism. I'd like to make a suggestion that there is a way to build such an architecture. BTW, you are my favorite author. The system I am talking about is already here, almost but unrecognized, as yet. On the one side we have what I refer to as Minsky's Heinz `57 capitalisms. On the other we have the Heinz `57 totalitarianisms. None of these are satisfactory. Yet, the answer lies somewhere inthe middle between the two. BushCo wants to implement an outrageously totally free [for the corporations that is] capitalism. China, on the other hand is moving from totalitarianism toward BushCo's totally free corporate capitalism. If it goes all the way this would be a big mistake, as the perfect mixed market capitalism lies in between.

What I'm talking about here is the world has a chance to help China develop the first perfectly balancedmixed economy of public and private enterprise. I use this example as the developed nations will not yet listen to common sense. Now, I know from reading your books and articles you can easily grasp this. If China were to naturally evolve to a state of 20% public enterprise markets and 80% private enterprise markets we would have a chance to witness something truly amazing in economic history, if properly organized at this % mix. As, at this total market mix the 20% public enterprise market could be used to keep inflation/deflation permanently in check throughout the 80% private enterprise market, thus allowing a fiat money system unlimited potential. I mention this about China as it is the only experiment in the world heading toward and most likely to reach this % threshold. It would be a great loss to the world if we do not recognize this once in earth's lifetime chance to grant the world a new path. E=1/5X is a formula for perfect competition capitalism.

The 20% public enterprise mix must be a total % market organization of all production, goods, and services in order to check inflation/deflation throughout the 80% totally free private enterprise side. A tripple entry banking system can be set up to finance. Alfred Marshall, at the turn of the century, mentioned such a similar mix with his units of purchasing power. This is the same thing, so to speak, at a much expanded macro level. If you can actually see this system, which I think you can, you must see the advantages a fiat system would possess when inflation/deflation can be market controlled, it frees the printing press to have free reign to build an unbelievably wealthy, healthy, strong, and viable moral capitalism.

If China were to discover this capitalism key, the rest of the world would be forced to emulate - gladly as debts and taxes would vanish or could be used productively. They most likely will cross the 1/5X threshold sometime in the near future as they are privatizing at a fast rate - almost 50% already. There is no need for them to cross it in disarray as is the case with many of Europe's social democracies and Russia's failed transition. They only need be shown the simple facts. Please dialogue with me to work out the details. The world needs us George.

I wrote three books about this system through the `80's and `90's. Trouble is they are very crude web published material - not enough free time. I am now retired and have the time to finish. My work will be rewritten and republished this winter. My first paper will be 20 to 30 pages long on global credit productivity - a totally new macroeconomic subject.
just a start, I have more,
everyone, dialogue with me,
Lloyd


Friday, May 30, 2014

Preliminaries — definitions of concepts of logical truth and necessity:

Preliminaries — definitions of concepts of logical truth and necessity:

The hierarchy of stable sets, then, consists at least of the empty  set, the set of logical necessities, the set of physical necessities, and the set of all truths. Since any proper subset of the set of logical truths fails to be logically closed, the set of logical truths is the smallest nonempty stable set. Marc Lange

1. Boltzmann’s continuum hypothesis (necessarily incomplete)(admitted by Boltzmann)

2. Boltzmann’s ergodicity (necessarily incomplete as to exact equilibrium)

3. Ramsey’s ergodicity (tends toward equilibrium)

4. Wittgenstein’s foundational logic for mathematics (as interpreted by Ramsey)(sum of all propositions possible represents logical infinity as a fundamental ground of math)(symbolically useful/used as to computer math software)

5. Cantor’s w incompleteness (as per Brower’s intuitionistic logic)(para-consistent logic)(logic is deeper still)

6. Are set-theoretical truths mathematical or logical (why the most basic set is logical)(the non-empty stable set)(logical truths form a stable set under CH and ØCH counterfactual necessity)(stable sets form a heiarchy)

7. Physical necessity and/vs. logical necessity (two definitions of logical necessity —classical and ergodic)(where ergodic applies to non-fixed/non-linear universal logic, i.e., logic of the universal mechanics, not exact universal logic, i.e., what exists in macro structures vs. what exists in micro structures of black holes — as per theory, also QM at super-positioning limit)

