Aristotle\u27s Theory of Principles: A Rationalistic-Empirical Bipolarity

Primarily, this paper attempts to analyze Aristotle\u27s notion of principle as it is uniquely applied throughout his works. Principle is a basic notion; and it is, moreover, the basic notion in Aristotle\u27s philosophy. The purpose here is to establish as precisely as possible the meaning of \u27principle\u27 and the role that it plays in Aristotelian thought. It is shown that the meaning of principle involves a certain bipolar tension which strains between a logico-epistemic pole and an on tic pole. This tension grounds a philosophy which constantly vacillates between a rationalistic idealism and an empirically oriented naturalism. The Greek term under consideration is ἀρχή although it should be noted that Aristotle does not aIways use the term in a technical sense; and, at times, when he refers to principle in a technical sense, he may not always use ἀρχή. In Chapter I, we claim that Aristotle\u27s basic and primary assumption-that there is a real world which is intelligible--necessarily involves a notion of principles that somehow connects the real world with intelligible expressions of it. In other words, principles manifest a bipolar condition of being both mental (the intelligible expression) and real (objectively grounded in the world). Descartes is seen as the first philosopher to challenge seriously the objective pole of principles. For Descartes, philosophical inquiry begins with principles of knowledge rather than with principles of being. The Cartesian assault on Aristotle\u27s principles may be unwarranted if it is realized that his (Aristotle\u27s) search after principles of being included the cognitional pole so that being is never really separated from one\u27s clear and distinct understanding of it. Chapter II investigates the bipolarity of Aristotelian principles in the realm of perishable entities. Through his notion of principles, Aristotle attempts to solve an enigma of being and knowing. How can sensible entities be individual and yet definable, unique and yet intelligible? How can a world of particulars be admitted when knowledge is of the universal ? Principles provide both the concrete unity and the ground for universal understanding in Aristotle\u27s attempt to solve the problem. It is the ontic pole of principles that is explanatory of the concreteness and unity of individuals, while it is the logico-epistemic pole which serves as the basis for univers ·ality and intelligibility. Four specific characteristics of principles as applied to perishable entities are then revealed. Principles are seen to be as: 1) referential or relational; 2} potential for universality; 3) irreducible contraries; and 4) analogous. Concerning the first, principles are to be viewed not as entities or things but rather as certain ways whereby things are known. The second characteristic pursues in specific detail the problem of universal knowledge versus individual entities. From the point of view of a being\u27s potentiality, one may realize a universal ground of being many things. From the point of view of a being\u27s actuality, one grasps the individual entity in an immediate sensory awareness. The third characteristic remolds the pre-Socratic and Platonic notions of contrariety. The pre-Socratic notion of archai as contraries (according to Aristotle) cannot be true principles, since being material elements they are not basic and irreducible. Plato\u27s contrary forms cannot be true principles since they are separate from what they purport to explain. Aristotle\u27s bipolar principles can be irreducible and contrary and yet be simultaneously in things (e.g., act-potency). The fourth characteristic allows both sameness and difference to permeate the various levels of being so that any hierarchy of being is freed from an uncompromising fixity or rigidity. Analogous principles explain a hierarchy of horizontal levels of classes with a vertical continuity running through the class structures (i.e., the genera and species). In Chapter III, Aristotle\u27s imperishable realm (ἄφθαρτος) is compared with his sublunar realm. The two realms are seen to be different and yet similar, and it is analogous principles that effect these differences and similarities. Aristotle\u27s application of the same principles to both realms allows him to include both perishables and imperishables under the realm of nature. This spanning of the whole range of nature by principles warrants a transcendental character of principles that is contrasted with Aristotle\u27s search in the Physics and the Metaphysics for a Transcendent One. Again, a bipolarity is indicated which strains between a rationalistic tendency toward a Transcendent Being which might explain the whole of reality and a tendency toward more naturalistic explanations in terms of transcendental principles. The last Chapter traces the role of principles in the realm of reason where archaiare applied to Aristotle\u27s theory of demonstration and his general notion of science. Two basic kinds of demonstration are seen as permeating Aristotle\u27s theory of methodology. The first we label axiomatic demonstration. This is demonstration in the strict sense of deducing certain and necessary conclusions from self-evident principles. These worthy and noble first principles (ἀξιώματα) are the source of intellectual delight and contain more intrinsic worth than the conclusions that are drawn from them. The second kind of demonstration is termed hypothetical demonstration. This is demonstration in a looser sense in which principles are difficult to know and demonstration proceeds from hypotheses and postulates. Conclusions arrived at by means of this type of deduction tend toward probability rather than certitude. Concerning the problem of how one acquires knowledge of the first principles, we again maintain that Aristotle vacillates between the poles of rationalism and realism. The former pole involves an analytic intuition in which the world of experience is shunned and a mere analysis of terms and concepts reveals the primary axioms. The latter advocates an inductive intuition in which experience plays a necessary role in one\u27s grasping of the principles. Finally, it is shown that there is more than one meaning to Aristotle\u27s concept of science (ἐπιστήμη)

