Formal validity in problem solving

200 Pages·09.585 MB·English

by  Bradley, Earl Edsel

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NORTHWESTERN UNIVERSITY
FORMAL VALIDITY IN PROBLEM SOLVING
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degre®
DOCTOR OF PHILOSOPHY
SCHOOL OF SPEECH
BY
EARL EDSEL BRADLEY
EVANSTON, ILLINOIS
AUGUST, 1950
ProQuest Number: 10061016
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TABLE OP CONTENTS
Pag©
PREFACE............................... i
I. INTRODUCTION.......................... 2
II. OBJECT OP THE EXPERIMENT.............. 6
III. EXPERIMENTAL PROCEDURE . * .......... . 8
IV. RESULTS . .................... 30
V. CONCLUSIONS............................ 36
VI. COMMENTS.............................. 38
APPENDICES
APPENDIX A. SURVEY OP LITERATURE
Introduction..................... .. 1A
Literature Pertaining to Rhetoric • • 4A
Literature Pertaining to Logic , . . • 14A
Experimental Literature...... 26A
APPENDIX B. MANUAL AND TESTS
I. Introduction ............. IB
A. The relation of Formal Validity to
Problem Solving .............. IB
B. The Laws of Thought • IB
C. The Nature of Formal L o g i c ....... 2B
D. Validity and Form . . • • . ....... 3B
E. Form or Structure in Argument • • • • 4B
II. Terms, Propositions, Premises . . . . . . 6B
A. On the Nature of T e r m s ...... 6B
1. On the Representation of Terms • . 7B
2. Assignment on Terms . . . . . . . 7B
B. On the Nature of Propositions • • • • 8B
1. Propositions as to Quality and
Quantity..................... 8B
2. The distribution of Terms . . . . 8B
3. Assignment on Propositions . . . . 9B
*
:
Page
C. The Proposition as a Premise........ 10B
1. The structure of a Syllogism.... 10B
2. Assignment on Premises..... 10B
D. Assignment materials on Section II.. 11B
III. The Categorical Syllogism.......... 13R
A. The Nature of the Syllogism.... 13B
B. Rules of the Syllogism.......... 14B
1. Rule 1..........................- 14B
2. Rule 2.......................... 15B
3. Rule 3...................... 15B
4. Rule 4...................... 1CB
5 . Rule 5 . .... 16B
6 . Rule 6 . . . ............ 1-7B
7 . Rule 7...... ............... 17B
8. Assignment on Rules of the
Syllogism.................. 17B
C. Moods and Figures of the Syllogism.. IBB
1. The First Figure............... 19B
2. The Second Figure.............. 19B
3. The Third Figure............... 19B
4. The Fourth Figure.............. 20B
D. Assignment materials on the Syllogism 21B
IV. Of Conditional Arguments........... 24B
A. Of H^potheticals . ........ 24B
B. Of Disjunctives................. 25B
V. The Enthvrneme.................
VI. Glossary of Terms.............
VII. Suggested Readings ............
VIII. Test, Form A .................. .
Eh Test, Form B....... .......... .
APPENDIX C TABLES
Part I. Original Lata
Part II. Validity....
Part Ill* Reliahilitv..
Part IV. Item Analysis
Part V. Results ......
APPENDIX D BIBLIOGRAPHY
Part I, Psychology: of Thinking. . . . ID
Part II. Argumentation and I>Lnte.« 4D
Part III. Logic and Reasoning...... 5D
PREFACE
THE PLACE OF THE SYLLOGISM
IN RHETORICAL THEORY
The rhetorical and logical systems developed by
Aristotle have exerted a tremendous influence for more
than 2000 years. These systems as conceived by Aristotle
are closely related, as the following statement from the
Rhetoric^* reveals t
01?thymeme, again, Is a kind of syllogism: now
every kind of syllogism falls within the province of
Dialectic, and must be examined under Dialectic as a
whole, or under some branch of it. Consequently the
t^e clear©st insight into the nature of
syllogisms, who knows from what premises and in what
?6y may 5® COI*structed, will also be the most
ent3?yra^s* once he had mastered
special province th3-ngs contingent and
uncertain such as human actions and their consequen­
ces:), and has learnt the differences between
enthymemes and logical syllogisms.
The Middle Ages, dominated by the authoritarianism
the Church, witnessed the decadence and distortion of
both the rhetorical and logical systems. Rhetoric, during
this period, was concerned primarily with style and
delivery. Logic was used as a coercive device for support
of dogmatic views of the Church. The "Logic of Consistency"
conceived by Aristotle became a "Logic of Authority" during
this period.
Cooper (translator), The Rhetoric
y - Aristotle. New Yorks D. Appleton-Century Company, 1932,
ieX P* 5. t
Th® Renaissance and Reformation brought about a new
era in history* Men began to examine the world about them
in a new way* "What are the facts?" became a paramount
question* The revolt against the authoritarianism of the
Middle Ages witnessed men like Peter Ramus defending such
theses as "Everything that Aristotle said is falsa."
Explanation for this revolt in its several forms can be
