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Between the two world wars, Stanislaw Lesniewski (1886-1939),
created the famous and important system of foundations of
mathematics that comprises three deductive theories: Protothetic,
Ontology, and Mereology. His research started in 1914 with studies
on the general theory of sets (later named `Mereology'). Ontology
followed between 1919 and 1921, and was the next step towards an
integrated system. In order to combine these two systematically he
constructed Protothetic - the system of `first principles'.
Together they amount to what Z. Jordan called `... most thorough,
original, and philosophically significant attempt to provide a
logically secure foundation for the whole of mathematics'. The
volume collects many of the most significant commentaries on, and
contributions to, Protothetic. A Protothetic Bibliography is
included.
The book is divided into chapters, but several themes run across
them. This is, in fact, the reason for writing a book rather than a
number of independent articles; for it appears that several moments
of Kant's work are characterized by similar problems, and
consequently we might be unable to see the impact of these on a
more 1 i mi ted canvas. But further, and perhaps no less
importantly, the shared problems are likely to be indicative of the
nature of the whole area under discussion. Given this, to
concentrate our attention on them should provide clarification not
accessible in any other way. It is one of the objects of the
present book to obtai n thi s clarification, and to apply it to the
area itself, rather than merely to utilize the results in Kantian
exegesis and elucidation. Thus the aim is not predominantly
historical. Of the various themes, the theme of Space and Time
turns out to be of prime importance to the whole picture presented,
and within it, the theme of space. This is not perhaps surprising,
for Kant's central task is to provide for objectivity; i. e. , to
explain how a "subjective" stream of perceptions can amount to a
perception of the world in which there are both subjective and
objective moments.
Stanislaw Lesniewski (1886-1939) was one of the leading Polish
logicians and founders of the Warsaw School of Logic whose
membership included, beside himself, Jan Lukasiewicz, Tadeusz
Kotarbinski, Alfred Tarski, and many others. In his lifetime
LeSniewski published only a few hundred pages. He produced many
important results in many areas of mathematics; these stood in
various relations to each other, and to materials produced by
others, and, in time, created more and more editorial problems.
Very many were left unpublished at the time of his death. Then in
1944 in the fire of Warsaw the whole of this material was burned
and lost -a considerable loss since a great deal of what is
important could have been reconstructed from these notes. The
present publication aims at presenting unique Lesniewski's
materials from alternative sources comprising lecture notes taken
during some of Lesniewski's lectures and seminars delivered at the
University of Warsaw be tween the two world wars. The editors are
aware of the limitations of student notes which cannot compensate
for the loss of the original materials. However, they are unique in
reflecting Lesniewski's ideas as he himself presented them. Already
at the time of his death it was realized that these notes would
provide a unique access to Lesniewski's own thought as well as a
valuable record of some of the activities of the Warsaw School of
Logic."
Section 1 One of the big problems facing us is the need to plan for
the betterment and improvement of society. In any status quo there
are many unsatisfactory moments and experience shows that with
changing conditions, even those elements of our communal structure
that work well will often get out of step and become a problem. We
need then to introduce devices both to alleviate present troubles
and, if possible, to anticipate future ones. On the whole, it might
appear to the untutored eye that the matter is relatively simple.
For instance, if we keep increasing prices of commodities without
increasing incomes, and especially if we allow inflation to proceed
unfettered as well, the situation will certainly deteriorate. What
we need to
l. THE GENERAL PROBLEM OF EPISTEMOLOGY There is a philosophical
issue that surely precedes all other possible questions. It
concerns the very possibility of our thinking about some thing to
some purpose. Short of this no philosophy, theory or research would
be possible. But it is not immediately clear that we are assured
that what purports to be effective thought, and cognition is such
in reality. What guarantee is there for instance that when one is
under the impression that one is thinking that "the cat is on the
mat" it is in fact the case that one is thinking this? One could
not be thinking at all, only having a misleading mystic experience.
And then even if one was thinking, one might not be really thinking
of the cat being on the mat, but only that one wishes there was a
cat, and wonders whether if there was it would be on the mat, and
yet the subjective impression was that one was thinking: "The cat
is on the mat" (the same picture might stand for both the thoughts
mentioned). Then one might in some way try to think 'the cat is on
the mat. ' yet be mistaken in that there aren't any material
objects at all, and all one does is to inventory god's perceptions.
