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All the books listed below are now available as quality paperbacks
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Logic - FUTURE
Categorical and Conditional Deduction
of the Natural, Temporal, Extensional, and Logical
Future Logic is an original, and wide-ranging treatise of formal logic. It deals with
deduction and induction, of categorical and conditional propositions, involving
the natural, temporal, extensional, and logical modalities.
and Modern logic have covered in detail only formal deduction from actual
categoricals, or from logical conditionals (conjunctives, hypotheticals, and
disjunctives). Deduction from modal categoricals has also been considered,
though very vaguely and roughly; whereas deduction from natural, temporal and
extensional forms of conditioning has been all but totally ignored. As for
induction, apart from the elucidation of adductive processes (the scientific
method), almost no formal work has been done.
is the first work ever
to strictly formalize the inductive processes of generalization and
particularization, through the novel methods of factorial analysis, factor
selection and formula revision.
is the first work ever
to develop a formal logic of the natural, temporal and extensional types of
conditioning (as distinct from logical conditioning), including their
production from modal categorical premises.
a great many other new discoveries, organized into a unified, consistent and
empirical system, with precise definitions of the various categories and types
of modality (including logical modality), and full awareness of the
epistemological and ontological issues involved. Though strictly formal, it uses
ordinary language, wherever symbols can be avoided.
its other contributions: a full
list of the valid modal syllogisms (which
is more restrictive than previous lists); the main formalities of the
logic of change (which introduces a dynamic instead of merely static
approach to classification); the first formal definitions
of the modal types of causality;
a new theory of class logic, free of
the Russell Paradox; as well as a critical review of modern metalogic. But
it is impossible to list briefly all the innovations in logical science -- and
therefore, epistemology and ontology -- this book presents; it has to be read
for its scope to be appreciated.
Basing Knowledge On Appearance. (2003; expanded 2005)
is the study of appearance as such. It is a branch of both Ontology and
Epistemology, since appearing is being known. By an
‘appearance’ is meant any existent which impinges on consciousness, anything
cognized, irrespective of any judgment as to whether it be ‘real’ or
‘illusory.’ The evaluation of a particular appearance as a reality or an
illusion is a complex process, involving inductive and deductive logical
principles and activities. Opinion has to earn the status of strict knowledge.
Knowledge develops from appearances, which may be: (a) objects of
perception, i.e. concrete phenomena in the physical or mental
domains; (b) objects of intuition, i.e. one’s subjective self,
cognitions, volitions and valuations (non-phenomenal concretes); and/or
(c) objects of conception, i.e. simple or complex abstracts of
preceding appearances. Abstraction relies on apprehensions of sameness
and difference between appearances (including received or projected
appearances, and projected negations of appearances). Coherence in
knowledge (perceptual, intuitive and conceptual) is maintained by
apprehensions of compatibility or incompatibility.
facilitate our construction of conceptual knowledge, thanks to their
intentionality. The abstract concepts most words intend are common characters or
behaviors of particulars (concrete material, mental or subjective experiences).
Granting everything in the world is reducible to waves, ‘universals’ would
be equalities or proportionalities in the measures of the features, motions and
interrelations of particular waves. Such a theory of universals would elucidate
sensation and memory.
to retrace the development of conceptual knowledge from experience, we may refer
to certain major organizing principles. It is also important to keep track of
the order of things in such development, interrelating specific concepts and
specific experiences. By proposing a precise sequence of events, we avoid
certain logical fallacies and are challenged to try and answer certain crucial
questions in more detail. Many more
topics are discussed in the present collection of essays, including selfhood,
adduction and other logical issues, the status of mathematical concepts and
- JUDAIC LOGIC:
A Formal Analysis of Biblical, Talmudic
and Rabbinic Logic.
Logic is an
original inquiry into the forms of thought determining Jewish law and belief,
from the impartial perspective of a logician. Judaic Logic attempts to
honestly estimate the extent to which the logic employed within Judaism fits
into the general norms, and whether it has any contributions to make to them.
