If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability (...) to recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF PHYSICS By Antonino Drago, formerly at Naples University “Federico II”, Italy – drago@unina,.it (Size : 391.800 bytes 75,400 words) The book summarizes a half a century author’s work on the foundations of physics. For the forst time is established a level of discourse on theoretical physics which at the same time is philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics, kinds of (...) logic). This double side of the two dichotomies assures a deep comprehension of theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis, each manifestly insufficient for representing all the aspects of theoretical physics. Among the many formulations of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, Instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, within Mathematics either the classical one or the constructive one(2); within Mathematical Logic either the classical logic or the intuitionist one(3). Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s,(4) whose mathematics is no more than algebraic-trigonometric and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, as in intuitionist logic occurs. By considering these two dichotomies as the foundations of the physical theories, each couple of choices upon them fashions one out four models of scientific theory, which are baptized through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence four versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5) All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds amid the so numerous physical theories. By taking these dichotomies as interpretative categories, a new interpretative history of Physics including both classical and modern physics results according to a quadrilinear development. The birth of modern physics is characterized by the two theories - Einstein’s paper on special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses the discrete mathematics; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6) Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori transcendental categories represent the physical interpretation of the two choices out of the four pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics, Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist logic. The book starts by a comparison of different formulations of thermodynamics in order to recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A quickly history of the other classical physical theories is illustrated in chapter 3; it results a foundational conflict between the last two theories, and hence a conflict between their opposite couples of choices. The two main theories of modern physics, special realtivity and quantum mechanics confirm the foundational role played by the two dichotomies which gives reason for the radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of choices gives reason of the crisis in theoretical physics in the early 1900s. As a global result, the book represents the first interpretation of the entire history of Physics, both classical and modern; This fact proves that the four models of scientific theories can works as a compass (that of the front cover) suggesting a direction among the many physical theories. This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies. Their interpretative categories are interpreted and explained through the two dichotomies so that it is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as the suitable categories for interpreting the alternative theories to Newton’s mechanics. All that suggests a new interpretation of the crucial step in the history of Western philosophy of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them in order to construct the well-known four cosmological proofs, which however he misinterpreted as leading to contradictions, instead to tow different methods of investigation corresponding to the two different kinds of logic.(7) Bibliography 1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III. 2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill. 3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland. 4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation: Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9. 5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151. 6. Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234. 7. This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne. (shrink)

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of (...) K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type. (shrink)

We discuss central aspects of history of the concept of an affine differentiable manifold, as a proposal confirming the need for using some quantitative methods (drawn from elementary Model Theory) in Mathematical Historiography. In particular, we prove that this geometric structure is a syntactic rigid designator in the sense of Kripke-Putnam.

The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic approach of (...) the rings of operators; 3) Morchio and Strocchi’s improving Dirac’s analogy between commutators and Poisson Brackets into an exact equivalence; 4) the recent foundation of quantum mechanics upon the algebra of perturbations. Some considerations on alternating theoretical importance of the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices to group theory and C*-algebras but has not led to a definition of the foundations of physics; in particular, an algebraic formulation of QM organized as a problem-based theory and an exclusive use of constructive mathematics is still to be discovered. (shrink)

A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.

In this paper, we wish to highlight, within the general cultural context, some possible elementary computational psychoanalysis formalizations concerning Matte Blanco’s bi-logic components through certain very elementary mathematical tools and notions drawn from theoretical physics and algebra. NOTE: This is the corrected version of the paper which had to be published but that instead has been wrongly uploaded in the related published proceedings.

John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development of (...) algebra [Jacob Klein, English translation, Greek mathematical thought and the origin of algebra, especially pp. 154–157, M.I.T. Press, Cambridge, Mass., 1968]. -/- It is universally agreed that the method of analysis begins by “assuming the thing sought after” (e.g., in geometry, the truth of the proposition to be proved or the existence of the geometric figure to be constructed). Aside from this, little else can be taken for granted. There is disagreement concerning the “direction of analysis”, i.e. whether one is to seek implications of the assumption or whether one is to seek implicants of it. There is also disagreement concerning what is to be “anatomized” (analyzed), i.e., whether one analyzes mathematical objects (figures), mathematical propositions (the axioms, known theorems, and analytic assumption) or an imagined proof (of the analytic assumption from axioms and known theorems). (shrink)

