We obtain an equivalent implicit characterization of Lp Banach spaces that is amenable to a logical treatment. Using that, we obtain an axiomatization for such spaces into a higher order logical system, the kind of which is used in proof mining, a research program that aims to obtain the hidden computational content of mathematical proofs using tools from mathematical logic. As an aside, we obtain a concrete way of formalizing Lp spaces in positive-bounded logic. The axiomatization is followed (...) by a corresponding metatheorem in the style of proof mining. We illustrate its use with the derivation for this class of spaces of the standard modulus of uniform convexity. (shrink)

A famous theorem by van der Waerden states the following: Given any finite coloring of the integers, one color contains arbitrarily long arithmetic progressions. Equivalently, for every q,k, there is an N = N(q,k) such that for every q-coloring of an interval of length N one color contains a progression of length k. An obvious question is what is the growth rate of N = N(q,k). Some proofs, like van der Waerden's combinatorial argument, answer this question directly, while the topological (...) proof by Furstenberg and Weiss does not. We present an analysis of (Girard's variant of) Furstenberg and Weiss's proof based on monotone functional interpretation, both yielding bounds and providing a general illustration of proof mining in topological dynamics. The bounds do not improve previous results by Girard, but only—as is also revealed by the analysis—because the combinatorial proof and the topological dynamics proof in principle are identical. (shrink)

In this paper, we present another case study in the general project of proof mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation developed in Kohlenbach , Oxford University Press, Oxford, 1996, pp. 225–260) to analyze Cheney's simplification 189) of Jackson's original proof 320) of the uniqueness of the best L1-approximation of continuous functions fC[0,1] by polynomials pPn of (...) degree n. Cheney's proof is non-effective in the sense that it is based on classical logic and on the non-computational principle WKL . The result of our analysis provides the first effective uniform modulus of uniqueness . Moreover, the extracted modulus has the optimal ε-dependency as follows from Kroó 331). The paper also describes how the uniform modulus of uniqueness can be used to compute the best L1-approximations of a fixed fC[0,1] with arbitrary precision. The second author uses this result to give a complexity upper bound on the computation of the best L1-approximation in Oliva 66–77). (shrink)

Hilbert’s program: • Formalize abstract, infinitary, nonconstructive mathematics. • Prove consistency using only finitary methods.

It is well-known that an element of a commutative ring with identity is nilpotent if, and only if, it lies in every prime ideal of the ring. A modification of this fact is amenable to a very simple proof mining analysis. We formulate a quantitative version of this modification and obtain an explicit bound. We present an application. This proof mining analysis is the leitmotif for some comments and observations on the methodology of computational extraction. In (...) particular, we emphasize that the formulation of quantitative versions of ordinary mathematical theorems is of independent interest from proof mining metatheorems. (shrink)

In view of an enhancement of our implementation on the computer, we explore the possibility of an algorithmic optimization of the various proof-theoretic techniques employed by Kohlenbach for the synthesis of new effective uniform bounds out of established qualitative proofs in Numerical Functional Analysis. Concretely, we prove that the method of “colouring” some of the quantifiers as “non-computational” extends well to ε-arithmetization, elimination-of-extensionality and model-interpretation.

We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style of proof mining, a research programme that aims to obtain the hidden computational content of ordinary mathematical proofs using tools from proof theory.

In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...) this empirical study suggest that mathematical explanations do occur in research articles published in mathematics journals, as indicated by the occurrence of explanation indicators. When compared with the use of justification indicators, however, the data suggest that justifications occur much more frequently than explanations in scholarly mathematical practice. The results also suggest that justificatory proofs occur much more frequently than explanatory proofs, thus suggesting that proof may be playing a larger justificatory role than an explanatory role in scholarly mathematical practice. (shrink)

\noindent\textbf{Introduction} Online interventions hold great potential for Therapeutic Change Process Research (TCPR), a field that aims to relate in-therapeutic change processes to the outcomes of interventions. Online a client is treated essentially through the language their counsellor uses, therefore the verbal interaction contains many important ingredients that bring about change. TCPR faces two challenges: how to derive meaningful change processes from texts, and secondly, how to assess these complex, varied and multi-layered processes? We advocate the use text mining and (...) multi-level models (MLMs): the former offers tools and methods to discovers patterns in texts; the latter can analyse these change processes as outcomes that vary at multiple levels. \noindent\textbf{Method} We (re-)used the data from \cite{Lamers2015} because it includes outcomes and the complete online intervention for clients with mild depressive symptoms. We used text mining to obtain basic text-variables from e-mails, that we analysed through MLMs. \noindent\textbf{Results} We found that we could relate outcomes of interventions to variables containing text-information. We conclude that we can indeed bridge text mining and MLMs for TCPR as it was possible to relate text-information (obtained through text mining) to multi-levelled TCPR outcomes (using a MLM). \noindent\textbf{Discussion} Text mining can be helpful to obtain change processes, which is also the main challenge for TCPR. We showed how MLMs and text mining can be combined, but our proposition leaves open how to obtain the most relevant textual operationalization of TCPR concepts. That requires interdisciplinary collaboration and discussion. The future does look bright: based on our proof-of-concept study we conclude that MLMs and text mining can indeed advance TCPR. (shrink)

We will apply the methods developed in the field of ‘proof mining’ to the Bolzano-Weierstraß theorem BW and calibrate the computational contribution of using this theorem in proofs of combinatorial statements. We provide an explicit solution of the Gödel functional interpretation as well as the monotone functional interpretation of BW for the product space Πi ∈ℕ[–ki, ki] . This results in optimal program and bound extraction theorems for proofs based on fixed instances of BW, i.e. for BW applied (...) to fixed sequences in Πi ∈ℕ[–ki, ki]. (shrink)

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie “non-computational” proofs from the mainstream literature. To this end, we establish (...) logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches. (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by (...) the ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

This paper addresses the strength of Ramsey's theorem for pairs ($RT^2_2$) over a weak base theory from the perspective of 'proof mining'. Let $RT^{2-}_2$ denote Ramsey's theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König's Lemma and a substantial amount of $\Sigma^0_1$-induction (enough to prove the totality of all primitive recursive functions but not of all primitive recursive functionals). (...) In the resulting theory we show the extractability of primitive recursive programs and uniform bounds from proofs of $\forall\exists$-theorems. There are two components of this work. The first component is a general proof-theoretic result, due to the second author, that establishes conservation results for restricted principles of choice and comprehension over primitive recursive arithmetic PRA as well as a method for the extraction of primitive recursive bounds from proofs based on such principles. The second component is the main novelty of the paper: it is shown that a proof of Ramsey's theorem due to Erdős and Rado can be formalized using these restricted principles. So from the perspective of proof unwinding the computational content of concrete proofs based on $RT^2_2$ the computational complexity will, in most practical cases, not go beyond primitive recursive complexity. This even is the case when the theorem to be proved has function parameters f and the proof uses instances of $RT^2_2$ that are primitive recursive in f. (shrink)

The task of this article is to propose an alternative method for adjudicating truth claims between various paradigms. Informed by sources such as Augustine, Aquinas, Heidegger, Gadamer, and Kuhn, I argue for a form of reasoning which aspires to credibility, plausibility, and explanatory capacity, rather than absolute proof. Instead of representing a flight from scientific standards, I argue that such an approach ultimately represents the best hope of safeguarding the essence of science and rationality as such.