The author ranges far and wide in Jewish lore, finding clear evidence of both
inductive and deductive reasoning in the Torah and other books of the Bible, and
analyzing the methodology of the Talmud and other Rabbinic literature by
means of formal tools which make possible its objective evaluation with
reference to scientific logic. The result is a highly innovative work - incisive
and open, free of clichés or manipulation.
Judaic Logic succeeds in translating vague and confusing
interpretative principles and examples into formulas with the clarity and
precision of Aristotelean syllogism. Among the positive outcomes, for logic in
general, are a thorough listing, analysis and validation of the various forms of
a-fortiori argument, as well as a
clarification of dialectic logic.
However, on the negative side, this demystification of Talmudic/Rabbinic modes
of thought (hermeneutic and heuristic) reveals most of them to be, contrary to
the boasts of orthodox commentators, far from deductive and certain. They are
often, legitimately enough, inductive. But they are also often unnatural and
arbitrary constructs, supported by unverifiable claims and fallacious
other thought-processes, used but not noticed or discussed by the Rabbis, are
identified in this treatise, and subjected to logical review. Various more or
less explicit Rabbinic doctrines, which have logical significance, are also
examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its
universal aspects and its peculiarities.
regard to Biblical studies, one notable finding is an explicit formulation
(which, however, the Rabbis failed to take note of and stress) of the
principles of adduction
in the Torah, written long before the acknowledgement of these principles in
Western philosophy and their assimilation in a developed theory of knowledge.
Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish
Bible) contains a lot more than ten instances of qal
vachomer (a-fortiori) reasoning.
In sum, Judaic Logic elucidates
and evaluates the epistemological assumptions which have generated the Halakhah
(Jewish religious jurisprudence) and allied doctrines. Traditional
justifications, or rationalizations, concerning Judaic law and belief, are
carefully dissected and weighed at the level of logical process and structure,
without concern for content. This foundational approach, devoid of any critical
or supportive bias, clears the way for a timely reassessment of orthodox Judaism
(and incidentally, other religious systems, by means of analogies or contrasts).
Judaic Logic ought, therefore, to be
read by all Halakhists, as well as Bible and Talmud scholars and students; and
also by everyone interested in the theory, practise and history of logic.
Critical Analysis of Nagarjuna’s Arguments.
The 2nd Century CE Indian philosopher
Nagarjuna founded the Madhyamika (Middle Way) school of Mahayana Buddhism, which
strongly influenced Chinese, Korean and Japanese (Ch’an or Zen) Buddhism, as
well as Tibetan Buddhism. Nagarjuna is regarded by many Buddhist writers to this
day as a very important philosopher, who they claim definitively proved the
futility of ordinary human cognitive means.
His writings include a series of arguments purporting
to show the illogic of logic, the absurdity of reason. He considers this the way
to verbalize and justify the Buddhist doctrine of “emptiness” (Shunyata).
These arguments attack some of the basic tenets and techniques of reasoning,
such as the laws of thought (identity, non-contradiction and the excluded
middle), conceptualization and predication, our common assumptions of self,
entities and essences, as well as our beliefs in motion and causation.
The present essay demonstrates the
involved in Nagarjuna’s arguments. He uses double standards, applying or
ignoring the laws of thought and other norms as convenient to his goals; he
manipulates his readers, by giving seemingly logical form (like the dilemma) to
his discourse, while in fact engaged in non-sequiturs or appealing to
doubtful premises; he plays with words, relying on unclear terminology,
misleading equivocations and unfair fixations of meaning; and he ‘steals
concepts’, using them to deny the very percepts on which they are based.
Although a critique of the Madhyamika philosophical
interpretation and defense of “emptiness”, Buddhist Illogic is not
intended to dissuade readers from Buddhism. On the contrary, its aim to enhance
personal awareness of actual cognitive processes, and so improve meditation. It
is also an excellent primer on phenomenological epistemology.
Logic of Causation
- Causal Logic: THE
LOGIC OF CAUSATION:
Definition, Induction and Deduction of Deterministic Causality.
