Studies in Computational Intelligence 991 Enric Trillas Settimo Termini Marco Elio Tabacchi Reasoning and Language at Work A Critical Essay Studies in Computational Intelligence Volume 991 Series Editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland The series “Studies in Computational Intelligence” (SCI) publishes new developments and advances in the various areas of computational intelligence—quickly and with a high quality The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution, which enable both wide and rapid dissemination of research output Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago All books published in the series are submitted for consideration in Web of Science More information about this series at https://link.springer.com/bookseries/7092 Enric Trillas · Settimo Termini · Marco Elio Tabacchi Reasoning and Language at Work A Critical Essay Enric Trillas Accademia Nazionale di Scienze Lettere e Arti di Palermo Palermo, Italy Settimo Termini Accademia Nazionale di Scienze Lettere e Arti di Palermo Palermo, Italy Marco Elio Tabacchi Dipartimento di Matematica e Informatica Università degli Studi di Palermo Palermo, Italy ISSN 1860-949X ISSN 1860-9503 (electronic) Studies in Computational Intelligence ISBN 978-3-030-86087-5 ISBN 978-3-030-86088-2 (eBook) https://doi.org/10.1007/978-3-030-86088-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Dedicated to the memory of Professors Luis A Santaló (1911–2001) and Abe Mamdani (1942–2010) Series Editor’s Foreword This insightful book—maybe short in size but big in ideas, and deep explanations and inspirations concerning relevant aspects and relations—is concerned with many issues that are crucial for the human cognition, thinking, and acting, and also related issues that are also crucial for some artificial systems mimicking the humans exemplified by multi-agent systems, and also artificial intelligence-based (AI) systems that take science and technology by storm Briefly speaking, the authors deal with fundamental aspects of, first, reasoning which is the key element of all kinds of systems, both human-centric and artificial, that are meant for broadly perceived problem solving, notably decision making In such systems, we have some premises, for instance some evidence and judgments, and we have to find conclusions which can then possibly be employed for some purposeful activities like to find some best option from available or feasible ones Second, since natural language is the only fully natural means of articulation and communication for the human being, the authors consider natural language, in particular methods, to represent and then handle its syntax and semantics What differentiates this book from similar treatises on similar topics is that the authors, first, consider these above-mentioned topics in a broadly perceived logical framework Second, to adequately represent an inherent imprecision in the meaning of linguistic terms and relations, expressed by the humans in the form natural language, they explicitly refer to the pioneering works by the late Lotfi A Zadeh on the concept of a fuzzy set, then fuzzy logic, and finally computing with words, sometimes called computing with words and perceptions Moreover, the book contains extremely valuable references to many concepts and problems considered in various classical and extended logics, often using different languages and motivations More specifically, the authors provide an extremely valuable and insightful exposition of, first, some basic more general types of reasoning, that is, deductive, inductive, and abductive However, they also refer the reader to various non-standard types of reasoning, notably those that have recently appeared, for instance in relations to multivalued, uncertain, temporal, etc., logics As examples, one can cite here defeasible, paraconsistent, probabilistic, or statistical reasoning, to just name a few Particular emphasis is put on the broadly perceived approximate reasoning, vii viii Series Editor’s Foreword and the role of fuzzy sets and fuzzy logic has been underlined The authors go even deeper and discuss commonsense reasoning, notably expressed by using elements of the fuzzy logic-based paradigm of computing with words, the inclusion of which can be decisive for the development and implementation of all kinds of artificial intelligence-based (AI) systems To summarize, the book is a remarkable source of information, explanations, and inspirations which may be a basic reference for all readers, both novice and advanced, interested in an insightful and inspiring exposition of the topics covered, notably logics, reasoning, fuzzy logic, natural language, computing with words, commonsense language, and related topics It is highly recommendable! Warsaw, Poland May 2021 Janusz Kacprzyk Preface Wege nicht Werke (Martin Heidegger) What follows is not a proper text on fuzzy logic, the basic field of research which has seen the now retired first two authors active for around 50 years, and the third for over twenty Instead, it is but a booklet containing a collection of reflections that fly further from fuzzy logic by continuing where some previous papers by the three authors have left Such reflections are a tentative way to show that fuzzy logic is not only fertile due to its being relevant in many technologic fields Indeed, it is also as a facilitator for building reflections on thinking, language, reasoning, and its mechanization, in a way that intermingles both ‘scientific’ and ‘philosophical’ aspects It is something that, consequently, can be seen as able to generate a new ‘Humanistic Culture’ for the twenty-first century, not too far from what prevailed along the seventeenth-century century’s European Enlightening, and including science, as today nobody can doubt it is a relevant part of culture A possible, innovative field of debate this booklet presents, especially, to the young scientists and philosophers A general consensus in the community exists that the good scientists begin reasoning on a delimitated subject, of which some previous knowledge exists, looking at first for questions that are new as well as good, and subsequently find adequate answers Such answers are even more satisfactory when their fertility expands to fields different from the one in which the problem was initially posed The goodness of a question and its fertility are obviously linked One could also say that, perhaps, the evaluation of a satisfactory judgment cannot but be retrospective: A question ‘was’ a good one if the obtained answers are subsequently demonstrated to be fertile Just to exemplify, let us recall the questions asked by