Logic is first of all an instinctive art. We all, from an early age, try to ‘sort out’ our experiences and ‘make sense’ of the world around us — and this thought process is to varying degrees ‘logical’. It is logical to the extent that we try to consider the evidence, avoid contradictions, and try to understand. We call this using ‘common sense’.
On a higher level, logic is a science, which developed out of the self-awareness of thinkers. They began to wonder why some thoughts were more credible, forceful, and informative than others, and gradually discerned the patterns of logical intelligence, the apparatus of reasoning. A logic theorist is called a logician. Note that we also call ‘a logic’, any specific field of or approach to logical science.
Logic as a field of inquiry has two goals, then. On a practical level, we want it to provide us with a guide book and exercise manual, which tells us how to think straight and trains us to do so efficiently. On a theoretical level, we seek the assurance that human knowledge does, or can be made to, conform to reality. How these methodological and philosophical tasks are fulfilled, will become apparent as we proceed.
Logic is of value to all individuals, bettering their daily reasoning processes, and thus their efficacy in dealing with their lives, and their work. It teaches you organization, enabling you to arrive at the solution of problems more efficiently. It helps you to formulate more pondered opinions and values.
Be you an artist, a parent, a university professor, a doctor, a psychologist, a civil engineer, an auto-mechanic, a bank manager, an office worker, an investor, a planner, an organizer, a negotiator, a lawmaker, judge or lawyer, a politician or journalist, a systems analyst, a statistician, a computer or robot programmer, whatever your profession or walk of life — you are sure to find the study of logic useful.
It is of value to scientists of all disciplines, helping them to clarify issues and formulate solutions to problems. There is no area of human interest or endeavor where logic does not have a say, and where the study of logic would not be effective in improving our situation.
Logic is worth studying also, for the sheer esthetic joy of it. There is no describing the mind’s response to this beautiful, colorful achievement of the human spirit. I hope the reader will have as much fun reading this book, as I had writing it. It can be hard work, but it is rewarding. My own favorite topic is de-re modality; I find it closer to earth than logical modality.
Logic teaches us to pursue and verify knowledge. It is based on an acknowledgment of the possibility of human error, but also implies our ability to correct errors. Where veracity or falsity is hard to establish, it tells us at least how ‘reasonable’ or ‘forced’ our judgments are.
It is essentially a holistic science, teaching us to take everything into consideration when forming judgments. Truth is not to be found in a limited viewpoint, but through a global perspective, an awareness of all aspects of an issue, all proposed answers to a question.
Logical science shows us what to look for in the course of knowledge acquisition, by listing and clarifying the main forms of relation among things and ideas (whence the name ‘formal logic’). It is the ‘systems analysis’ of human thought.
Logic is concerned with the formalities of reasoning, without so much regard to its subject-matter. It allows for objective assessments of inferential processes, precisely because its principles make minimal references to specific contents of thought. It is emotionally detached, it has no double standards, it is open-minded and fair.
Logic is a tool of interpretation, understanding, and prediction. It is a method for drawing the maximum amount of useful information from new experiences, or enveloped in previous knowledge, so as to fully exploit the lessons of the world of matter and mind, appearing all around us all the time.
What logic does is to help us to take all impressions and intuitions in stride, and resolve any disagreements which may arise. What is sure, is that, in reality, things themselves can never be in contradiction. It is ideas which conflict with each other or with primary experiences. Sometimes it is the idea that there is a conflict which turns out to be wrong.
The job of logicians is, not to reword what is already known, but to uncover and enhance the logical capabilities of everyday language. This is achieved by first singling out any concept which seems to infiltrate all fields of human interest. Often, the colloquial expression relating to it has many meanings; in such case, we make an agreement to use those words in only the selected sense, which is usually their most common connotation. Once all risk of ambiguity or equivocation is set aside, we can develop a clear and rigorous understanding of the logical properties of the concept under consideration.
The so-called logical order of development is satisfying to trained logicians (from the general to the particular, as it were), and has also some didactic value. But it is often the opposite of the way an individual or a researcher normally arrives at knowledge (building up from specific discoveries, then formulating a comprehensive theory); sometimes, replicating the natural order is a more effective teaching method.
Sometimes these two kinds of orders coincide. In the last analysis, they are always to some extent both involved, working in tandem; logical practise is an integral part of logical theorizing.