Intra-molecular connectivity (that is, chemical structure) does not emerge from computations based on fundamental quantum-mechanical principles. In order to compute molecular electronic energies (of C 3 H 4 hydrocarbons, for instance) quantum chemists must insert intra-molecular connectivity “by hand.” Some take this as an indication that chemistry cannot be reduced to physics: others consider it as evidence that quantum chemistry needs new logical foundations. Such discussions are generally synchronic rather than diachronic —that is, they neglect ‘historical’ aspects. However, systems of (...) interest to chemists generally are metastable . In many cases chemical systems of a given elemental composition may exist in any one of several different metastable states depending on the history of the system. Molecular structure generally depends on contingent historical circumstances of synthesis and separation, rather than solely or mainly on relative energies of alternative stable states, those energies in turn determined by relationships among components. Chemical structure is usually ‘kinetically-determined’ rather than ‘thermodynamically-determined.’ For instance, cyclical hydrocarbon ring-systems (as in cyclopropene) are produced only in special circumstances. Adequate theoretical treatments must take account of the persistent effects of such contingent historical events whenever they are relevant—as they generally are in chemistry. (shrink)

By the middle of the seventeenth century we that find that algebra is able to offer proofs in its own right. That is, by that time algebraic argument had achieved the status of proof. How did this transformation come about?

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

In this paper, a formal theory is presented that describes syntactic and semantic mechanisms of philosophical discourses. They are treated as peculiar language systems possessing deep derivational structures called architectonic forms of philosophical systems, encoded in philosophical mind. Architectonic forms are constituents of more complex structures called architectonic spaces of philosophy. They are understood as formal and algorithmic representations of various philosophical traditions. The formal derivational machinery of a given space determines its class of all possible architectonic forms. Some of (...) them stand under factual historical philosophical systems and they organize processes of doing philosophy within these systems. Many architectonic forms have never been realized in the history of philosophy. The presented theory may be interpreted as falling under Hegel’s paradigm of comprehending cultural texts. This paradigm is enriched and inspired with Propp’s formal, morphological view on texts. The peculiarity of this modification of the Hegel-Propp paradigm consists of the use of algebraic and algorithmic tools of modeling processes of cultural development. To speak metaphorically, the theory is an attempt at the mathematical and logical history of philosophy inspired by the Internet metaphor. And that is why it belongs to the tradition of doing metaphilosophy in The Lvov-Warsaw School, which is continued today mainly by Woleński, Pelc, Perzanowski, and Jadacki. (shrink)

In their seeking of simplicity, scientists fall into the error of Whitehead's "fallacy of misplaced concreteness." They mistake their abstract concepts describing reality for reality itself--the map for the territory. This leads to dogmatic overstatements, paradoxes, and mysteries such as the deep incompatibility of our two most fundamental physical theories--quantum mechanics and general relativity. To avoid such errors, we should evoke Whitehead's conception of the universe as a universe-in-process, where physical relations perpetually beget new physical relations. Today, the most promising (...) interpretations of quantum mechanics exemplify this Whiteheadian idea, formalizing physical systems, and the universe itself, as ongoing histories of actualizations of potential states, where actual states and potential states exist in mutually implicative relation as two separate categories of reality—an idea first proposed by Aristotle and rehabilitated by Heisenberg. In these interpretations, the classical conception of a history as a derivative story about fundamental physical objects is reversed: the classical physical object becomes the derivative story about fundamental histories of quantum states. The consistent histories interpretation of Robert Griffiths and the decoherent histories interpretation of Roland Omnès are cardinal examples of this approach to quantum mechanics. Another example, the relational realist interpretation, begins with the decoherent histories approach and formalizes it explicitly as a Whiteheadian interpretation, taking his “algebraic method” and applying it to quantum mechanics via algebraic topology. This branch of mathematics can be thought of as a “de-concretized” geometry in that it focuses only on the logical relations among objects and regions (and relations of these relations) rather than the fixed magnitudes of lines, planes, and other such rigid intervals. It has all the robust logical structure of geometry yet allows for an elasticity of relations that makes topological mathematical structures inherently immune misplaced concretization. (shrink)

The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the (...) way epistemology might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)

The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it (...) from the pre-Socratics to the Pythagoreans). Husserl’s phenomenology and Heidegger’s derivative “fundamental ontology” as well as his later doctrine after the “turn” are the starting point of the research as established and well known approaches relative to the newly introduced conception of ontomathematics, even more so that Husserl himself started criticizing his “Philosophy of arithmetic” as too naturalistic and psychological turning to “Logical investigations” and the foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as a relation of locality and nonlocality, respectively as a motion from nonlocality to locality if both are physically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from the pre-Socratics' “Logos” or Heideger’s “Language” (after the “turn”) to the Pythagoreans “Numbers” or “Arithmetics” as an inherent and fundamental philosophical doctrine. Then, a leap to contemporary physics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’s opposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowing for the “creation from nothing” instead of the quasi-scientific myth of the “Big Bang”. Furthermore, ontomathematics needs another interpretation of arithmetic, propositional logic and set theory in the foundations of mathematics, where the latter two ones are both identified with Boolean algebra, and the former is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it after doubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of the foundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where the latter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newly introduced substance of quantum information being physically dimensionless and generalizing classical information measured in bits. The substance of information, whether classical or quantum, visualizes the way of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic and Hilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics to the Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity, is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectless choice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by Michel Foucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as the philosophy of locality ends the study. (shrink)