Einstein on motion, those of Kekulé on the Benzene’s molecule, and Cajal’s ones on the nervous cell Their answers did all have a noteworthy import in other fields: For instance, Kekulé’s discover is one of the bases on which the German Chemical Industry of Colorants developed ix x Preface Most of the current technology of information and communication, as well as many results of the pharmaceutical industry (but those two cases are not exhaustive), come from fertile answers to science’s good questions Currently, the percentage of GNP devoted to R&D is in direct proportion with the true power of a nation and all developed countries have to with what is called ‘Politics for science,’ or ‘Scientific Politics’ which, frankly, sounds horrible Such more or less obvious considerations are stated here—at the beginning of these pages—keeping in mind some remarks done by Isaac Rabi, Nobel Prize for Physics, and the great geometer and thinker Karl Menger They are also tuned with the spirit informing the book ‘Combining Experimentation and Theory’ which articulates and develops an homage to the late Abe Mamdani, just starting from the relationships existing between the two concepts present in the title [1] We are tempted to state that fruitful new ideas—be they in definitive shape or still in an informal state—can provoke the asking of unusual, vitalizing questions which, when answered, can allow us to see things from a new, different and, in some cases, enlarged perspective ‘Good thinking,’ then, means that it is not enough to ‘think’ and ‘reason’ correctly against an untouchable background of general presuppositions which cannot be questioned, but it also requires, la Nietzsche, systematically, meticulously doubting of what is considered already well known and definitely assessed Submitting thinking to a rigorous control, pushing it outside the borders of the ‘received view,’ must be considered, then, an issue of intellectual hygiene It is just in such sense that this small book is presented as a ‘Critical Essay’, the choice of terms signaling, respectively, that it raises some doubts even if these not always turn into an explicit criticism, and that this is a surface level ‘survey’, with the aim of focusing the attention on some issues more than treating them in detail, and in a relatively contained number of pages It tries to rethink already known topics by looking at them from a point of view that is new as well as naïve, the term used in the same sense in which it characterizes ‘Naïve Set Theory.’ In somewhat a kind of joke, the authors try to ‘shake before drinking’ what they previously believed as well known for what concerns reasoning Notwithstanding, such ‘critical’ approach is not only outward directed against what others express, but as well and mainly inward, against what the authors believe is an acquired knowledge Years and years of debate among the authors have not produced any certainty, but in a serious twist for practitioners of fuzziness, a number of uncertainties It is, partly, due to such uncertainties that the critical approach is not always explicit in this essay Einstein once observed that ‘Science comes from refining the usual thinking,’ underlining both the important continuity between the known and unknown, and where differences reside The same idea underlies the efforts done by deep authors when writing ponderous volumes on known subjects with the didactical intention of 94 14 Looking for Some Historical Roots There are still other important elements which make the status of mathematical entities relative.” And more “A condition sine qua non for being able to operate efficiently with abstract mathematical entities is to experience ("see") them clearly - clar et distinct -, nearly as concrete objects The corresponding state of mind cannot be communicated or completely described And still more: Another, similar element, but on a somewhat higher level, is manifest if we try to use mathematics and logic as tools for the explication of new phenomena; in particular, for an analysis of some basic concepts of mathematics themselves This proves impossible unless we sufficiently clearly “understand” what we are doing Such an understanding, especially if connected with the establishment of a new conceptual base, is usually not the result of a merely deductive or combinatorial manipulation of old concepts, but is simultaneously related to new insights and intuitions - and decisions; The aim of his analysis, although only briefly outlined, is very ambitious and supplies some “proviso” and warnings about the paths to be followed when trying to use mathematics and mathematical methods in completely new domains—especially in the case in which elements of vagueness are substantially present and embodied in the problem, and as such not easily eradicable That, in a sense, is exactly our case 14.8 In our travel back to the past with Dante, Bacon, and Ockham, Jiˇrí Beˇcváˇr meant a step ahead to the present, but there is again another contemporary thinker that influenced us, Ebrahim (Abe) Mamdani, who unfortunately passed away in 2010 and to the memory of whom this book is dedicated Let’s devote a few lines to one of his views Bertrand Russell stated that Pure Mathematics was created by George Boole And without any desire to debate against Russell, what can be added is that Boole, an excellent autodidactic mathematician, did arrive at the then new ‘symbolic mathematics’ through more or less ‘applied’ necessities For instance, the so-called operator D he introduced to solve linear differential equations by means of an algebraic equation, responded to the need of quickly solving such differential equations His later great idea, further called ‘Boolean Algebra’, appeared with the aim of regimenting, or mathematically modeling, the Human Thought It is just at this point that Mamdani said what follows, in the already mentioned book edited in homage to him, ‘Experimentation and Theory’: In fact, that an algebra can be created which, under certain interpretations of its symbols, be shown to capture some aspects of human reasoning must have been quite exciting to George Boole But his ‘Laws of Thought’ did not have the same scientific reality as Newton’s Law of Gravity or Darwin theory of Evolution That shortcoming of mathematical logic needs to be understood to start with Mamdani’s words reinforce the old enlightening empiricist idea that what follows from formal proofs, even of a mathematical character, should be tested against reality That, consequently, the study of the associated Natural Phenomena of Language and Reasoning, for saying nothing on the wider Natural Phenomenon of