8. Godel’s incompleteness of his incompleteness theorem = hypothesis (new discovery sheds new light on Godel’s math being short of its full logic knowledge)

9. Necessary counterfactuals (i.e., by the necessity of a space-time continuum being mathematically un-closable, counterfactuals function as physical necessities for logical necessity, i.e., positive and negative charges of qm fundamental substance matter, except in the possibilities of theoretical black-hole super-positioning mechanics, thus allowing the two positions of logic over math impossibilities)(such a relational logic can’t be written into numbers, at this level of super-positioning)(maybe in the future, it can be mathematized; but, this is un-necessary to absolute foundations of logic, where such logic dictates its own closure by necessity of charge counterfactuals and the c-laws of physics — light, or charge as light velocity-spin collisions, is its own absolute governor on logic’s possibilities and necessities)

Summary of the concept of logical truth and necessity:
Since the time of Thales, Anaximander and Heraclitus we’ve been confronted with the fact of how the mind logically necessarily mechanically functions as to “argument to exhaustion”, or in modern terminology, “counterfactuals”. What is it about us bio-beings that allows us such high level of both logical and mathematical interpretation? I mean; Is it the mind’s eye’s geometric necessary mechanics of scalable intelligence only, or is there a deeper fundamental mechanical necessity in operation? For the last 4 or 5 years, I’ve thought it mainly the bio-organic mechanics of the mind’s eye’s geometric functioning, but I was having trouble grounding such mechanics, other than highly complex compounding of the many truth and proof systems available, but I now see another path — that of a more fundamental counterfactually necessary CH and ØCH logic.

We know the trouble really reared its ugly head with the logic and mathematical crises of the latter part of the 19th century, when non-linear logic and maths were discovered, placing all fundamental classical logic and math in jeopardy. And, even with all the work done in math and logic since, from Piano axioms, Cantor and ZF set theory and its variants up through Von Neumann, Church-Turing, Godel, Tarski, Cohen, etc., and many other non-standard analyses since, there’s still been the nagging question of incompletenesses, in many areas, especially as to absolute foundations; foundations which could not be fully derived, either from the universal laws, maths or logics, without using the often fudged axioms. What would or could replace the questionable axioms? Many of us have surmised it to be some more basic system of math or logic, not yet discovered, and that is what I’ve discovered — At least, as far as I can see.

I just happened to wake up yesterday morning thinking about “The tensor scalability of imagination”, i.e., “Empires scale up and down over time, mainly by law, money and intelligence; and/or, the lack of intelligence, money and by symmetric and asymmetric law confusions, conflations and changes”; “Quantifiable truth requires a physical ground, even if only qm space”; “Linguistics’ over-formalization of non-fundamental formalization, i.e., Chomsky — Psychology can-not be formalized”; “So far, the only successful “Universal Languages” that’s ever been developed are logic and math; and then, there’s 137+ different formal logics and many more maths”; “Philosophy is a formal methodology of thinking about thinking, as abstraction, conceptualism, logic, etc., and being formal is thus an objective science” — When it dawned on me that what I was looking at was a fundamentally new way of looking at formalizable foundations in logic and math, from a perspective I’d never considered — That of; “The foundation of all quantifiable logic, math and truth systems is the fact that a completed continuum hypothesis is “Impossible of Proof” in any of these systems, thus acts as the counter-factual fact to found such physical realities upon — The Ø symbol is the foundation symbol of all truth proof systems, i.e., “Factual Incompleteness” is the foundation of all truth systems’ proofs.” ØCH extends all the way back to Thales’ counter-factuals, or arguments to exhaustion. Exhaustion only exists due to the incompleteness of ØCH possible. Logic, math and truth systems would not function without ØCH incompleteness, as there’d be no logical or physical counterfactuals to base such systems and thinking upon. CH Completeness must remain incomplete for our knowledge systems to function. The CH is only “Ergodic” — “Tends Toward Equilibrium” — But, ØCH complete — by necessity of logic, math and truth functionality — Otherwise; Counterfactuals could not exist to base any knowledge system upon. All logic, math and truth systems are true up to “Ergodicity”; But, ØCH complete… (Ø meaning “never” here)(CH complete would destroy all possibility of logic, math and truth functionality)(Realize this is just an early summary of my yet pregnant ideas, while the concept is complete in my mind — It’ll take me a while yet to polish and complete it)