This essay is a contribution to the historical phenomenology of science, taking as its point of departure Husserl’s later philosophy of science and Jacob Klein’s seminal work on the emergence of the symbolic conception of number in European mathematics during the late sixteenth and seventeenth centuries. Sinceneither Husserl nor Klein applied their ideas to actual theories of modern mathematical physics, this essay attempts to do so through a case study of the conceptof “spacetime.” In §1, I sketch Klein’s account of (...) the emergence of the symbolic conception of number, beginning with Vieta in the late sixteenth century. In §2,through a series of historical illustrations, I show how the principal impediment to assimilating the new symbolic algebra to mathematical physics, namely, thedimensionless character of symbolic number, is overcome via the translation of the traditional language of ratio and proportion into the symbolic language of equations. In §§3–4, I critically examine the concept of “Minkowski spacetime,” specifically, the purported analogy between the Pythagorean distance formula and the Minkowski “spacetime interval.” Finally, in §5, I address the question of whether the concept of Minkowski spacetime is, as generally assumed, indispensable to Einstein’s general theory of relativity. (shrink)

The aim of this paper is to make sense of the Keynes–Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show how this structure is to be handled by means of a semantics of partition, thus computing logical relations between matching formulas with a semantic method that combines model theory and Boolean algebra.

In this paper, we make a short history about: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures. Afterwards, their generalizations to refined neutrosophic set, respectively refined neutrosophic numerical and literal components, then refined neutrosophic numbers and refined neutrosophic algebraic structures.

2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and (...) Sriram Nambiar, I have written several publications trying to set the record straight—but so far to little avail. This encyclopedia entry is one more attempt to set the record straight in a way that can be appreciated by non-experts.Also see https://www.academia.edu/10161999/Booles_criteria_of_validity_and_invalidity . (shrink)

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to (...) Gauss and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

We give a brief overview of the evolution of mathematics, starting from antiquity, through Renaissance, to the 19th century, and the culmination of the train of thought of history’s greatest thinkers that lead to the grand unification of geometry and algebra. The goal of this paper is not a complete formal description of any particular theoretical framework, but to show how extremisation of mathematical rigor in requiring everything be drivable directly from first principles without any arbitrary assumptions actually (...) leads to relaxing the computational difficulty along with maximal conceptual clarity. With this, we consider a revision of the foundations of elementary geometry and algebra based on the work of Grassmann and Clifford and apply it to conceptual and practical problems of past and present modern mathematics and mathematical physics. (shrink)

The global relation between logical empiricism and American pragmatism is one of the more difficult problems in history of philosophy. In this paper I’d like to take a local perspective and concentrate on the details that concern the vicissitudes of a philosopher who played an important role in the encounter of logical empiricism and American pragmatism, namely, Ernest Nagel. In this paper, I want to explore some aspects of Nagel’s changing attitude towards the then „new“ logical-empiricist philosophy. In the (...) beginning Nagel welcomed logical empiricism whole-heartedly. This early enthusiasm did not last. At the end of his philosophical career Nagel’s early positive attitude towards logical empiricism shown in the 1930s had been replaced by a much more reserved one. Nagel’s growing dissatisfaction with the Carnapian version of logical empiricist philosophy was clearly expressed in Nagel’s criticism of Carnap’s inductive logic and more generally in his last book Teleology Revisited and Other Essays on History and Philosophy of Science. There he critized harshly Carnap’s philosophy of science in general as ahistoric and non-pragmatist. One of the distinctive features of Nagel’s philosophy of science is the emphasis that he put on the role of history of science for philosophy of science. A compelling evidence for this attitude are his works on the history and philosophy of geometry and algebra One may say that Carnap and Nagel represented opposed possibilities of how the profession of a philosopher of science could be understood: Carnap as a „conceptual engineer“ was engaged in the task of inventing the conceptual tools for a better theoretical understanding of science, while Nagel was to be considered more as a „public intellectual“ engaged in the project of realizing a more rational and enlightened society. (shrink)

