Abstract A number is the number of a class which is an objective, nonactual, mathematical object. The concept of class is analyzed and it is concluded that a number is the number of a pure founded class. A tempting strategy of explaining numbers away is rejected. Some well?known definitions of numbers are analyzed and it is concluded that this analysis purports the thesis that the unique notion of number does not exist. Numbers are conventional. Nevertheless, an argument is offered purporting (...) the thesis that von Neumann's ordinal numbers are the ordinal numbers. Accordingly, the corresponding von Neumann's cardinal numbers are the numbers. (shrink)

Gentzen’s singular sequential system of first-order logic was an alternative notation for his system of natural deductions. His multiple sequential system was his symmetric generalization that was more appropriate to classical logic. Beth’s tableaus system was a system that was derived directly from the semantic analysis of connectives and quantifiers. It was soon realized that the Beth’s system and the Gentzen’s multiple system were only notational variants of each other. Kneale’s system of multiple natural deductions was a generalization of Gentzen’s (...) system of natural deductions. We prove that Kneale’s natural deductions are also a notational variant of Beth’s tableaus. (shrink)

We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which is actually unconvincing in the case of ultrafilters. As a bonus, we get a very simple proof of Łoś's theorem.

The idea that probability is a degree of rational belief seemed too vague for a foundation of a mathematical theory. It was certainly not obvious that degrees of rational belief had to be governed by the probability axioms as used by Laplace and other prestatistical probabilityst. The axioms seemed arbitrary in their interpretation. To eliminate the arbitrariness, the stat- isticians of the early 20th century drastically restricted the possible applications of the probability theory, by insisting that probabilities had to be (...) interpreted as relative frequencies, which obviously satisfied the probability axioms, and so the arbitrariness was removed. But the frequentist approach turned more subjective than the prestatistical approach, because the identifications of outcome spaces, the choices of test statistics, the declarations of what rejection regions are, the choices of null-hypothesis among alternatives, the contradictory choices between sizes and powers etc., depend on thoughts or even whims of the experimenter. Frequentists thus failed to solve the problems that motivated their approach, they even exacerbated them. The subjective Bayesianism of Ramsey and de Finetti did not solve the problems either. Finally Cox provided the missing foundation for probability as a degree of rational belief, which makes the Bayesian probability theory (which is based on this foundation) the best theory of probable inference we have. Hence, it is quite unbelievable that it is not even mentioned in recent philosophy textbooks devoted to the probable inference. The reason could be that it requires fairly sophisticated mathematics. But not even to mention it? We explain the history and prove Cox theorem in a novel way. (shrink)

The emphasis on the organization of entities and their activities and interactions has been labeled one of the most distinct contributions of mechanistic philosophy. In this paper I discuss the manner in which the organization of entities and their activities and interactions participates in bringing about phenomena. I present a well-known example from molecular biology—the functioning of the genetic switch in phage lambda—and discuss Marco J. Nathan’s notion of causation by concentration. Nathan introduces causation by concentration to account for the (...) irreducible causal role that the concentration ratio between two kinds of proteins possesses in the genetic switch mechanism in phage lambda. I discuss what the irreducibility of this causal role amounts to and provide a mechanistic interpretation of Nathan’s causation by concentration; that is, I explain this irreducible causal role as one organizational feature of this mechanism. The paper concludes that biological mechanisms need a causal pluralist framework [similar to Glennan’s account in, and but slightly modified] where organizational features such as the concentration ratio have a causally relevant role, yet all the causally productive relations occur at the level of entities or individuals. (shrink)

Bošković's explanatory procedure and his concept of explanation represents a certain departure from Newton's causal theory and his theory of explanation. Apart from particular elements of causal explanation, Bošković developed an alternative, non‐causal explanatory strategy. In this paper two different elements of this strategy are discussed: (i) the micro‐reductive explanatory strategy based on Bošković's idea of determination, and (ii) a type of explanation of a theory by means of a more general law, through a thought‐experiment. In addition, an outline of (...) the proposed (iii) ‘argument theory’ of explanation in his mature period is made. These aspects are considered with respect to the realist and anti‐realist elements in Bošković's epistemology. (shrink)

This important volume covers ethics and integrity in health and life sciences research. It addresses concerns in gene editing, dual use and misuse of biotechnologies, big data and nutritional science in health and medicine, and covers attempts at ensuring ethical practices in such fields are shared internationally.