Thinking, deserve to be considered after cautious, planned and controlled experimentation’s 14 Looking for Some Historical Roots 95 processes, designed by means of some theory supported in the Neurosciences; and that, in view of its mechanization through digital computers, will need of some mathematical model like it is, for instance, that of the Skeleton presented in the previous Chapters Part of the reason why there is—surprising as that can be—a continuity between our actual point of view and the before mentioned Middle Ages perspectives, possibly lies in a lack of variation along time of what Commonsense Reasoning is: the same formal Skeleton that today seems to be valid for it, was valid as well in the 13th, the 14th, and the 17th Centuries There is no substantial difference in how Dante, Bacon and Ockham were reasoning then, and how the authors of this essay reason today What is new are the mathematical models of specialized reasoning, like that of Quantum Physics and those reasoning with imprecise terms All this looking back shown by what precedes is, possibly, a consequence of the authors wishes (perhaps in line with the Saint Francis Pray) of trying to comprehend the others before trying to comprehend themselves In any case, all the cited views coincide in the direction towards the need of a ‘Physics of Language and Ordinary Reasoning’ Let us return to ‘our Franciscans’ Roger Bacon and William of Ockham for a moment, and in the words attributed to the former, “Mathematics is the gate and key to science”, and on those attributed to the latter, “Why bother with nonprime numbers when the primes can everything” Statements that, if we overlook for a moment their authors, could easily pass for the words of a contemporary, or at least a modern thinker Both Bacon and Ockham belong to the Middle Age “Franciscan Line of Thought” that flourished in Great Britain after the incredible work of Robert Grosseteste during the 13th Century; a line of thought that competed intellectually with the theologians and philosophers of Paris, and contributed to the later European Enlightening Grosseteste was an antecedent of Bacon who in turn was an antecedent of Ockham 14.9 Let us conclude this Chapter To look for historical roots usually means to pick up some crucial points of the development of a certain discipline (or sector of study) as well as some relevant forerunners (usually, not too distant in time) In the present case what is in question is—in a certain sense—a rethinking of a research program which has evolved along more than 50 years of continuing investigation on fuzzy sets and Fuzzy Logic This rethinking has shown that interesting and challenging paths can be followed—which can be very similar to the original spirit of 50 years ago—outside the mainstream which has become a sort of new orthodoxy An orthodoxy in the presence of which the authors openly declare their heterodoxy; if the former mainly looks at possible and often dubious applications, the latter just attests—in line with K.G Jacobi—the honor of the human genus It is worth recalling that even if Abe Mamdani—who actually introduced Fuzzy Control—repeatedly stated that the success of ‘Fuzzy Control’ can’t serve as a justification for Fuzzy Logic, it is nevertheless obvious that such branch of applications shows that some of the questions initially posed by Zadeh proved to be ‘good questions’: the answers that were found for them were ‘fertile’ in not initially provided 96 14 Looking for Some Historical Roots fields Fertile up to the extreme that in many books and papers devoted to the learning of Fuzzy Logic, and after presenting the basics of Fuzzy Control, the question: ‘Can Machines think?’ appears So, this is an attempt at analyzing some aspects of “language in action”, in the hope of taming and regimenting it through an initial, simple mathematical model, subject to a strong empirical verification to be done We implicitly asked ourselves what could be the background epistemological attitudes that could help in carrying out such program In a sense, it is not strange that in order to grasp useful indications we went back to the historical period before the general, shared indications of the Century of scientific revolution: the 17th Century, with the great contributions due not only to Galileo and other scientific giants but also to the other Bacon, Francis, the Lord Chancellor Their epistemological considerations were devised and developed when the time was ripe for the turn synthesized by the triad “Copernicus-Galileo-Newton”; a time in which reasoning did need to become more and more specialized But some more elementary questions, in an unknown land, were asked by people living three centuries before And they developed an epistemology that was "good” for that stage of development It is not strange that the contemporary connections quoted above have to with deep thinkers outside the mainstream References P Feyerabend, Against Method, 4th Ed Verso Books (New York, 2010) R Bacon, Opus Maius (Oxford University Press, 1928) S Termini, Aspects of vagueness and some epistemological problems related to their formalization, in Aspects of Vagueness (Springer, Dordrecht, 1984a), p 218 S Termini, Aspects of vagueness and some epistemological problems related to their formalization, in Aspects of Vagueness (Springer, Dordrecht, 1984b), p 224 M E Tabacchi, Fuzziness: came for the view, stayed for the same, in Fuzziness: came for the view, stayed for the same, eds R Seising, E Trillas, C Moraga, S Termini (Springer, 2013) pp 660–661 Trillas, Enric and Mamdami, Abe: Correspondence between an Experimentalist and a Theoretician In Combining Experimentation and Theory: A Hommage to Abe Mamdani edited by Enric Trillas, Piero P Bonissone, Luis Magdalena, Janusz Kacprzyk Springer, 2012 G Gerla, Vagueness and formal fuzzy logic: some criticisms Logic and Logical Philosophy, 26(4), 431–460 (2017) J Beˇcváˇr, Notes on Vagueness and Mathematics, in Aspects of Vagueness, eds H.J Skala, S Termini, E Trillas (Kluwer Academic Publishers, 1984), 1–11 Joseph Kupfer, “The father of empiricism: Roger not Francis”, Vivarium, XII, (1974) pages 52– 62 The End: General Conclusions As complexity rises, precise statements lose meaning and meaningful statements lose precision (Lotfi A Zadeh) I It is unusual—and could also appear a little bit presumptuous—the desire to communicate, in the book’s final pages, what have been some general points characterizing the dialogue among the authors ‘Presumptuous’ one could say since there is no reason for which the reader should be interested in knowing such personal considerations The question, however, is different since