1. Tributes
For many years my own knowledge of the book
was based on three brief accounts of it.
In 1975 I read an article by Boleslaw Sobocinski
, written at the time of Lukasiewicz's death.
Speaking of this book, he says:
We find a detailed analysis of all the passages
in Aristotle which relate to this topic [i.
e., to the principle of contradiction]. All
possible interpretations of these texts are
presented and discussed thoroughly. The problems
raised by the principle of contradiction
are presented in so clear and precise a way
that even a mind untrained in philosophy
can understand them at once. Moreover, Lukasiewicz
for the first time used the methods of symbolic
logic in order to obtain a strict analysis
of the problems under investigation.... The
influence of this book was extremely great
on Polish philosophers of that generation,
regardless of their philosophical schools.
This book set Lukasiewicz at the forefront
of the Polish philosophers of his time. Looking
back on it over a span of forty-six years,
we can say that its historical and analytic
parts are still the best that have appeared
on this subject. Even now, if this book were
translated into other languages, it would
gain fresh renown (Sobocinski 1956, pp. 10-11).
He goes on to say that on its logical side
the book is dated and sometimes in error;
for our knowledge and understanding of logic
have grown, partly of course in consequence
of Lukasiewicz's own later discoveries. Because
Sobocinski's article is admittedly a eulogy
of Lukasiewicz, we must read it with some
caution to filter out some of its excessive
enthusiasm.
Later in 1975 I was reading the philosophical
autobiography of Stanislaw Lesniewski, where
I found the following:
In 1911, during my years as a student, I
came across Jan Lukasiewicz's book On the
Principle of Contradiction in Aristotle.
In its time this book significantly influenced
the intellectual development of a succession
of Polish 'philosophers' and 'philosophising'
scholars of my generation, and it was in
many respects a revelation to me personally.
From it I learned for the first time of the
existence of 'symbolic logic', of Bertrand
Russell, and of his 'antinomy' concerning
'the class of the classes which are not elements
of themselves’ (Lesniewski 1927, p. 169).
Finally in the Encyclopedia of Philosophy
I found an article on Lukasiewicz by Czeslaw
Lejewski , which states:
On the Principle of Contradiction in Aristotle
was one of the most influential books in
the early period of the twentieth-century
logical and philosophical revival in Poland.
It must have stood high in the author's own
estimation, for in 1955 he began translating
it into English (Lejewski 1967, p. 104).
These tributes aroused my interest, but for
many years I was unable to obtain a copy
of the book, and there matters rested.
Lukasiewicz did publish in 1910, the year
in which the book appeared, a German summary
of it, which is twenty-three pages long,
about one tenth of the length of the book
(Lukasiewicz 1910a). This summary has been
reprinted (in German), and has appeared in
two English translations, and once in French.
These summaries have been the primary means
of access to the original for most European
readers. Clearly a short summary must omit
most of the content of the longer work.
2. History
I now have some understanding of why this
book was so influential. Like many of Lukasiewicz's
other works, it covers a wide variety of
topics. Some readers might have felt the
book contains too much peripheral matter,
but most found something in it that encouraged
them to read it. Shortly after its publication,
Lukasiewicz became very well known. In 1915
he was appointed Professor of Philosophy
in the Faculty of Mathematics at the newly
reopened University of Warsaw. Two years
later he was elected Rector of the University.
For a year in 1919 he joined the Cabinet
as Minister of Education. Later his textbook,
The Elements of Mathematical Logic, was popular
in schools and universities. These circumstances
surely encouraged and maintained interest
in his works.
Moreover, Lukasiewicz was a good stylist.
He was always clear and persuasive. He was
a gifted orator, and his writings are said
to read well aloud. His works thus appealed
to many readers who knew little of the subjects
he discussed. There were articles in Polish
which mention symbolic logic as early as
1888, but this book, which appeared in the
same year as Whitehead and Russell's Principia
Mathematica, became the first popular introduction
to the theory in Poland. One copy, which
was part of a library for Polish soldiers
in England during the Second World War, contains
many underlinings and marginal notes by at
least two of its readers.