Let the chain antichain principle (CAC) be the statement that each partial order on $\mathbb{N}$ possesses an infinite chain or an infinite antichain. Chong, Slaman, and Yang recently proved using forcing over nonstandard models of arithmetic that CAC is $\Pi^1_1$-conservative over $\text{RCA}_0+\Pi^0_1\text{-CP}$ and so in particular that CAC does not imply $\Sigma^0_2$-induction. We provide here a different purely syntactical and constructive proof of the statement that CAC (even together with WKL) does not imply $\Sigma^0_2$-induction. In detail we show using (...) a refinement of Howard's ordinal analysis of bar recursion that $\text{WKL}_0^\omega+\text{CAC}$ is $\Pi^0_2$-conservative over PRA and that one can extract primitive recursive realizers for such statements. Moreover, our proof is finitary in the sense of Hilbert's program. CAC implies that every sequence of $\mathbb{R}$ has a monotone subsequence. This Bolzano-Weierstraß}-like principle is commonly used in proofs. Our result makes it possible to extract primitive recursive terms from such proofs. We also discuss the Erdős-Moser principle, which—taken together with CAC—is equivalent to $\text{RT}^2_2$. (shrink)

Kohlenbach's proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel's pioneering work on the so-called unwinding of proofs. The proof mining of classical mathematics is rather restricted in scope due to the existence of sentences without computational content which are provable from the law of excluded middle and which involve only two quantifier alternations. By contrast, we show that the proof (...) class='Hi'>mining of classical Nonstandard Analysis has a very large scope. In particular, we will observe that this scope includes any theorem of pure Nonstandard Analysis, where 'pure' means that only nonstandard definitions are used. In this note, we survey results in analysis, computability theory, and Reverse Mathematics. (shrink)

This article presents a parametrized functional interpretation. Depending on the choice of two parameters one obtains well-known functional interpretations such as Gödel's Dialectica interpretation, Diller-Nahm's variant of the Dialectica interpretation, Kohlenbach's monotone interpretations, Kreisel's modified realizability, and Stein's family of functional interpretations. A functional interpretation consists of a formula interpretation and a soundness proof. I show that all these interpretations differ only on two design choices: first, on the number of counterexamples for A which became witnesses for ¬A when (...) defining the formula interpretation and, second, the inductive information about the witnesses of A which is considered in the proof of soundness. Sufficient conditions on the parameters are also given which ensure the soundness of the resulting functional interpretation. The relation between the parametrized interpretation and the recent bounded functional interpretation is also discussed. (shrink)

Recently, the second author, Briseid, and Safarik introduced nonstandard Dialectica, a functional interpretation capable of eliminating instances of familiar principles of nonstandard arithmetic—including overspill, underspill, and generalizations to higher types—from proofs. We show that the properties of this interpretation are mirrored by first-order logic in a constructive sheaf model of nonstandard arithmetic due to Moerdijk, later developed by Palmgren, and draw some new connections between nonstandard principles and principles that are rejected by strict constructivism. Furthermore, we introduce a variant of (...) the Diller–Nahm interpretation with two different kinds of quantifiers, similar to Hernest’s light Dialectica interpretation, and show that one can obtain nonstandard Dialectica by weakening the computational content of the existential quantifiers—a process called herbrandization. We also define a constructive sheaf model mirroring this new functional interpretation, and show that the process of herbrandization has a clear meaning in terms of these sheaf models. (shrink)

Some quantitative results obtained by proof mining take the form of Herbrand disjunctions that may depend on additional parameters. We attempt to elucidate this fact through an extension to first-order arithmetic of the proof of Herbrand’s theorem due to Gerhardy and Kohlenbach which uses the functional interpretation.

This paper discusses what kind of quantitative information one can extract under which circumstances from proofs of convergence statements in analysis. We show that from proofs using only a limited amount of the law-of-excluded-middle, one can extract functionals , where L is a learning procedure for a rate of convergence which succeeds after at most B-many mind changes. This -learnability provides quantitative information strictly in between a full rate of convergence and a rate of metastability in the sense of Tao (...) . In fact, it corresponds to rates of metastability of a particular simple form. Moreover, if a certain gap condition is satisfied, then B and L yield a bound on the number of possible fluctuations. We explain recent applications of proof mining to ergodic theory in terms of these results. (shrink)

In this paper we study with proof-theoretic methods the function(al) s provably recursive relative to Ramsey's theorem for pairs and the cohesive principle (COH). Our main result on COH is that the type 2 functional provably recursive from $RCA_0 + COH + \Pi _1^0 - CP$ are primitive recursive. This also provides a uniform method to extract bounds from proofs that use these principles. As a consequence we obtain a new proof of the fact that $WKL_0 + \Pi (...) _1^0 - CP + COH$ is $\Pi _1^0 $ -conservative over PRA. Recent work of the first author showed that $\Pi _1^0 + CP + COH$ is equivalent to a weak variant of the Bolzano-Weierstraß principle. This makes it possible to use our results to analyze not only combinatorial but also analytical proofs. For Ramsey's theorem for pairs and two colors $\left( {RT_2^2 } \right)$ we obtain the upper bounded that the type 2 functionals provable recursive relative to $RCA_0 + \sum\nolimits_2^0 {IA + RT_2^2 } $ are in T₁. This is the fragment of Gödel's system T containing only type 1 recursion—roughly speaking it consists of functions of Ackermann type. With this we also obtain a uniform method for the extraction of T₁-bounds from proofs that use RT2..... Moreover, this yields a new proof of the fact that $WKL_0 + \sum\nolimits_2^0 {IA} + RT_2^2 $ is $\Pi _1^0 $ -conservative over $RCA_0 + \sum\nolimits_2^0 { - IA} $ . The results are obtained in two steps: in the first step a term including Skolem functions for the above principles is extracted from a given proof. This is done using Gödel's functional interpretation. After this the term is normalized, such that only specific instances of the Skolem functions are used. In the second step this term is interpreted using $\Pi _1^0 $ -comprehension. The comprehension is then eliminated in favor of induction using either elimination of monotone Skolem functions (for COH) or Howard's ordinal analysis of bar recursion (for $RT_2^2 $. (shrink)

In recent years, proof theoretic transformations that are based on extensions of monotone forms of Gödel’s famous functional interpretation have been used systematically to extract new content from proofs in abstract nonlinear analysis. This content consists both in effective quantitative bounds as well as in qualitative uniformity results. One of the main ineffective tools in abstract functional analysis is the use of sequential forms of weak compactness. As we recently verified, the sequential form of weak compactness for bounded closed (...) and convex subsets of an abstract Hilbert space can be carried out in suitable formal systems that are covered by existing metatheorems developed in the course of the proof mining program. In particular, it follows that the monotone functional interpretation of this weak compactness principle can be realized by a functional Ω∗ definable from bar recursion of lowest type. While a case study on the analysis of strong convergence results that are based on weak compactness indicates that the use of the latter seems to be eliminable, things apparently are different for weak convergence theorems such as the famous Baillon nonlinear ergodic theorem. For this theorem we recently extracted an explicit bound on a metastable version of this theorem that is primitive recursive relative to Ω∗.In the current paper we for the first time give the construction of Ω∗ . As a corollary to the fine analysis of the use of bar recursion in this construction we obtain that Ω∗ elevates arguments in Tn at most to resulting functionals in Tn+2 . In particular, one can conclude from this that our bound on Baillon’s theorem is at least definable in T4. (shrink)