In his Tractatus, Wittgenstein sets out what he calls his N-operator notation which can be used to calculate whether an expression is a tautology. In his Laws of Form, George Spencer Brown offers what he calls a “primary algebra” for such calculation. Both systems are perplexing. But comparing two blurry images can reduce noise, producing a focus. This paper reveals that Spencer Brown independently rediscovered the quantifier-free part of the N-operator calculus. The comparison sheds a flood light on each (...) and from the letters of correspondence we shall find that Russell, as one might have surmised, was a catalyst for both. (shrink)

The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses (...) to these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics. (shrink)

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying (...) principles through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation. (shrink)

Determinismus und Indeterminismus in der modernen Physik is one of Cassirer’s least known and studied works, despite his own assessment as “one of his most important achievements”. A prominent theme locates quantum mechanics as a yet further step of the tendency within physical theory towards the purely functional theory of the concept and functional characterization of objectivity. In this respect DI can be considered an “update”, like the earlier monograph Zur Einsteinschen Relativitätstheorie: Erkenntnistheoretische Betrachtungen, to Substanzbegriff und Funktionsbegriff, a seminal (...) work considering only classical and pre-relativistic physics. But how does DI cohere with the three volumes of The Philosophy of Symbolic Forms providing a systematic survey of symbolic meanings in diverse aspects of culture, each with its own mode of “objectification” via self-created signs and images? Cassirer’s “phenomenology of cognition” via distinct types of symbolic form locates Dirac’s Principles of Quantum Mechanics as an exemplar within physical theory of purely symbolic thought, a realm of pure relations and their correlated meanings. In particular, Dirac’s characterization of the new notion of “physical state” in quantum mechanics by a “symbolic algebra of observables” severed from particular representations points to a limiting pole of the Bedeutungsfunktion, the third and highest mode of symbolic formation. (shrink)

The chapter begins with an initial survey of ups and downs of contextualist history of philosophy during the twentieth century in Britain and America, which finds that historically serious history of philosophy has been on the rise. It then considers ways in which the study of past philosophy has been used and is used in philosophy, and makes a case for the philosophical value and necessity of a contextually oriented approach. It examines some uses of past texts and (...) of history that reveal limits to noncontextual history, including Strawson's Kant, Rorty's grand diagnosis of the Western tradition, and Friedman on Kant's philosophy of mathematics. It then considers ways in which the history of philosophy may become philosophically deeper by becoming more historical, and instances in which history of philosophy of various stripes has or may deliver a philosophical payoff. Along the way, it urges historians of philosophy to attend not only to individual philosophers and their problems and projects, but also to the larger shape of the history of philosophy and its narrative themes. (shrink)

Human biological memory systems have adapted to use technological artifacts to overcome some of the limitations of these systems. For example, when performing a difficult calculation, we use pen and paper to create and store external number symbols; when remembering our appointments, we use a calendar; when remembering what to buy, we use a shopping list. This chapter looks at the history of memory artifacts, describing the evolution from cave paintings to virtual reality. It first characterizes memory artifacts, memory (...) systems, and the two main functions such artifacts have, which are to aid individual users in completing memory tasks and as a cultural inheritance channel (section 2). It then outlines some of our first symbolic practices such as making cave paintings and figurines, and then moves on to outline several key developments in external representational systems and the artifacts that support these such as written language, numeral systems and counting devices, diagrams and maps, measuring devices, libraries and archives, photographs, analogue and digital computational artifacts, the World Wide Web, virtual reality, and smartphones (section 3). After that, it makes some brief points about the cumulative nature of the cultural evolution of memory artifacts and speculates about the possible future of memory artifacts, arguing that it is very difficult to look beyond an epistemological horizon of more than five years (section 4). (shrink)

The professionalization of the study of history in the Nineteenth Century made possible a new way of thinking about the history of philosophy: the thought emerged that philosophy itself might be relative to time, historical culture, and nationality. The simultaneous demise of speculative metaphysics scattered philosophers’ confidence that the historical variance of philosophical systems could be viewed in terms of the teleological self-realization of reason. Towards the late Nineteenth Century, philosophers began to explicitly address the worry that all (...) philosophical systems might have only relative validity. This paper compares two key figures in late-nineteenth-century debates concerning historical relativism: Wilhelm Windelband and Wilhelm Dilthey. Beneath the deep disagreements between these two authors, it reveals their common concern to immunize philosophy from the threat of historical relativism. The paper traces how both philosophers sought to fend off relativism by defending the idea of an ahistorical and permanent stratum of philosophical thinking. And it argues that although they succeeded in blocking historical versions of relativism, they did so at the cost of incurring a relativism vis-à-vis philosophical systems. This relativism turned out to be rooted not in the historicity of philosophy but in the timeless essence of philosophical reasoning itself. (shrink)