At the end of that war, Lukasiewicz and his
wife escaped from Warsaw only two weeks before
the Uprising, which destroyed everything
they left behind. They intended to go to
Switzerland, but ended up in Belgium, where
Lukasiewicz taught children in a Polish refugee
camp. He brought a few of his papers with
him, but no books. Early in
1946 the Irish government invited him to
Dublin, to lecture on logic at University
College. On his way to Dublin, he spent two
days in London, where he happened to meet
one of his former students, Czeslaw Lejewski,
who later completed his second doctorate
at the University of London under Karl Popper.
Lukasiewicz was asked to come to London to
be Lejewski's external examiner, and there
Lejewski presented him with a copy of The
Principle of Contradiction in Aristotle which
he had obtained there. It was this copy that
Lukasiewicz used when he began his English
translation of the book less than a year
before his death.
Lukasiewicz suffered from severe kidney problems,
and he was unable to complete the translation
before he died in Dublin on February 13,
1956. 1 believe his wife placed the Polish
copy of the book in his coffin. Lejewski
was asked to take charge of Lukasiewicz's
remaining papers. It was he who saw the second
edition of Aristotle's Syllogistic through
to publication, correcting the proofs of
the new chapters and enlarging the index.
He brought Lukasiewicz's incomplete translation
of the older book back to England, and in
1994 he asked me to revise and complete the
project.
1.3. Lukasiewicz's English version
Lukasiewicz was a methodical worker. He produced
at least two draughts of everything he wrote,
even letters. The first draught of his English
version is lost, and was probably not much
longer than the second draught, of which
we have what appears to be a carbon copy.
It begins on April 6, 1955-almost every page
is dated at the top-and it ends in the middle
of a sentence at the bottom of a page on
September 27 of the same year. It is possible
that further pages have been lost. He wrote
one page of translation every day, except
apparently when travel or illness prevented
him. There are 100 pages, which cover pages
1 to 118 of the original book, which was
212 pages long.
The first page may serve to illustrate the
difficulties of revision. I think you can
'taste' Lukasiewicz's oratorical style even
in translation:
There are two moments in the history of philosophy
when contr6versy about the principle of contradiction
excited the minds: with one of them is connected
the name of Aristotle, with the other the
name of Hegel. Aristotle has formulated the
principle of contradiction as the highest
law of thinking and being. In a stubborn
polemic, in which indignation and contempt
is vibrating, he persecuted all those who
would not accept this law.. .. [I skip over
their names.] He has won this fight, and
so great was the force of his arguments,
or so right the cause defended by him, that
through whole centuries nobody dared to deny
that highest principle. Only, Hegel revived
the opinions buried by Aristotle, i [the
Polish word for 'and'] let us believe that
reality is reasonable and contradictory at
the same time. He restored the esteem to
the Greek Sophists, and included the statements
of Heraclitus into his system of logic. This
doctrine caused again an ardent discussion:
they strived to bury Hegel with the words
of Aristotle. These contr6versies have now
died away, and the problem of the principle
of contradiction is not actual. The better,
as it can be considered sine ira.
Instead of reading out my own version of
this passage, I shall point out some of the
difficulties in this one:
1. The word 'moments' does not express 'extended
periods of time'.
2. 'Excited the minds of philosophers'.
3. It is Aristotle, not the polemic, who
is stubborn.
4. 'Vibrating' does not work. Lukasiewicz
intends to suggest that Aristotle is unusually
upset, that he has lost his self-control.
5. 'So great was the force': the word 'evidently'
has been omitted.
6. 'So right the cause': it would be better
to say 'so just the cause' to make it clear
that moral values are involved.
7. 'Only Hegel': the original actually says
'but Hegel', but the translation sounds as
if it means 'Hegel alone'.
8. 'Opinions buried by Aristotle': the phrase
'long before' is omitted.
9. 'The problem of the principle of contradiction
is not actual': the word 'actual' in English
does not mean 'a subject of current interest'.
10. The expression 'sine ira' is not a Latin
phrase familiar to most English readers.
Besides these specific points, Lukasiewicz
has the usual difficulties with definite
and indefinite articles and with word order
in English, though I must admit that some
other Poles are worse.
Lukasiewicz's translation is fairly intelligible
and does present a valuable guide to the
original text. Moreover it expresses his
wish to change the format of the text slightly.