As for the historical order, it follows the natural order pretty closely, though with some redundancies. Some other consciousness must precede self-consciousness. Logic has developed on both the deductive and inductive sides alternately, and not in a systematic fashion.
The goal of logic is to make the facts and their relations transparent; it teaches us to focus the object until its most firm manifestation is captured. Logic cannot immediately solve all problems, but it always brings us closer to the solutions.
For the individual, this self-discipline is the source of realism and understanding. ‘Think for yourself’, do your own thinking, ‘use your head’, be creative, think things through. The goal is not a mind a-buzz with words, a slave to words; but the inner peace and self-respect of efficacy.
In communication with others, transparency means expressing one’s thoughts clearly, so that, as far as possible at the time, there is no doubt or ambiguity as to just what one is trying to say, and on the basis of what processes. ‘Say what you mean, and mean what you say’. Information is freely and helpfully shared; points or areas of ignorance or error are easily admitted.
This is the idea of ‘glasnost‘, transparency, a mutual respect and openness policy, a cooperative attitude, without unnecessary frictions. Too often, politicians, media, and others, use words to hide or distort, and do not in turn pay attention to input. You may prove something to them incontrovertibly; they remain unfazed, comme si de rien n’était.
Clarity of expression, accuracy of observation and thought, passing knowledge on honestly, reasonableness on all sides, are essential to vibrant democracy and social peace. Logic is a civilized way to resolve disputes.
This means self-criticism, the ability to review one’s own proposals, and anticipate possible objections, and try to deal with them as well as one can. We often gloss over possible problems in our own ideas, hoping no one will spot them; but this wastes one’s time, and everybody else’s. Logic is taking the time to double check one’s projects, shifting them this way and that way, to see how well focused they are in the largest context.
On the other hand, when receiving ideas, one’s should not look at them with an overly-critical eye, at least until one has properly understood them. Like rigid bone, hasty and excessive skepticism can inhibit the growth of knowledge. ‘Stop, look, listen’, hear, consider, make the effort to assimilate it. Learn before you try to teach.
While I am not of the opinion that logic is relative and arbitrary, there is more often than not at least some helpful truth to be found in other people’s concerns. One should not reject offhand, though still reserve one’s judgement. One should neither fool nor be fooled. Be humble, but keep your standards high.
I get some very funny reactions from people at the mention of the word ‘logic’. One should not reject logic offhand, because of a mistaken notion of what it is about.
Logic is not a method of inferring all knowledge from a limited number of abstract premises; it is not a magical tool of omniscience. It depends for its action on moment by moment impressions or intuitions, which in some cases turn out to be unfounded. Nor is logic merely a mechanized manner of pursuing solutions to specific problems.
People often wrongly regard and use logic as a square-headed, narrow-minded activity. But in my opinion, logic is, straight and tough on a level of details, but overall very broad and open minded. Obstinacy and prejudice, are rather attributes of people unwilling to listen to reason, not even to at least consider alternative viewpoints. This is the very antithesis of a logician’s attitude.
People often oppose ‘logic’ to feeling; they believe it discards the emotional side of life. But logic does not mean ignoring feelings, but rather recommends taking the feelings — including their inner meaning, their intuited significance — as one set of data among others in the total picture; rationalistic data must also, however, be given their due weight.
Some people complain that ‘logic’ sometimes leads to evil conclusions. But value-judgments involve inferences from standards. So either the norms are unsound, or they have not been given their due weights in comparison to other norms, or the proposed means are not the exclusive ways to achieve the norms. Thus, the failure involved may precisely be a weakness in logical abilities, rather than any inherent coldness of logic.
Logic is only a tool — it cannot be blamed for errors made in its name, nor can it control the moral choices of individuals who utilize it. Its only possible danger is that the efficacy it endows on thought and action may be used for nefarious ends. But even then, a person who sees things truly clearly, with the broad conception logic gives, is less likely to have twisted values.
Logic is an important component of both mental health and moral responsibility. It requests that we face facts and listen to the voice of reason: this does not exclude having a heart or paying attention to one’s intuition. A person who does not keep in close touch with reality, can easily develop unhealthy emotions and make counter-productive choices. Rationality is a sign of maturity.
Another wrong impression people have of logic is that it is a meaningless manipulation of symbols, or at best a branch of mathematics. One man recently told me the following sad story. He thought of himself as a ‘logical person’, and being inclined to constantly improve his education, he enrolled for a University course on the subject in San Francisco. He was so put off by the lessons he attended, that he now hesitates to call himself ‘logical’!