we not want to dwell on personal remnants We want to clarify these ‘general points’ since they have floated in the background of these pages being neither their bulk nor content The chosen topics and tools are clear, and we synthetically recall them again A little bit of (deliberately) simple mathematics used to model something (language and reasoning) caught in its most immediate form And stressing the necessity of doing some direct experimentation for a subsequent refinement of hypotheses and results, without forgetting the words of William of Ockham: “Whenever two hypotheses cover the facts, use the simpler of them” For what regards the content, the fruit of our efforts is now in the hands of the readers, and theirs are both the right and the duty to judge the results, as it is implicitly part of the pact between writers and readers We limit ourselves to say that we think such hypotheses and results are very limited and circumscribed but, perhaps, are ‘new’ in a general sense; or at least show a line of thought previously unforeseen We really hope that someone will strongly criticize them; this would say that our point of view has been seriously taken into some form of consideration © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 E Trillas et al., Reasoning and Language at Work, Studies in Computational Intelligence 991, https://doi.org/10.1007/978-3-030-86088-2 97 98 The End: General Conclusions II But why did we embark ourselves in a project characterized by the choices mentioned above and which is far from be completed? Too ‘minimalistic’ one could say, and outside the tradition of both logic and language studies Moreover, considerations of (and on) old thinkers are mixed with more or less technical pages and with the position of contemporary scientists An uncommon mix Perhaps an attempt to exit from the classical scientific tradition? What was the hidden motivation? Was there a ‘method’ in the folly that guided us in following this path? The path that led us first to converge on the project and, immediately after, to focus on what, but only improperly, can be called ‘method’ was, in fact, tortuous We can say two things: first, this is not a ‘methodology’ in the usual sense of the word; second, our way of doing and proceed wants to strictly remain in the scientific tradition, the one of the ‘Enlightenment’ we dare to say, but in the minimal (and crucial) sense expressed by Immanuel Kant when he wrote that this word means, mainly, ‘the exit of man from the state of minority’ III What we not share are many interpretations, prevailing in the bulk of some political establishments, often the ones guiding the scientific research, which tend to carry on the legacy of the Enlightenment (and also of modernity, and scientific revolution) in a standardized, mechanical way As if there exists an immutable set of rules which scientists should apply to the solution of any problem, in order to appear ‘scientific’ and ‘modern’ or ‘contemporary’ Our dissatisfaction with this almost frozen, bureaucratic and not at all creative vision of scientific progress led us to also focus our attention on old approaches, on neglected thinkers that tried to see problems in a fresh way, following Kant’s recommendation We hope to transmit these feelings also to the reader by adding that bureaucracy is like an antidote for creativity, one antonym of which is mediocrity; if creativity is, in the words of Albert Einstein, contagious, also mediocrity is so and with the intellectual danger of its easiness We humbly beg our possible if improbable young readers to escape from the evils of bureaucracy, mediocrity and endogamy, joint causes of most of the bad illnesses affecting research today These pages, in fact—referring to the motto preceding the foreword—are not a ‘work’ but only a few ‘steps in a path’ we invite to follow We, then, cannot but wish a good meandering to our twenty-five readers,1 and remembering them that almost all ‘scientific results’ have, like yoghourt, an expiration date, that may or may not The number 25 is brought (better, ‘stolen’) from the first Chapter of the novel “The Betrothed” by Alessandro Manzoni In this novel the author, periodically, interrupts the narration, turning to the reader And the first time he does this, he declares to have 25 readers The End: General Conclusions 99 be known in advance Jointly with the different motto preceding this last chapter, this should help to curb the, seldom deserved, excessive pride of the authors IV Let us conclude by focusing on a word that appeared many times in this essay, ‘reality’ It tries to baptize, give name, to a basic concept for the empiricists: The ground on which all is and always happens, and whose actual existence, its own ‘reality’, is but a hypothesis For instance, people see what surrounds them in all the colors of the rainbow, but what is seen is related to the sensibility of the human eyes to light wavelengths (a specific range) Dogs see the same surroundings but only in black and white; what for a person is his/her garden, does not coincide with what the same garden is for his/her dog: a mixture of looks, smells, tastes, sounds, and touches, all from a short distance from the ground Even if avoiding cultural aspects, my concept of my garden, its reality for me, does not coincide with the reality it has for my dog We see and conceptualize the physical world as our senses allow us to do, and it is uniform for almost all people For instance, a person suffering of colorblindness will not see the same colors than a non-colorblind; the world’s percentage of colorblind people is 8% among man, and 0.5% among woman: they are a reduced minority whose views not influence the majority of people that consider colorblindness as a kind of illness, a lack of vision It should be pointed out, that humans amplified their own senses by means of artifacts build up exactly with this scope, such as glasses, magnifying glasses, telescopes, microscopes, headsets, radio-telescopes, etc The coexistence of ‘Homo Faber’ and ‘Homo Sapiens’ from the very beginning, permits a lot of things that our most close relatives in the animal world, like are some apes, can’t have, build, do, or ‘know’ The human possibilities of thinking, speaking, telling and guessing, finally leading to building up some complex artifacts and to computing, as well as highlighting its intrinsic limitations, make of ‘Homo Sapiens Sapiens’ a very special mammal with self-conscience, the own perception of being a person, word coming from the Latin persona, whose meaning was ‘an actor’s mask’ Actually, people are conscious of masking, as they hide in themselves many thoughts