Usual narratives among prehistoric archaeologists consider typological approaches as part of a past and outdated episode in the history of research, subsequently replaced by technological, functional, chemical, and cognitive approaches. From a historical and conceptual perspective, this paper addresses several limits of these narratives, which (1) assume a linear, exclusive, and additive conception of scientific change, neglecting the persistence of typological problems; (2) reduce collective developments to personal work (e.g. the “Bordes’” and “Laplace’s” methods in France); and (3) presuppose (...) the coherence and identity of these “methods” over time. It explores the case of the “Structural and analytical typology” method, developed in France, Spain, and Italy from the 1950s to the 2000s by Georges Laplace and his collaborators for lithic implements. This paper (1) provides a detailed historical account of the evolving content of this collective endeavour over five decades; (2) it addresses the epistemological question of what makes the identity and unity of a scientific method, demonstrating that the core component of the “analytical typology” lies in its particular way to represent real-world phenomena through its notation system; and (3) it reveals how this little known but significant episode of advances in the methods and theory of archaeology, contemporary but independent of the “New Archaeology” trend in English-speaking archaeology, was instrumental in the continuation of evolutionary perspectives in France and in the development of quantitative and formal methods in archaeology in southwestern Europe, foreseeing crucial knowledge representation issues raised today by digital methods in archaeology and data curation. (shrink)

Logical positivism is often characterized as a set of naive doctrines on meaning, method, and metaphysics. In recent decades, however, historians have dismissed this view as a gross misinterpretation. This new scholarship raises a number of questions. When did the standard reading emerge? Why did it become so popular? And how could commentators have been so wrong? This essay reconstructs the history of a “caricature” and rejects the hypothesis that it was developed by ill-informed Anglophone scholars who failed to (...) appreciate the subtleties of European scientific philosophy. It argues that the received view has a more complicated history and was frequently promoted by the European positivists themselves. The essay shows that the view has roots in both American and European scientific philosophy and emerged as a result of the complex interplay between the two communities in the years before the intellectual migration. (shrink)

This bibliographical guide gives a comprehensive overview of the historiography of philosophy and thought in the Japanese language through an extensive and thematically organized collection of relevant literature. Comprising over one thousand entries, the bibliography shows not only how extensive and complex the Japanese tradition of philosophical and intellectual historiography is, but also how it might be structured and analyzed to make it accessible to a comparative and intercultural approach to the historiography of philosophy worldwide. The literature is categorized and (...) organized according to thematic focus areas such as geographical regions and continents, nations or peoples, religious traditions and philosophical teachings such as Buddhism, Islam, Shintō, and Confucianism, as well as disciplines such as ethics, aesthetics, and political thought. The bibliography is accompanied by an introduction outlining the research method as well as quantitative and qualitative approaches to analyzing the material, followed by a chronological overview of the historiography of philosophy and thought in the Japanese language and of the Japanese tradition of writing “world histories of philosophy.” As a first step towards a “history of the historiography of philosophy” in non-European languages, we hope that this guide will provide a useful tool for interculturally oriented scholarship aimed at a non-Eurocentric and diversified historiography of philosophy in a global perspective. (Open access, see link below.). (shrink)

Digital ethics, also known as computer ethics or information ethics, is now a lively field that draws a lot of attention, but how did it come about and what were the developments that lead to its existence? What are the traditions, the concerns, the technological and social developments that pushed digital ethics? How did ethical issues change with digitalisation of human life? How did the traditional discipline of philosophy respond? The article provides an overview, proposing historical epochs: ‘pre-modernity’ prior to (...) digital computation over data, via the ‘modernity’ of digital data processing to our present ‘post-modernity’ when not only the data is digital, but our lives themselves are largely digital. In each section, the situation in technology and society is sketched, and then the developments in digital ethics are explained. Finally, a brief outlook is provided. (shrink)

Permissivism is the view that for some body of evidence E there may be more than one rational doxastic attitude that inquirers may take towards some proposition. This paper examines the aims and processes involved in doing the history of philosophy. It argues that the complexities involved in the process of doing the history of philosophy motivates hermeneutical permissivism.

