What sort of entities are electrons, photons and atoms given their wave-like and particle-like properties? Is nature fundamentally deterministic or probabilistic? Orthodox quantum theory (OQT) evades answering these two basic questions by being a theory about the results of performing measurements on quantum systems. But this evasion results in OQT being a seriously defective theory. A rival, somewhat ignored strategy is to conjecture that the quantum domain is fundamentally probabilistic. This means quantum entities, interacting with one another probabilistically, must differ radically from the entities of deterministic classical physics, the classical wave or particle. It becomes possible to conceive of quantum entities as a new kind of fundamentally probabilistic entity, the “propensiton”, neither wave nor particle. A fully micro realistic, testable rival to OQT results.

According to a model defended by some authors, dispositional predicates, or concepts, can be legitimately used in causal explanations, but such a use is not necessary. For every explanation couched in dispositional terms, there is always a better, and complete, explanation that makes use of a different vocabulary, that of categorial bases. In what follows, I will develop this view, and then argue that there is a kind of use of dispositions in explanations that does not fall within this model. That is, I will argue that we would miss some explanations if we were to forsake dispositional concepts and dispositional explanations.

To come to know what to do is to have a thought which itself consists of an awareness of its bringing about an action, or a rearrangement of one’s causal powers...The causal dimension of practical thinking is the coalescence of contemplation and the causation of that contemplation, and the contemplation of that causation.

A similarity index allowing comparisons of human populations has been defined as the common “Percentage of Isoactive Genes” or PIG, which can be calculated from any gene frequency distribution characterizing two populations. The complement to one of this value has been proved to be a distance, a measure which can be used in most techniques of cluster analysis as well as in usual representations of multivariated data (dendrograms, etc...). Furthermore, the formula can be generalized to a set of populations. From a biological point of vue, PIG values are particularly meaningful, whereas other previously defined indices which tend to measure similarity or difference between populations neither have such an advantage, nor can they be expressed by a single and clear number like a percentage. Moreover,comparisons using PIG indices depend at first on the fluctuations of the most frequent genes of a distribution; on the other hand, different measures principally reflect the variations of low frequency genes, which unfortunately are nearly always poorly estimated, due to weak samples of populations.Interestingly, PIG values can be applied to any frequency distribution of any kind of objects. They can also extend to a whole set of distributions by using a mean value. When applying these measures to a series of polymorphic genetical systems such as ABO, Rhesus, MNSs, Gm and HLA, one can account for the variability or the homogeneity particular to the different human groups, with simple and objective criteria.

There are three kinds of nature singled out according to the physical contact with the man: “nature immune from man”, “nature touched by man”, and “nature transformed by man”. The latter type is of highest relevance for the man’s present dilemmas. The extrapolation of present tendencies of the man-nature relations is summarized in the two basic dilemma: ecological dilemma/either the development of the modern technologies or the destruction of human ecological environment/, and peace dilemma /either to continue the nuclear arms race or the total nuclear disarmament/. There are four types of situations facing the man when avoiding the negative results of trends in the transformation of nature, which are linked with legal phllosophy. The man-nature relations are axiologically ambivalent because the transformed nature is the challenge, but calls for looking at nature as apart of our life, and to exist with it in in it.

An arithmetical language, whose words are natural numbers written in hexadecimal numeration system, is defined and its applications for the representation, analysis and decision of formulae of some logical and normative systems are described and illustrated.The formulae, operations and relations of the represented system are associated as follows respectively to the numbers and the arithmetical operations and relations of the proposed language:1. Each well-formed-formula of the system is associated to a number of a set of natural numbers between zero (associated to all tautologies and theses) and the binary supremum Φ of the set (Φ is associated to all contradictions and antitheses and his value is 2n-1, n depending on system’s dimensions and structure).2. Negation of a formula and disjonction and conjonction of t wo other more formulae of the system are associated respectively to the binary complement Φ-N(f) of the number associated to the first and to the binary infimun and supremum of the numbers associated to the last.3. The logical relations “f1 implies f2” (f1 -> f2), “f1 is incompat.ible with f2” (f1|f2), “f1 is the contradictory opposite of f2” (f1wf2) and “f1 is alternative to f2” (f1vf2) are true in the represented system if and only if the associated arithmetical relations, respectively “N(f1) absorbs arithmetically N(f2)”, “binary supremum of N(f1) and N(f2) is equal to Φ”, “sum of of N(f1) and N(f2) is equal to Φ” and “binary infimum of N(f1) and N(f2) is equal to 0”, are true.The applications of the proposed arithmetical language as very rapid and simplified tool of analysis and decision method are shown for the following systems: propositional logic, syllogistic, some deontic and alethic modal systems and some normative systems of statutory law:1. In the propositional logic, after fixing the maximum of variables considered, the numbers associated to these variables and to the contradictions are calculated. On this permanent basis, the evaluation of a farmula (especially in the case of many occurrences of many variables) is performed by the calculation of the associated number faster as in the traditional way.2. In the syllogistic, after the calculation of the number associated to each type of premise or conclusion, an arithmetical table of syllogisms shows that a proposed syllogism is valid if and only if the binary supremum of the numbers associated to the premises absorbs arithmetically the number associated to the conclusion. It is well-known that the search of this sort of arithmetization of syllogistic and the study of its possibilitiy has been a recurrent topic in modern logic, from Leibniz to Łukasiewicz and to-day.3. In a deontic equivalent:ial system who includes Von Wright’s deontic system of 1982 far norms of the first order, the calculation of the numbers associated to an types of permission and obligation sentences allows the im mediate arithmetical verification of an the classical relations between those sentences. The same is shown for an alethic modal system including the modlities of the first order of Lewis’s S5.4. For normative systems of statutory law, the arithmetical verification of the logical and normative relations is shown in precedent author’s papers -especially in recent “The ‘Ars Judicandi.’ Programme”-, though not yet in hexadecimal numeration system but only in binary and decimal ones.In all the represented systems, the arithmetical verification of the metalogical properties of the system -consistency and completeness- is performed in a very easy and rapid manner, after the arithmetic representation of the axiomatic basis of the latter by a system of equations.