O zasięgu twierdzenia Lindenbauma o nadsystemach zupełnych

Allatum est die 19 Septembris 1960     

О правилах исчисления предложе ий

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Evaluation of drug toxicity in clinical trials

An increasing number of drugs removed from the market because of unacceptable toxicity raises concerns regarding preapproval testing of drug safety. In the present paper it is postulated that the non-inferiority type of trial should be abandoned in favor of the superiority trial with active controls and less stringent (p<0.1, both for efficacy and toxicity) statistics. This approach will increase sensitivity of detection of drug-induced adverse effects at the expense of increasing false positive results regarding the difference in efficacy between the tested and reference drug. Such a move will increase the protection of future patients. In addition, the proposed design is far more acceptable from the clinical (e.g. no need to specify the statistically expected “unimportant” number of deaths) and ethical points of view, as well as being favored by the strong incentive of involved parties. In the second part of this paper arguments are presented in favor of the hypothesis that placebo (still used in some superiority trials) does not induce adverse effects. The assertion that placebo may induce adverse effects is probably biased by the nature of the clinical experiment. Such a conclusion is supported by studies indicating that placebo-induced adverse effects are disease — and treatment — specific. The modification of clinical trials according to the proposed changes may increase the trials’ sensitivity at detecting adverse effects of drugs. A lecture on the subject of this paper was presented at the 6th International Bioethics Conference on the subject of ‘The Responsible Conduct of Basic and Clinical Research’, held in Warsaw, Poland, 3–4 June 2005.     

The Pentus Theorem for Lambek Calculus with Simple Nonlogical Axioms

The Lambek calculus introduced in Lambek [6] is a strengthening of the type reduction calculus of Ajdukiewicz [1]. We study Associative Lambek Calculus L in Gentzen style axiomatization enriched with a finite set Γ of nonlogical axioms, denoted by L(Γ).It is known that finite axiomatic extensions of Associative Lambek Calculus generate all recursively enumerable languages (see Buszkowski [2]). Then we confine nonlogical axioms to sequents of the form p → q, where p and q are atomic types. For calculus L(Γ) we prove interpolation lemma (modifying the Roorda proof for L [10]) and the binary reduction lemma (using the Pentus method [9] with modification from [3]). In consequence we obtain the weak equivalence of the Context-Free Grammars and grammars based on L(Γ).     

Number of Extensions of Non-Fregean Logics

We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.     

On field's argument for substantivalism

In this article I subject to criticism Field's argument, according to which field theory takes space‐time to be à substance since it ascribes field properties to space‐time points. There is petitio principii error made in this reasoning because Field does not give any justification for his controversial assumption that fields are properties of space‐time points. What is more, I suggest, Field's interpretation of field theory is incompatible with the way this theory is understood and utilized by its users, namely scientists. My criticism is based on the assumption that one cannot propose an ontology of a given scientific theory, at the same time imposing on it an interpretation which clashes with the interpretation current among its users. I also suggest that in order to establish the ontology of a scientific theory one should also take into account the way it has been constructed. According to this criterion, field theory does indeed take space‐time to be a substance.     

A new formulation of discussive logic

S. Jakowski introduced the discussive prepositional calculus D ₂as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Costa and L. Dubikajtis, On Jakowski's discussive logic, in Non-Classical Logic, Model Theory and Computability, A. I. Arruda, N. C. A da Costa and R. Chuaqui edts., North-Holland, Amsterdam, 1977, 37–56). D ₂has afterwards been extended to a first-order predicate calculus and to a higher-order logic (cf. the quoted paper). In this paper we present a natural version of D ₂, in the sense of Jakowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus (with equality). A semantics for the new calculus is also presented.     

What is non-fregean in the semantics of Wittgenstein'sTractatus and why?

From J.M. Bocheski's Rady starego filozofa [Advice of the old philosopher]: 6. Pytaj sie Zawsze (i) co to znaczy? i (ii) dlaczego? [Ask always (i) what does it mean? and (ii) why?]