According to the antirealist argument known as the pessimistic induction, the history of science is a graveyard of dead scientific theories and abandoned theoretical posits. Support for this pessimistic picture of the history of science usually comes from a few case histories, such as the demise of the phlogiston theory and the abandonment of caloric as the substance of heat. In this article, I wish to take a new approach to examining the ‘history of science as a (...) graveyard of theories’ picture. Using JSTOR Data for Research and Springer Exemplar, I present new lines of evidence that are at odds with this pessimistic picture of the history of science. When rigorously tested against the historical record of science, I submit, the pessimistic picture of the history of science as a graveyard of dead theories and abandoned posits may turn out to be no more than a philosophers’ myth. (shrink)

During the first quarter of the twentieth century, the French philosopher Henri Bergson became an international celebrity, profoundly influencing contemporary intellectual and artistic currents. While Bergsonism was fashionable, L. Susan Stebbing, Bertrand Russell, Moritz Schlick, and Rudolf Carnap launched different critical attacks against some of Bergson’s views. This book examines this series of critical responses to Bergsonism early in the history of analytic philosophy. Analytic criticisms of Bergsonism were influenced by William James, who saw Bergson as an ‘anti-intellectualist’ ally (...) of American Pragmatism, and Max Scheler, who saw him as a prophet of Lebensphilosophie. Some of the main analytic objections to Bergson are answered in the work of Karin Costelloe-Stephen. Analytic anti-Bergsonism accompanied the earlier refutations of idealism by Russell and Moore, and later influenced the Vienna Circle’s critique of metaphysics. It eventually contributed to the formation of the view that ‘analytic’ philosophy is divided from its ‘continental’ counterpart. (shrink)

One of the most influential ideas of twentieth-century art history and aesthetics is that vision has a history and it is the task of art history to trace how vision has changed. This claim has recently been attacked for both empirical and conceptual reasons. My aim is to argue for a new version of the history of vision claim: if visual attention has a history, then vision also has a history. And we have some (...) reason to think that at least in certain contexts, visual attention does have a history. (shrink)

This essay is a case study of the self-destruction that occurs in the work of a social-constructionist historian of science who embraces a radical philosophy of science. It focuses on Thomas Laqueur's Making Sex: Body and Gender from the Greeks to Freud in arguing that a history of science committed to the social construction of science and to the central theses of Kuhnian, Duhemian, and Quinean philosophy of science is incoherent through self-reference. Laqueur's text is examined in detail in (...) order to make the main point; a similar phenomenon in the work of the feminist historian of science Evelyn Fox Keller is then briefly discussed. (shrink)

The book is a history of the concept of experience in philosophy. Minakov focuses mainly on Western 19-20th century philosophical movements and their use of the experience concept. Author uses topological method to describe growth of the conseptual content of experience, as well as decline in its use in the end of 20th century.

This is the first chapter of Mark Julyan's 'History of the Heavens' which, as a whole, focuses on the many different interpretational problems that emerge within the controversial and previously unavailable appendix to Kant's 'Universal Natural History and Theory of the Heavens'. The first chapter makes the contention that we should interpret J.L. Austin's curious and otherwise eccentric capitalization of the font in the word KANT (twice on pp.2-3) of his 'How to do Things with Words' (1962), through (...) pp.13-14 of the 'Elementum: eine Vorarbeit zum Griechischen und Lateinischen Thesaurus' of Hermann Diels (1899), where Diels describes the Thesaurus of the font based on Aristotle's description of ancient atomism (twice in the Metaphysics and Gen et Corr). This, alongside a play on the words of the name Bernard de Fontenelle and the provocative nature of Austin's obviously false statements regarding Kant, suggest he had seen Kant's astonishingly scandalous opening statement to the appendix; and that he was making a cryptic, but nonetheless fairly tangible reference to it, by means of showing us How To Do Things With Words by embodying a witticism ass encryption, an instance of his theory into his text. (shrink)

This paper examines the fortunes of non-European philosophies in histories of philosophy written by European and American philosophers from the 17th century to the present day. It charts the shift from inclusive histories of philosophy, which included non-European philosophies, to exclusive histories of philosophy, which excluded and/or marginalized non-European philosophies, at the end of the 18th century. This shift was motivated by racial Eurocentrism, which cast a long shadow over histories of philosophy written during the 19th and 20th centuries. The (...) paper also considers recent attempts to produce a more inclusive history of philosophy. By examining the history of the inclusion and exclusion of non-European philosophies in histories of philosophy, this paper seeks to challenge the assumption that philosophy began and has been practised exclusively by European or western thinkers. (shrink)

Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...) for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)

Bergson offers an epistemological critique of Darwin’s theory that focuses on his gradualism: for Darwin variation is “minute”, and Bergson glosses “insensible.” His main argument is that if variations are insensible, they cannot confer an advantage to the organism and therefore be selected. Yet, for Darwin, the selected variation is not insensible: to be selected, it must be beneficial to its bearer in the struggle for existence. This article aims at understanding the origin of this misunderstanding by tracing the (...) class='Hi'>history of this critique. To do this, we will study Bergson’s sources, showing that his interpretation of Darwin is in line with the critique of many biologists at the turn of the 20th century, albeit in a confused way. This will lead us back to the origin of this critique: the work of Mivart. In this study, we wish to reveal the anchor of the Bergsonian interpretation in the debates of his time, and the shifts from the traditional exposition of the argument that led Bergson to formulate this false paradox. This article will also analyze more precisely the counterexample of the “analogy of structure” to show that, despite Bergson’s misunderstanding, he did point to actual limits of the Darwinian theory. (shrink)