For example, in the original book Greek,
German, Latin, and other foreign quotations
appear in the text, followed by a Polish
translation. But in the manuscript Lukasiewicz
moves most of the foreign text into footnotes;
only the English translations appear in the
text.
Incidentally, Lukasiewicz's knowledge of
English dates back many years. He had at
least a reading knowledge of it by 1905,
when in collaboration with Kazimierz Twardowski
he produced a Polish translation of Hume's
Essay concerning Human Understanding, which
(being a translation) does not usually appear
in the lists of Lukasiewicz's publications.
I don't believe he tried to speak English
before he went to Dublin in 1946, and his
first article actually written in English
was published two years later, in 1948.
Before we continue I should like to point
out that the epigraph at the top of the first
page is a twist on a phrase by Aristotle.
He wrote
M G 6 1011 a 12 They look for a proof of
things which have no proof.
and Lukasiewicz says
We look for a proof of things, which do have
a proof.
4. Summary of the book
The book consists of an introduction, twenty-one
sections each about eight pages long, and
an appendix containing nine further sections.
In the introduction, Lukasiewicz remarks
that the study of the philosophical foundations
of arithmetic and geometry led to a better
understanding of those fields and to new
developments in them. So too reexamining
the foundations of logic should prove fruitful.
He knew that such work had begun-he mentions
Russell, Couturat, Frege, Peano, Hilbert,
and others-but he saw in Aristotle the historical
origin of logic in a way in which Western
logicians did not.
Western (by which I mean mostly English-speaking)
logicians (British, American, and later Australian
logicians) often hold Aristotle in contempt,
but in Poland, at least before the Second
World War, Aristotle was more highly respected,
and most Polish logicians felt that they
were building on and developing his tradition
rather than replacing it. If the Western
view is largely due to Bertrand Russell,
the Polish view is certainly indebted to
Lukasiewicz. Besides Lukasiewicz himself,
Stanislaw Lesniewski, Tadeusz Kotarbinski
, Jan Slupecki , Czeslaw Lejewski, and others
lectured on and wrote about Aristotle's logic.
Lukasiewicz also promoted a new interest
in and understanding of the Stoics and of
medieval logicians. A respect for the logical
tradition is evident throughout the Principle
of Contradiction in Aristotle.
The first fifteen sections of the book are
concerned more directly with Aristotle; we
shall look at these more closely later. The
next five sections are more concerned with
contemporary ideas. For example, section
18, 'The principle of contradiction and mental
constructs', discusses Meinong's complete
and incomplete objects, abstraction, Dedekind's
idea that mathematical theories are 'free
creations of the human spirit', the foundations
of set theory, Russell's and other antinomies.
Here Lukasiewicz suggests that, while the
principle of contradiction does obtain in
the 'real world', it may not apply to 'free
creations of the human spirit', that there
may possibly be 'contradictory a priori objects'.
This view he later rejected.
At the end of the main part of the book,
Lukasiewicz sees the principle of contradiction
as our only weapon against error and falsehood.
He wants it to be true, but feels that we
can never establish it with certainty. Still,
he says, we ought to accept it as probable,
at least as far as the 'real world' is concerned.
Aristotle feared the consequences of rejecting
it, and so accepted it as an axiom, as unassailable
dogma.
The Appendix, an introduction to symbolic
logic, was evidently written before Lukasiewicz
came to be familiar with the 'theory of deduction',
later known as the 'propositional calculus',
as a distinct branch of logic. For this reason
he based his presentation on the better known
turn-of-the-century logicians, and particularly
on a textbook by Couturat. Nevertheless it
contains some ideas which Lukasiewicz originated,
and which had some influence on later Polish
philosophers. For example, in the following
section he classifies valid reasoning into
four divisions. He says
The relation of consequence is an asymmetric
relation; that is, when it occurs in the
direction from a to b, it can but need not
occur in the direction from b to a. This
feature is the basis for dividing reasoning
into deduction and reduction. Deductive reasonings
run in the direction of the relation of consequence,
and reductive reasonings run contrary to
the direction of this relation. So I reason
deductively when from a given judgment a
I infer a judgment b, which follows from
a. I reason reductively when for a given
judgment b I find a judgment a from which
b follows.
