Preproceedings 2006 - Austrian Ludwig Wittgenstein Society

group theory for obtaining the basic invariants of the
theory.(18) Fifty years later, by reiterating the same crucial
word “adjunction” Galois applied the same method to
algebra.
Aldo Capitini, the first Western, active non-violent
individual in the 20 th century, offered a philosophical basis
for Gandhian non-violence, by considering the whole
development of Western philosophy. Kant recognised that
human reason unsuccessfully attempted to know noumena;
man can, however, grasp reality through an ethical move,
characterised as an “adjunction”;(33) this notion originated in
Hegel's philosophy Absolute Spirit's aufhebung. Instead,
Capitini considered only personal ‘adjunctions’ as the typical
moves performed by “an individual persuaded for the cause
of non-violence”, aiming to rise above the level of an even
distressing situation of interpersonal realtionships, and
hence to apperceive a higher viewpoint from which to
achieve a "choral" solution.(3,2) Indeed, the process of nonviolent
solution of a conflict can be modelled by attributing to
the notion "adjunction" the same role it plays in scientific
theories.(16)
In Freud’s psychoanalysis the patient, by desribing his
dreams to analyst, “adjoins” them to his psychical “system”
for its clarification. A therapist analysing patient’s diseases,
obtains a hint for the solution by adding a second negation
to each patient’s negated statement, (27). Marx wanted to
add, as a trigger eliciting the desired change in the history of
mankind, historical consciousness to the proletariat.
Among strategic theories, L. Carnot’s defensive one is
expressly based upon the term ‘adjunctions’. He maintains
that the best strategy is a step-by-step strategy. When the
besieged of a stronghold is threatened by a besieger
applying a step-by-step strategy for approaching with
impunity the stronghold, then the besieged has to 'adjoin' to
his defensive activity some quick sorties, in order to break
the besieger's strategy, and hence to preserve the best
strategy withinthe stronghold.(8)
4. A formal interpretation
iv) The above parallelisms among so disparate theories can
be qualified in formal terms. The law of double negation
holds true in classical logic (e.g., “It is not true that 2+2 is not
4” is equivalent to "2+2=4"); its failure (e.g., a court
judgement of “lack of guilt evidence” is not equivalent to its
corresponding positive judgement of “honesty”)
characterises non-classical logic.(26,40) The founders of the
above-mentioned scientific theories wrote books where one
recognises a lot of double negated sentences, whose
corresponding positive sentences are not true for lack of
scientific evidence (= DNSs). For instance: “It is impossible
that matter is divisible in a not finite way” (chemists of 19 th
Century); “Infinitesimals are not chimerical (=not real)
beings”;(6) “It is impossible a perpetual (= without an end)
motion”;(4,7); “It is not contradictory the hypothesis of two
parallel lines to a given straight line.”(37)"... we can attribute
no absolute (= not relative) meaning to simultaneity."(26).
Hence, all these theories are governed by non-classical
logic.
Non-violence is essentially merged in non-classical
logic, since the word itself, non-violence, is a doubly negated
word (being violence a negation of a lot of values), which
cannot be appropriately substituted by a concrete, positive
word. The best candidate in Gandhi's eyes, the word
'Satyagraha' (= force of Truth), in fact sublimates the original
meaning in an abstract word, hanging over human life.
Christian people commonly think that positive word ‘love’ is
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The Rational Structure of Non-Violent Worldview- Antonino Drago
equivalent to “non-violence”; yet, ‘love’ is a multi-purposed
word, as it is proved by the social history of Christendom.
Furthermore, any typical non-violent slogan is appropriately
expressed by two negations: e.g., “It is impossible that this
man is my enemy”, "Nobody is without a soul", "Eye for eye
(=vengeance) makes blind the world".
A celebrated methodological paper by Freud equates
a patient's negation to a trauma repression; which has to be
solved by the analyst by denying the patient's
negation.(27,24)
It is well known that Marx wanted to illustrate his
theory by means of dialectics, where a synthesis is obtained
by the "negation of the negation" of the starting thesis.
In the alternative strategic theories the main goal is
not to win always, but to result in-vincible, a word including
two negations.(41) Moreover, the celebrated Clausewitz'
statement is "War is nothing else diplomacy through other
means" (never he wrote the corresponding positive
statement, wrongly quoted by almost all scholars).(10)
v) Leibniz sketched a 'Science of Science'(14) whose
two basic principles are the principle of non-contradiction
and the principle of sufficient reason; the latter one being a
DNS ("Nothing is without a reason") constitutes the best
introduction to non-classical logic within an alternative
theory.(17) There is not enough space to identify in each of
the above theories the translation of the latter Leibniz'
principle in a particular DNS, working as its specific
methodological principle.
vi) Some of the above-mentioned theories present
one more feature; the mere sequence of DNSs within an
original text faithfully synthesises the core of the respective
theory. This can be found in S. Carnot's booklet on
thermodynamics,(22) Lobachevsky's new geometry (20),
Freud's psychoanalysis,(24) the above strategic
theories.(11,1,25) 2
It cannot be overemphasised the fact that all the
above scientists, although unaware of non-classical logic,
consistently built entire theories by means of DNSs.
vii) Some of the above theories attained their crucial
results through ad absurdum theorems, e.g., the celebrated
S. Carnot’s theorem in thermodynamics. 3
The eventual result of the non-violent method is
obtained by reducing an argument ad absurdum, e.g., “It is
absurd that my opponent is not my brother, otherwise God
does not exists”, or “… otherwise universal brotherhood is
impossible”. Gandhi often argued in such a way.(35, ch.4,
no.s 8,43,52,76)
Also both L. Carnot’s and Clausewitz’ theories end
with ad absurdum arguments.(1,10)
viii) At last, we have characterised the both logical
and alternative organisation(20) of non-violence as a
theory. 4 Thus, conflict theory is linked with scientific theories.
2 See (19,23) for more such reconstructions.
3 Ad absurdum argument is rejected by non-classical logic when one,
complying with classical logic, imposes the conclusion, really a DNS ¬¬T,
onto the positive sentence T. But when a theory argues on the basis of DNSs,
this step is not necessary, because the last DNS works as a methodological
principle for the following argument. Only in the final argument of the theory,
when ¬¬T achieves universal evidence for all problems at issue, then the
author feels justified to change both logic and organisation of the theory, by
assuming T as a new hypothesis from which to draw all possible derivations.
This move is recognised in both S. Carnot's and Lobachevsky's theories.(20)
4 Non-violence can be also characterised by its privileged attention to the
development of interpersonal relationships, rather than to the development of
material objects, institutions or abstract ideals. By adding this option to the
above one, one obtains two dichotomic variables, generalising the variables