We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix $${\mathbb {A}}$$ with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i,j =?. The method allows us to decide whether to declare a i,j = 0 or a i,j = 1 or a i,j =? (...) undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences. (shrink)

This is the first critical edition since the nineteenth century of Bacon's principal philosophical work in English, The Twoo Bookes of Francis Bacon. Of the proficience and advancement of Learning, divine and humane - traditionally known as The Advancement of Learning.

The present paper investigates why logical empiricists remained silent about one of the most philosophy-laden matters of theoretical physics of their day, the principle of least action (PLA). In the two decades around 1900, the PLA enjoyed a remarkable renaissance as a formal unification of mechanics, electrodynamics, thermodynamics, and relativity theory. Taking Ernst Mach's historico-critical stance, it could be liberated from much of its physico-theological dross. Variational calculus, the mathematical discipline on which the PLA was based, obtained a new rigorous (...) basis. These three developments prompted Max Planck to consider the PLA as formal embodiment of his convergent realist methodology. Typically rejecting ontological reductionism, David Hilbert took the PLA as the key concept in his axiomatizations of physical theories. It served one of the main goals of the axiomatic method: ''deepening the foundations.'' Although Moritz Schlick was a student of Planck's, and Hans Hahn and Philipp Frank enjoyed close ties to Gottingen, the PLA became a veritable Shibboleth to them. Rather than being worried by its historical connections with teleology and determinism, they erroneously identified Hilbert's axiomatic method tout court with Planck's metaphysical realism. Logical empiricists' strict containment policy against metaphysics required so strict a separation between physics and mathematics to exclude even those features of the PLA and the axiomatic method not tainted with metaphysics. (shrink)

Ambiguity is not the polysemy most words display as dictionary entries but results from the context's blocking of the reader's choice among competing meanings, as when, to use an example from Derrida, a French context hinders the reader from deciding whether plus de means "lack" or "excess" .1 In this case, the undecidability is due entirely to the fact that the reader is playing a score, the syntax, that will not let him choose. This must be because the score is (...) badly written; yet it is precisely this sort of willful neglect that critics have labeled poetic license, thereby underlining its literary nature. Undecidability has become a central feature in Derrida's analyses of literariness, and it is also the main underpinning of his creative writing.2 Better still, his own critical discourse has put undecidability to use, not a rare case of metalanguage imitating the very devices of the language it purports to analyze. My example are therefore drawn from Derrida on the assumption that his conscious practice of écriture, backed up by a sophisticated theory, will be particularly illuminating. For my own analysis of these phenomena, I shall be using a special word that Derrida has adopted and adapted from the terminology of ancient rhetoric. He proposes it in his commentary on this sentence of Mallarmé's: "La scène n'illustre que l'idée, pas une action effective, dans une hymen . . . entre le désir et l'accomplissement, la perpétration et son souvenir."3 Our critic points out that the grammar prevents the reader from choosing between hymen as "marriage," a symbolic union or fusion, and as "vaginal membrane," the barrier is broken through if desire is to reach what it desires. Undecidability is the effective mechanism of pantomime as an art form since from mimicry alone, without words, the spectator cannot tell whether a dreamed, or a remembered, or a present act is being set forth. This, in turn, Derrida shows to be fundamental to Mallarmé's concept of poetry. It is simply a pun or, as Derrida prefers to call it, a "syllepsis,"4 the trope that consists in understanding the same word in two different ways at the same time, one meaning being literal or primary, the other figurative.5 The second meaning is not just different from and incompatible with the first: it is tied to the first as its polar opposite or the way the reverse of a coin is bound to its obverse—the hymen as unbroken membrane is also metaphorical in both its meanings is irrelevant to its undecidability. What makes it undecidable is not that it is an image but that it embodies a structure, that is, the syllepsis. · 1. See Jacques Derrida's La Dissémination , p. 307.· 2. Because Derrida is a philosopher by trade, one would expect his undecidability to reflect the very precise logical and mathematical concepts of that discipline - which is to say, the limitations inherent in the axiomatic method. Kristeva, for example, tries to do this in her Le Texts du roman: Approche sèmiologique d'une structure discursive transformationnelle , pp. 76-78. So far as I can make out, however , Derrida's critical theory and reading practice do not pack more into the word "undecidable" than does the definition I offer in this paper.· 3. Stephane Mallarmé, Mimique, Oeuvres complètes , p. 310: "the scene [a drama, or rather a pantomime] bodies forth only an idea, not an action: it is like a hymen between desire and its realization, or between an act committed and the memory of it"; here and elsewhere, my translation unless otherwise cited. Derrida's commentary, "La Double Séance," has been rpt. in La Dissémination, pp. 199-317; see esp. pp. 240 ff.· 4. See La Dissémination, p. 249.· 5. This definition has prevailed ever since Dumarsais' treatise, Des Tropes . That syllepsis must be distinguished from the so-called grammatical syllepsis or the zeugma is apparent in Heinrich Lausberg's Handbuch der literarischen Rhetorik , pars. 702-7; on the acceptation chosen by Derrida, see pars. 7-8. Michael Riffaterre, Blanche W. Knopf Professor of French Literature and chairman of the department of French and Romance literatures at Columbia University, is the editor of Romantic Review. He is the author of Semiotics of Poetry, La Production du Texte, Typology of Intertextuality and A Grammar of Descriptive Poetry. "Syllepsis" developed out of seminars he led at the Irvine School of Criticism and Theory and at Johns Hopkins University. (shrink)

