The paper proposes a typology of the scientific theories based on the modality of mathematizing (relying on the kind of mathematics which participates to the theory edification and the level of mathematical organizing of the theoretical frame). This gives us, like the classification of the geometries from the famous -Erlagen Program- initiated by Felix Klein, an internal principle for the connection of the different forms or levels of the theorizing, a constructive basis for the understanding of the complex structural nets of the mature scientific disciplines.

The aim of my paper is to explore in some detail some epistemological issues concerning moral theorizing on global warming. First, I consider the issue of the structure of the theoretical approach in a field of inquiry requiring normative assessments. How do theoretical principles work here? What is to be regarded as a normative evidence for such a theory? Second, the criteria to determine which part, if any, of the theory gets normatively constrained, and which does not, are discussed. Third, I focus on the procedures to reach an equilibrium between such a theory and its evidence and to reach it, changes might be required on the normative side of the theory, rather than on its non-normative one

This paper presents aprevalent representation about the objectivity and impartiality of scientific knowledge that emerges from the structure and style of the standard research paper. This representation is critically examined considering some rather untypical scientific papers reporting controversies between researchers in a certain field of experimental science. The role of personal preconceptions and intellectual prejudices in the assessment of scientific theories is emphasized by reference to Einsteinls grounds for his general theory of relativity.

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence.

Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional logic -results traditionally credited to Bernays (1918) and Post (1921). These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its soundness and completeness: a sentence is provable if and only if valid. By 1917, strongly influenced by PM, Hilbert accepted the theory of types and logicism -a surprising shift. But by 1922 he abandoned the axiom of reducibility and then drew back from logicism, returning to his 1905 approach of trying to prove the consistency of number theory syntactically.

The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s, before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory (with particular attention to Carnap and Tarski), Quine’s work is our central concern, since he was seemingly the most outstanding logicist around 1940, though he would shortly abandon that viewpoint and promote first-order logic as all of logic. Quine’s class-theoretic systems NF and ML, and his farewell to logicism, are examined. The last section attempts to summarize the motives why set theory was preferred to other systems, and first orderlogic won its position as the paradigm logic system after the great War.

Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical omnibus discipline logic into new philosophical subdisciplines and separate disciplines such as psychology, epistemology, philosophy of science, and formal (symbolic, mathematical) logic. In the 19th century a growing foundational need in mathematics provoked the emergence of a structural view on mathematics and the reformulation of logic for mathematical means. As a result formallogic was taken over by mathematics in the beginning of the 20th century as is shown by sketching the German example.

In this paper, Tarskis notion of Logical Consequence is viewed as a special case of the more general notion of being a theorem of an axiomatic theory. As was recognized by Tarski, the material adequacy of his definition depends on having the distinction between logical and non logical constants right, but we find Tarskis analysis persuasive even if we dont agree on what constants are logical. This accords with the view put forward in this paper that Tarski indeed captures the more inclusive notion of theoremhood in an axiomatic theory. The approach to logical consequence via axiomatic theories leads us to grant centrality to inference schemas rather than to full-fledged arguments and to view the logically valid schemas as a subclass of generally valid schemas.

Nonreductive naturalism holds that we can preserve the (scientifically valued) metaphysical truth of physicalism while averting the methodological mistakes of reductionism. Acceptable scientificexplanation need not (in some cases cannot and in many cases, should not) be formulated in the language of physical science. Persuasive arguments about the properties of phenomenal consciousnesspurport to show that physicalism is false, namely that phenomenal experience is a nonphysical fact. I examine two recent, comprehensive efforts to naturalize phenomenal consciousness and argue thatnonreductive naturalism yields a dilemma of reductionism or panpsychism.

This paper points out several difficulties to understand Putnam’s views in his recent “Dewey Lectures”, which involve a certain move away from his “internal realism”. The main goal is to set into relief tensions in Putnam’s thinking probably provoked by his philosophical development. Two such tensions are touched upon. In the first place, Putnam wants to reject an account of phenomenal consciousness (sensory experience in particular) he had subscribed to during his realist times, which he calls “Cartesianism cum Materialism”, CM. He puts forward what he takes to be an alternative, apparently based on the traditional Chisholmian “Theory of Appearing”. The paper suggest firstly that, in view of the facts to be accounted for, a theory along those lines cannot count as a real alternative to CM. In the second part, the paper develops an analogous tension between the views on truth Putnam seems to be willing to defend in the Dewey Lectures, and previous criticisms of the semantic conception of truth by hirn that heclaims still to be willing to subscribe.

Armstrong (1983) poses two requirements that law-statements must satisfy in order to support the corresponding counterfactuals. He also argues that law-statements can not satisfy one of these requirements if they merely express regularities, although both requirements are satisfied if law-statements are interpreted as expressing relations between universals. I try to show that Armstrong’s argument can be raised against Armstrong’s own solution by adding three premisses to it: the inference thesis, the contingency thesis and a principle whose rationality I also argue for. Finally, I offer a more reasonable alternative condition for nomic counterfactual supporting which is satisfied by law-statements if they are interpreted as expressing relations between universals, but not so if we interpret them as mere regularities.

En este trabajo se define formamente el concepto de representacion en química utilizando homomorfismos desde estructuras algebraicas, que llamamos sistemas de tipo C, en otras estructuras especiales de símbolos muy relacionados con los que son habituales en la qímica experimental. Para la definicion de los sistemas de tipo C se ha seleccionado un conjunto minimo de relaciones y funciones, que son necesarias para expresar proposiciones significativas en química. Tambien se define un lenguaje formal de primer orden adecuado a los sistemas de tipo C, que llamamos L(C). EI resultado principal que se demuestra es que toda representación que verifica las mismas sentencias de L(C) que un sistema de tipo C, es necesariamente isomorfo a él. Se concluye por lo tanto que puede existir un problema linguístico subyacente en la aplicacion que de la mecaníca cuántica se hace en la química teórica.The concept of representation in chemistry bas been formallv defined by means of homomorphisms from algebraical structures, which we call type-C systems, to some special sets of symbols which can be related to the symbols ordinarily used in experimental chemistry. A minimum number of relations and functions, which would suffice to express significant propositions in chemistry, have been chosen to define type-C systems. A first order formal language L(C) adequate to type-C systems has been defined. It has been shown that each representation that verifies the same sentences of L(C) as a type-C system is necessarily isomorphic to it. It is concluded that a systematic study of the representation problem in chemistry is in order because a deep language problem underlies the application of quantum mechanies to chemical problems.

The essay begins with a detailed consideration of the introduction of incommensurability by Feyerabend in 1962 which exposes several historically inaccurate claims about incommensurability. Section 2 is a coneise argument against causal theories of reference as used as arguments against incommensurability. We object to this strategy because it begs the question by presupposing realism. Section 3 introduces and discusses a hypothesis that w'e call meta-incommensurability which provides the reason for the wide-spread accusation of question-begging and use of circular argumentation among the proponents of both realist and non-realist interpretations of science.

Does incommensurability threaten the realist’s claim that physical magnitudes express properties of natural kinds? Some clarification comes from measurement theory and scientific practice. The standard (empiricist) theory of measurement is metaphysically neutral. But its representational operational and axiomatic aspects give rise to several kinds of a one-sided metaphysics. In scientific practice. the scales of physical quantities (e.g. the mass or length scale) are indeed constructed from measuring methods which have incompatible axiomatic foundations. They cover concepts which belong to incomensurable theories. I argue, however, that the construction of such scales conmmits us to a modest version of scientific realism.