ØCH and ØØCH can both be true, as in unified black-holes’ neutron charge non-existence, and all other natural phenomena of universal charges +’s and –’s counterfactual necessities outside black-holes and neutron stars — Thus; Physical necessity is not always logical necessity, allowing for absolute counterfactual facts and truths. The smallest non-empty stable set of pure logic is the ergodic ØCH. E = MC2 except at limit — Limit = “Absolute Hydrodynamic Spin-Time Compression” in black-holes, where opposing charges neutralize — When all electrons and atomic structure merge into “Super-Super-Positioning”. No math exists for the above conditions — Only ØCH Logic — The sums and products of truths and counterfactual truths of the propositions involved. These facts alone are the reason logic is the more stable set, over and above set math.

If you follow this at all, give me some honest criticism, as imo, I’m looking at; The #1 Universal Law of ØCH Modal Necessity — CH Counterfactuals Absolutely Must Exist — Which actually changes and enhances the entire foundations of logic, and the logical foundations of math.

P.s.
Sorry for the mostly note infused prelim and summary. I’ll work it into a more condensed and presentable paper later. Just wanted to give you some idea what I’m working on.

Monday, April 15, 2013

Fundamental Motion In Motion...

The “motion and rest-motion” indiscernibility apex of CM/QM/RM There exists no such state, as linear motion is “eternally” exchanging motion states, with angular motion and spin states “Eternally” one to the other Va = Vr « Vu

Wednesday, April 10, 2013

A Rational Morality

A Rational Morality
By, http://intelligentparty.wordpress.com/

I’ve found on a number of occasions that people who conceive of morality as something handed down from on high don’t understand how there could be any alternative to that view. “If you don’t get your morals from [deity of choice], where do you get them?”The frequency with which this line of questioning appears demonstrates a profound misunderstanding of what sort of a concept morality is and how we can coherently define it. The assumption at the heart of the misunderstanding is that morals must be things in the world—not necessarily that they must be tangible, but that they have an existence independent of the human mind. For a person holding this view, morals are fixed, constant, and external.
(Continued below the fold.)

The Source
This notion of external moral values is equally ludicrous whether the perceived source is a deity or a dictator. Morality is a value-based judgment system, a human-created way of applying conceptual labels to human interaction and decision-making. These labels, the words of moral judgment—good, bad, right, wrong, just, unjust—have no real-world referent, the way ‘pencil’ or ‘babboon’ do. They only exist in the abstract, which is to say that they only exist as products of the human mind, and this is the only way they really make any sort of sense—as linguistic constructions for describing and evaluating human behavior. People intuitively understand this, I think, but they persist in thinking of moral values as something existing independent of human reason (and often not even accessible to human reason).
Nature certainly doesn’t make sense as a source for morality, given that nature (pathetic fallacy aside) has no particular interest in whether we act “morally” or “immorally.” This is to say that two actions, one “moral” and one “immoral,” may have markedly different consequences, but nature has no real investment in one over the other for the sake of adhering to a moral system. Examined in this light, moral actions are not qualitatively different from immoral actions from any perspective other than a human one. The only distinction between actions, from a natural standpoint, is due to a difference in the direct consequences of those actions. Any attempt to claim the natural world as a source for arbitrarily chosen moral values is bogus, and is most likely an attempt to rationalize a supernaturally-based view of morality.

Defining the System
It is important for us to understand why morality exists, what purpose it serves in human discourse. Morality is most readily understood as a system we impose in order to make our lives easier—in terms of both individual quality of life and overall utility—and to turn them into something other than ‘kill or be killed.’ In its rational form (as distinct from the sense of ‘public morality,’ where things are arbitrarily chosen as ‘good’ or ‘bad’ for no logical reason), it is a product of extrapolating from rational self-interest. The impulse towards morality is not, fundamentally speaking, an impulse towards treating people justly or fairly for its own sake, but rather an impulse towards treating people justly and fairly in the hopes that they will treat us in such a way. An appropriately chosen moral value within such a system is one that strikes the right balance between self and other, in the sense that the negatives of obeying it ourselves are balanced out by the positives of everyone else obeying it. The most obvious example is the widely held moral prohibition against killing for reasons other than self defense. This is an appropriate moral value for us to hold, because we can reasonably (there’s that word again) expect that the desire to not be killed is more or less universal, that the convenience of not worrying about being murdered will outweigh the inconvenience of not being able to slit the throat of someone who pisses us off. That this is often overlooked in moments of passion in no way invalidates it as an ethos—it just means that there are situations in which people will make decisions based on something other than morality.