Analogously, people talk on things by wrapping them into meaning, and, in fact, scientific theories or even philosophical thinking serve to give meaning to what is in the physical world, and also to what is virtual The same is done—independently from personal beliefs—to what is considered transcendent In the same way in which a distinction is done between ‘natura naturans’ and ‘natura naturata’, let’s remark the obvious thing that reality is always a ‘thought reality’ or, better, ‘thought’ on the basis of what we can observe; on the basis not only of our experimentations and the advancing of our technologies but, also, on the structure of our (cerebral) morphological structures and the features of our thoughts, 100 The End: General Conclusions in whatever way we interpret, now, this concept and will be able to in the future, presumably in new, different ways A very Kantian theme, indeed We are not trying to enter surreptitiously in these very difficult themes Whether ‘true reality’ (the ‘noumenon?) can be, before or later, attained is not a question within the reach of any whatsoever reflection we can But we can observe the fine experimentations done thanks to such complex machines as the Great Colliders at the CERN What they show is that the “presumed reality” is not static but dynamic The confirmation of what was previously theoretically forecasted is searched together with a complete openness towards the appearance of new things that can change what was thought before In the words attributed to Roger Bacon, “To ask the proper question is half of knowing” V So, along this path, ‘progress’ is reached not only by successive refinements inside an everlasting, general scheme: this same scheme must be changed and modified In this sense the progress is not always linear and cumulative as the ‘scientific turns’ of last Century have shown The process of changes and modifications of the background will not, presumably, reach a final stage The problem of the existence of a presumed Aristotle’s ‘Hypokeimenon’, a world’s underlying and fixed ‘subjectum’, a true reality ending all speculations on perceived realities, should be left open for the future One can imagine that more advanced knowledge of the human brain’s inner working, today pursued by the neuroscientists in such endeavor as the ‘Brain Project’, will certainly suggest new paths to be followed also in relation to the themes treated in this Essay Using the title of the memories of the late Sir Karl R Popper, true scientific research is but an ‘un-ended quest’ A quest that must go on along different lines looking for a continuous interaction and dialogue among them Continuously thinking on Ordinary Reasoning, on Language at Work, can contribute to this endless dialogue, especially if the scientists working on it are true researchers and not just professors In the line indicated by the words of the great mathematician and former leader of Integral Geometry, L A Santaló (1911–2001), to whom this booklet is also dedicated, “those that occasionally not publish a new result, can be professors but they are not actual mathematicians” Besides sharing Santaló’s distinction between true researchers and just professors, we want to pinpoint another aspect: the way in which scientific investigation is (and can be) done We are, presently in a situation where, up to a certain degree, research is increasingly becoming an entrepreneurial activity University researchers are increasingly dependent on funding coming from companies or, anyway, related to specific applications; even Governments Policies on Science encourage this behavior It is convenient, at this respect, to underline how relevant it is that researchers continue to have The End: General Conclusions 101 a strong connection with high level teaching, according to von Humboldt’s vision of the University which has produced so many extraordinary results They should continue to truly supervise Ph.D candidates along the perspective of a free investigation Usually, close contact with students can encourage researchers to refrain from copying some bad behavior and unethical habits merely considering the “honor of mankind” An example of this type of problem is shown by the current debates on the use of “Data’s Language” for the implementation of new algorithms used directly or indirectly to evaluate people As is commonly known today, this can produce flagrant injustices against human rights VI One must disagree with the tendency prevailing today, also from another point of view Not for defending an “ivory tower” attitude or for considering unimportant economic and productive issues Exactly for the opposite reason Science is both engine and fuel for the true and long lasting innovations along all the chain leading to the production of goods present in everyday life However, in order for this to happen and continue to happen, it is first of all necessary to respect a fair division of tasks and respect for the methodologies of each sector of human activity On what are the best ways for this to happen we have many indications that come from a quick glance at our past Without bothering Galilei or Bacon (Francis, this time, the Lord Chancellor, not Roger)—although a quick glance at the visionary planning of the latter as well as of the way in which the former connected technological innovations and advances in pure research could be extremely useful—the main example is provided by the great project that come out from the interaction between Vannevar Bush and the US President Franklin Delano Roosevelt to make permanent, in peacetime, the great technological leap made by the USA in wartime due to the intense dialogue that took place with the scientific community The project was subsequently presented by Bush to Harry Truman, successor of Roosevelt who, suddenly, died on April 1945 Despite the fact that the most innovative aspects of the Bush project have not been implemented, this paradigm shift has helped to allow the United States to play a role of absolute primacy in the world for over fifty years The idea was that Science with its endless frontier (words taken from the title of the Report) could be the key tool In fact, he writes: One of the peculiarities of basic science is the variety of paths which lead to productive advance … Today, it is truer than ever that basic research is the pacemaker of technological progress … A nation which depends upon others for its new basic scientific knowledge will be slow in its industrial progress and weak in its competitive position in world trade, regardless of its mechanical skill Of course, such strategy can, as any other do, harbor potential dangers For