In this fascinating autobiography from the foremost genius of twentieth-century physics, Max Planck tells the story of his life, his aims, and his thinking. Published posthumously, the papers in this volume were written for the general reader and make accessible his scientific theories as well as his philosophical ideals, including his thoughts on ethics and morals. Max (Karl Ernst Ludwig) Planck was a German physicist and philosopher known for his quantum theory, for which he won the Nobel Prize in Physics (...) in 1918. Planck was born in Kiel, Germany, in 1858 to an academic family, and he valued education from a young age. He attended the Universities of Munich and Berlin to study physics under the great scientific leaders Kirchhoff and Helmholtz. His early work mainly focused on the study of thermodynamics, and in 1900 he published a paper on his quantum theory that would change the face of modern physics. Planck worked as a professor at Berlin University his entire life, and he also served as the president of the Kaiser Wilhelm Society for the Promotion of Science. During World War II, Planck experienced great hardships while he remained in Germany but openly opposed the Nazi regime. One of his two sons was executed during this time for an unsuccessful attempt on Hitler's life, and Planck's home in Berlin was eventually bombed. He continued to write on physics and philosophy until his death in 1947. (shrink)

In the sixth section of his light quantum paper of 1905, Einstein presented the miraculous argument, as I shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the macroscopic, thermodynamic properties of high frequency heat radiation carry a distinctive signature of finitely many, spatially localized, independent components and so inferred that it consists of quanta. I describe how Einstein’s other statistical papers of 1905 had already developed and exploited the idea that the ideal (...) gas law is another macroscopic signature of finitely many, spatially localized, independent components and that these papers in turn drew on his first two, “worthless” papers of 1901 and 1902 on intermolecular forces. However, while the ideal gas law was a secure signature of independence, it was harder to use as an indicator that there are finitely many components and that they are spatially localized. Further, since his analysis of the ideal gas law depended on the assumption that the number of components was fixed, its use was precluded for heat radiation, whose component quanta vary in number in most processes. So Einstein needed and found another, more powerful signature of discreteness applicable to heat radiation and which indicated all these properties. It used one of the few processes, volume fluctuation, in which heat radiation does not alter the number of quanta. (shrink)

In the sixth section of his light quantum paper of 1905, Einstein presented the miraculous argument, as I shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the macroscopic, thermodynamic properties of high-frequency heat radiation carry a distinctive signature of finitely many, spatially localized, independent components and so inferred that it consists of quanta. I describe how Einstein's other statistical papers of 1905 had already developed and exploited the idea that the ideal gas (...) law is another macroscopic signature of finitely many, spatially localized, independent components and that these papers in turn drew on his first two, "worthless" papers of 1901 and 1902 on intermolecular forces. However, while the ideal gas law was a secure signature of independence, it was harder to use as an indicator that there are finitely many components and that they are spatially localized. Further, since his analysis of the ideal gas law depended on the assumption that the number of components was fixed, its use was precluded for heat radiation, whose component quanta vary in number in most processes. So Einstein needed and found another, more powerful signature of discreteness applicable to heat radiation and which indicated all these properties. It used one of the few processes, volume fluctuation, in which heat radiation does not alter the number of quanta. © 2005 Elsevier Ltd. All rights reserved. (shrink)