The two kinds of deductive reasoning are
inference and testing. Inference occurs when
the point of departure of reasoning is a
judgment, which is certain, and I prove some
consequences from it. [I omit the examples
Lukasiewicz gives for each kind of reasoning.]
Testing occurs when the point of departure
of reasoning is an uncertain judgment, which
I try to make probable by finding true consequences.
[He means also that if he finds false consequences,
the starting point fails the test.] The two
kinds of reductive reasoning are proof and
explanation. Proof occurs when the point
of departure of reasoning is an uncertain
judgment for which I seek true grounds. [In
other words, if he can infer it by valid
inferences from premises, which are certain,
he has proved it.] Explanation occurs when
the point of departure of reasoning is one
or more certain judgments, and I seek some
reason from which these judgments follow.
Note that here Lukasiewicz regards the traditional
process of induction as just one kind of
‘explanation’.
I hope you can see that the Principle of
Contradiction in Aristotle covers a wide
range of subjects, most of which continued
to interest Lukasiewicz for the rest of his
life. And now I would like to look more closely
at his interpretation of Aristotle.
5. Formulations of the principle of contradiction
Aristotle has several formulations of the
principle of contradiction, which Lukasiewicz
classifies into three groups.
The ontological principle of contradiction
states that no object can have and not have
the same property. Here are two of the texts
which Lukasiewicz says express this form
of the principle:
1. M G 3 1005 b 19-20 For the same [property]
cannot together belong and not belong to
the same [object] and in the same respect.
2. M B 2 996 b 29-30 And it is impossible
together to be and not to be.
The logical principle of contradiction states
that two contradictory sentences cannot both
be true. A text expressing this formulation
is:
3. M G 6 1011 b 13-14 So that this is the
most certain of all opinions: contradictory
sentences are not together true.
The psychological principle of contradiction
states that two beliefs corresponding to
contradictory sentences cannot exist together
in the same mind. A text expressing this
formulation is:
4. M G 3 1005 b 23-26 For it is impossible
for someone to believe that the same is and
is not, as some people think Heraclitus said,
but it isn't necessary that someone believes
what he [someone] says.
Lukasiewicz translates upolambanein as 'believes',
but he takes great pains to justify this,
referring not only to the commentators Schwegler
and Maier but also to a series of passages
taken mostly from the de Interpretatione.
He might have used the word 'judgment' instead
of 'belief' if he were not already using
this term to mean 'sentence' in harmony with
the usage of late nineteenth century philosophers.
He says that a belief (doxa or upolepsis)
is a psychic act or decision accepting something
as true. I would distinguish this belief
from pistis, which seems to be a state of
mind resulting from making a judgment.
Lukasiewicz asks whether it is possible that
the three formulations, which Aristotle does
not explicitly distinguish, express three
distinct principles or just one principle
in three different ways. To answer this he
asks, when do two sentences express the same
thought in different ways? The sentences
'Aristotle was the creator of logic' and
'the Stagyrite was the creator of logic'
appear to express the same thought in different
words, because they both refer to the same
object, the same man. Two sentences are equivalent
when the first follows from the second and
the second follows from the first. (In Aristotle's
Syllogistic Lukasiewicz presents a more mature
version of the same notion as deductive equivalence.)
Two sentences are synonymous when they both
attribute or deny the same property to the
same object.
From this it follows that synonymous sentences
are always equivalent to each other, but
some equivalent sentences are not synonymous.
For example, 'Aristotle was a pupil of Plato'
and 'Plato was a teacher of Aristotle' are
clearly equivalent, but since the first sentence
is about Aristotle, while the second is about
Plato, they are not synonymous. (In his later
works, Lukasiewicz proposes a more complex
notion of synonymity because of his rejection
of the Aristotelian notion that every sentence
asserts or denies that some object has some
property. Even here he states that he feels
his definition of synonymity is not generally
adequate, but that it is sufficient for his
present purpose.)
If we accept these ideas, however qualified,
we can see that the three formulations of
the principle of contradiction are not synonymous,
because the ontological formulation refers
to objects and properties, the logical formulation
to sentences, and the psychological to beliefs.