instance, that of ‘secrecy’: to hide some results or possible results to protect one 102 The End: General Conclusions against the other It is an attitude that is contrary to Jacobi’s “honor of the human genus”; a sin which the authors of this essay firmly want to avoid, by openly offering their thoughts—thoughts they firmly believe in Let’s come back to our favorite theme As has been repeated throughout this essay, reasoning and language are intertwined; but reasoning is more than language, it is not just speaking Not everything in language is necessary in every reasoning It should not be forgotten that, as Bertrand Russell observed in the early twentieth century, mathematics only needs mastering a limited collection of words, but life requires all words At this point, it is worth mentioning what Nobel laureate Sir Peter H Medawar wrote in his book “The Limits of Science” (Harper and Row 1984): No process of logical reasoning can enlarge the informational content of the axioms and premises or observational statements from which it [Science] proceeds An objection that every ‘theoretician’ has, in different forms, heard from his colleagues ‘experimentalists’ and to which a satisfactory answer is due To actually expand the initial information, to arrive at something truly new, the deduction is insufficient and speculation, the inferential zigzag, acquires all its relevance Without observational assertions and inductions, as well as without formal and abstract concepts and deductions, progress in the knowledge of the physical world by Galileo, Newton and Einstein would not have been achieved and similar results will not be achieved in any field: It can’t be forgot by those pursuing the goal of constructing machines that can properly think, and not only deductive reasoning For the reaching of such goal, building computers endowed with the capacity of ‘zigzagging autonomously’, by themselves, around a known factual statement could be a starting point VII Concerning which parts of science are connected with the topics of this Essay, let us observe that if internally is Neuroscience, externally is Computation If the first can be a support, the second can be supported by what is presented here Probably it is this second contact that can be closer in time Now that we are concluding this common journey and parting our ways, let us borrow Alessandro Manzoni’s famous ending: Ai posteri l’ardua sentenza Afterword Our reasoning is a part of our thinking With reasoning, our thinking can move from one idea to a related idea Through reasoning, we reach decisions In order to share our thoughts with others, that is, to be able to transmit them, and in order to be able to receive the thoughts of others, in short, to communicate, we have to transform our thoughts into symbol structures that are part of a system we call language Our languages have evolved naturally; humankind has developed many different languages in different places and in different cultures They not only consist of different elements, symbols, words, sentences, they also differ structurally Languages cannot be translated one-to-one and the individual elements are not unique Communicating linguistic information requires intelligent behavior because we need to choose the correct symbols from a plethora of possibilities and then “send” these symbols, assembled into messages In order for our messages to be (a) correctly transmitted, (b) correctly understood, and (c) to have the desired effect, the symbols forming them must be well chosen Claude Shannon addressed the first of these problems in his "Mathematical Theory of Communication” (1948) [1], claiming that “The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point” [2] Obviously, he conceived of communication purely as the transmission of messages—completely detached from the meaning of the symbols However, we humans are not machines When we communicate, we associate meanings and intentions with the transmission of signs or messages Fundamental problems of communication besides (a) the technical problem highlighted by Shannon are therefore also (b) the semantic and (c) the pragmatic problems of information transmission In an essay explaining and extending Shannon’s theory, Warren Weaver considered these latter two problems as absolutely central to any genuine information theory [3] Will the receiver also grasp the meaning meant by the sender with the symbols received from the sender? Will the information transmission also achieve the desired intentions? © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 E Trillas et al., Reasoning and Language at Work, Studies in Computational Intelligence 991, https://doi.org/10.1007/978-3-030-86088-2 103 104 Afterword A general information theory therefore needs to offer solutions not only to the technical problems, but also to the semantic and pragmatic ones This demand is self-evident when it comes to the communication of information between people, because people want to share not only data or messages but also information and thus meanings and intentions Since the advent of digital computers and the socalled Artificial Intelligence research programs became established, questions have been raised about whether computers can be intelligent and whether they can think In that context, Alan Turing proposed an imitation game In this game, a human decides whether she has communicated with another human or a machine based on the answers she receives to her questions A machine would succeed in deceiving a human being in this game if the human thought she had communicated with a fellow human being and not with a machine In that case, Turing said, the machine could be called a “thinking machine” because it had successfully imitated human intelligent behavior Of course, he knew that calculating and processing symbols— these abilities were attributed to computers at that time—and thinking—this ability had been attributed to humans only—represent different activities, but he seemed to have ignored this Turing did not want to make any essential distinction between thinking and the imitation of thinking In fact, he assumed that by the end of the twentieth century the use of words and the connotations would have changed in such a way that one would then speak of “thinking machines” as a matter of course [4] This prophecy has not yet come true, and today, we still not consider machines capable of thinking However, many people think that in the future machines will be able to think! The vision of thinking machines survived Turing, who died in 1954, and it persists to this day Turing himself could not experience the developments of Artificial Intelligence