The AirWand: Design and Characterization of a Large-Workspace Haptic Device

Almost all commercially available haptic interfaces share a common pitfall, a small shoebox-sized workspace; these devices typically rely on rigid-link manipulator design concepts. In this paper we outline our design for a new kinesthetic haptic system that drastically increases the usable haptic workspace. We present a proof-of-concept prototype, along with our analysis of its capabilities. Our design uses optical tracking to sense the position of the device, and air jet actuation to generate forces. By combining these two technologies, we are able to detach our device from the ground, thus sidestepping many problems that have plagued traditional haptic devices including workspace size, friction, and inertia. We show that optical tracking and air jet actuation successfully enable kinesthetic haptic interaction with virtual environments. Given an appropriately large volume high-pressure air source, and a reasonably high speed tracking system, this design paradigm has many desirable qualities when compared to traditional haptic design schemes

\u3ci\u3eThis Strange Creature\u3c/i\u3e: Plato and Conversion Experiences

In Plato’s corpus, the Greek word ἐξαίφνης appears precisely thirty-six times. Translated generally as “all of a sudden” or “the instant” in his Parmenides, ἐξαίφνης emerges in some of the most significant passages of Plato’s dialogues. Put simply, ἐξαίφνης connotes illumination of the highest realities and philosophical conversion experience. In addition to providing a review of Plato’s conception and use of ἐξαίφνης in Parmenides, Republic, Symposium, and the Seventh Letter, our paper brings an ancillary link to light. Namely, the appearance of ἐξαίφνης as a mark for conversion experiences in the New Testament’s Acts of the Apostles and Plotinus’s Enneads. We reveal how the same pattern and employment of ἐξαίφνης established by Plato emerge in both Acts and the Enneads. This pattern suggests a prolonged period of thinking and training, followed by a flash of understanding. Thus ἐξαίφνης, as evidenced by our survey of its strange instantiation in Plato’s dialogues and then subsequently in Acts and the Enneads, becomes a sign for enlightenment, assimilation with the divine, and conversion experience

Real-Time Graphic and Haptic Simulation of Deformable Tissue Puncture

A myriad of surgical tasks rely on puncturing tissue membranes (Fig. 1) and cutting through tissue mass. Properly training a practitioner for such tasks requires a simulator that can display both the graphical changes and the haptic forces of these deformations, punctures, and cutting actions. This paper documents our work to create a simulator that can model these effects in real time. Generating graphic and haptic output necessitates the use of a predictive model to track the tissue’s physical state. Many finite element methods (FEM) exist for computing tissue deformation ([1],[4]). These methods often obtain accurate results, but they can be computationally intensive for complex models. Real-time tasks using this approach are often limited in their complexity and workspace domain due to the large computational overhead of FEM. The computer graphics community has developed a large range of methods for modeling deformable media [5], often trading complete physical accuracy for computational speedup. Casson and Laugier [3] outline a mass-spring mesh model based on these principles, but they do not explore its usage with haptic interaction. Gerovich et al. [2] detail a set of haptic interaction rules (Fig. 2) for one dimensional simulation of multi-layer deformable tissue, but they do not provide strategies for integrating this model with realistic graphic feedback

