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7/25/2019 Dumitriu, Anton. History of Logic 370-371
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History of Logic by Anton DumitriuThe Journal of Symbolic Logic, Vol. 45, No. 2 (Jun., 1980), pp. 370-371Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2273199.
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7/25/2019 Dumitriu, Anton. History of Logic 370-371
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370 REVIEWS
rather a viewing of
clippings
from
the
original
reels. The
result
is,
as
one
would
expect,
that he
has produced
a
report
rather than a
history;
it is often full
of welcome and
little-known details of
history of logic, but
interpretation
is
bland
or even
non-existent. The cast of
the net
has also been
rather
too
wide.
For
example,
the
chapters
on
the
application
of
logic
to
twentieth-century prob-
lems embrace quantum mechanics, relativity, dialectics, linguistic philosophy, induction, and the
logic
of
scientific
discovery; fifty
sections have
only
pages
62-132
of
Volume III to
make their
points, so
that each section is too brief to state
satisfactorily
either the
logic
involved or the
ap-
plication being
made.
The same criticism
applies
to
Dumitriu's
rapid presentation
of
the
post-
Romantic
logicians
(Vol. III, pp. 235-259)
and their
psychologistic
contemporaries (Vol. III, pp.
311-352).
Dumitriu's
historiography
is
put
to
a
severe
test in the last
volume,
for the
history
of mathe-
matical
logic
has
been
fraught
with controversies over the nature of
logic
and
its
relationship
with
set
theory
and
mathematics
in
general,
and
handicapped by
the
slow
recognition
of
metalogic
as
separate
from
logic.
How
would
a film
director
cope
with this? The
chapter
on
algebraic logic
(pp. 39-50)
is
exceedingly
disappointing;
the usual
things (but nothing
else)
are said about
Boole,
Peirce receives just over a page, Schroder thirteen lines. Among the later developments, those on
many-valued logics
(including
modal
logics, pp.
145-181)
and
formalism
and proof theory (pp.
182-223)
include
some
longer takes, though
the
text
usually
reads
like a
script (A
did
this,
B
did
that,
and so
on).
And regrettably,
some
developments
that have
aroused
great
interest are either
ignored
or
given
only
the briefest
exposure:
for
example,
the
substitutional
interpretation
of
quantification
(indeed,
little
is
said about
quantification
anywhere),
free
logic,
natural
deduction
(five
lines
on
p. 143,
with
Popper's
contributions
overlooked),
and
Quine's
logical systems
(eight
lines on
p. 141).
No
points
of
substance are
made
anywhere
about Cantor
or
Lesniewski,
despite
the
variety
of their influences on
logic;
the absence of
Lesniewski
from
the
chapter
on the
paradoxes
and
their
solutions
(pp. 113-117)
is
particularly painful.
In the more substantial chapters, only the familiar scenes are shown. The Frege chapter (pp.
51-63)
is
devoted
largely
to
the
elementary parts
of
his
symbolism; there is not even an
indication
of
how his
logicist
thesis is
articulated.
The Peano
chapter (pp. 64-86)
similarly
runs over the
logical,
set-theoretical,
and arithmetical
notions, though
there is also a useful
passage
on
Peano's
attention
to
definitions
(pp. 77-80).
The
chapter
on
Principia
mathematics
(pp. 87-112)
involves
a
basic
mistake for
any history
of
logic:
The
prehistory
of
the work in
Russell
and
Whitehead's
earlier
writings
is
overlooked,
with the
result that the
motivations
to
its
principal
ideas
are
lacking.
Judgements,
when
made
at
all,
are
tendentious. For
example, on pages 88-89 the need to
axioma-
tise
logic
is
ascribed
to
Hilbert's
influence,
whereas Russell
was so
removed from Hilbert's views
that
he
did
not even assess the
consistency and
independence
of
his
axiom system. Again,
the
critical
comments
on
Russell's
admittedly curious remarks on definitions
(p. 111) overlook the
important use made in Principia mathematics of contextual definition.
The above
assessment
is
presented
with
a
keen sense of
my
own
ingratitude. I have done enough
historical
study
to
know
how much
hard work it
involves, and the
labour required here from
author, translators, and publisher
to
put nearly thirteen
hundred pages on the market must have
been immense.
Yet
the
result
is
disappointing, chiefly because of
Dumitriu's conception of his
task,
with
his
open book view
that
the
texts alone,
or
condensed
versions of
them,
will
constitute
a
history
of
logic.
He
quotes
with
approval
Aristotle's
comment that he who
does
not
philoso-
phize, philosophizes (Vol. I, p. x), but he
himself exemplifies the rider
that such inexplicit
philo-
sophy
can be
the
least
valuable
of
all.
If I
were
to
compare
this
history
with its
predecessors,
then
I would describe it as Bocheiiski
writ large. Those familiar with Bochefiski's History of formal logic (cf. XXV 57) will recall the
cinematographic
style used
there-brief extracts strung together,
newsreel-style, as
sequences of
short
takes. Dumitriu
summarises more than
he quotes, but the effect is
the same.
Bochefiski's
readers
are also
grateful for his extensive
bibliographies and indexes, and
by and large they are
well
served
by
Dumitriu
also.
Neither
author, however,
allows
himself to
go
beyond
these limits-
which is
a
pity,
for
beyond film-watching
is
creative
film-writing, where
history becomes interesting
and
important.
I.
GRATTAN-GUINNESS
ANTON
DUMITRIU. Istoria
logical.