found in at least two circumstances: (1) It must be remem­
bered that during the Middle Ages the Rhetoric of Aristotle
and the better logical works of Aristotle and other
Classical writers were lost; (2) It must also be kept in
mind that the criticisms of this period by men like Ramus
were not criticisms of the "real" Aristotle but of the
"received" Aristotle. Therefore, it is only natural that,
once started, criticisms of the logical system of Aristotle
have continued to the present day* These criticisms center
on the "deductive" syllogism as treated in the Prior
Analytics* The criticisms stem from two principal sources*
First, justified criticism of the syllogism as distorted by
Medieval Scholasticism, and second, criticisms arising from
a lack of understanding of the nature and fuction of the
syllogism.
The writings of Locke,1 Campbell,2 Bacon,3 Schiller,4
SIdgwick,5 and others have perpetuated these criticisms,
^John Locke, An Essay Concerning Human Understanding,
23rd ed. London: 1817“:; ' a
r
and they are oft repeated in the writings of today.
What are some of these cCriticisms and how valid
are they? Campbell, tacking his point of view from Locke,
condemns the syllogism as useless since f,it does not aid
in the discovery of truth*11 This objection is answered
clearly in the following statement by Edney:
It is evident that Campbell had given Aristotlefs
discovery the benefit of no more study than had John
Locke* Campbell*s discussion Ignores Aristotle*s
acknowledgment that the first principles of science
are learned by Induction as well as the fact that
Aristotle’s only purpose in proposing the syllogism
waa to lay down the conditions by which science
could "be sure of the validity of each step it takes*n
Campbell makes a second indictment that has been
made by many other writers that the syllogism Is useless
because of an alleged inherent petitio princlppii * This
charge Is answered by Whatel^as follows:
Such an objection against Aristotle’s dictum* no
one has ever attempted to establish by any kind of
proof; but it has often been taken for granted; it
being (as has been stated) very commonly supposed*
without examination, that the syllogism is m distinct
kind of argument, and that the rules of It accord-
ingiy"cTo not apply, nor were Intended to apply, to all
2
George Campbell, The Philosophy of Rhetoric, 7th ed
London: 1823.
^Francis Bacon, Novum Organum. London: W. Pickering,
1850. “
^P*C*S* Schiller, Formal Logic: A Scientific and
Social Problem. London: Macmillan and Company, Limited7~ 1912
5Alfred Sidgwick, The Application of Logic. London:
Macmillan and Company, Limited, 1910•
^■C.W. Edney, ”George Campbell’s Theory of Logical
Truth," Speech Monographs * Vol. XV, 1948, 19-32. (p. 31)
ill.
reasoning whatever. Under this misapprehension, Dr.
Campbell labors with some ingenuity, and not without
an air of plausibility, to show that every syllogism
must be futile and worthless, because the premises
virtually assert the conclusion: little dreaming, of
course, that his objections, however specious, lie
against the process of reasoning Itself, universally;
and will therefore, o? course, apply to those very
arguments which he is himself adducing.
Among modern writers, Nichols,^* taking his point
of view from SIdgwick deals most severely with the syllo­
gism. The following Is the essence of the criticism*
It remained for Professor Alfred Sidgwick in
comparatively modern times to deal syllogistic
logic a truly desperate thrust. He exposed the
fact that whenever any actual, truth-discovering
reasoning was necessary, the middle term was always
ambiguous, it was never identical; and the syllo­
gism was merely an ex post facto structure, forak-
ulated after the actual reasoning had been done*
Thus when we follow Professor Sidgwick*s exposure
to Its ultimate consequence, the syllogism is
discovered to be almost useless. If the middle term
is obviously the Same, as in the "mortality of
Socrates" example, then the conclusion is self-
evident; and even Euclid did not think it necessary
to reason about axioms. On the other hand, If the
middle terms in both premises are not obviously
identical, then we must compare them, and again the
syllogism Is futile. It cannot assure us of the
Identity of the middle term, hence It cannot guar­
antee its conclusion; and the correct conclusion Is
after all the entire objective of reasoning* In the
first Instance the syllogism is puerile; In the second
It is Incompetent*
This criticism is answered effectively by Whately2
In the following statement:
2Richard Whately, Elements of Logic. New York:
William Jackson, 1832, pp. 26-27.
^*Alan Nichols, Discussion and Debate. New York:
Harcourt, Brace and Company, 1$4i, pp. 3&4-337.
2Whately, op* eit.» p. 122.
iv*