This paper was written to study the order of medical advances throughout history. It investigates changing human beliefs concerning the causes of diseases, how modern surgery developed and improved methods of diagnosis and the use of medical statistics. Human beliefs about the causes of disease followed a logical progression from supernatural causes, such as the wrath of the Gods, to natural causes, involving imbalances within the human body. The invention of the microscope led to the discovery of microorganisms which (...) were eventually identified as the cause of infectious diseases. Identification of the particular microorganism causing a disease led to immunization against the disease. Modern surgery only developed after the ending of the taboo against human dissection and the discovery of modern anesthesia and the discovery of the need for anti-septic practices. Modern diagnostic practices began with the discovery of x-rays and the invention of medical scanners. Improved mathematics, especially in probability theory, led to statistical studies which led to a much greater ability, to identify the causes of disease, and to evaluate the effectiveness of treatments. These discoveries all occurred in a necessary and inevitable order with the easiest discoveries being made first and the harder discoveries being made later. The order of discovery determined the course of the history of medicine and is an example of how social and cultural history has to follow a particular course determined by the structure of the world around us. (shrink)

In recent decades, perspectivism has developed into an epistemological research program claiming its independence. This autonomy stems from Perspectivism’s potential ability to resolve the contradictions between realist and constructivist programs. Perspectivism is based on the idea that the object depends on perspective, which constitutes any subjective attempt to cognize it. Perspectivists reconstruct and explain the factors involved in the formation of perspective, identifying the conditionality of epistemic acts, using concepts such as “position”, “point of view”, “view”, “angle”, “horizon”, “focus”, “picture”, (...) “context”, “aspect”, etc. Although these concepts are part of the perspectivist’s toolkit, their meanings and interrelation have so far been taken for granted and have not yet been critically and comprehensively analyzed. The purpose of this article is to take steps toward clarifying the conceptual basis for defending perspectivism as an epistemological program. Once consistently uncovered and correlated in a conceptual model, Perspectivist concepts can be used as a tool for a detailed analysis of theories, positions, and beliefs. The article begins with a preliminary description of the concept of perspectivism and its brief history as an epistemological program. In particular, the first modern attempts to outline perspectivist epistemology are described in the works of F. Kaulbach (1990), W. Stegmaier (2008), and M. Massimi (2017, 2020). The problem of identifying the special a priori status of perspectivist notions as a strategy for justifying the autonomy of Perspectivism is then posed. A method for demonstrating such a status, based on Kant’s transcendentalism and P. Strawson’s descriptive metaphysics, is then suggested. (shrink)

The endeavor of this bibliographical guide is inscribed in the broader effort to reframe the discipline of Philosophy in a global perspective through the account of its history. With the present work readers will gain a broad overview of the materials available in Italian on the histories of philosophy in different regions of the world from the first editions, in the 15th century, to the present. Some of these materials are presented in the extensive introduction to the bibliography, which (...) has been organized according to geographical regions, such as continents and nations, as well as thematic focuses, such as religions, doctrines, or disciplines. Moreover, the introduction discusses two main themes, namely the strong historiographical tradition in Italy and its close connection with political agendas, and the influence of the history of philosophy in the schools. One outcome of the work is the mapping of leading research areas as well as neglected areas, and even the uncovering of some blind spots. (shrink)