2nd ed. 2003, 3rd ed. 2010)
The Logic of Causation is a treatise of formal logic and of
aetiology. It is an original and wide-ranging investigation of the definition of
causation (deterministic causality) in all its forms, and of the deduction and
induction of such forms. The work was carried out in three phases over a dozen
years (1998-2010), each phase introducing more sophisticated methods than the
previous to solve outstanding problems. This study was intended as part of a
larger work on causal logic, which additionally treats volition and allied
cause-effect relations (2004).
The Logic of Causation deals with the main technicalities relating
to reasoning about causation. Once all the deductive characteristics of
causation in all its forms have been treated, and we have gained an
understanding as to how it is induced, we are able to discuss more intelligently
its epistemological and ontological status. In this context, past theories of
causation are reviewed and evaluated (although some of the issues involved here
can only be fully dealt with in a larger perspective, taking volition and other
aspects of causality into consideration, as done in Volition and Allied
Phase I: Macroanalysis. Starting with the paradigm of causation, its most
obvious and strongest form, we can by abstraction of its defining components
distinguish four genera of causation, or generic determinations, namely:
complete, partial, necessary and contingent causation. When these genera and
their negations are combined together in every which way, and tested for
consistency, it is found that only four species of causation, or specific
determinations, remain conceivable. The concept of causation thus gives rise to
a number of positive and negative propositional forms, which can be studied in
detail with relative ease because they are compounds of conjunctive and
conditional propositions whose properties are already well known to logicians.
The logical relations (oppositions) between the various determinations (and
their negations) are investigated, as well as their respective implications (eductions).
Thereafter, their interactions (in syllogistic reasoning) are treated in the
most rigorous manner. The main question we try to answer here is: is (or when
is) the cause of a cause of something itself a cause of that thing, and if so to
what degree? The figures and moods of positive causative syllogism are
listed exhaustively; and the resulting arguments validated or invalidated, as
the case may be. In this context, a general and sure method of evaluation called
‘matricial analysis’ (macroanalysis) is introduced. Because this (initial)
method is cumbersome, it is used as little as possible – the remaining cases
being evaluated by means of reduction.
Phase II: Microanalysis. Seeing various difficulties encountered in the
first phase, and the fact that some issues were left unresolved in it, a more
precise method is developed in the second phase, capable of systematically
answering most outstanding questions. This improved matricial analysis (microanalysis)
is based on tabular prediction of all logically conceivable combinations and
permutations of conjunctions between two or more items and their negations
(grand matrices). Each such possible combination is called a ‘modus’ and is
assigned a permanent number within the framework concerned (for 2, 3, or more
items). This allows us to identify each distinct (causative or other, positive
or negative) propositional form with a number of alternative moduses.
This technique greatly facilitates all work with causative and related forms,
allowing us to systematically consider their eductions, oppositions, and
syllogistic combinations. In fact, it constitutes a most radical approach not
only to causative propositions and their derivatives, but perhaps more
importantly to their constituent conditional propositions. Moreover, it is not
limited to logical conditioning and causation, but is equally applicable to
other modes of modality, including extensional, natural, temporal and spatial
conditioning and causation. From the results obtained, we are able to settle
with formal certainty most of the historically controversial issues relating to
Phase III: Software Assisted
Analysis. The approach in the second phase was very ‘manual’ and
time consuming; the third phase is intended to ‘mechanize’ much of the
work involved by means of spreadsheets (to begin with). This increases
reliability of calculations (though no errors were found, in fact) – but
also allows for a wider scope. Indeed, we are now able to produce a
larger, 4-item grand matrix, and on its basis find the moduses of
causative and other forms needed to investigate 4-item syllogism. As
well, now each modus can be interpreted with greater precision and
causation can be more precisely defined and treated.
In this latest phase, the
research is brought to a successful finish! Its main ambition,
to obtain a complete and reliable listing of all 3-item and 4-item
causative syllogisms, being truly fulfilled. This was made technically
feasible, in spite of limitations in computer software and hardware, by
cutting up problems into smaller pieces. For every mood of the
syllogism, it was thus possible to scan for conclusions ‘mechanically’
(using spreadsheets), testing all forms of causative and preventive
conclusions. Until now, this job could only be done ‘manually’, and
therefore not exhaustively and with certainty. It took over 72’000 pages
of spreadsheets to generate the sought for conclusions.