Improving weighted least squares inference

These days, it is common practice to base inference about the coefficients in a hetoskedastic linear model on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can also used to base valid inference on a weighted least squares estimator and using such an estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on asymptotic approximations with plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. Similarly, tests can have null rejection probabilities that are above the nominal level. It is shown that under unknown hereroskedasticy, a bootstrap approximation to the sampling distribution of the weighted least squares estimator is valid, which allows for inference with improved finite-sample properties. For testing linear constraints, permutations tests are proposed which are exact when the error distribution is symmetric and is asymptotically valid otherwise. Another concern that has discouraged the use of weighting is that the weighted least squares estimator may be less efficient than the ordinary least squares estimator when the model used to estimate the unknown form of the heteroskedasticity is misspecified. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals

Automatic Filter Design for Synthesis of Haptic Textures from Recorded Acceleration Data

Sliding a probe over a textured surface generates a rich collection of vibrations that one can easily use to create a mental model of the surface. Haptic virtual environments attempt to mimic these real interactions, but common haptic rendering techniques typically fail to reproduce the sensations that are encountered during texture exploration. Past approaches have focused on building a representation of textures using a priori ideas about surface properties. Instead, this paper describes a process of synthesizing probe-surface interactions from data recorded from real interactions. We explain how to apply the mathematical principles of Linear Predictive Coding (LPC) to develop a discrete transfer function that represents the acceleration response under specific probe-surface interaction conditions. We then use this predictive transfer function to generate unique acceleration signals of arbitrary length. In order to move between transfer functions from different probe-surface interaction conditions, we develop a method for interpolating the variables involved in the texture synthesis process. Finally, we compare the results of this process with real recorded acceleration signals, and we show that the two correlate strongly in the frequency domain

Dimensional Reduction of High-Frequencey Accelerations for Haptic Rendering

Haptics research has seen several recent efforts at understanding and recreating real vibrations to improve the quality of haptic feedback in both virtual environments and teleoperation. To simplify the modeling process and enable the use of single-axis actuators, these previous efforts have used just one axis of a three-dimensional vibration signal, even though the main vibration mechanoreceptors in the hand are know to detect vibrations in all directions. Furthermore, the fact that these mechanoreceptors are largely insensitive to the direction of high-frequency vibrations points to the existence of a transformation that can reduce three-dimensional high-frequency vibration signals to a one-dimensional signal without appreciable perceptual degradation. After formalizing the requirements for this transformation, this paper describes and compares several candidate methods of varying degrees of sophistication, culminating in a novel frequency-domain solution that performs very well on our chosen metrics

Refined Methods for Creating Realistic Haptic Virtual Textures from Tool-Mediated Contact Acceleration Data

Dragging a tool across a textured object creates rich high-frequency vibrations that distinctly convey the physical interaction between the tool tip and the object surface. Varying one’s scanning speed and normal force alters these vibrations, but it does not change the perceived identity of the tool or the surface. Previous research developed a promising data-driven approach to embedding this natural complexity in a haptic virtual environment: the approach centers on recording and modeling the tool contact accelerations that occur during real texture interactions at a limited set of force-speed combinations. This paper aims to optimize these prior methods of texture modeling and rendering to improve system performance and enable potentially higher levels of haptic realism. The key elements of our approach are drawn from time series analysis, speech processing, and discrete-time control. We represent each recorded texture vibration with a low-order auto-regressive moving-average (ARMA) model, and we optimize this set of models for a specific tool-surface pairing (plastic stylus and textured ABS plastic) using metrics that depend on spectral match, final prediction error, and model order. For rendering, we stably resample the texture models at the desired output rate, and we derive a new texture model at each time step using bilinear interpolation on the line spectral frequencies of the resampled models adjacent to the user’s current force and speed. These refined processes enable our TexturePad system to generate a stable and spectrally accurate vibration waveform in real time, moving us closer to the goal of virtual textures that are indistinguishable from their real counterparts