In this paper we develop a method for finding, under general conditions, explicit and highly uniform rates of convergence for the Picard iteration sequences for selfmaps on bounded metric spaces from ineffective proofs of convergence to a unique fixed point. We are able to extract full rates of convergence by extending the use of a logical metatheorem recently proved by Kohlenbach. In recent case studies we were able to find such explicit rates of convergence in two concrete cases. Our novel (...) method now provides an explanation in logical terms for these findings. This amounts, loosely speaking, to general conditions under which we in this specific setting can transform a ∀∃∀-sentence into a ∀∃-sentence via an argument involving product spaces. This reduction in logical complexity allows us to use the existing machinery to extract quantitative bounds of the sort we need. (shrink)

Let ${2-\textsf{RAN}}$ be the statement that for each real X a real 2-random relative to X exists. We apply program extraction techniques we developed in Kreuzer and Kohlenbach (J. Symb. Log. 77(3):853–895, 2012. doi:10.2178/jsl/1344862165), Kreuzer (Notre Dame J. Formal Log. 53(2):245–265, 2012. doi:10.1215/00294527-1715716) to this principle. Let ${{\textsf{WKL}_0^\omega}}$ be the finite type extension of ${\textsf{WKL}_0}$ . We obtain that one can extract primitive recursive realizers from proofs in ${{\textsf{WKL}_0^\omega} + \Pi^0_1-{\textsf{CP}} + 2-\textsf{RAN}}$ , i.e., if ${{\textsf{WKL}_0^\omega} + \Pi^0_1-{\textsf{CP}} + 2-\textsf{RAN} (...) \, {\vdash} \, \forall{f}\, {\exists}{x} A_{qf}(f,x)}$ then one can extract from the proof a primitive recursive term t(f) such that ${A_{qf}(f,t(f))}$ . As a consequence, we obtain that ${{\textsf{WKL}_0}+ \Pi^0_1 - {\textsf{CP}} + 2-\textsf{RAN}}$ is ${\Pi^0_3}$ -conservative over ${\textsf{RCA}_0}$. (shrink)

It is well known that for a given continuous function f : [0, 1] → ℝ and a number n there exists a unique polynomial pn ∈ Pn which best L1-approximates f. We establish the first upper bound on the complexity of the sequence n∈ ℕ, assuming f is polynomial-time computable. Our complexity analysis makes essential use of the modulus of uniqueness for L1-approximation presented in [13].

We prove a result relating the author's monotone functional interpretation to the bounded functional interpretation due to Ferreira and Oliva. More precisely we show that largely a solution for the bounded interpretation also is a solution for the monotone functional interpretation although the latter uses the existence of an underlying precise witness. This makes it possible to focus on the extraction of bounds while using the conceptual benefit of having precise realizers at the same time without having to construct them.

We revisit Naturalized Epistemology and the Law of Evidence, published twenty years ago. The evolution of the relative plausibility theory of juridical proof is offered as evidence of the advantage of a naturalized approach to the study of the field and law evidence. Various alternative explanations of aspects of juridical proof from other disciplines are examined and their shortcomings described. These competing explanations are similar in their reductive, a priori approaches that are at odds with an empirically oriented (...) naturalized approach. The shortcomings of the various a priori approaches are driven by their common methodological commitments to employing weird hypotheticals to engage in intuition mining about the American legal systems that in turn ignore important aspects of the actual legal systems and consistently make impossible epistemological demands. As a result, both their descriptions of and prescriptions for American legal systems are implausible, unlike the relative plausibility theory. (shrink)

Collaborative filtering technology is currently the most successful and widely used technology in the recommendation system. It has achieved rapid development in theoretical research and practice. It selects information and similarity relationships based on the user’s history and collects others that are the same as the user’s hobbies. User’s evaluation information is to generate recommendations. The main research is the inadequate combination of context information and the mining of new points of interest in the context-aware recommendation process. On the (...) basis of traditional recommendation technology, in view of the characteristics of the context information in music recommendation, a personalized and personalized music based on popularity prediction is proposed. Recommended algorithm is MRAPP. The algorithm first analyzes the user’s contextual information under music recommendation and classifies and models the contextual information. The traditional content-based recommendation technology CB calculates the recommendation results and then, for the problem that content-based recommendation technology cannot recommend new points of interest for users, introduces the concept of popularity. First, we use the memory and forget function to reduce the score and then consider user attributes and product attributes to calculate similarity; secondly, we use logistic regression to train feature weights; finally, appropriate weights are used to combine user-based and item-based collaborative filtering recommendation results. Based on the above improvements, the improved collaborative filtering recommendation algorithm in this paper has greatly improved the prediction accuracy. Through theoretical proof and simulation experiments, the effectiveness of the MRAPP algorithm is demonstrated. (shrink)

During the first half of the twentieth century, the mining industry in Britain was subject to recurrent disputes about the risk to miners’ lungs from coal dust, moderated by governmental, industrial, medical and mining bodies. In this environment, precise measurements offered a way to present uncontested objective knowledge. By accessing primary source material from the National Archives, the South Wales Miners Library and the University of Bristol's Special Collections, I demonstrate the importance that the British Medical Research Council (...) (MRC) attached to standardized instrumental measures as proof of objectivity, and explore the conflict between objective and subjective measures of health. Examination of the MRC's use of spirometry in their investigation of pneumoconiosis (miner's lung) from 1936 to 1945 will shed light on this conflict and illuminate the politics inherent in attempts to quantify disability and categorize standards of health. (shrink)

Clifton, Butterfield, and Redhead [1989] have constructed two separate arguments that bear some resemblances to a proof of mine pertaining to the nonlocal character of quantum theory. Their arguments have flaws, which they point out. I explicate my proof by explaining in detail both how it differs logically from the two arguments they have constructed, and how it avoids the pitfalls of both. *This work was supported by the Director, Office of Energy Research, Office of High Energy and (...) Nuclear Physics, Division of High Energy Physics of the U. S. Department of Energy under Contract DE-ACO3-76SF00098. (shrink)

This volume comprises a selection of contributions to the theorizing about argumentation that have been presented at the 9th conference of the International Society for the Study of Argumentation, held in Amsterdam in July 2018. The chapters included provide a general theoretical perspective on central topics in argumentation theory, such as argument schemes and the fallacies. Some contributions concentrate on the treatment of the concept of conductive argument. Other contributions are dedicated to specific issues such as the justification of questions, (...) the occurrence of mining relations, the role of exclamatives, argumentative abduction, eudaimonistic argumentation and a typology of logical ways to counter an argument. In a number of cases the theoretical problems addressed are related to a specific type of context, such as the burden of proof in philosophical argumentation, the charge of committing a genetic fallacy in strategic manoeuvring in philosophy, the necessity of community argument, and connection adequacy for arguments with institutional warrants. The volume offers a great deal of diversity in its breadth of coverage of argumentation theory and wide geographic representation from North and South America to Europe and China. (shrink)

This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes (...) emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. -/- Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition. (shrink)