Contrary to the received view, I argue that Gettier’s counterexamples to the tripartite analysis of knowledge as justified true belief failed, because the justification condition and especially truth condition for knowledge in these cases are not unambiguously fulfilled. For the propositions believed are semantically ambiguous and cannot be clearly said to be either true or false and, therefore, to be the objects of justified true beliefs. This is due to the puzzling semantic role played by a definite description and an (...) exclusive disjunction. Therefore, neither of Gettier’s alleged counterexamples does in fact refute the tripartite analysis as such, but only an interpretation of it. Gettier’s cases can be at best construed as demanding a modification and improvement of the traditional analysis and not as demanding its replacement. Some other Gettier-like cases, e.g. those proposed by Lehrer and Feldman, can be treated in an analogous manner. (shrink)

Suprotno općeprihvaćenom mišljenju, argumentiram da Gettierovi protuprimjeri za trodijelnu analizu znanja kao opravdanoga istinitog vjerovanja nisu uspjeli zato što uvjet opravdanja, a pogotovo uvjet istinitosti za znanje u tim slučajevima nisu jednoznačno ispunjeni. Jer sudovi u koje se vjeruje jesu semantički ambivalentni te se za njih ne može jasno reći jesu ili istiniti ili neistiniti, pa stoga ni jesu li predmeti opravdanih istinitih vjerovanja. To je zbog zbunjujuće semantičke uloge koju igra odreðeni opis i ekskluzivna disjunkcija . Stoga nijedan od (...) Gettierovih navodnih protuprimjera zapravo ne opovrgava trodijelnu analizu kao takvu, nego samo jednu njezinu interpretaciju. Gettierovi se slučajevi mogu u najboljem slučaju protumačiti kao oni koji zahtijevaju modifikaciju i poboljšanje tradicionalne analize, a ne kao oni koji zahtijevaju njezino zamjenjivanje. Neki se drugi gettierovski slučajevi, npr. oni koje su iznijeli Lehrer i Feldman, mogu razmatrati na analogan način.Contrary to the received view, I argue that Gettier’s counterexamples to the tripartite analysis of knowledge as justified true belief failed, because the justification condition and especially truth condition for knowledge in these cases are not unambiguously fulfilled. For the propositions believed are semantically ambiguous and cannot be clearly said to be either true or false and, therefore, to be the objects of justified true beliefs. This is due to the puzzling semantic role played by a definite description and an exclusive disjunction . Therefore, neither of Gettier’s alleged counterexamples does in fact refute the tripartite analysis as such, but only an interpretation of it. Gettier’s cases can be at best construed as demanding a modification and improvement of the traditional analysis and not as demanding its replacement. Some other Gettier-like cases, e.g. those proposed by Lehrer and Feldman, can be treated in an analogous manner. (shrink)

One of the most famous problems in the decision-making literature is the “bat and a ball” problem from the cognitive reflection test (CRT; Frederick, 2005). The problem goes as follows: „A bat and...

Boskovic treated unobservables in two different ways. During his earlier period (1741-48) the difference between observables and unobservables was a significant element of his specific semantic instrumentalism. The sentences of unobservables (such as absolute space, time and motions) were treated only as convenient tools conceived to provide for the empirical success of a theory. Later, especially in his Theory of Natural Philosophy (1763), Boskovic relativized this distinction by positing absolute properties (continuity and impenetrability), which are common to both observables and (...) unobservables. As a scientific realist he was committed to his original unobservable entities, i.e. “points of matter”. Due to the intrinsic paradox contained in the concept of these points, his realist position was led to the absurd, which demands an anti-realist interpretation of Boskovic's theory. (shrink)

Personal data protection is an ethical issue. In this study we analyzed how research ethics committees (RECs) and data protection officers (DPOs) handle personal data protection issues in research protocols. We conducted a mixed-methods study. We included heads (or delegated representatives) of RECs and DPOs from universities and public research institutes in Croatia. The participants provided information about data protection issues in research and their mutual collaboration on those issues through structured interviews that contained closed and open-ended questions. Qualitative description (...) was used to analyze open-ended questions. The results showed that 55% of the REC representatives were not aware who was DPO in their institution. Among RECs, 65% never contacted the DPO. There were 61% of RECs who reported that they received no training from the organization on personal data protection. When asked about barriers to personal data protection in their institutions, 26% of REC members highlighted the lack of a clear protocol for assessing personal data protection issues, while 30% of DPOs mentioned lack of knowledge among researchers about personal data. In conclusion, we found that when it came to protecting personal data in research protocols, RECs and DPOs hardly ever worked together. When developing future personal data protection policies for academic and scientific research institutions, it is essential that RECs and DPOs should collaborate and both continue to expand/update their knowledge on personal data protection procedures. (shrink)

The first beginnings of modern logic in Croatia are recognizable as early as in the middle of the 19th century in Vatroslav Bertić. At the turn of the 20th century, Albin Nagy, who was teaching in Italy, made contributions to algebraic logic and to the philosophy of logic. At that time, a distinctive author Mate Meršić stood out, also working on algebraic logic. In the Croatian academic philosophy, until the publication of Gajo Petrović's textbook (1964) and the contributions by Heda (...) Festini, a critical or indifferent attitude toward modern logic prevailed. The first comprehensive modern logic textbook in Croatian was written by mathematician Vladimir Devidé (1964), known, for example, for his axiomatizations of natural numbers and classical propositional logic. In the Croatian philosophy of the 1980s and 1990s, influential logicians are Goran Švob and mathematician Zvonimir Šikić. At the turn of the 21st century, logical investigations are being intensified and extended to various branches of the contemporary logic. (shrink)