Robert Burns and true contradictions

Lorenzo Penya Laurentius at
Tue Nov 21 16:30:14 MST 1995

On Sat, 11 Nov 1995, Robert P. Burns wrote:

      A fundamental principle in logic is the principle of
      non-contradiction -- the principle that tells us that it is
      incorrect, illogical to assert a logical contradiction. How
      could natural science investigate, explain, or discover this
      principle -- for doesn't every form of rational inquiry,
      including natural science presuppose it? How otherwise could
      we distinguish good science from bad science, rational
      assertion from irrational assertion? Does not the scientific
      investigation of nature presuppose the very normative
      validity of reason you disdain as the "high-falootin"
      projections of our own speciesist metaphysical abstractions?
      Or are you quite content to assert logical contradictions,

There are true [logical] contradictions. At least, many people think so.
The days are past when logical contradictions were frightening. The
reason is that we now can avail ourselves of paraconsistent logics --
logics, that is, wherein a logical contradiction does not entail
everything. In overconsistent (or non-paraconsistent) logics, from a pair
of sentences, ``p'' and ``not-p'' everything follows. If the NEP was and
wasn't capitalism, then all people under communist regimes die before
reaching adulthood. Classical logic (the logic founded by Gottlob Frege
and Bertrand Russell) was overconsistent, but so have turned out to be
most nonclassical logics. Instead, Peirce can be claimed to have
anticipated paraconsistent logic, but the first logician to have devised
a rigorous system of paraconsistent logic is Polish logician St.
Sobocinski in 1948. One of his motivations was that of implementing a
rigorous approach to dialectical materialism. Unfortunately dialectical
materialists themselves at that time had no use for Sobocinski's
theoretical construction.
      It is only in the 70's and later that paraconsistent logics have
developed. There are many of them. Some of them are weaker than classical
logic. Some of them are stronger than classical logics. The latter kind
is constituted by systems which do in fact contain the whole of classical
logic, but under a certain translation. Thus, e.g., some paraconsistent
logics develop Engels's considerations in his Dialectics of Nature (and
elsewhere) about the contradictorial characteristic of boundaries and
borderline entities in order to introduce two different negations: a
strong negation, read as `not at all', which never allows any
contradiction; and a weaker or simpler negation, a mere `not' which does
allow contradictions. To take Engels's own example, some German dialects
are and are not Hoch-Deutsch. Since all languages are fuzzy entities,
there are lots of dialects which only to some extent belong to a certain
language, while also to some extent belonging to a different language.
Periods of time, socio-economic formations, juridically relevant features
etc are, most of them, fuzzy properties. Any such property is such that
many things do to some extent possess the property but also to some
extent lack it. In at least some of those cases it seems appropriate to
assert that the thing does have the property, but also to assert that it
lacks the property. (Unless of course only what is entirely true may be
legitimately asserted, which sounds very odd; such a maxim would condemn
us to silence most of the time: we could not say that it's cold, nor that
it's not cold, nor that it neither is nor fails to be cold, nor ...
Nothing, just silence!)
      By the way, the principle of noncontradiction is one thing, the
rule of avoidance of contradictions is quite another (what you call `the
principle that tells us that it is incorrect, illogical to assert a
logical contradiction'). The principle of noncontradiction says nothing
of the sort. It limits itself to saying that, for any sentence ``p'', the
following is true: ``Not: p-and-not-p''. Mind you, most (not all)
paraconsistent logicians accept the validity of the principle of
noncontradiction. They think that every instance thereof is true. But not
wholly or completely true. To some extent, yes, it is not the case that
Papiamento is-and-is-not a Spanish dialect. Since to the extent it is
Spanish, it is not the case that it is not Spanish. And conversely. But
while accepting every instance of noncontradiction, many people reject
the rule which prohibits contradictions, the rule to the effect that
every contradictorial theory has to be junked.
      Of course, Robert, your point (with which I disagree, by the way)
can be put in terms which do not assume the necessary validity of an
overconsistent logic. For instance, since every logic complies with
certain canons, and indeed enforces certain standards, you can argue it
is irrational to profess a theory that makes every statement assertible
or true. Call such a rule (`Avoid committing yourself to a system of
beliefs according to which everything is true') the Maxim of Minimal
Consistency, MMC for short. You can proceed in the same manner as you did
with respect to [what you took to be] the principle of noncontradiction,
namely by arguing that any rational inquiry presupposes MMC and so MMC
itself cannot be inferred through a process of empirical assessment (a
la John Stuart Mill), but must be arrived at a priori; and that such a
principle must belong to an irreducibly nonnatural and nonempirical
realm. I still disagree with you on such issues, but that is another
      (By the way, I may surprise you by claiming that I do not disagree
with you -- not quite -- as regards God. But, please, Robert, a natural
God, a force -- as powerful as you want, even almighty, in a sense --
within our natural world, as a unifying ground for cohesiveness and
harmony to be reached through disharmony; or something like that. I
sometimes think polytheists may be closer to truth.)
Gent (Belgium) in July 1997. Inquiries: WCP97 at

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