| Future Logic – FUTURE LOGIC:
Categorical and Conditional Deduction and Induction
of the Natural, Temporal, Extensional, and Logical Modalities. (1990, revised 1996) |
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. Traditional 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. This 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.
This 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. Future Logic contains 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. Among 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. |
| Phenomenology – PHENOMENOLOGY: Basing Knowledge On
Appearance. (2003; expanded 2005) |
Phenomenology 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. Words 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. In attempting 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 theology. |
| Judaic Logic – JUDAIC LOGIC:
A Formal Analysis of Biblical, Talmudic and
Rabbinic Logic. (1995, Slatkine 1997) |
Judaic 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 techniques.
Many 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. With 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<![if !supportFootnotes]>[1]<![endif]>[2] 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. |
| Buddhist Illogic – BUDDHIST ILLOGIC: A Critical Analysis of Nagarjuna’s Arguments. (2002) |
Buddhist Illogic. 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 many sophistries 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. |
| The Logic of Causation – Causal Logic: THE LOGIC OF CAUSATION: Definition,
Induction and Deduction of Deterministic Causality. (1st ed.
1999, 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 Causal Concepts). 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
causation. 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. |
Volition 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. Volition
(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. The 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. Volitional 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 variously
influenced. Volition 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. |
| Ruminations –RUMINATIONS: Sundry notes and essays on Logic. (2005) |
Ruminations 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 negation. Additionally, 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
Judaic Logic, as well as a historical essay; a brief analysis of Islamic
logic. |
Meditations. A meditation is a voluntary exercise intended to increase
awareness, sustained over some time. The 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. After 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 here. |
Logical and Spiritual Reflections is a collection of shorter
philosophical works, in two parts. The first part, consisting of Logical Reflections,
includes: | 
| 
| 
| 
| 
| 
|
Hume’s Problems with Induction, which 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. A 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 stead. In 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. The second part, consisting of Spiritual Reflections,
includes: More Meditations, 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. Zen Judaism, 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
theodicy. No to Sodom, which is an essay against homosexuality, using biological,
psychological, spiritual, ethical and political
arguments. |