research in the USA, the birth of which is often said to have been the 1956 “Summer Research Project on Artificial Intelligence” organized by John McCarthy, Marvin Minsky, Nathaniel Rochester, and Claude Shannon at Dartmouth College in Hanover, New Hampshire [5] Turing could not have known about the “Logic Theorist” written by programmer John Clifford Shaw based on a draft by Herbert Simon and Alan Newell either [6]: a first theorem prover for mathematical theorems as stated and proved in Bertrand Russel and Alfred North Whitehead’s “Principia Mathematica” [7] Simon and Newell presented it at the Dartmouth Summer School Its function, like their later program “General Problem Solver” , was based on the manipulation of data structures built from symbols and relations Minsky and Rochester then developed the idea for a proof program of geometric theorems, which Herbert Gelernter and Carl Gerberich realized [10] On McCarthy’s advice, they extended the computer language Fortran with some list operations to FLPL (Fortran List Processing Language), inspiring McCarthy and Rochester to construct LISP as a more powerful “list processing” language two years later [11] Neither could Turing see the publication of the volume “Automata Studies” in 1956 by Shannon and McCarthy [12] To this volume, psychiatrist William Ross Ashby contributed the essay “Design for an Intelligence-Amplifier”—incidentally, this is the only contribution of the volume with the word “intelligence” [13] As the Times wrote See [8, 9] Afterword 105 in its May 7, 1956 issue, “Dr W Ross Ashby of Britain, a mathematically minded psychiatrist, believes that such machines can at least “amplify” human intelligence just as the engine of a bulldozer amplifies the muscle power of the man who controls it.” They quoted from Ashby’s contribution in “Automata Studies” to explain, “how an intelligence amplifier might be constructed «It has often been remarked,» he says, «that any random sequence, if long enough, will contain all the answers.» So a machine for solving problems too complex for the human brain should contain a mechanism that presents for consideration all the possible solutions The machine’s job will be to select the right one when it comes along It will the job by a kind of testing system One part of the machine is adjusted in such a way that it “has a veto” over any proposed solution that does not check It says no, no, no, perhaps a billion times no At last the right set of answers comes along The critical part of the machine is satisfied It signals its O.K., and the whole machine stops, displaying the right answers winnowed out of a billion wrong ones.”3 In his “Introduction to Cybernetics” also in 1956 Ashby referred to the so-called intelligence tests of that time, writing: “It is also clear that many of the tests used for measuring «intelligence» are scored essentially according to the candidate’s power of appropriate selection Thus, one test shows the child a common object and asks its name: out of all words the child must select the proper one Another test asks the child how it would find a ball in a field: out of all the possible paths, the child must select one of the suitable few Thus, it is not impossible that what is commonly referred to as “intellectual power” may be equivalent to “power of appropriate selection” Indeed, if a talking Black Box were to show high power of appropriate selection in such matters—so that, when given difficult problems it persistently gave correct answers—we could hardly deny that it was showing the behavioral equivalent of ‘high intelligence’” [15] With Weaver’s additions to Shannon’s theory, we can therefore conclude that an intelligent being performs this selection process at all three levels of information transmission: addressing syntax, semantics, and pragmatics Intelligent communication means selecting a message from a pool of the many possible messages, selecting the correct meaning from the set of all possible meanings of that message, and selecting the intended meaning from all possible associated intentions In the context of signal transmission, Lotfi A Zadeh described an interesting mathematical problem in a 1952 lecture for the Section on Mathematics and Technology of the New York Academy of Sciences Referring to Shannon’s communication theory, Zadeh said, If a signal coming from the sender is transmitted over a possibly disturbed channel, the signal received at the receiver may differ from the transmitted signal However, it can be recovered under certain conditions Zadeh described this process mathematically: Signals were represented as ordered pairs of points in a signal space embedded in a function space To measure the difference of the points from each other, he provided the space with a distance function, which has the properties of a metric To recover the originally transmitted signal, the receiver evaluates the “distance” calculated between the received signal and all possible transmitted signals using a suitable distance function It then selects the signal that is “closest” to the See [14] 106 Afterword received signal with respect to this distance function In other words, the signal that has the smallest distance value from the originally transmitted signal is transmitted [16] After reflecting on this problem Zadeh conceded that “in many practical situations it is inconvenient, or even impossible, to define a quantitative measure, such as a distance function, of the disparity between two signals In such cases we may use instead the concept of neighborhood, which is basic to the theory of topological spaces” [17] This problem was one of the problems that initiated Zadeh’s thoughts about not precisely specified quantitative measures, i.e cloudy or fuzzy quantities About 13 years later, he proposed his new ‘concept of neighborhood’, which became the basis of the theory of fuzzy sets and systems [18] While some computer scientists began trying to translate human thinking into computer-friendly languages to realize communication between humans and machines, others were pondering ways to make a computer’s computation, deduction, and behavior more like a human’s Building machines that could think and learn like humans was specifically formulated as a goal of AI research “Creating Computers to Think like Humans” was the title of the December 7, 1980 New York Times Magazine cover story, and a portrait of Minsky completely filled the magazine’s cover page [19] Zadeh used an almost identical title for his paper in the IEEE Spectrum in August 1984, “Making Computers Think Like People” [20] To achieve this goal he brought into play his mathematical theory of fuzzy