Extrapolation and Universality
You will undoubtedly notice a certain degree of speculation within such a system. This is unavoidable, practically speaking, given the overwhelming numbers of people on the earth; it’s not even remotely feasible that we interview the entirety of the human population, in order to have a truly universal representation of human desires. We must rely on experience and reason to give us a sense of what humans value, and which of these values must/should be considered unimpeachable—life, liberty, property, pursuit of happiness, etc. As we’ve previously established, reason is the only universal language available to us for discussing and analyzing these issues; emotion is not irrelevant, especially when utility and happiness are so closely linked, but the fact that something makes us feel good doesn’t in and of itself make it a universal good in any sense. And there is a need for morality to come from a universally accessible source, because otherwise it becomes meaningless as a system for human behavior. If, say, concepts of morality were bestowed by Hypothetical Supernatural Entity #1, and Hypothetical Supernatural Entity #1 was only perceptible to a certain subset of the population, then the rest of the population couldn’t be fully participating in the system, in the sense that they wouldn’t have any direct access to these “moral values.” Likewise, there is a need for some sort of universal morality in our increasingly global culture; if ever there was a time when different cultures could function with drastically different moral systems without affecting each other, that time is long since gone.

To What End?
The end result of this sort of moral reasoning (post-conventional, under Kohlberg’s very useful rubric, which I expect I’ll discuss again at some future point) is less clear than the merits and methods of the process itself. The only coherent theory of morality, it seems to me, is one which falls under the heading of a social contract, given the lack of justification for drawing moral values from external (non-human) sources. We identify, by careful reasoning, certain values which we all implicitly agree to live by, in order that we may enjoy the advantages of civilization over a more animalistic, survival of the fittest system. The logistics of this are troublesome, as is determining the ideal relationship of morality and law, but the point is that we must embrace a rational definition of morality, wherein we recognize that moral frameworks exist only insofar as we create them and impose them on ourselves and, by extension, on others. It should also be recognized that morality is not, from a broad perspective, a necessity; rather, it is a particularly useful system we’ve concocted to keep from killing and raping and stealing from each other (which is to say: to keep from being killed or raped or stolen from). The sooner we recognize the necessarily rational nature of moral judgments and stop trying to assign some absolute “moral” status to random beliefs and prejudices, the more just and pleasant our world will become, and the less we will abridge the fundamental rights of others.
Urizen

Sunday, December 23, 2012

N.A. Vasiliev's "Imaginary" Experimental Modal Logic...

Evolutionary Thinking in Past Scientific Theories: A Logical Analysis by Antonino Drago, Dept. Phys. Sci., Univ. “Federico II”, Naples, Italy
Abstractions lead us to shape ideas, about which our minds argue by means of logic. An evolutionary thinking occurs when these ideas are not linked together by means of mechanistic deductions, but in a creative way. In this sense evolutionary thinking pushes us to shape a broader kind of logic. The phenomenon of a double negated statement whose corresponding positive statement is lacking of scientific evidence (=DNS) will be examined. It represents a failure of the double negation law; this law constitutes the borderline between classical logic and, broadly speaking, non-classical logic (in particular, intuitionistic logic). In fact, several scientific theories born in past times include in an essential way DNSs. In particular, quantum logic can be represented by means of DNSs inside intuitionistic logic. When DNSs pertain in an essential way to a theory, no more – as a comparative analysis upon the several instances shows – a deductive organization of the theory is possible; rather, the theory puts an universal problem by means of a DNS, then some double negated methodological principles (e.g.: “It is impossible a motion without an end”) follow in order to achieve a new scientific method, capable to solve the problem at issue. This arguing evolves through a cyclic pattern, according to the synthetic method as it was improved by L. Carnot. The crucial step in this pattern is an ad absurdum theorem (likely as in thermodynamics S. Carnot’s theorem is). This theorem reaches evidence for a possible conclusion, still enunciated by means of a DNS. Then by a move like Markoff principle this DNS is changed in a positive statement; it can now be put as a new hypothesis from which to develop a full deductive system. This move is illustrated at best in Lobachevsky’s – maybe first – presentation of a non-Euclidean geometry, but can be recognised also in S. Carnot’s thermodynamics, Avogadro’s atomic theory, Einstein’s founding special relativity. This pattern of arguing is examined by means of paraconsistent logic. In correspondence to the use by theoretical scientific research, of respectively paraconsistent logic, intuitionistic logic and classical logic about statements which are potentially principles for a theory, three kinds of principles are recognized; i.e., a guess, a methodological principle, an axiom-principle. These differences are expressed in a lucid way by Einstein again in his celebrated paper on special relativity: “We will raise the conjecture (the substance of which will be hereafter called the “[axiom-]principle of relativity”) to the state of a [methodological] postulate”