Jakob Friedrich Fries is one of the most important representatives of the Critical Philosophy, someone who built immediately on the original Kantian philosophy. -/- Fries was born in 1773 in Barby (on the Elbe). In 1805 he was extraordinary professor for philosophy in Jena and in the same year was ordinary professor for philosophy in Heidelberg. Returning to Jena in 1816, one year later he was compulsorily retired because of his participation at the nationalistic and republican Wartburg Festival. In 1924 (...) he obtained a professorship for physics and mathematics, and in 1838 he was given back a professorship for philosophy. He died in 1843 in Jena. -/- The book summarizes the research results of the DFG-Project "Jakob Friedrich Fries' Influence on the Sciences of the 19th Century". The research project was carried out by Dr. Kay Herrmann (Institute of Philosophy, Jena University) and Prof. Dr. Wolfram Hogrebe (Institute of Philosophy, Bonn University). Such a study has special importance. There is available a large amount of literature about the "speculative contemporaries" of Fries, like Fichte, Schelling, and Hegel. In contrast to the "speculative philosophy", there has been published only a few studies about the Friesian natural philosophy. Fries was, in his natural-philosophical studies, looking for a link between philosophy and modern sciences, wheras his "speculative philosophical" contemporaries felt obligated to stick primarily to a descriptive, phenomenal view of nature. So far the question "How was mathematical natural philosophy regarded by scientists and mathematicians of the 19th century?" has hardly been investigated. Archival studies showed that this gap in Fries-research can be filled. The Friesian correspondence turned out to be a rich gold mine. -/- The present publication is more than a research report. The monographic first part is intended to introduce the foundations of the Friesian theory of cognition, the Friesian methodology, and the Friesian natural philosophy. This should facilitate entry into Friesian philosophy. -/- The Friesian theory is analyzed from two points of view: •How did Fries suceed in continuing and improving the Kantian approach? Is Fries able to remove the weak points of Kantian philosophy? -/- •What is the current significance of the Friesian approach? There are some interesting similarities between the Friesian approach and modern philosophical theories (such like Chomsky's theory of "universal grammer"). The lasting core of the Friesian theory of cognition is: To use empirical studies for working on philosophical problems. -/- Chapters 3 and 4 are scientific-historically oriented. These chapters analyze the Friesian position in scientific and mathematical debates (debates about the a priori foundations of physics, the problem of the identification of physics as an independent discipline, the problem of the boundary between chemistry and physics, the problem of mathematization of the sciences, the theory of the imponderabilia, the systematics and structure of sciences and mathematics, problems of infinity, the differential calculus, the theory of parallel lines) and the relation between Fries and the scientists of the 19th century. The book contains the latest findings gained by evaluation of the Friesian unpublished work (for example the correspondence with W. Weber, C. F. Gauß, E. F. Apelt, O. Schlömilch, Ch. Reichel, B. A. v. Lindenau, L. Gmelin, E. G. Fischer, A. N. Scherer, J. S. C. Schweigger) -/- One result of the research project is that some important scientists took a favourable view of the Friesian theory, but the influence of the Friesian philosophy on the sciences of the 19th century was very limited. The causes are very complex: An anti-natural-philosophical spirit of age, the limits of the Kantian inspired philosophy and some unfavourable aspects in the biography of Fries. -/- For the first time the voluminous Fries-Reichel-correspondence was evaluated. The Fries-Reichel-correspondence contains the Friesian approach to prove the 11th Euclidean axiom, and the whole transcript of the Friesian attempt at proof is given. // Der erste Teil des Buches will in die Grundprobleme Fries’scher Erkenntnis­theorie, Methodenlehre und Naturphilosophie einführen, wobei das Hauptaugenmerk auf die Fortführung der kantischen Ansätze durch Fries sowie auf die aktuelle Interpretation der Fries’schen Lehre gerichtet ist. Der wissenschaftshistorisch ausgerichtete zweite Teil analysiert Fries’ Stellung zu naturwissenschaftlichen und mathematischen Diskussionsrichtungen (Probleme der Identifizierung der Physik als eigenständige Disziplin, der Grenzziehung zwischen Physik und Chemie, der Mathematisierung der Naturwissenschaften, der Imponderabilientheorie, der Systematik von Naturwissenschaft und Mathematik, des Unendlichen, der Parallelentheorie usw.) sowie sein Verhältnis zu Naturwissenschaftlern und Mathematikern seiner Zeit. Das Buch enthält neue Erkenntnisse, die aus der Auswertung zahlreicher Nachlassmaterialien gewonnen wurden. Erstmalig wird unter dem Blickwinkel „Fries als Naturwissenschaftler und Mathematiker“ auch der sehr umfangreiche Reichel-Briefwechsel ausgewertet. Dem Reichel-Briefwechsel entstammt auch Fries’ Versuch eines Beweises des Parallelenaxioms, der in diesem Buch erstmalig in transkribierter Form vollständig vorliegt. -/- . (shrink)

This volume comprises a selection of contributions to the theorizing about argumentation that have been presented at the 9th conference of the International Society for the Study of Argumentation, held in Amsterdam in July 2018. The chapters included provide a general theoretical perspective on central topics in argumentation theory, such as argument schemes and the fallacies. Some contributions concentrate on the treatment of the concept of conductive argument. Other contributions are dedicated to specific issues such as the justification of questions, (...) the occurrence of mining relations, the role of exclamatives, argumentative abduction, eudaimonistic argumentation and a typology of logical ways to counter an argument. In a number of cases the theoretical problems addressed are related to a specific type of context, such as the burden of proof in philosophical argumentation, the charge of committing a genetic fallacy in strategic manoeuvring in philosophy, the necessity of community argument, and connection adequacy for arguments with institutional warrants. The volume offers a great deal of diversity in its breadth of coverage of argumentation theory and wide geographic representation from North and South America to Europe and China. (shrink)

Preface/Introduction: The question under discussion is metaphysical and truly elemental. It emerges in two aspects — how did we come to be conscious of our own existence, and, as a deeper corollary, do existence and awareness necessitate each other? I am bold enough to explore these questions and I invite you to come along; I make no claim to have discovered absolute answers. However, I do believe I have created here a compelling interpretation. You’ll have to judge for yourself. -/- (...) What follows is the presentation of three essays I have worked on over the past several years seeing publication for the first time. “Hollows of Experience” was written first as an invited chapter for a collection on the ontology of consciousness. However, when cuts became necessary, my chapter got the knife. Its length has prohibited it from publication in any print journal. “Myth and Mind” was written next as a journal article, but as my involvement with it grew so did its length, so it has also idled on my websty awaiting its call. “From Panexperientialism to Conscious Experience” was written most recently, but it is the only one to have been available to the public elsewhere than my own website. Under the name, “The Continuum of Experience”, it was Target Article #95 on the recently closed Karl Jaspers Forum (for discussion purposes only). -/- I have put them in a different sequence here, for reasons of logical sense. Up first, “Panexperientialism” deals with an idea difficult for many to accept, namely that conscious experience is a particular mode of symbolically reflected experience that is largely unique to our species. However, I aver that experienced sensation in itself (as found, for example, in autonomic sensory response systems) goes “all the way down” into nature, and thus the title, panexperientialism. -/- Understanding this idea is helpful to dealing with the focus on language in Part I of “Hollows”, next, since here speech and general symbolic interaction in general are found to be the catalysts for the creation of our consciously experienced world (our “lived reality”). In Part II, however, I explore how experienced sensations must be coeval with existence, and, with even greater temerity, how all this sensational existence might have arisen within some literally inconceivable background of awareness-in-itself that yet has a dynamism that occasionally breaks into existence as experiential events and entities. (The latter may sound wacky, but physicists and cosmologists are themselves attempting to come to terms with that which seethes with vast potential energy in what they refer to as the quantum vacuum.) -/- “Myth and Mind” was put third since it deals with a major lacuna in “Hollows” — that presumed prehistoric period when members of our species made the painful crossing of the symbolic threshold into the beginnings of cultural consciousness. Speech plays a central role here, too, but I look more at narrative structures from the dawn of self-awareness when ritual and myth became vital to human survival. Why would fantastic stories and bizarre rituals be necessary? I speculate that growing foresight led to the unavoidable realization of certain mortality, from which, in turn, emerged the secondary realization that we were now alive. In contrast to our yet-to-come death, we have life here and now, and by ritually identifying with a symbolically expanded mythic, i.e., sacred, reality, we may continue to live on after bodily death, just as our ancestors and loved ones must also do. Language and mythmaking are necessary to avoid mortal despair and they remain at the core of human consciousness. -/- As Ernst Cassirer (1944) has noted, language and myth are “twin creatures”, both metaphoric webs over a reality we can never wholly comprehend. We live in the symbolic and construct our works of imagination and wars of conquest to make life meaningful, to feel immortal, and to sense that we ourselves participate in a reality greater than ourselves. No doubt we do, but this does not mean our culturally constructed self-identities survive the death of our bodies, and it does not imply that our symbolic concepts can ever indicate the ultimate truth. We simply must symbolize an extended reality that was sacred to our ancestors: “Is it not our way, as illusory as it may be, to force continuance on our world and our life in the face of their inevitable ending? Are we not compelled to extend those imaginary horizons as far as we can despite the terror and the sometime joy their extension incites? Is their closure not a form of death?” (Crapanzano, p. 210) -/- Of course, this leaves me in the uncomfortable position of being forced to admit that this venture of mine must inevitably be another attempt at meaningful mythmaking. But what else could it be? This is certainly not a scientific proof though it is indeed an academically rigorous exploration. (Just try to count the citations!) I hope the reader will judge my thesis on the basis of its coherence, the sense of meaning it evokes, my intellectual responsibility, and, finally, the engagement it inspires. If you have read my expositions and found yourself immersed in the timeless questions I here call forth, I would call these writings successful (even if you violently disagree with my answers). -/- I am very grateful to Huping Hu for granting me this special issue of JCER in which to present my ideas in some detail. He has patiently dealt with my exuberant approach and allowed the many changes I kept coming up with right until the final publication date. I also wish to thank the many potential commentators who politely replied to my invitation, and, even more, I thank those who made time to write actual commentaries. -/- References -/- Cassirer, E. (1944). An Essay on Man: An Introduction to a Philosophy of Human Culture. New Haven/London: Yale UP. -/- Crapanzano, V. (2004). Imaginative Horizons: An Essay in Literary-Philosophical Anthropology. Chicago: U of Chicago Press. -/- Gregory M. Nixon University of Northern British Columbia Prince George, British Columbia, Canada Email: [email protected] Websty: http://members.shaw.ca/doknyx. (shrink)

This essay takes up a challenge recently posed by Graham Oppy: to clearly express, in premise-conclusion form, Hegel's version of the ontological argument. In addition to employing this format, it seeks to supplement existing treatments by locating a core component of Hegel's argument in a slightly different place than is common. Whereas some prominent recent treatments (Williams, Bubbio, Melechar) focus on Hegel's definition of the Absolute as the Concept, from the third part of his Science of Logic (the Doctrine of (...) the Concept), mine focuses on earlier definitions from the first (the Doctrine of Being). As I hope to show, there are even more resources in Hegel's Logic for an ontological argument than those emphasized in recent treatments: the concept, the Idea, etc. Already in the first third of the Logic, we find a compelling response to a famous Kantian counter-argument to the ontological proof. The counter-argument is summed up in the phrase ‘existence [Sein] is not a real predicate’. Hence, Hegel's response as I interpret it will take the form of a competing analysis of Being, a Lehre vom Sein (Doctrine of Being). What do we learn when we put the ontology back into Hegel's ontological argument? That Being is neither predicate, nor subject, nor copula, but a monist (or ‘infinite’) category. The larger importance of this exercise to our understanding of Hegel's thought lies in the way it clarifies his profound debt to even non-idealist conceptions of God, such as the one espoused by Spinoza. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Descartes’s Dualism by Marleen RozemondSteven J. WagnerMarleen Rozemond. Descartes’s Dualism. Cambridge: Harvard University Press, 1998. Pp. xx + 279. Cloth, $24.00.Rozemond gives particular attention to questions of mind-body distinctness vs. union and to the status of sensory ideas. Her historical emphasis, backed by impressive scholarship, is Descartes’s relation to the late scholastics. Rozemond is clear, alert to detail, and fair-minded. While the text is too long (esp. in (...) chapters 4–5), this study is indeed rich, its scope and architecture justified.Any good reading of a philosopher is defined—both enhanced and limited—by certain decisions. I have mentioned one of Rozemond’s: her account of Descartes’s dialogue with such predecessors as Suárez and Fonseca sheds important light. It makes one ask, further, whether standard histories are not just as wrong to ignore scholastic concerns in, say, Hobbes, Spinoza, and Locke. Yet Rozemond is less helpful with issues that make more sense when we read forward from the 1640s, not back. An historian also sets a level of philosophical engagement. One chooses between presenting a meaningful narrative, and struggling with the endless problems of detail that can both doom [End Page 678] a philosophical position and give it life. Rozemond inclines toward narrative, often stopping just short of hard questions. Yet she shows curiosity and intelligence throughout. As in the first case, another decision would not have been better or worse but simply yielded a different kind of history.Fundamental is a third choice. A philosopher’s thought may appear as an orderly structure; or as a mix of fixed points and shifting, inconsistent tendencies. Most of us are trained to the former style of representation (although we let philosophers “develop” over time). Rozemond’s Descartes, too, turns out this way. He occupies definite positions. Within each position he knows whether Ρ is a premise for Q, vice versa, or neither. This way of presenting a body of thought, i.e., as a determinate structure admitting logical assessment, is an indispensable tool for historians. Its value in any particular case is, however, a matter of judgment. Rozemond attacks textual problems with skill, often improving decisively on the competition, but the going looks smoother than it is. Sometimes she carries the privilege of selective reading too far. At other times, she overlooks the poor mutual fit of separately smooth solutions, or rests with an outcome that could not have satisfied Descartes. Some examples:1. There is an old question how far Descartes goes towards proving dualism in the Second Meditation, how much is left for the Sixth. Rozemond basically champions the Second Meditation. Although some texts favor this, she ignores important contrary passages. Her reconstruction of the “argument from separability” also fails completely to carry over to Descartes’s alternate proof (AT VII, 85–6) from the indivisibility of mind.2. Rozemond identifies (“pure”) intellection with thought or mind (56). This leaves a problem how sensation could be a mode of thought, given that for her sensations differ from pure thoughts in being ‘modes of the mind as united to the body’ (201, emphasis mine). She remarks that sensations are not ‘straightforward modes of the mind’; yet her earlier chapters have no place for obscure modal hybrids and indeed require the tidy metaphysical scheme that is now denied.3. Although Rozemond handles Descartes’s anti-empiricism well, the discussion of empty space (95–7) no sooner suggests than it drops a crucial question. Descartes traces belief in the void to a childhood prejudice according to which all bodies are perceptible; rejecting the prejudice is supposed to remove support for the hypothesis of the void. But can Descartes really pick up the doctrine of childhood prejudice, an anti-Aristotelian weapon, and turn it against the radically different atomist framework? Rozemond passes on the attendant philosophical and textual problems (cf. 133–7).4. Rozemond’s extensive treatment of sensory perceptions and qualities rewards study (particularly on the importance, for dualism, of problems about body). But she misses the chance for more. Her Descartes firmly “places sensory qualities in the mind.” The real one struggled repeatedly over whether sensory ideas can or must... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Response to Robert Zydenbos' Review of An Introduction to Mādhva VedāntaDeepak SarmaIntroductionI am grateful to the editors of Philosophy East and West for asking me to write a response to Zydenbos' review of my book, An Introduction to Mādhva Vedānta. To this end, I will address four issues: typographical errors, unfounded claims about my translations, content and problems of method and theory, and the future of scholarship in Mādhva (...) Vedānta.Typographical DoṣasFirst, I wish to thank Zydenbos for pointing out the typographical errors. I take full responsibility for them and I intend to correct them in future editions. These are unintentional mistakes and should not be taken as an accurate indicator of my academic ability. I invite readers to examine my other publications on Mādhva Vedānta and to decide for themselves. Jayatīrtha (1365-1388 C.E.), a renowned Mādhva commentator, explained the reasons for such errors in his Pramāṇapad-dhati. He held that defective eyes, whether from cataract, jaundice, or the like,1 [End Page 670] can give rise to defective knowledge, and further, that if an object is too far away, too near, too small, obstructed, or even mixed with similar things, then this will give rise to incorrect knowledge.2 I knew that such errors were likely to occur (especially given the size of the fonts in the page proofs!), which is why I wrote the following in my acknowledgments: "Errors that remain in this text are entirely my own responsibility. If any are found I beg your forgiveness and hope that they inspire you to further study Mādhva Vedānta!" (p. xi). Perhaps all of the undue attention paid by Zydenbos to typographical errors (he devoted a significant portion of his review to them) will inspire further study!TranslationsI am delighted that Zydenbos found my translations to be "not badly done" and disappointed that he incorrectly "assumes" that they are not my own. Rest assured that they are mine. I was assisted by Professor Lawrence McCrea and scholars of the Pūrṇaprajña Saṃśodhana Mandiram (PPSM) and have dutifully acknowledged all of them in my book (p. xii). Zydenbos should know better than to speculate about matters he has no knowledge of.Content and Methodological IssuesThe typographical errors and accusations of plagiarism are far less interesting than the points that were raised about the content of my book. Disputes in the West about interpretations of Mādhva Vedānta are recent; it has been largely ignored in favor of Buddhism and the crypto-Buddhist school, namely Advaita Vedānta. There have been very few books on Mādhva Vedānta written by outsiders, and those few are no longer in print, are poorly written, use dated language, or are in a language that is not available to most lay Mādhvas. Interpretations of Mādhva doctrines made by their authors have remained unquestioned by Western readers given the relative novelty and obscurity of Mādhva Vedānta, while Mādhva insiders have ignored most of them. It is wonderful, then, that Zydenbos doubts my interpretations. After all, his disputes are among the first ones published by an outsider concerning the interpretation of Mādhva doctrines.3Zydenbos' skepticism is reason for celebration for it indicates that Western scholarship on Mādhva Vedānta has come of age. There are now enough scholars of Mādhva Vedānta (or, rather, scholars who claim knowledge of Mādhva Vedānta) in the West that such a debate can occur. I invite others to investigate the points of dispute and to join this expanding community!Zydenbos has also faulted me on the organizational principles of my introductory text. I have, as he correctly notes, intentionally ignored issues of contemporary politics, a topic that he finds essential. Although some historical and political issues are relevant, I find that philosophical discourse sans context is far more intellectually appealing. I am well aware of my biases and have acknowledged the limitations of my historical analysis: [End Page 671]... the history presented here is not intended to be comprehensive. Instead, it is intended... (shrink)

In this article we assume that the kantian a priori juridical-political theory can be reconstructed according to the a priori synthetic satisfiability proof theory, initially declared in Kritik der reinen Vernunft and extended to practical domain in Kritik der praktischen Vernunft. In particular, it is assumed that the aim to prove that synthetic judgments, such as “this object of external usage is mine”, can a priori invigorate in private law and public law in general – from the determination of (...) their possibility conditions in the executable actions domain by the free human agent – was carried out in Metaphysische Anfangsgründe der Rechtslehre. In what concerns the demonstration of the effectiveness of the law a priori synthetic judgments Kantian theory, i.e., to decide which juridical proposals actually invigorate or not, accepted that this work was not treated on a systematic way by the philosopher Königsberg. There are fragments, spread through many works. Therefore, the task to be developed in this article, aiming to present a field of effectiveness to the law doctrine, is to organize (synthetically) Kant´s statements about politics as a law doctrine exercise, according to the proof theory problems from the a priori synthetic proposals in general. (shrink)

In article <[email protected]> [email protected] writes: Reminds me of a friend of mine who claims that the number 17 is "the most random" number. His proof ran as follows: pick a number. It's not really as good a random number as 17, is it? (Invariable Answer: "Umm, well, no...") This reminds me of a little experiment I did a couple of years ago. I stood on a busy street corner in Oxford, and asked passers by to "name a random number (...) between zero and infinity." I was wondering what this "random" distribution would look like. (shrink)

1. IMPORTANCE OF THE SUBJECT In 1900, in A Critical Exposition of the Philosophy of Leihniz, Russell made the following assertion: "That all sound philosophy should begin with an analysis of propositions is a truth too evident, perhaps, to demand a proof". 1 Forty years later, the interest aroused by this notion had not decreased. C. J. Ducasse wrote in the Journal of Philosophy: "There is perhaps no question more basic for the theory of knowledge than that of the (...) nature of 2 propositions and their relations to judgments, sentences, facts and inferences". Today, the great number of publications on the subject is proof that it is still of interest. One of the problems raised by propositions, the problem of deter mining whether propositions, statements or sentences are the primary bearers of truth and falsity, is even in the eyes of Bar-Hillel, "one of the major items that the future philosophy oflanguage will have to discuss". 3 gave a correct summary of the situation when he wrote in his Ph. Devaux Russell : Since Peano and Schroder who, in fact, adhered more faithfully to Boole's logic of classes, the logical and epistemological status of the proposition together with its analysis have not ceased to be the object of productive philosophical controversies. And especially so since the establishment of contemporary symbolic logic, the foundations 4 of which have been laid out by Russell and Whitehead. * 2. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Response to Robert Zydenbos' Review of An Introduction to Mādhva VedāntaDeepak SarmaIntroductionI am grateful to the editors of Philosophy East and West for asking me to write a response to Zydenbos' review of my book, An Introduction to Mādhva Vedānta. To this end, I will address four issues: typographical errors, unfounded claims about my translations, content and problems of method and theory, and the future of scholarship in Mādhva (...) Vedānta.Typographical DoṣasFirst, I wish to thank Zydenbos for pointing out the typographical errors. I take full responsibility for them and I intend to correct them in future editions. These are unintentional mistakes and should not be taken as an accurate indicator of my academic ability. I invite readers to examine my other publications on Mādhva Vedānta and to decide for themselves. Jayatīrtha (1365-1388 C.E.), a renowned Mādhva commentator, explained the reasons for such errors in his Pramāṇapad-dhati. He held that defective eyes, whether from cataract, jaundice, or the like,1 [End Page 670] can give rise to defective knowledge, and further, that if an object is too far away, too near, too small, obstructed, or even mixed with similar things, then this will give rise to incorrect knowledge.2 I knew that such errors were likely to occur (especially given the size of the fonts in the page proofs!), which is why I wrote the following in my acknowledgments: "Errors that remain in this text are entirely my own responsibility. If any are found I beg your forgiveness and hope that they inspire you to further study Mādhva Vedānta!" (p. xi). Perhaps all of the undue attention paid by Zydenbos to typographical errors (he devoted a significant portion of his review to them) will inspire further study!TranslationsI am delighted that Zydenbos found my translations to be "not badly done" and disappointed that he incorrectly "assumes" that they are not my own. Rest assured that they are mine. I was assisted by Professor Lawrence McCrea and scholars of the Pūrṇaprajña Saṃśodhana Mandiram (PPSM) and have dutifully acknowledged all of them in my book (p. xii). Zydenbos should know better than to speculate about matters he has no knowledge of.Content and Methodological IssuesThe typographical errors and accusations of plagiarism are far less interesting than the points that were raised about the content of my book. Disputes in the West about interpretations of Mādhva Vedānta are recent; it has been largely ignored in favor of Buddhism and the crypto-Buddhist school, namely Advaita Vedānta. There have been very few books on Mādhva Vedānta written by outsiders, and those few are no longer in print, are poorly written, use dated language, or are in a language that is not available to most lay Mādhvas. Interpretations of Mādhva doctrines made by their authors have remained unquestioned by Western readers given the relative novelty and obscurity of Mādhva Vedānta, while Mādhva insiders have ignored most of them. It is wonderful, then, that Zydenbos doubts my interpretations. After all, his disputes are among the first ones published by an outsider concerning the interpretation of Mādhva doctrines.3Zydenbos' skepticism is reason for celebration for it indicates that Western scholarship on Mādhva Vedānta has come of age. There are now enough scholars of Mādhva Vedānta (or, rather, scholars who claim knowledge of Mādhva Vedānta) in the West that such a debate can occur. I invite others to investigate the points of dispute and to join this expanding community!Zydenbos has also faulted me on the organizational principles of my introductory text. I have, as he correctly notes, intentionally ignored issues of contemporary politics, a topic that he finds essential. Although some historical and political issues are relevant, I find that philosophical discourse sans context is far more intellectually appealing. I am well aware of my biases and have acknowledged the limitations of my historical analysis: [End Page 671]... the history presented here is not intended to be comprehensive. Instead, it is intended... (shrink)

Publications in Science, Technology, & Human Values need to have an author. For this reason, I have put my name at the head of this text. I have also provided the title.1 But I must emphasize that the words below are not mine. I have done nothing more, in this case, than transcribe an audio-tape recording2 that has recently come into my possession and submit it to the journal's editor. This latter step seemed to me to be appropriate in view (...) of the tape's unique character. If you choose to read on, it will soon become clear why I came to believe that wider distribution was essential. It is no exaggeration, I believe, to suggest that the publication of this transcript may mark a turning-point in human history. As a result, there are likely to be many enquiries about its authenticity. Let me, therefore, state that I have been given conclusive proof that the tape is genuine. I cannot reveal more in this public forum. However, toward the end of the tape, the speaker throws some light on these matters. The tape seems to have been recorded at some kind of academic confer ence. On the original version, there is background noise and evidence of a live audience. This transcription presents only the words of the main speaker. The speaker is female. (shrink)

The philosophy of mathematics has long been concerned with deter- mining the means that are appropriate for justifying claims of mathemat- ical knowledge, and the metaphysical considerations that render them so. But, as of late, many philosophers have called attention to the fact that a much broader range of normative judgments arise in ordinary math- ematical practice; for example, questions can be interesting, theorems important, proofs explanatory, concepts powerful, and so on. The as- sociated values are often loosely classied (...) as aspects of \mathematical understanding." Meanwhile, in a branch of computer science known as \formal ver- ication," the practice of interactive theorem proving has given rise to software tools and systems designed to support the development of com- plex formal axiomatic proofs. Such eorts require one to develop models of mathematical language and inference that are more robust than the the simple foundational models of the last century. This essay explores some of the insights that emerge from this work, and some of the ways that these insights can inform, and be informed by, philosophical theories of mathematical understanding. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Men with Muskets, Women with Lyres: Nationality, Citizenship, and Gender in the Writings of Germaine de StaëlSusanne HillmanOn 23 May 1812 Germaine de Staël (1766–1817), Europe’s best-known enemy of Napoleon Bonaparte, set out from her estate on Lake Geneva to escape to England. In her reminiscences, she reflected on the pivotal event as follows:[A]fter ten years of ever-increasing persecutions [...] I was obliged to leave two homelands as a (...) fugitive, Switzerland and France, by order of a man less French than I. For I was born on the banks of the Seine, where his only claim to citizenship is his tyranny. He saw the light of day on the island of Corsica, practically within Africa’s savage sway. His father did not, like mine, devote his fortune and his sleepless nights to defending France from bankruptcy and famine; the air of this beautiful country is not his native air; how can he understand the pain of being exiled from it, when he considers this fertile land only as the instrument of his victories. [End Page 231] Where is his patrie? It is any country that accepts his domination. His fellow-citizens? They are whatever slaves obey his orders.1In this passage, de Staël deliberately links nationality and citizenship. In her view, citizenship status was acquired simply by being born on French soil. Her family’s tireless labors on behalf of the nation added another irrefutable proof of Frenchness. In addition, growing up in France and breathing the country’s invigorating air had created an emotional attachment that a person raised elsewhere simply could not fathom. We thus have a triad of birth/service/sentiment that connects the deserving individual to his or her nation (in this case la grande nation).In this essay I explore de Staël’s understanding of the twin concepts of nationality and citizenship through the lens of gender. Nationality and citizenship were of perennial concern to her thought, partly because of the turbulent times she lived in, partly because of her personal experience in exile. Influenced by history and literature, she early on admired the gallant men with muskets who heroically sacrificed their lives for the glory of the nation. But it was the exceptional women with lyres who were destined to act as the nation’s unifying agents by recreating the gallants’ deeds in writing. By imagining the nation these women fulfilled the supreme task of citizenship. In what follows I will argue that de Staël conceived of the ideal citizen as a woman writer or artist who served her nation by inspiring its members with enthusiasm and virtue.2 In elaborating her view of the superior woman as citoyenne and national muse she made an important contribution to the debate on the nation and the citizen.The only daughter of Louis XVI’s finance minister Jacques Necker and the salonnière Suzanne Curchod-Necker, of Genevan and Vaudois citizenship respectively, de Staël gained fame and notoriety through her brilliant conversational talents, political intrigues, and unconventional relationships with famous men. Though she considered herself a “true Frenchwoman” (véritable française),3 she was a citizen of Geneva and a Swedish subject by marriage, at least until 1803 when she took advantage of the Code Civil [End Page 232] and officially claimed French citizenship.4 Considering this multiplicity of conflicting loyalties, it is not surprising that her major writings reveal a sustained preoccupation with these issues.Despite their undeniable significance for early nineteenth-century European intellectual history, historians have so far devoted scant attention to de Staël’s writings. In fact, in the US, Staëlien studies have largely been dominated by literary criticism and theory.5 This has had the effect of prioritizing her novels over her non-fiction, downplaying the historical context of her oeuvre and, most grievously, ignoring de Staël’s historical contribution to socio-political thought.6 As a result of the complex ways in which her personal experience informed her writing, her oeuvre is best examined as a unified, though certainly inconsistent, whole. Her writings were rarely “products of intense deliberation, but rather reflections... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Iddo Landau responds:I believe that there is much to learn from Gilead's arguments, and that his paper adds to the understanding of the themes presented in the original discussion. However, in the end I do not think that the claims I made are rebuffed.Gilead should be commended for expanding the discussion of the Mandarin thought experiment (henceforth: Mandarin) from the existentialist context, to which it was limited in my (...) original article, to the Kantian one. This is a fruitful move. However, we should keep in mind that in Kantianism—unlike existentialism—to be autonomous is to be moral. Thus, some of my claims may be understood differently in existentialist and Kantian contexts. I wrote, "I would like to argue, however, that it [the Mandarin thought experiment] also casts doubt on an important and central existentialist notion: the value of being an authentic, autonomous individual, who behaves as he or she does not because of fear of what others would say, but because he or she genuinely chooses this or that course of action" ("To Kill a Mandarin," p. 95). But to claim, in a Kantian context, that the Mandarin casts doubt on the value of being autonomous is to suggest that the Mandarin casts doubt on the value of being moral, which it certainly does not. Similarly, in a Kantian context it cannot be the case that "if we were true, autonomous individuals... we would have killed an unknown person," since a Kantian autonomous individual is moral and would not kill an innocent person. In the existentialist context, however, things are different; there, autonomy is not tantamount to morality, and the suggestion that we should be autonomous creates many risks. When reading Gilead, I at times felt that he was examining certain expressions that had originally been set in an existentialist context, where autonomy does not equal morality, as though they had been presented in a Kantian one.Gilead also seems to overstate my position on the ability to behave morally when social supervision is revoked. He suggests that, in my [End Page 158] view, "in order to behave morally, respecting the moral law or value is certainly less than enough" and that I regard as "self-deception or simply wishful thinking... any attempt at thinking... that other motives (such as the respect for the moral law) are sufficient to behave morally." However, I do not make such strong claims. I do not think that respecting the moral law is insufficient for behaving morally, only that many (even if not all) will not choose to mind the moral law. Nor do I think that, when there is no external social supervision, it is impossible to remain moral, or that no one can successfully withstand the temptation that the Mandarin presents, or that any view that people are able to withstand the temptation and act morally without social supervision is self-deception. However, I do believe that the number of people who can withstand the temptation, and act morally when there is no social supervision, is significantly smaller than we like to think. Unfortunately, if complete secrecy is guaranteed and the return value for wrongdoing is sufficiently high, many, including "nice" people like you and me, who condemn immoral behavior and are considered by others and themselves as perfectly decent, will either kill an innocent person or have significant difficulties in refraining from doing so.But I should point out, first, that this is an empirical, objective question, and thus not in line with the subjectivist, personal character of much of the original paper. Second, I should note that while I cannot present a satisfactory empirical proof for my assessment, there is nevertheless some basis for it: too many people, upstanding people like you and me, told me time and again that they would accept the Mandarin deal, or at least find it difficult to resist it. Gilead thinks that only very few would so respond, but does not present any empirical evidence for this claim, not even as limited and unscientific as mine, stating that he simply believes "the opposite to be the case." He also feels the suggestion to be annoying. I agree that it is... (shrink)

This release includes the data and code used in: Malaterre, C., F. Lareau (2023) Inferring social networks from unstructured text data: A proof of concept detection of “hidden communities of interest”. Text and Data Analytics for Policy.

In lieu of an abstract, here is a brief excerpt of the content:Response to Robert Zydenbos' Review of An Introduction to Mādhva VedāntaDeepak SarmaIntroductionI am grateful to the editors of Philosophy East and West for asking me to write a response to Zydenbos' review of my book, An Introduction to Mādhva Vedānta. To this end, I will address four issues: typographical errors, unfounded claims about my translations, content and problems of method and theory, and the future of scholarship in Mādhva (...) Vedānta.Typographical DoṣasFirst, I wish to thank Zydenbos for pointing out the typographical errors. I take full responsibility for them and I intend to correct them in future editions. These are unintentional mistakes and should not be taken as an accurate indicator of my academic ability. I invite readers to examine my other publications on Mādhva Vedānta and to decide for themselves. Jayatīrtha (1365-1388 C.E.), a renowned Mādhva commentator, explained the reasons for such errors in his Pramāṇapad-dhati. He held that defective eyes, whether from cataract, jaundice, or the like,1 [End Page 670] can give rise to defective knowledge, and further, that if an object is too far away, too near, too small, obstructed, or even mixed with similar things, then this will give rise to incorrect knowledge.2 I knew that such errors were likely to occur (especially given the size of the fonts in the page proofs!), which is why I wrote the following in my acknowledgments: "Errors that remain in this text are entirely my own responsibility. If any are found I beg your forgiveness and hope that they inspire you to further study Mādhva Vedānta!" (p. xi). Perhaps all of the undue attention paid by Zydenbos to typographical errors (he devoted a significant portion of his review to them) will inspire further study!TranslationsI am delighted that Zydenbos found my translations to be "not badly done" and disappointed that he incorrectly "assumes" that they are not my own. Rest assured that they are mine. I was assisted by Professor Lawrence McCrea and scholars of the Pūrṇaprajña Saṃśodhana Mandiram (PPSM) and have dutifully acknowledged all of them in my book (p. xii). Zydenbos should know better than to speculate about matters he has no knowledge of.Content and Methodological IssuesThe typographical errors and accusations of plagiarism are far less interesting than the points that were raised about the content of my book. Disputes in the West about interpretations of Mādhva Vedānta are recent; it has been largely ignored in favor of Buddhism and the crypto-Buddhist school, namely Advaita Vedānta. There have been very few books on Mādhva Vedānta written by outsiders, and those few are no longer in print, are poorly written, use dated language, or are in a language that is not available to most lay Mādhvas. Interpretations of Mādhva doctrines made by their authors have remained unquestioned by Western readers given the relative novelty and obscurity of Mādhva Vedānta, while Mādhva insiders have ignored most of them. It is wonderful, then, that Zydenbos doubts my interpretations. After all, his disputes are among the first ones published by an outsider concerning the interpretation of Mādhva doctrines.3Zydenbos' skepticism is reason for celebration for it indicates that Western scholarship on Mādhva Vedānta has come of age. There are now enough scholars of Mādhva Vedānta (or, rather, scholars who claim knowledge of Mādhva Vedānta) in the West that such a debate can occur. I invite others to investigate the points of dispute and to join this expanding community!Zydenbos has also faulted me on the organizational principles of my introductory text. I have, as he correctly notes, intentionally ignored issues of contemporary politics, a topic that he finds essential. Although some historical and political issues are relevant, I find that philosophical discourse sans context is far more intellectually appealing. I am well aware of my biases and have acknowledged the limitations of my historical analysis: [End Page 671]... the history presented here is not intended to be comprehensive. Instead, it is intended... (shrink)