This is a book on logic, a formal and detailed study.
I called it ‘Future Logic’ to dedicate it to the future, to suggest its potential for improvement of human thinking and doing. It is also a logic about the future, aimed at knowledge of the possible and necessary. Lastly, it is futuristic, in that it is new, not of the past, unbound by previous limits. Hence, it is a young and optimistic logic, for and of the future, full of strength and energy.
I also called it ‘Future Logic’, because writing it has seemed an endless process. And it is really without end; I have left many things unsaid, only hinting at directions future logicians may take.
I would subtitle the book ‘modal logic’, to stress that all logic is ‘modal’, but not to imply that it concerns a specific sector of logic. The book ranges over virtually the whole of logic, constructing a well-integrated and fruitful system of logic, by means of an investigation of modality. A ‘system’ in the grand, traditional sense, not in the narrow sense used by modern logicians with reference to certain manipulations of limited scope.
‘Modality’, simply put, refers to concepts like possibility and necessity, which pervade knowledge in many different senses. Thought without modality is very limited in scope; much of our thinking depends on conceiving what the alternative possibilities are.
Modality is an incredibly creative force, which, like a crystal instantly solidifying a liquid, rushes through every topic and restructures it in new and interesting ways. I want to show how logic is forcefully pushed in a multitude of directions, as soon as modality and its ramifications are taken into account.
In writing this book my ambition was to invigorate logic — to contribute to the science, and to revive interest in it by all segments of society.
Thus, it is intended equally for laypersons and scientists, for students and educators, and for professional logicians. It is equally a popularizing book, a text-book, and a research report.
My goal is not only to explore new avenues for the science of logic, but especially to make its teachings accessible to a wide public. For this reason, even while attempting to write a scholarly treatise, I do my best to keep it readable by anyone.
The book is full of ground-breaking discoveries, which should impress any logic theorist, and perhaps put him or her back to work. I mean, not just a peppering of incidental insights, but entirely original areas of concern, directions, and techniques, as will be seen. Though well-nigh encyclopedic in scope, it is not a compilation, but presents a unified system.
Although addressed to a wide audience, this is not an elementary work; it is an attempt to transmit advanced logic to everyone. My faith is that we have all reached a level of education high enough to absorb it and use it.
The book moves from the more obvious to the less so, from the simple to the complex, and from the old to the new, so that a layperson or student lacking any previous acquaintance with the subject-matter can grasp it all, granting a little effort. The order of development is thus natural and didactic, rather than strictly ‘logical’ in the sense of geometry. It is easy, at the end, when we know what we are talking about, to review the whole, and suggest a ‘logical’ ordering which consolidates it.
My approach is strongly influenced by Aristotle; all I do is push his methods into a much broader field. The primary purpose of logic should be to teach people to think clearly. For this reason, I try to develop the subject in ordinary language, and avoid any excessive symbolization.
Modern logicians have managed to overturn the very spirit of the discipline of logic, and made it cryptic, obscure, and esoteric. This was a disservice to the public, depriving it of an important tool for living, since most people lack the patience to decipher symbols.
Logical science as such has also suffered from this development. Logic has no intrinsic need of symbols other than those provided by ordinary language. An artificial language in principle adds nothing to knowledge, just as renaming things never does. Symbolization as such is just a quaint footnote to logic, not a real advance.
Symbols are to some extent valuable, to summarize information in a minimum of space, or to discover and highlight patterns in the data. But taken to an extreme, symbolism can lock us into simplistic mind-sets, and arrest further insight, limiting us to making trivial embellishments. Worse still, it can distance us from empirical inputs, turning logic into a game, a conventional, mechanical manipulation of arbitrary constructs, without referents, divorced from reality.
Also, I try as much as possible in this volume to avoid philosophical issues and metaphysical speculations, anything too controversial or digressive — and to concentrate on the matter at hand, which is formal logic. Some comments on such topics are inserted at the end, for the record.
A logician is of course bound to get involved in some wider issues. Every logical analysis intimates something about ‘thought processes’ and something about ‘external reality’. Logic somehow concerns the interface of these parallel dimensions of epistemology (the study of knowing) and ontology (the study of being), and it is hard to draw the lines.
I try to be brief. But I also try and touch on all relevant topics. Every issue is of course many-faceted, and capable of interminable treatment, with every layer uncovered seemingly more crucial than the previous. I still have great quantities of unused manuscript, and therefore know how much more remains to be said. But the reader may find that his questions at any stage, are readily answered in a later stage, in a wider context. One cannot do everything at once.