LINK:
In a previous paper I obtained a relevant result regarding paraconsistent logic. The

founder of paraconsistent logic, N.A. Vasiliev, stated as a characteristic feature of his logic,

three kinds of sentence, i.e., "S is A", "S is not A", "S is and is not A" ("indifferent judgment"). I was able to show that they hold true even when one substitutes "¬¬A" for "S" and "-->" for "is". One obtains respectively: "¬¬A-->A ", "¬¬A fails to -->A", "¬¬A-->A and ¬¬A fails to -->A".(substitute necessity [box] for --> everywhere)

Let us remark that the three cases represent three different roles played (in) a sentence in an

argument.

i) ¬¬A-->A represents as an affirmative sentence, i.e. a sentence well-supported by

scientific evidence;

ii) ¬¬A fails to -->A represents a logical problem, i.e., it can represent a sentence still

insufficiently supported by scientific evidence;

iii) ¬¬A-->A and ¬¬A fails to -->A represents a sentence whose truth and falsity is not yet decided in scientific terms; this kind of sentence may be considered inside a theoretical

framework as a guess, whose scientific qualification it is still yet to be decided. The last kind of sentence qualifies the characteristic sentence of paraconsistent logic as pertaining to a theory in construction. Antonino Drago

 

Imaginary(meaning sheet of assertions in imagination) Experimental Modal Logic:

¬¬A-->A(classical linear deduction)

¬¬A fails to -->A(non-classical/non-linear induction)

¬¬A-->A and ¬¬A fails to -->A(non-classical/non-linear abduction, hypothesis, theory)Antonino Drago on N.A. Vasiliev(my additions in italics)

 

Infinity__ Where all doubts are allowed…

Let us consider Lobachevskii's geometry. By substituting "two straight lines meet" for A

and "It is not true that two straight lines do not meet" for ¬¬A, i.e. Vasiliev's S, the three

Vasiliev's above sentences describe respectively

i) ¬¬A-->A, i.e. the hyperbolic secant lines,

ii) ¬¬A fails to-->A, i.e. the hyperbolic ultra-parallel lines and,

iii) ¬¬A-->A and ¬¬A fails to -->A, i.e. the parallel lines - which meet at a point which is located at infinity, i.e. where all doubts are allowed. This last meaning is presented by

Lobachevskii himself in his most relevant writing; there, Lobachevskii refers to the meeting

point at infinity by means of the following words: "In the uncertainty...", just the meaning of

Vasiliev's third kind of sentence. That vindicates Vasiliev's reiterated claim, i.e. his logic
represents just the logic of Lobachevskii's geometrical theory.

"Handle two sorts of negations (logical and ontological)"; as paraconsistent logic does.

 

Conclusions

The three main kinds of logic correspond to three characteristic ways of organizing a set

of scientific data in a systematic way. Paraconsistent logic is a relevant logic since it represents

the logic of the work of a scientist in his guessing new hypotheses for a given set of scientific

data.

I would add that the above exploration of the different roles played by the three kinds of logic has introduced us to a new kind of study, which can be called experimental logic; it is based upon evidence coming from the characteristic features of past scientific theories rather

than the characteristic features of natural languages. Antonino  Drago
Vasiliev affirmed, only ''positive'' sensations are possible, by which we can distinguish only contrary qualities. This is the basis of qualitatively different types of judgments - affirmative and negative. If one imagines a world in which not only positive but negative sensations are possible, then such a world will indeed require a different logic, and the introduction of supplementary qualitative judgments…