Ideas will always resist single-statement definitions, but in a rough attempt at generalization one can say that they either play or are attributed a very special role in thinking and expressive processes, in perhaps all domains of human culture. People who specialize in creating, receiving, transforming, and disseminating them are usually called “intellectuals”—even if they do not monopolize those social practices. The constitution and circulation of ideas as structures of thinking and expression, the settings in which they originate and to (...) which they respond, the material supports in which they are conveyed as well as the intellectual agents specialized in dealing with them are studied by the history of ideas and its neighboring fields. These include intellectual history, history of concepts, histoire des mentalités, Geistesgeschichte, history of books, and even cultural history, sociology of knowledge, and the histories of science, philosophy, literature, and the humanities. As it is obvious, such labels do not support a clear-cut division of labor, nor can they be lined up in an organogram that would fix constant hierarchical relations between them. They show up with incommensurable frequency, displaying different connotations within different academic cultures. This explains why in some cases—as in Geistesgeschichte, Begriffsgeschichte, or histoire des mentalités—equivalent English terms are considered problematic or unnecessary. Having flourished, spread, and sometimes also decayed within different national, disciplinary, and generational contexts, the fields designated by them can only have intricate and overlapping limits. A good way to understand the traditions connected to the history of ideas is hence to look closely to their messy border zones. The closest and most intricate connections are those between “history of ideas” and “intellectual history,” which is reflected in the fact that these terms are often employed interchangeably—a use that will be noted also in the remainder of the present text. Even so, “intellectual history” clearly emerged as preferential designation in the English-speaking world in the final decades of the twentieth century. A reason for this is the spread of the suspicion that “ideas” are burdened by essentialist traits that would render us insensitive to historical discontinuity. The notion of ideas is also sometimes regarded as much too oblivious of the way language conditions thought, and accordingly some analysts suggest that it would be out of line with the best theoretical intelligence established since the so-called linguistic turn (see Kelley 2002a: 310–14). However, others claim that ideas should not be equaled to expressed words, as they refer to occurrences that are best described with psychological terms such as beliefs and attitudes, and, further, that there would be non-essentialist ways of addressing them . What seems more uncontroversial is that, in comparison to “history of ideas,” “intellectual history” opens up an enlarged space of ambivalence as regards the analytical focus, which can then toggle from intellectual products to intellectual producers, consumers, and the cultural frameworks in which they interact. There are also important crossroads between the history of ideas and conceptual history (or Begriffsgeschichte), as both terms signal to the historical study of basic structures of thought. Conceptual history, however, at least in its most well-known variety, which was very much inspired by social-historical approaches, tends to be less centered on biographical and psychological issues and to introduce concepts as more depersonalized linguistic entities. Such and other connections and disconnections between the various ways of attending to “the reflective communal life of human beings in the past” (Burrow) will be further discussed in the following from the perspective of a geographically multicentered historical synopsis. Hopefully, its many limitations will be compensated by the possibilty of bringing to the fore relations that otherwise would not become so salient. (shrink)

Digital ethics, also known as computer ethics or information ethics, is now a lively field that draws a lot of attention, but how did it come about and what were the developments that lead to its existence? What are the traditions, the concerns, the technological and social developments that pushed digital ethics? How did ethical issues change with digitalisation of human life? How did the traditional discipline of philosophy respond? The article provides an overview, proposing historical epochs: ‘pre-modernity’ prior to (...) digital computation over data, via the ‘modernity’ of digital data processing to our present ‘post-modernity’ when not only the data is digital, but our lives themselves are largely digital. In each section, the situation in technology and society is sketched, and then the developments in digital ethics are explained. Finally, a brief outlook is provided. (shrink)

PHILOSOPHY OF SCIENCE, vol. 52, number 1, pp.44-63. R.M. Nugayev, Kazan State |University, USSR. -/- THE HISTORY OF QUANTUM THEORY AS A DECISIVE ARGUMENT FAVORING EINSTEIN OVER LJRENTZ. -/- Abstract. Einstein’s papers on relativity, quantum theory and statistical mechanics were all part of a single research programme ; the aim was to unify mechanics and electrodynamics. It was this broader program – which eventually split into relativistic physics and quantummmechanics – that superseded Lorentz’s theory. The argument of this paper (...) is partly historical and partly methodological. A notion of “crossbred objects” – theoretical objects with contradictory properties which are part of the domain of application of two different research programs – is developed that explains the dynamics of revolutionary theory change. (shrink)

The conception of truth-making, albeit in a rudimentary form, could already be discerned in the writings of G. E. Moore and E. Husserl in the early 1900s. A few years later it was more extensively exploited by William James. It was Wittgenstein, however, who gave the concept a precise meaning. In 1913/1914 Wittgenstein advanced a theory of possible worlds, only one of which was real. Every proposition suggests a part of a possible world which does or does not correspond to (...) parts of the real world. In the first case the proposition is true, in the second case false. Moreover, the part of the real world makes the sentence true. This part is a truth-maker, and the sentence is a truth-bearer. Surprisingly enough, Wittgenstein’s concept of truth-making had its family resemblance with William James’s conception of truth. In 1915 Wittgenstein stopped using the concept of truth-making—it was also not men-tioned in the Tractatus. Unfortunately, Russell did not notice this and in 1918 he adopted the concept of truth-making. In the 1930s, it was used by some second generation analytic philosophers (Schlick, Stebbing, and Wisdom). However, it became rather popular among analytic philosophers only in the 1980s. (shrink)