Often I am obliged to stop the further development of ideas. If I feel that an idea is already drawn clearly enough, and there would be boring repetitions of previously encountered patterns, I merely indicate the expected changes in pattern, and call on the reader to explore further on his or her own. This may be likened to the use of perspective and shading in artwork. Knowledge is infinite anyway, and as the saying goes ‘there is no end to words’.
The informed reader may find that there is too much elementary logic — but I am forced to include some at first, to make the discussion comprehensible to all, and to show the more advanced developments in their proper context. In any case, even in a discussion of traditional logic, an expert may find novel details or viewpoints, as the various aspects of a topic are unraveled.
I apologize to the novice for my failure to give many examples, but this disadvantage seems to me outweighed by the advantage of brevity. I assume the reader capable of searching for appropriate examples, and it is a good exercise. The neophyte reader is warned to beware of our use of many words in selective, specialized senses, which may be based on common connotations or even be neologisms; the context hopefully always makes the intention clear.
I also keep historical notes to a minimum in the course of the text, more intent on being a logician than a historian of logic. However, an effort to attribute authorship of the main lines of thought, is made towards the end, when I seek to place my own contributions in their historical context. My critical evaluations of modern trends in logic are also included at that stage.
My style of writing is no doubt not uniformly good. Repeated editing is bound to sometimes result in obscure discontinuities in the text. Little errors may creep in. I hope the reader will nevertheless be tolerant, because the substance is well worth it.
The book is divided into 7 parts, with a total of 68 chapters; each of the chapters is split into on average 4 sections.
Part I starts with the three ‘laws of thought’, then presents the logic of actual categoricals (propositions of the form ‘X is Y’), including their features, their oppositions and immediate inferences, and syllogistic argument. Most of the credit for this seminal work can be attributed to Aristotle, although many later logicians were involved in the further development and systematization of his findings.
Part II defines the modalities called ‘de re‘, and develops the logic of modal categoricals, following the same pattern as was established in the previous part. Although Aristotle wrote a great deal about concepts like potentiality, and described some modal arguments, he did not investigate this area of logic with the same thoroughness as the previous; nor have logicians since done much more, in my opinion. I introduce some new techniques, and arrive at some original results.
This part also, for the sake of completeness, analyses other forms of categorical proposition (among which, those concerning change) and other logical processes (such as ‘substitution’), some of which seem to have been previously ignored or underrated.
Part III defines logical modality, and analyses logical conditioning. This concerns ‘if-then’ (and ‘either-or’) propositions, which have been dealt with in great detail by modern logicians. While my own results concur with theirs on the whole, my approach differs in many respects; especially different are the definitions of logical modalities, but there are many significant technical innovations too (such as ‘production’).
Part IV introduces ‘de re‘ conditioning, whose properties are found to be very distinct from those of logical conditioning. This is (to my knowledge) an entirely new class of propositions for logical science to consider, although commonly used in our everyday thought. The research emerged from the insights into modality obtained in part II, and provides us with original and important formal tools for the study of causality (and, incidentally, a better understanding of subsumption).
Part V begins with a new logic of classes (including a definitive solution of the Russell Paradox). Then I present the now-traditional discussion of scientific method (confirmation and discrediting of hypotheses), but from the viewpoint of logical modality.
Part VI contains an altogether original theory of induction based on ‘factorial analysis’. Consideration of modality in its various senses gives rise to a need for a completely new area of logic: how to induce modal propositions and how to resolve contradictions between them. The problems of generalization and particularization are solved systematically, using very formal techniques. Every aspect of this research — the tasks set, and the ways they are fulfilled — is a major breakthrough for logic.
The practical importance of factorial induction cannot be overstated. How far and in what direction can one generalize any finding? What happens when conflicting data is uncovered — how far and in what direction should one retreat from previous positions? What is the middle ground or compromise position or synthesis between competing views?
Part VII considers some of the ontological and epistemological implications of all my previous findings, with a sketch of my theory of cognition. The last few chapters provide a critical, historical and philosophical review of the whole field; this segment is more of interest to academic logicians than to the ordinary reader. Finally, the work is summarized, and I point out some of the opportunities for further research.
The reader is invited to peruse the table of contents for a more precise overview. I recommend that you return to it from time to time, so as to place the topic you are studying in its proper perspective.