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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