This argument has a considerable influence
on other Polish philosophers; for example,
a few years later Lesniewski argues against
Whitehead and Russell that the sentences
'p' and 'it is true that "p" cannot
be synonymous, since, for example, the sentence
'Warsaw is a city on the river Vistula' refers
to Warsaw, while the sentence 'it is true
that "Warsaw is a city on the river
Vistula"' does not refer to Warsaw,
though it does refer to another sentence
which refers to Warsaw.
Even if two sentences are not synonymous,
they may be equivalent. Lukasiewicz argues
that although Aristotle does not state this
explicitly, the ontological and logical principles
of contradiction are equivalent on Aristotelian
grounds. For example,
5. E 9 18 a 39-18 b 1 If it is true to say
that something is white or not white, then
it must be white or not white.
The context, says Lukasiewicz, makes it clear
that this example is typical; that is, that
any property at all can replace 'white'.
Therefore
a) If we had an exception to the logical
principle of contradiction, we would have
two true contradictory sentences.
b) One of these sentences would affirm that
some object has some property, and the other
would deny that the same object has the same
property.
c) Following Aristotle's example, we must
infer from the first true sentence that the
object does have the property, and from the
second that it does not have the property.
This violates the ontological principle of
contradiction.
In other words, if the logical principle
fails, so does the ontological principle.
Therefore if the ontological principle holds,
so does the logical principle. The converse
is also true if we accept certain other statements
by Aristotle. For example,
6. E 9 18 b 1-2 And if [something] is white
or not white, it would be true to affirm
or deny this.
7. M Q 10 1051 b 3-4 So that he speaks truly
who regards what is disjoint as being disjoint,
and what is conjoint as being conjoint.
From examples like these Lukasiewicz infers
that for Aristotle, if an object has a property,
a sentence which affirms that the object
has the property is true, and that if an
object does not have a property, a sentence
which denies that the object has the property
is true. Therefore
a) If there were an exception to the ontological
principle of contradiction, some object would
both have and not have some property.
b) According to Aristotle, a sentence affirming
that the object has the property, and a sentence
denying that the object has the property,
are both true.
c) These true sentences are contradictory.
This violates the logical principle of contradiction.
In other words, if the ontological principle
fails, the logical principle fails as well.
Therefore if the logical principle holds,
so does the ontological principle. If Aristotle
would accept these arguments based on his
own views, he would accept that each of the
principles, ontological and logical, follows
from the other, so that, while they are not
synonymous, they are deductively equivalent.
Lukasiewicz feels this is in complete harmony
with Aristotle's well-known definition of
truth: 1011b
8. M G 7 1011 b 27 Truth is to say of what
is that it is, and of what is not that it
is not.
Moreover Aristotle makes statements which
suggest that he would say that, while the
two principles are logically equivalent,
they are in some sense not really equivalent.
For example,
9. M Q 10 1051 b 6-9 For you are not white
because we hold truly that you are white,
but because you are white we who say so tell
the truth.
Hence if a sentence is true which ascribes
some property to some object, it follows
logically that that object has that property,
but the circumstance that the object has
the property is not only a logical reason
for the sentence being true, but also the
real cause why it is true. Lukasiewicz says
that, if Aristotle had been clearly aware
of this distinction, he would have accepted
it, as passage 9 shows.
6. The psychological principle of contradiction
Aristotle assumes tacitly that the ontological
and logical principles of contradiction are
equivalent, and emphasises that they are
ultimate principles and not provable. But
he does try to prove the psychological principle
explicitly from the other two. The proof
has two parts, of which the first is found
in this passage:
10. M G 3 1005 b 26-32 If it is not possible
for contrary properties to belong together
to the same [object], and contrary beliefs
correspond to contradictory sentences, then
clearly it is impossible for someone to believe
together that something is and is not, for
he would then have contrary beliefs together,
being mistaken in that respect.