This is a historic breakthrough
for causal logic and logic in general. Of course, not all conceivable
issues are resolved. There is still some work that needs doing, notably
with regard to 5-item causative syllogism. But what has been achieved
solves the core problem. The method for the resolution of all
outstanding issues has definitely now been found and proven. The only
obstacle to solving most of them is the amount of labor needed to
produce the remaining (less important) tables. As for 5-item syllogism,
bigger computer resources are also needed.
and Allied Causal Concepts is a work of
aetiology and metapsychology. Aetiology is the branch of philosophy and logic
devoted to the study of causality (the cause-effect relation) in all its forms;
and metapsychology is the study of the basic concepts common to all
psychological discourse, most of which are causal.
(or free will) is to be distinguished from causation and natural spontaneity.
The latter categories, i.e. deterministic causality and its negation, have been
treated in a separate work, The Logic of Causation. Volition may
be characterized as personal causality, a relation between an agent (the self or
soul) and his actions (acts of will). Unlike causation, this relation cannot be
entirely defined using conditional (if–then) propositions. Although we can say
that the agent is a sine qua non of his actions, we cannot say that the agent is
invariably (in all or specific circumstances) followed by his actions. It
appears that both an act of will and its negation remain possible to a soul in
any given set of circumstances. This defines freedom of the will, and implies
the responsibility of the agent for his actions. Introspection provides
knowledge of particular acts of will.
existence of freewill implies a distinction between necessary causation
(determinism independent of volition) and inertial causation (determinism,
except when some contrary will interferes). An act of will occurs on a spiritual
plane. It may have natural (mental or physical) consequences; those that
inevitably follow it may be regarded as directly willed, whereas those that vary
according to circumstances must be considered indirectly willed. Volition
presupposes some degree of consciousness. So-called involuntary acts of will
involve a minimum of attention, whereas mindful acts are fully conscious. Even
pure whim involves intention. Most volitions moreover involve valuation, some
sort of projection of goals, deliberation on means, choice and decision. To
judge responsibility, various distinctions are called for, like that between
intentional, incidental and accidental consequences.
action can be affected through the terms and conditions of the world surrounding
its agent, but also more intimately through the influence of concrete or
abstract aspects of that world that the subject has cognized. The causal concept
of influence, and its implication of cognition (of inner or outer information,
including emotions), are crucial to measuring the effort involved in volition.
Influences make willing easier or harder, yet do not curtail its essential
freedom. All the causal concepts used in psychological explanation –
affections, appetites, instincts, habits, obsessions, compulsions, urges and
impulses – can be elucidated thanks to this important finding. Much of human
(and animal) behavior can thus be both acknowledged as volitional and as
and Allied Causal Concepts is a work of
ambitious scope, intent on finally resolving philosophical and logical issues
that have always impeded progress in psychology. It clarifies the structure and
workings of the psyche, facilitating hygienic and therapeutic endeavors. The
relation between volition and physical laws is discussed, as is the place of
volition in biology. Concepts used in biology, analogous to that of purpose, are
incidentally analyzed. Theological issues are also dealt with, as are some
topics in ethics and law.
notes and essays on Logic. (2005)
is a collection of sundry notes and
essays on Logic. These complement and enrich the author’s past writings,
further analyzing or reviewing certain issues. Among the
many topics covered are: the importance of the laws of
thought, and how they are applied using the logic of paradox; details of formal logic,
including some important new insights on the nesting, merger and splitting
up of hypothetical propositions; details of causal logic,
including analogical reasoning from cause to cause; a phenomenological analysis of
this volume is used to publish a number of notes and essays previously only
posted in the Internet site www.TheLogician.net, including: a thoroughly revised version of
an essay on J.S. Mill’s Methods; various addenda and diagrams for
Logic, as well as a historical essay; a brief analysis of
meditation is a voluntary exercise intended to increase awareness,
sustained over some time.