The exegesis of sacred rites in the Talmud is subject to a restriction on the iteration and composition of inference rules. In order to determine the scope and limits of that restriction, the sages of the Talmud deploy those very same inference rules. We present the remarkable features of this early use of self-reference to navigate logical constraints and uncover the hidden complexity behind the sages? arguments. Appendix 11 contains a translation of the relevant sugya. 1Hebrew and Aramaic transliteration approximates (...) traditional Sephardic pronunciation, which is closer to academic standard transliteration than the various Ashkenazic pronunciations, yet is legible. Specific references follow the convention of folio (number), side (a or b), number of lines from the top or (if negative) bottom of the page. (shrink)

One of the central pillars of Vygotsky’s contribution to social science is his concept of mediation: the process through which the social and the individual mutually shape each other. His rich, complex and challenging texts focus on a nuanced notion of mediation that was not necessarily visible to those active in the command-and-control climate of the Stalinist era. The article focuses on this notion of the lack of visibility in mediation.

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev, is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to (...) the truth values of its elementary constituents, Hj, and to the truth functions of their corresponding FBST structures Mj, respectively. (shrink)

We consider conditionals of the form A ⇒ B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals.Three main aspects will be investigated: Inverse causality from future to past, where a future condition can influence a legal event in the past (this is a man made causality).Comparison with similar features in modern law.New types of temporal logics arising (...) from modelling the Talmudic examples. We shall see that we need a new temporal logic,which we call Talmudic temporal logic with linear open advancing future and parallel changing past, based on two parameters for time. (shrink)

Discusses mental processes, the role of humans in nature, experience, and the connection between myth, religion, and science.

Preface to paperback edition -- Why Schelling? why naturephilosophy? -- The powers due to becoming: the reemergence of platonic physics in the genetic philosophy -- Antiphysics and neo-Fichteanism -- The natural history of the unthinged -- "What thinks in me is what is outside me". phenomenality, physics and the idea -- Dynamic philosophy, transcendental physics -- Conclusion: transcendental geology.

When the New Organon appeared in 1620, part of a six-part programme of scientific inquiry entitled 'The Great Renewal of Learning', Francis Bacon was at the high point of his political career, and his ambitious work was groundbreaking in its attempt to give formal philosophical shape to a new and rapidly emerging experimentally-based science. Bacon combines theoretical scientific epistemology with examples from applied science, examining phenomena as various as magnetism, gravity, and the ebb and flow of the tides, and anticipating (...) later experimental work by Robert Boyle and others. His work challenges the entire edifice of the philosophy and learning of his time, and has left its mark on all subsequent philosophical discussions of scientific method. This volume presents a new translation of the text into modern English by Michael Silverthorne, and an introduction by Lisa Jardine that sets the work in the context of Bacon's scientific and philosophical activities. (shrink)

The main goal of this article is to use the epistemological framework of a specific version of Cognitive Constructivism to address Piaget’s central problem of knowledge construction, namely, the re-equilibration of cognitive structures. The distinctive objective character of this constructivist framework is supported by formal inference methods of Bayesian statistics, and is based on Heinz von Foerster’s fundamental metaphor of objects as tokens for eigen-solutions. This epistemological perspective is illustrated using some episodes in the history of chemistry concerning the definition (...) or identification of chemical elements. Some of von Foerster’s epistemological imperatives provide general guidelines of development and argumentation. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations that (...) are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of using (...) the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

Heinz Von Forester characterizes the objects “known” by an autopoietic system as eigen-solutions, that is, as discrete, separable, stable and composable states of the interaction of the system with its environment. Previous articles have presented the FBST, Full Bayesian Significance Test, as a mathematical formalism specifically designed to access the support for sharp statistical hypotheses, and have shown that these hypotheses correspond, from a constructivist perspective, to systemic eigen-solutions in the practice of science. In this article several issues related to (...) the role played by language in the emergence of eigen-solutions are analyzed. The last sections also explore possible connections with the semiotic theory of Charles Sanders Peirce. (shrink)

Decoupling is a general principle that allows us to separate simple components in a complex system. In statistics, decoupling is often expressed as independence, no association, or zero covariance relations. These relations are sharp statistical hypotheses, that can be tested using the FBST - Full Bayesian Significance Test. Decoupling relations can also be introduced by some techniques of Design of Statistical Experiments, DSEs, like randomization. This article discusses the concepts of decoupling, randomization and sparsely connected statistical models in the epistemological (...) framework of cognitive constructivism. (shrink)

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on (...) the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)

In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by Cognitive Constructivism and the FBST (Full Bayesian Significance Test). The constructivist framework is contrasted with the traditional epistemological settings for orthodox Bayesian and frequentist statistics provided by Decision Theory and Falsificationism.

Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.

The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.