At first glance this passage appears to confuse
contradiction (antifasis) with contrariety
(enantiousis). A solution was found by Alexander
of Aphrodisias and accepted by Maier; it
is based on a long passage in the de Interpretatione,
chapter 14, p. 23 a 27-24 b 3. Lukasiewicz
explains the passage as follows: According
to Aristotle, the relation of contrariety
exists between properties at extreme ends
of a series. Sentences are not properties,
so we cannot strictly speaking say that they
are contraries. But sentences expressed in
words correspond to beliefs in the psyché
and Aristotle treats beliefs as properties
of the mind in which they exist. Being properties,
beliefs can be contraries. Aristotle then
tries to show that beliefs which correspond
to an affirmation and a negation about the
same object are contraries; for example,
the belief that Callias is just and the belief
that Callias is not just. Lukasiewicz concludes
that the following represents Aristotle's
view:
A doxa or upolepsis is a psychic act which
exists in thought (en te dianoia) or in the
soul (en te psyché). In language (en te foné)
of this as a symbol (symbolon) there is a
sentence, which is either an affirmation
(katafasis) or a negation (apofasis).
Lukasiewicz believes that the following statement
in the de Anima supports his interpretation:
11. Y G 3 428 a 20-21 For it is not possible
for someone who has an opinion not to believe
in his opinion.
I must say that to me this suggests that
'belief' is the wrong way to translate ‘doxa’,
since it is a different kind of belief from
'pistis', unless Lukasiewicz means that 'pisteuein'
and 'doxazein' and 'upolambanein' are the
same, which I don't think he does. At any
rate, it is the above interpretation which
he feels justifies him in translating 'enantia
d’esti doxa doxe e tes antifaseos’ in passage
10 as 'contrary beliefs correspond to contradictory
sentences'.
Bearing all this in mind, Lukasiewicz rephrases
the first part of Aristotle's proof of the
psychological principle of contradiction
as follows:
No object can have contrary properties at
the same time. If someone could believe that
something is and at the same time believe
that it is not, he would have two contrary
beliefs, so that his mind would have two
contradictory properties. Therefore no one
can believe that something is, and at the
same time believe that it is not. In other
words, two beliefs corresponding to contradictory
sentences cannot exist together in the same
mind.
To prove the psychological principle of contradiction,
Aristotle has only to prove that no object
can have two contrary properties at the same
time. To do this he makes use of the logical
principle of contradiction, reasoning as
follows (This is my paraphrase of Lukasiewicz's
paraphrase of Aristotle):
Whenever two properties are contrary, there
must be some property which one contrary
involves having, while the other contrary
involves lacking it. Thus, for example, white
and black are contrary properties. There
must be some property, such as reflecting
light, that being white involves having,
while being black involves not having. So
if some object is white and the same object
is black, it follows that it is true that
the object has the property of reflecting
light, and it is true that it does not have
the property of reflecting light. This violates
the logical principle of contradiction. Therefore
no object can be together black and white.
Similar considerations obtain for any other
contrary properties.
To support this claim, Lukasiewicz cites
passage 12:
12. M I 4 1055 b 18 Every contrariety contains
lack of one of the contrary properties.
though he admits that this is not as clear
as it might be. But he feels that this same
principle is invoked in passage 13:
13 M G 1011 B 15-21 Since it is impossible
for contradictory sentences to be together
true of the same object, it is evident also
that contrary properties cannot together
belong to the same object. For one of two
contraries is no less a defect, a defect
of a thing. [That is, it is the lack of something
as well as being a contrary.] But defect
is negation of a certain kind. Therefore,
if it is impossible together to affirm and
to deny truly, is also impossible for contrary
properties to exist together.
The two parts of the proof establish the
psychological principle of contradiction
from the logical principle.
7. The proof of the psychological principle
of contradiction
Is Aristotle right to say that two beliefs
which correspond to contradictory sentences
must contain a contrariety, a hidden contradiction?
In the de Interpretatione Aristotle defines
contraries as follows:
14. E 14 23 b 22-23 Contrary properties are
those most different in the same respect.
So Aristotle needs some principle which establishes
an order among beliefs, and hence determines
two extreme ends of a series, which are contrary
to each other. In chapter 14 of the de Interpretatione,
just before passage 14, he argues that there
is a scale of truer and falser beliefs, with
the truest belief being one which ascribes
an essential property to an object, while
the falsest belief denies to an object an
essential property which it actually has.
Lukasiewicz argues:
It is impossible to agree with this. We cannot
accept that there are differences of degree
in truth or falsity. If a sentence ascribes
to an object a property which it has, the
sentence is true regardless of whether the
property is essential or accidental, or belongs
to the object permanently or temporarily..
.. If we want to accept the existence of
sentences which are more true or less true,
we must change the definition of truth.
He has a more serious objection to Aristotle's
argument about contrary beliefs and contrary
sentences. He says,
In chapter 14 of the de Interpretatione there
appears, probably for the first time in the
history of philosophy, a now too common confusion
of logical with psychological questions.
. .. In order to solve... a logical problem,
Aristotle tacitly assumes the false supposition
that the relations between sentences are
the same as the relations between beliefs.
He goes on to say that, being unable to give
an accurate psychological analysis of the
relations between beliefs, Aristotle actually
treats them as sentences. He ascribes to
beliefs relations which exist only between
sentences, such as the relation of consequence,
and properties which belong only to sentences,
that is, truth and falsity. After several
pages of argument, Lukasiewicz concludes:
The continuous confusion of beliefs and sentences
is why the psychology of knowledge consists
chiefly of logical analyses based on a priori
suppositions instead of on experience. The
argument in chapter 14 of the de Interpretatione
belongs to such pseudo psychological analyses.
And therefore Aristotle's proof of the psychological
principle of contradiction is a failure.
The fact that an argument is bad does not
make its conclusion false. But Lukasiewicz
argues that beliefs are mental phenomena,
and that such objects of experience have
relations which cannot be investigated adequately
by reasoning from a prioristic premises.
We could, of course, assume axioms and infer
conclusions from them. We could demonstrate
that such an axiom is false by deriving false
conclusions from it, but even if we found
only true conclusions, the axioms would never
become certain, only probable at best, since
we would be employing the kind of reasoning
he calls 'testing'. In the light of these
considerations, the psychological principle
of contradiction is at best an empirical
law. After examining some arguments from
Husserl, Lukasiewicz comes to doubt that
the psychological principle of contradiction
is in fact true. Looking at the history of
philosophy, he finds three possible counter
examples:
a) Heraclitus, although no actual instance
of contradictory beliefs appears to have
survived in Heraclitus's own words.
b) Hegel, who says clearly and unambiguously,
'Something is in movement ... because in
one and the same 'now' it is here and not
here, and in that here it simultaneously
is and is not.
c) Lukasiewicz, because he accepts the Athanasian
creed, which contains apparently contradictory
statements.
He admits that none of these examples disproves
the psychological principle of contradiction
to anyone else, because after all, counter
examples must exist in one person's mind,
and so cannot be exhibited to someone else.
You may claim to have contradictory beliefs,
but, as Aristotle says in passage 4, it is
not necessarily the case that someone believes
what he says. But whether you accept Lukasiewicz's
arguments or not, he feels that the psychological
principle of contradiction is uncertain and
doubtful, and hence not suited to be a fundamental
principle of logic, so that we can dismiss
it from further consideration. He concludes,
'The way to the fundamental principles of
logic does not lead through psychology'.
And this conclusion was readily accepted
by all the Polish philosophers whom I have
studied.
8. Conclusion
In the remainder of his book, Lukasiewicz
explains why he feels that Aristotle becomes
upset by the possibility that someone might
reject the logical or ontological principle
of contradiction, why he insists that they
are indemonstrable, how he nevertheless tries
to prove them in five different ways, and
that each proof either proves something else,
something which is not the principle of contradiction,
or else commits some logical error which
makes it invalid. After examining the relations
between the principle of contradiction and
other laws, Lukasiewicz observes that it
is not in fact very useful as a logical tool,
and consequently he calls into question its
status at the most fundamental of all principles.
We do not have the time to examine these
arguments in detail. But I hope that what
I have said has convinced you of three things:
First, that Lukasiewicz's disagreements with
Aristotle are based on a careful examination
of a large number of texts in several of
Aristotle's works. Consequently the summary
of this book (which is more accessible to
those who do not read Polish) does not give
a complete or adequate account of its contents.
Second, that it is reasonable to accept the
statements by Sobocinski, Lesniewski, Lejewski,
and myself. this book appealed to a wide
variety of readers, and so had a considerable
influence on the development of Polish thought
in the early part of this century.
Finally, that this work is still of interest
today, so that if I am able to complete a
translation of the book, you might be willing
to read it.
|
Evans Experientialism 