Editura Didacticg
?i
Pedagogici,
Bucharest
1969, 1049
pp.
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7/25/2019 Dumitriu, Anton. History of Logic 370-371
3/3
REVIEWS
371
ANTON DUMITRIU. Istoria logicii.
Second, revised and enlarged, edition of the preceding and
Roumanian original of History
of
logic. Editura Didacticd
?i
Pedagogicd,
Bucharest 1975, 1212
PP.
ROBERT
BLANCHE. La Logique et son histoire: d'Aristote a'Russell. Collection U. Librairie
Armand
Colin, Paris
1970, 366 p.
Il
n'existait jusqu'ici
aucune histoire de
la
logique
un peu developpee due
a
un auteur
de langue
franqaise.
L'ouvrage
de Robert
Blanche comble cette lacune
pour une periode
qui va de la logique
grecque
a
la naissance de la logique
contemporaine. L'ouvrage
clairement
redige,
ecrit
dans une
bonne langue,
se lit avec plaisir.
Mais il
faut bien constater que,
en depit du sous-titre, I'auteur
a consacre
proportionnellement
beaucoup plus de place
a la logique classique et
aux premieres
tentatives de mathematisation
de
la
logique
qu'aux oeuvres de pionniers
comme
Frege et Russell. Pour tout ce
qui concerne
la logique
classique
l'information
est abondante et
a
jour
si l'on tient compte de
la date de parution
de
l'ouvrage
et de son
dMlai
d'elaboration. L'expose
ne neglige
ni les commentaires traditionnels
ni
les recherches entreprises a la lumiere de la logique mathematique contemporaine. L'auteur s'efforce
de degager une vue synthetique
faisant
place sans parti pris
aux differents
apports et il y parvient
souvent avec bonheur.
Les chapitres
consacres a Aristote, aux
megariques, aux stoiciens
illustrent
bien sa maniere.
De meme la logique medievale,
les apports
de la Renaissance et Leibniz
sont
traits egalement d'agreable
faqon.
La situation
change
quand on aborde la logique
posterieure
a
1850. La quality de la
presentation
demeure. Mais, surtout
en ce qui concerne
les tres grands noms,
l'information semble moins
solide.
On
peut
comprendre qu'a propos
de Boole l'auteur
n'ait pas voulu entrer
dans des
details tech-
niques.
Il est regrettable
que l'amateur de details
soit
renvoye
en tout et pour tout
a
l'ouvrage
de
Liard (1878),
Les logiciens anglais
contemporains (413), et
au Treatise de
Jorgensen (4241). De
meme, en ce qui concerne Frege et Russell, l'expose est a la fois acceptable en ce sens, qu'il ne
contient pas d'affirmation
erronee, et insuffisant
en ce qu'il manque de relief
et
ignore
tout
ce
que,
depuis
bien des
annees,
les
recherches sur
Frege
et Russell
ont apporte.
Des references bien choisies
auraient pu aider le lecteur;
en fait, au
fur et
a
mesure que
l'on
avance vers la
fin
de l'ouvrage,
elles sont de moins en moins nombreuses
et de plus
en plus
arbi-
trairement choisies.
Malgre ce desequilibre,
ce livre
rendra de grands services
aux etudiants
depourvus
de culture
mathematique,
interesses surtout
par la logique ancienne et
classique.
Pour
ce
qui
concerne
les
cent dernieres annees,
ils trouveront
une esquisse qui ne
saurait
les dispenser
de
recourir
a des
etudes
plus
etoffees.
ROGER
MARTIN
ALEX
ORENSTEIN.
Willard Van Orman Quine.
Twayne's world leaders series, no.
65.
Twayne Publishers,
Boston
1977, 180
pp.
Rather bravely,
Orenstein
sets out
to furnish
the uninitiated
reader with an integrated
view
of Quine's
philosophical
thought
in
less than sixty thousand
words.
The treatment
is
sympathetic,
the book
mainly uncritical.
To a certain extent,
the present work is ordered
to reflect
Quine's
intellectual
development.
The principal
topics
are ontological
commitment,
meaning and
refer-
ence, logical
truth,
analyticity,
holism,
indeterminacy
of
translation, and behaviorism;
there
is
little on technical
logic.
Presuppositions
are
meagre; even
truth-functions
and quantifiers are presented
as
if
they
might
be new
to the reader.
To place
Quine's philosophy
in perspective,
Orenstein supplies
the needed
sketches of doctrine from Frege, Russell, Carnap, Tarski, and others. He quotes very liberally
from
Quine's own
writings.
Indeed the
reviewer
finds that
the most
successful
portions of the
book
are those that
are thickest
with
quotation.
For
it is difficult to improve
on
Quine through
para-
phrase, given
the
lucidity and
elegance
of his prose.
Orenstein is a responsible
expositor of
Quine's
philosophy.
Some of his summaries are
sharp
and crisp (as of
Duhemian
holism and
of Quine's
clash
with Chomsky's
innateness hypothesis),
others somewhat cloudy
(on observation
sentences
and on views
of '2 plus
2 equals 4'). He
is skilled
at keeping
his
account
simple without
great
sacrifice of accuracy.
The book
is thoughtfully
organ-
ized, though there
is occasional
flitting
from topic to
topic.
As is inevitable
in so short
a treatment
of so broad a subject,
there is some lack
of depth. On balance,
Orenstein
may
be seen as
moderately
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