www.TheLogician.net © Avi Sion - all rights reserved
© Avi Sion
All rights reserved
Avi Sion, 1990 (Rev. ed. 1996) All rights reserved.
CHAPTER 1. INTRODUCTION.
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
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
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 nιtait.
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
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
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
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.