And so on, and so on These are of course the kind of problem that
the layman habitually views with disdainful alarm."
Philosophy flourished in Australia after the war. There was
spectacular growth in both the number of departments and the number
of philosophers. On top of this philosophy spread beyond the
philosophy departments. Serious studies, and interest in philosophy
is now common in faculties as diverse as law, science and
education. Neither is this development merely quantitative, the
Australian researcher has come of age and contributes widely to
international debates. At least one movement originated in
Australia. This makes the study of philosophy in Australia timely,
evidenced by the number of articles concerned with this area that
begin to appear in international journals. In Australia itself
there is growing interest in the history of the country's
philosophical development. There are discussions in conferences and
meetings: the matter is now the subject of courses.
Between the two world wars, Stanislaw Lesniewski (1886-1939),
created the famous and important system of foundations of
mathematics that comprises three deductive theories: Protothetic,
Ontology, and Mereology. His research started in 1914 with studies
on the general theory of sets (later named `Mereology'). Ontology
followed between 1919 and 1921, and was the next step towards an
integrated system. In order to combine these two systematically he
constructed Protothetic - the system of `first principles'.
Together they amount to what Z. Jordan called `... most thorough,
original, and philosophically significant attempt to provide a
logically secure foundation for the whole of mathematics'. The
volume collects many of the most significant commentaries on, and
contributions to, Protothetic. A Protothetic Bibliography is
included.
l. THE GENERAL PROBLEM OF EPISTEMOLOGY There is a philosophical
issue that surely precedes all other possible questions. It
concerns the very possibility of our thinking about some thing to
some purpose. Short of this no philosophy, theory or research would
be possible. But it is not immediately clear that we are assured
that what purports to be effective thought, and cognition is such
in reality. What guarantee is there for instance that when one is
under the impression that one is thinking that "the cat is on the
mat" it is in fact the case that one is thinking this? One could
not be thinking at all, only having a misleading mystic experience.
And then even if one was thinking, one might not be really thinking
of the cat being on the mat, but only that one wishes there was a
cat, and wonders whether if there was it would be on the mat, and
yet the subjective impression was that one was thinking: "The cat
is on the mat" (the same picture might stand for both the thoughts
mentioned). Then one might in some way try to think 'the cat is on
the mat. ' yet be mistaken in that there aren't any material
objects at all, and all one does is to inventory god's perceptions.
And so on, and so on These are of course the kind of problem that
the layman habitually views with disdainful alarm."
Philosophy flourished in Australia after the war. There was
spectacular growth in both the number of departments and the number
of philosophers. On top of this philosophy spread beyond the
philosophy departments. Serious studies, and interest in philosophy
is now common in faculties as diverse as law, science and
education. Neither is this development merely quantitative, the
Australian researcher has come of age and contributes widely to
international debates. At least one movement originated in
Australia. This makes the study of philosophy in Australia timely,
evidenced by the number of articles concerned with this area that
begin to appear in international journals. In Australia itself
there is growing interest in the history of the country's
philosophical development. There are discussions in conferences and
meetings: the matter is now the subject of courses.
Stanislaw Lesniewski (1886-1939) was one of the leading Polish
logicians and founders of the Warsaw School of Logic whose
membership included, beside himself, Jan Lukasiewicz, Tadeusz
Kotarbinski, Alfred Tarski, and many others. In his lifetime
LeSniewski published only a few hundred pages. He produced many
important results in many areas of mathematics; these stood in
various relations to each other, and to materials produced by
others, and, in time, created more and more editorial problems.
Very many were left unpublished at the time of his death. Then in
1944 in the fire of Warsaw the whole of this material was burned
and lost -a considerable loss since a great deal of what is
important could have been reconstructed from these notes. The
present publication aims at presenting unique Lesniewski's
materials from alternative sources comprising lecture notes taken
during some of Lesniewski's lectures and seminars delivered at the
University of Warsaw be tween the two world wars. The editors are
aware of the limitations of student notes which cannot compensate
for the loss of the original materials. However, they are unique in
reflecting Lesniewski's ideas as he himself presented them. Already
at the time of his death it was realized that these notes would
provide a unique access to Lesniewski's own thought as well as a
valuable record of some of the activities of the Warsaw School of
Logic."