sets: He intended to account for the fuzziness of human languages, which could be modeled with fuzzy sets by means of the “linguistic variables” introduced in 1968 Zadeh argued explicitly for programming languages that are—because of missing rigidness and preciseness and because of their fuzziness—more like natural languages.4 Fuzzy languages are fuzzy sets over a set of finite strings Their membership functions assign to each finite string its membership degree as an element of this fuzzy language The values attributed by a membership function to various strings as elements of fuzzy languages determine those who use that language This also depends on what meanings these people associate with it in each case In 1971, Zadeh wondered, “Can the fuzziness of meaning be treated quantitatively, at least in principle?”5 To this end, he considered a basic set U, its subsets, and the set T of names of these subsets As the meaning of such a name, say n, of a subset of U he defined then that fuzzy subset of U, whose elements lie in the subset of this name How meaningful the name n is for an element of the basic set U or the subset named n is expressed by the corresponding membership function For example, let U be the basic set of objects visible to us, and then a term set T would be given by the names for colors, “white”, “grey”, “green”, “blue”, “yellow”, “red”, “black” Each of them is the name of a fuzzy subset of the set of objects visible to us Then, Zadeh defined these fuzzy subsets as the meanings of their names For example, “red” is the name of the red elements in the set of objects visible to us and the meaning of “red” is the specified fuzzy subset of red objects See [21, 22] See [23] Afterword 107 Lotfi Zadeh passed away in September of 2017 We miss his reflective talks on ideas related to fuzzy sets and systems, fuzzy logic and precisiated logic, computing with words and the computational theory of perceptions To follow up on such reflections, Enric Trillas, Settimo Termini, Marco Elio Tabacchi, and I introduced the format of the “Saturday Scientific Conversations” (SSC) more than ten years ago Unfortunately, so far these conversations have happened only three times Fig A Enric Trillas, Rudolf Seising, Settimo Termini and Marco Elio Tabacchi after dinner in a street restaurant after a hard day’s work (Photo: Francesca Falconi) The SSC 2010 took place under the heading “Philosophy, Science, Technology and Fuzzy Logic” in Gijon, in the Asturias region of Spain, on May 15, 2010 The European Centre for Soft Computing organized it, and 15 young researchers attended The SSC 2011 was organized in the Palazzo Steri with support of the Università degli Studi di Palermo, on the Italian island Sicily, in May 14, 2011, and 22 young researchers from all over Europe participated This “essay” by Enric Trillas, Settimo Termini and Marco Elio Tabacchi is a renewed attempt to reflect philosophically on scientific activity I am very glad to have been part of some previous attempts and wish this book a lot of success! Rudolf Seising Munich, May 2021 108 Afterword References 10 11 12 13 14 15 16 17 18 19 20 21 22 23 C.E Shannon, The mathematical theory of communication, Bell Syst Tech J 27(3 & 4), 379–423 & 623–656 (1948) C.E Shannon, The mathematical theory of communication, p 379 W Weaver, The mathematics of communication, Sci Am 181, 11–15 (1949) A.M Turing, Computing Machinery and Intelligence, Mind 59, 433–460 J McCarthy, M Minsky, N Rochester, C Shannon, A proposal for the dartmouth summer research project on artificial intelligence http://www-formal.stanford.edu/jmc/history/dar tmouth/dartmouth.html (1955) A Newell, J Shaw, J Clifford, H Simon, Empirical explorations of the logic theory machine: A case study in heuristic, Proceedings of the Western Joint Computer Conference (Los Angeles, California, February 1957), pp 218–230 A.N Whitehead, B Russell, Principia Mathematica, (1 ed.), (Cambridge: Cambridge University Press, 1910), (1 ed.) (Cambridge, Cambridge: 1912) A Newell, J Shaw und H Simon: Report on a general problem-solving program, RAND Corporation P 1584, 30.12 1958 A Newell, H Simon: GPS, a program that simulates human thought, in: E Feigenbaum, J Feldmann, (Eds.): Computers and Thought, McGraw-Hill 1963 H Gelernter, Realization of a geometry theorem-proving machine, Proceedings of the International Conference on Information Processing (Paris, 1959) N Rochester, Symbol Manipulation Language Memo 5, Artificial Intelligence Project (RLE and MIT Computation Center, 20.11.1958) C.E Shannon, J McCarthy (Eds.), Automata Studies (Princeton, New Jersey: University Press, 1956) W.R Ashby, Design for an Intelligence-Amplifier, in Automata Studies, eds C Shannon, J McCarthy, pp 215–233 Time, Monday, May 07, 1956, p 70: Science: Intelligence Amplifier W.R Ashby, An Introduction to Cybernetics, (Chapman & Hall, London, 1956) L.A Zadeh, Some basic problems in communication of information, The New York Academy of Sciences, Series II 14(5), pp 201–204, p 201 (1952) L.A Zadeh, Some basic problems in communication of information, p 202 L.A Zadeh, Fuzzy Sets, in Information and Control 8, pp 338–353 (1965) S William, Creating computers to think like humans (Part of two parts), (New York Times Magazine, December 7, 1980), pp 40–43, pp 182–187 L.A Zadeh, Making computers think like people, in IEEE Spectrum, pp 26–32 (August 1984) L A Zadeh and E T Lee: Fuzzy Languages and their Acceptance by Automata In: Proceedings of the Third Annual Princeton Conference on Information Sciences and Systems, (Papers presented March 27–28, 1969), p 399 L A Zadeh: Fuzzy Languages and their Relation to Human and Machine Intelligence In: M Marois (Ed.): Man and Computer, in: Proceedings of the First International Conference on Man and Computer, Bordeaux, June 22–26, 1970 Basel: S Karger, 1972, pp 130–165, Round Table Discussions, pp 166–178, 1972 L A Zadeh: Similarity Relations and Fuzzy Orderings In: Information Sciences, 3, 1971, pp 177–200; L A Zadeh: Quantitative Fuzzy Semantics In: Information Sciences, 3, 1971, pp 159–176 ... deals with matter and energy, and whose dynamics are essential All in all, if Language and Reasoning are but Natural Phenomena, their study corresponds to, and requires, a Natural Science of Language. .. journal and is on the Editorial board of the ’Lettera Matematica’ journal He also serves as an ambassador at the FMsquare Foundation in Switzerland, and has been a member of the board of the Associazione... Italy, an Associate Researcher at Dipartimento di Matematica e Informatica at Università degli Studi di Palermo, Italy, adjunct at Accademia di Belle Arti di Palermo for etching and litography