No Matrix Term-Equivalent to Wroński's 3-element Matrix is Finitely Based

Motivated by a question of W. Rautenberg, we prove that any matrix that is term-equivalent to the well-known nonfinitely based matrix of A. Wroski is itself also nonfinitely based.     

Sergei Hessen, Neo-Kantian Dedicated to Professor Andrzej Walicki

This paper commemorates thepresentation of the honorary doctorate, in May2001 by the University of ód, toProfessor Andrzej Walicki. On this occasion,the Honorary Graduate delivered a lecturedevoted to his first philosophy teacher –Sergej Iosifovich Hessen, a prominent RussianNeo-Kantian philosopher and a liberal inmatters social and political. I try to analyzethe main features of Hessen's philosophicalneo-Kantianism, in particular the inevitabilityof a choice between the absolute and therelative both in epistemology and in ethics inthe context of contemporary philosophy.     

Placebo in the investigation of psychotropic drugs,especially antidepressants

The paper presents major ethical, legal and methodological problems related to the use of placebo in mental disorders, especially in depression. It is pointed out that although authoritative groups of experts and numerous publications in the field of psychopharmacology indicate advisability of the double blind design with placebo in clinical trials of antidepressants, in recent years there have been more and more voices questioning legitimacy of this method. Objections of an ethical nature are raised, and reliability of this approach is put into doubt from the methodological viewpoint. These issues are discussed in more detail in the paper. Available alternative solutions should be implemented in psychotropic drug studies. The author shares these objections and doubts of an ethical nature, and believes that the placebo procedure is not a necessity in clinical trials of antidepressants. An earlier version of this paper was presented at an international conference, “Placebo: Its Action and Place in Health Research Today,” held in Warsaw, Poland on 12–13 April, 2003.     

Clinical trials: active control vs placebo — What is ethical?

The quest for effective medicines is very old. In modern times two important tools have been developed to evaluate efficacy of drugs: superiority and non-inferiority types of clinical trials. The former tests the null hypothesis of μ (the difference between a tested drug and comparator) ≤ 0 against μ > 0; the latter tests the null hypothesis of μ ≤ - Δ against, μ > - Δ, where Δ is the clinical difference from the comparator. In a superiority trial, a new drug is tested against a placebo; in a non-inferiority trial, a new drug is tested against active treatment. In this paper, arguments are presented to show that a superiority trial against a placebo is scientifically sound but ethically unacceptable, whereas a non-inferiority trial against active treatment is ethically sound but scientifically not reliable. Switching from a superiority type of trial with placebo to a non-inferiority trial with an active-control — following the latest revision of Declaration of Helsinki — is in practice switching from the violation of the uncertainty principle to uncertainty of results. Given human and financial resources, it appears an academic question as to which is more unethical: to violate patients’ rights or to produce results without scientific value. All presented considerations lead to the conclusion that the use of a superiority trial of design with an active control instead of placebo will satisfy scientific needs, expectation of patients, and the ancient quest for effective medicines. In the era of Good (Clinical, Laboratory, Manufacture) Practice, the attention of those performing clinical trials is focused on the procedure, not always on its essence. However even the excellent performance of a trial which is not worth doing is fruitless. An earlier version of this paper was presented at an international conference, “Placebo: Its Action and Place in Health Research Today,” held in Warsaw, Poland on 12–13 April, 2003.     

Löb's Theorem in a Set Theoretical Setting

We present a semantic proof of Löb's theorem for theories T containing ZF. Without using the diagonalization lemma, we construct a sentence AUT _T, which says intuitively that the predicate autological with respect to T (i.e. applying to itself in every model of T) is itself autological with respect to T. In effect, the sentence AUT _T states I follow semantically from T. Then we show that this sentence indeed follows from T and therefore is true.     

Some Eighteenth Century Contributions to the Mind–Body Problem (Wolff, Taurellus, Knutzen, Bülfiger and the Pre-Critical Kant)

This work speaks about very special solution of the mind–body problem. This solution based on the so-called Principle of Co-existence stands out as one of the most interesting attempts at solving the mind–body problem. It states that substances can only exert a mutual influence on one another if they have something in common. This does not have to be a common property but rather, a binding relationship. Thus, substances co-exist when they remain bound by a common relationship, for instance, to an external subject. The Principle of Co-existence played an extremely important role in Kant’s philosophy, not only since it provided a framework for solving the mind–body problem, but since it captured the very basis of its existence. The Principle found also reflection in the works of Kant’s successors, such as Fichte, Schelling, Hegel or Feuerbach. It had significant—though often hidden—repercussions on later philosophy of mind. The notion of force and the principle of its operation became key concepts in resolving the mind–body problem. As a result, philosophy of mind concentrated on the search for a principle explaining the occurrence of two complementary types of phenomena. This established a tradition which, to a greater or lesser extent, has survived to our day.