Section 1 One of the big problems facing us is the need to plan for
the betterment and improvement of society. In any status quo there
are many unsatisfactory moments and experience shows that with
changing conditions, even those elements of our communal structure
that work well will often get out of step and become a problem. We
need then to introduce devices both to alleviate present troubles
and, if possible, to anticipate future ones. On the whole, it might
appear to the untutored eye that the matter is relatively simple.
For instance, if we keep increasing prices of commodities without
increasing incomes, and especially if we allow inflation to proceed
unfettered as well, the situation will certainly deteriorate. What
we need to
The book is divided into chapters, but several themes run across
them. This is, in fact, the reason for writing a book rather than a
number of independent articles; for it appears that several moments
of Kant's work are characterized by similar problems, and
consequently we might be unable to see the impact of these on a
more 1 i mi ted canvas. But further, and perhaps no less
importantly, the shared problems are likely to be indicative of the
nature of the whole area under discussion. Given this, to
concentrate our attention on them should provide clarification not
accessible in any other way. It is one of the objects of the
present book to obtai n thi s clarification, and to apply it to the
area itself, rather than merely to utilize the results in Kantian
exegesis and elucidation. Thus the aim is not predominantly
historical. Of the various themes, the theme of Space and Time
turns out to be of prime importance to the whole picture presented,
and within it, the theme of space. This is not perhaps surprising,
for Kant's central task is to provide for objectivity; i. e. , to
explain how a "subjective" stream of perceptions can amount to a
perception of the world in which there are both subjective and
objective moments.
The general purpose of this book differs from those of most of the
works found traditionally in the field of political philosophy.
Firstly, the present approach is in no way prescriptive or
normative, as the interest centres on explication rather than an
evaluative assess ment of this, that or another type of
arrangement, or act. 1 It will be clear that I am in complete
disagreement with Gewirth when he claims that "The central concern
of political philosophy is the moral evaluation of political power.
" It seems obvious that the under standing of political and social
forms of life, and a fortiori of political power, must come before
its evaluation. This cannot be provided by moral assessment alone.
Thus an analytical or explicative approach which promotes such
understanding must come first, and must be the "central concern" of
the appropriate philosophical discipline. This is not to say that
moral assessment is illegitimate, nor even that it cannot be one of
the concerns of political philosophy, but it is to deny that it can
be central, even though it might be somebody's central interest. To
the extent to which this book is successful it will provide an argu
mentin my favour - if the job can be done, obviously it is of
primary importance. But we should not assume that it cannot be done
unless we can show that there is no separate sphere of political
and/or social phenomena."
Franz Brentano 1 was an important philosopher, but for a long time
his importance was under-estimated. At least in the English
speaking countries, he came to be remembered best as the initiator
of a philoso phical position which he in fact abandoned for good
and sufficient 2 reasons. His ultimate and most important
contributions passed almost unnoticed. Even such a well-informed
and well-prepared book as Passmore's IOO Years of Philosophy
(Duckworth, I957), is open to the same comment; Passmore
concentrated his attention on the early Brentano, because he
regarded his influence on the British philo sophical scene as being
confined to Brentano's early work. Brentano's pupils, e. g.,
Husserl, Meinong, Marty and Twardowski, were often influential and,
often enough, they departed from the strict common sense and
advisedly cautious attitude of their great teacher. Thus even on
the continent, the public image of Brentano tended to be incomplete
(and sometimes distorted), outside the narrower circle of pupils,
followers, and people with special interest. This, or very nearly
this, was still the case in I955, when my contacts with the
followers of Twardowski made me turn towards the study of Brentano.
Since then there has been a gratifying revival of interest in his
work. His early book on Aristotle was reprinted in German and two
of his main positions, Psychologie and Wahrheit und Evidenz, are
appearing in English translations. Translations into other
languages, e. g."
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