main purpose of the present Meditations is to inspire and assist
readers to practice meditation of some sort, and in particular ‘sitting
meditation’. This includes practices such as: observing the mechanisms
of one’s thinking, stopping unnecessary thought, forgetting things about
one’s self and one’s life that are irrelevant to the current effort of
meditation, dealing with distractions, becoming aware of one’s breath,
being here and now.
such practice for some time, one gets to realize the value of meditation,
and one’s commitment to it grows. The need for behavioral improvement
becomes more and more obvious, and one finds it easy and natural to
put more discipline into one’s life. Various recommendations are given
in this regard.
Prior to such practical guidance, so as to prepare the reader for it, the
book reviews the theoretical teachings relating to meditation in the main
traditions of mankind. The ultimate goals of meditation, the various
methods or techniques used to achieve them, the experiential results of
meditation, and the interpretations given to them, are topics treated
collection of shorter philosophical works, in two parts.
first part, consisting of Logical Reflections, includes:
Problems with Induction,
is intended to describe and refute some of the main
doubts and objections David Hume raised with regard to inductive
reasoning. It replaces the so-called problem of induction with a
principle of induction. David Hume’s notorious skepticism was based on
errors of observation and reasoning, with regard to induction,
causation, necessity, the self and freewill. These are here
pointed out and critically analyzed in detail – and more accurate and
logical theories are proposed. The present work also includes
refutations of Hempel’s and Goodman’s alleged paradoxes of induction.
Short Critique of Kant’s Unreason, which is a brief critical
analysis of some of the salient epistemological and ontological ideas
and theses in Immanuel Kant’s famous Critique of Pure Reason. It shows
that Kant was in no position to criticize reason, because he neither
sufficiently understood its workings nor had the logical tools needed
for the task. Kant’s transcendental reality, his analytic-synthetic
dichotomy, his views on experience and concept formation, and on the
forms of sensibility (space and time) and understanding (his twelve
categories), are here all subjected to rigorous logical evaluation and
found deeply flawed – and more coherent theories are proposed in their
Defense of Aristotle’s Laws of Thought, which addresses, from a
phenomenological standpoint, numerous modern and Buddhist objections and
misconceptions regarding the basic principles of Aristotelian logic.
Many people seem to be attacking Aristotle’s Laws of Thought nowadays,
some coming from the West and some from the East. It is important to
review and refute such ideas as they arise.
second part, consisting of Spiritual Reflections, includes:
which is a sequel to the author’s earlier work, Meditations. It
proposes additional practical methods and theoretical insights relating
to meditation and Buddhism. It also discusses certain often glossed over
issues relating to Buddhism – notably, historicity, idolatry, messianism,
importation to the West.
which is a frank reflection on the tensions between reason and faith in
today’s context of knowledge, and on the need to inject Zen-like
meditation into Judaism. This work also treats some issues in ethics and
No to Sodom,
which is an essay against homosexuality, using biological,
psychological, spiritual, ethical and political arguments.
This module includes
'thematic compilations' (2008-9). These bring together essays relevant
to their title topic drawn from all of Avi Sion's past works. They are:
The Laws of Thought is an exploration of the deductive and inductive
foundations of rational thought. The author here clarifies and
defends Aristotle’s Three Laws of Thought – and introduces a Fourth
Law of Thought implicit in and crucial to them, viz. the Principle
Ethics is a collection of thoughts on the method, form and content
The Self is an inquiry into the concepts of self, soul, person, ego,
consciousness, psyche and mind – ranging over phenomenology, logic,
epistemology, ontology, psychology, spirituality, meditation, ethics
Theology is about God and Creation, or more precisely perhaps about
our ideas of them, how they are formed and somewhat justified,
although it is stressed that they can be neither proved nor
Also displayed here are various
notes and essays in English and French. Previews and other temporary
postings, .pdf files for download, etc.
All the books posted in The
Logician Website are now available as quality paperbacks
in The Logician Bookshop. To order online click on the following hyperlink: