Inductive Argument Research Articles

Is Philosophy Exceptional? A Corpus-Based, Quantitative Study

ABSTRACT Drawing on the epistemology of logic literature on anti-exceptionalism about logic, we set out to investigate the following metaphilosophical questions empirically: Is philosophy special? Are its methods (dis)continuous with science? More specifically, we test the following metaphilosophical hypotheses empirically: philosophical deductivism, philosophical inductivism, and philosophical abductivism. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we searched through a large corpus of philosophical texts mined from the JSTOR database (N = 435,703) to find patterns of argumentation. The results of our quantitative, corpus-based study suggest that deductive arguments are significantly more common than abductive arguments and inductive arguments in philosophical texts overall, but they are gradually and steadily giving way to non-deductive (i.e. inductive and abductive) arguments in academic philosophy.

Cohen-like first order structures

We study uncountable structures similar to the Fraïssé limits. The standard inductive arguments from the Fraïssé theory are replaced by forcing, so the structures we obtain are highly sensitive to the universe of set theory. In particular, the generic structures we investigate exist only in generic extensions of the universe. We prove that in most of the interesting cases the uncountable generic structures are rigid. Moreover, we provide a (consistent) example of an uncountable, dense set of reals with the group of integers as its automorphism group.

Lie algebra for rotational subsystems of a driven asymmetric top

We present an analytical approach to construct the Lie algebra of finite-dimensional subsystems of the driven asymmetric top rotor. Each rotational level is degenerate due to the isotropy of space, and the degeneracy increases with rotational excitation. For a given rotational excitation, we determine the nested commutators between drift and drive Hamiltonians using a graph representation. We then generate the Lie algebra for subsystems with arbitrary rotational excitation using an inductive argument.

A Probabilistic Method for a Class of Non-Lipschitz BSDEs with Application to Fund Management

The present work is devoted to a study of the solvability of a class of non-Lipschitz and noncanonical backward stochastic differential equations (BSDEs) that naturally arises from an intertemporal mutual fund management problem; to this end, we propose a method of combining the techniques of Malliavin calculus and a discussion on the Jacobian flow of the BSDE. Specifically, based on the intimate relationship between $Y_t$ and $Z_t$ of the BSDE via the Malliavin derivative of the former, namely, $D_tY_t=Z_t$, we construct an iterative Picard converging scheme for approximating the underlying solution pair by first obtaining $Z_t$ from the derived BSDE with respect to the Malliavin derivative and then recovering $Y_t$ from the underlying BSDE. A local unique existence result is first warranted over a short time horizon with carefully examined a priori estimates; indeed, each term in the iterative sequence is related to different Girsanov transforms for change of measure, and comparing them demands a delicate analysis. The use of Jacobian flow further enables us to properly control the lower and upper bounds for a certain product of the forward process and $Z_t$, which enables us to extend the solution globally by an inductive argument. Our proposed method is fundamentally different from other probabilistic methods that also involve estimating or bounding Malliavin traces such as [E. Pardoux and S. Peng, Some Backward SDEs with Non-Lipschitz Coefficients, Technical note, Université de Provence, Aix-en-Provence, France, 1996] and [M. C. Zedouri, Equations Différentielles Stochastiques Rétrogrades avec Générateurs Lipschitiziens Stochastiques, Master's Thesis, Université Mohammed Seddik Ben Yahia-Jijel, Jijel, Algeria, 2010]. We believe that our new approach proposed here can be potentially applied to resolve many other general non-Lipschitz forward-backward stochastic differential equations (FBSDEs) encountered in economics and finance, especially in the presence of generic utility functions.

Philosophical reasoning about science: a quantitative, digital study

In this paper, we set out to investigate the following question: if science relies heavily on induction, does philosophy of science rely heavily on induction as well? Using data mining and text analysis methods, we study a large corpus of philosophical texts mined from the JSTOR database (n = 14,199) in order to answer this question empirically. If philosophy of science relies heavily on induction, just as science supposedly does, then we would expect to find significantly more inductive arguments than deductive arguments and abductive arguments in the published works of philosophers of science. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we search through our corpus to find patterns of argumentation. Overall, the results of our study suggest that philosophers of science do rely on inductive inference. But induction may not be as foundational to philosophy of science as it is thought to be for science, given that philosophers of science make significantly more deductive arguments than inductive arguments. Interestingly, our results also suggest that philosophers of science do not rely on abductive arguments all that much, even though philosophers of science consider abduction to be a cornerstone of scientific methodology.

The Logic of Scientific Reasoning in Peer Review Process

We outlined the logical argumentation of scientific reasoning, focusing on peer-reviewed rebuttal letters. Initially, we compared the argumentation in the peer review process with that in writing papers, and distinguished between commonly used argumentation and those that are characteristic of rebuttal letters. First, commonly used forms of logical argumentation, such as deductive and inductive argumentation, are introduced, followed by examples of typical errors in reasoning. Subsequently, we explain the forms of logical argumentation characteristic of the peer review process, including the issue of incommensurability and the error of double standards. This article aims to improve our skills in responding to peer-review comments by being more aware of the logical argumentation used in peer review.

Philosophy’s gender gap and argumentative arena: an empirical study

While the empirical evidence pointing to a gender gap in professional, academic philosophy in the English-speaking world is widely accepted, explanations of this gap are less so. In this paper, we aim to make a modest contribution to the literature on the gender gap in academic philosophy by taking a quantitative, corpus-based empirical approach. Since some philosophers have suggested that it may be the argumentative, “logic-chopping,” and “paradox-mongering” nature of academic philosophy that explains the underrepresentation of women in the discipline, our research questions are the following: Do men and women philosophers make different types of arguments in their published works? If so, which ones and with what frequency? Using data mining and text analysis methods, we study a large corpus of philosophical texts mined from the JSTOR database in order to answer these questions empirically. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we search through our corpus to find patterns of argumentation. Overall, the results of our empirical study suggest that women philosophers make deductive, inductive, and abductive arguments in their published works just as much as male philosophers do, with no statistically significant differences in the proportions of those arguments relative to each philosopher’s body of work.

Loomis–Whitney inequalities in Heisenberg groups

AbstractThis note concernsLoomis–Whitney inequalitiesin Heisenberg groups$$\mathbb {H}^n$$Hn:$$\begin{aligned} |K| \lesssim \prod _{j=1}^{2n}|\pi _j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb {H}^n. \end{aligned}$$|K|≲∏j=12n|πj(K)|n+1n(2n+1),K⊂Hn.Here$$\pi _{j}$$πj,$$j=1,\ldots ,2n$$j=1,…,2n, are thevertical Heisenberg projectionsto the hyperplanes$$\{x_j=0\}$${xj=0}, respectively, and$$|\cdot |$$|·|refers to a natural Haar measure on either$$\mathbb {H}^n$$Hn, or one of the hyperplanes. The Loomis–Whitney inequality in the first Heisenberg group$$\mathbb {H}^1$$H1is a direct consequence of known$$L^p$$Lpimproving properties of the standard Radon transform in$$\mathbb {R}^2$$R2. In this note, we show how the Loomis–Whitney inequalities in higher dimensional Heisenberg groups can be deduced by an elementary inductive argument from the inequality in$$\mathbb {H}^1$$H1. The same approach, combined with multilinear interpolation, also yields the following strong type bound:$$\begin{aligned} \int _{\mathbb {H}^n} \prod _{j=1}^{2n} f_j(\pi _j(p))\;dp\lesssim \prod _{j=1}^{2n} \Vert f_j\Vert _{\frac{n(2n+1)}{n+1}} \end{aligned}$$∫Hn∏j=12nfj(πj(p))dp≲∏j=12n‖fj‖n(2n+1)n+1for all nonnegative measurable functions$$f_1,\ldots ,f_{2n}$$f1,…,f2non$$\mathbb {R}^{2n}$$R2n. These inequalities and their geometric corollaries are thus ultimately based on planar geometry. Among the applications of Loomis–Whitney inequalities in$$\mathbb {H}^n$$Hn, we mention the following sharper version of the classical geometric Sobolev inequality in$$\mathbb {H}^n$$Hn:$$\begin{aligned} \Vert u\Vert _{\frac{2n+2}{2n+1}} \lesssim \prod _{j=1}^{2n}\Vert X_ju\Vert ^{\frac{1}{2n}}, \qquad u \in BV(\mathbb {H}^n), \end{aligned}$$‖u‖2n+22n+1≲∏j=12n‖Xju‖12n,u∈BV(Hn),where$$X_j$$Xj,$$j=1,\ldots ,2n$$j=1,…,2n, are the standard horizontal vector fields in$$\mathbb {H}^n$$Hn. Finally, we also establish an extension of the Loomis–Whitney inequality in$$\mathbb {H}^n$$Hn, where the Heisenberg vertical coordinate projections$$\pi _1,\ldots ,\pi _{2n}$$π1,…,π2nare replaced by more general families of mappings that allow us to apply the same inductive approach based on the$$L^{3/2}$$L3/2-$$L^3$$L3boundedness of an operator in the plane.

Legal philosophy and the study of legal reasoning

In this paper, I argue that legal philosophers ought to focus more on problems of legal reasoning. This is a field with many philosophically interesting questions to consider, but also, a field in which legal philosophers can contribute the most to the study and the practice of law. Neither legal practitioners nor legal scholars reason with the same care and precision as philosophers do. Against this background, I suggest that the following three types of questions regarding legal reasoning are especially worthy of serious consideration. The first is that of the relevance of the theory of reasons holism to legal reasoning. The second is the question of how to analyze (first-order) legal statements in a way that does not undermine the rationality of legal reasoning. And the third is the question of whether legal arguments are to be understood as deductive arguments, inductive arguments, or both, and if so how.

MODERN CRITICISMS TO NATURAL THEOLOGY AND SWINBURNE’S PROBABILISTIC APPROACH

In this article I expound some of the main criticisms by David Hume and Immanuel Kant against the legitimacy of natural theology, the philosophical activity of presenting arguments for or against the existence of God. The aim is not to contribute to the scholarship in history of philosophy, but as a starting point for describing the main lines of Richard Swinburne’s approach to natural theology in terms of inductive probabilistic arguments. His proposal has been part of a current philosophical movement of re-establishing the argumentative debate on the existence and nature of God, an area that has been growing in quantity and quality since the 1970’s.

Through the Looking Glass: Assessing and Enhancing the Effectiveness of Bourdieu’s Theory of Practice to Understand the Achievement Gap in British Columbia's Inner-City Schools

This paper emerges from a 2016 conceptual study borne out of an ongoing practitioner inquiry in which I, as a practicing K-12 inner-city Canadian teacher, tried to understand, on a theoretical level, why the children at my inner-city school in Vancouver consistently underperform in an academic sense in spite of being provided with additional learning resources. The achievement gap that exists between British Columbia’s inner-city children and their more affluent peers cannot be adequately explained by differences in finances alone, but it has sociological roots, which I explored in this study. To understand the achievement gap, I chose to filter it through Pierre Bourdieu’s Theory of Practice (1992) and evaluate the effectiveness of his theory in being able to effectively explain the who, what, where, when, why, and how of this problem for me as an inner-city educator. Methodologically, I utilized the qualitative approach of hermeneutics (Gadamer, 2013) to fuse my horizon with that of Bourdieu so as to develop a deep understanding of his Theory of Practice and its core concepts of cultural capital, habitus, field, and symbolic violence, and their implications for inner-city school children. Hermeneutics permitted me to uncover multiple layers of theoretical evidence that I used ultimately to make an inductive argument that finds in favor of using theory of practice to understand academic underperformance among British Columbia’s inner-city school children. This paper is a presentation of the theoretical merits of Theory of Practice as an analytical lens for practitioners who wish to understand the achievement gap. This paper also explains how the efficacy of Theory of Practice can be enhanced when it is coupled with Lareau’s (2013) scholarship on class-based parenting practices. My second paper provides practitioner-scholars who are exploring this topic with recommendations as to how best to use Theory of Practice for maximum benefit.

THE TRUTH RELATIONS IN THE MAIN CHARACTER’S ENTAILMENT SENTENCES IN MURDER ON THE ORIENT EXPRESS MOVIE

This study analyzed entailment of the main character’s sentences in Murder on The Orient Express movie in the semantics field. The purpose of this study is to explain the truth in the sentence uttered by the main character in the movie and to prove the truth value from the interlocutor’s response in the sentence. This study focused on explaining the truth of Poirot’s sentences and proving the truth value from the interlocutor’s response. This study used a qualitative descriptive method and a propositional logic approach. This study found 16 data of entailment. The data were analyzed using the theory of entailment from Fasold and Saeed, and theory of logic from Goranko and Hurley. The entailment sentences are entered into the truth table which explains the truth value of the sentence accompanied by logical explanations which are divided into deductive and inductive arguments. The truth value of the entailment sentence can be seen through the response of the main character's interlocutors.

A simplified algorithm computing all [formula omitted]-[formula omitted] bridges and articulation points

Given a directed graph G and a pair of nodes s and t, an s-tbridge of G is an edge whose removal breaks all s-t paths of G. Similarly, an s-tarticulation point of G is a node whose removal breaks all s-t paths of G. Computing the sequence of all s-t bridges of G (as well as the s-t articulation points) is a basic graph problem, solvable in linear time using the classical min-cut algorithm (Ford and Fulkerson, 1956).We show a simplified and self-contained algorithm computing all s-t bridges and s-t articulation points of G, based on a single graph traversal from s to t avoiding an arbitrary s-t path, which is interrupted at the s-t bridges. Its proof of correctness uses simple inductive arguments, making the problem an application of merely graph traversal, rather than of the more complex maximum flow problem.

The Territories of Human Reason: Science and Theology in an Age of Multiple Rationalities

The Territories of Human Reason: Science and Theology in an Age of Multiple Rationalities

The mereology of thermodynamic equilibrium

The special composition question (SCQ), which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, the thermodynamic composition principle (TCP): Multiple systems in (generalized) thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, might form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, “thermal contact” can be analyzed using the mereotopological predicate “self-connectedness”. Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected.

Value management and model pluralism in climate science

Non-epistemic values pervade climate modelling, as is now well documented and widely discussed in the philosophy of climate science. Recently, Parker and Winsberg have drawn attention to what can be termed “epistemic inequality”: this is the risk that climate models might more accurately represent the future climates of the geographical regions prioritised by the values of the modellers. In this paper, we promote value management as a way of overcoming epistemic inequality. We argue that value management can be seriously considered as soon as the value-free ideal and inductive risk arguments commonly used to frame the discussions of value influence in climate science are replaced by alternative social accounts of objectivity. We consider objectivity in Longino's sense as well as strong objectivity in Harding's sense to be relevant options here, because they offer concrete proposals that can guide scientific practice in evaluating and designing so-called multi-model ensembles and, in fine, improve their capacity to quantify and express uncertainty in climate projections.

Space-time decay estimates of solutions to 3D incompressible viscous Camassa-Holm equations

In this paper, based on the parabolic interpolation inequality and inductive argument, we study the space-time decay estimates of higher-order time and spatial derivatives of strong solutions for the 3D incompressible viscous Camassa-Holm equations provided that the initial datum is well localized.

Incompatibility and the pessimistic induction: a challenge for selective realism

Two powerful arguments have famously dominated the realism debate in philosophy of science: The No Miracles Argument (NMA) and the Pessimistic Meta-Induction (PMI). A standard response to the PMI is selective scientific realism (SSR), wherein only the working posits of a theory are considered worthy of doxastic commitment. Building on the recent debate over the NMA and the connections between the NMA and the PMI, I here consider a stronger inductive argument that poses a direct challenge for SSR: Because it is sometimes exactly the working posits which contradict each other, i.e., that which is directly responsible for empirical success, SSR cannot deliver a general explanation of scientific success.

Decentralized Control of Multiple Strict-Feedback Systems With Unknown Control Directions

This paper is concerned with the decentralized control problem of networked high-order nonlinear systems that can be transformed into strict feedback forms with parameter uncertainties and unknown control directions under a directed communication graph. A decentralized controller is designed recursively for each agent to realize output synchronization and guarantee the overall system to be bounded. Instead of a Lyapunov-based argument which is commonly used in the literature, an inductive contradiction argument is employed. Moreover, not like other existing works, we use the Nussbaum function in the analysis function form rather than its derivative, which not only facilitates the proof but also enlarges the schedule’s application scope. Simulation results are presented to verify the effectiveness of the proposed scheme.

On the Bloch\u2013Kato conjecture for Hilbert modular forms

The aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.