Wisdom, Knowledge and Rationality

After surveying the strengths and weaknesses of several well-known approaches to wisdom, I argue for a new theory of wisdom that focuses on being epistemically, practically, and morally rational. My theory of wisdom, The Deep Rationality Theory of Wisdom, claims that a wise person is a person who is rational and who is deeply committed to increasing his or her level of rationality. This theory is a departure from theories of wisdom that demand practical and/or theoretical knowledge. The Deep Rationality Theory salvages all that is attractive, and avoids all that is problematic, about theories of wisdom that require wise people to be knowledgeable.     

Wisdom: Understanding and the Good Life

I argue that a necessary condition for being wise is: understanding how to live well. The condition, by requiring understanding rather than a wide variety of justified beliefs or knowledge, as Ryan and Whitcomb respectively require, yields the desirable result that being wise is compatible with having some false beliefs but not just any false beliefs about how to live well—regardless of whether those beliefs are justified or not. In arguing for understanding how to live well as a necessary condition for wisdom, I reject the view, proposed by both Ryan and Whitcomb, that subjects such as chemistry lies within the domain of wisdom. I show that the argued for condition yields the desirable result that being wise is not a common achievement, but that it is not something that can only plausibly be achieved in the modern era.     

Basic Knowledge and Easy Understanding

Reliabilism is a theory that countenances basic knowledge, that is, knowledge from a reliable source, without requiring that the agent knows the source is reliable. Critics (especially Cohen 2002) have argued that such theories generate all-too-easy, intuitively implausible cases of higher-order knowledge based on inference from basic knowledge. For present purposes, the criticism might be recast as claiming that reliabilism implausibly generates cases of understanding from brute, basic knowledge. I argue that the easy knowledge (or easy understanding) criticism rests on an implicit mischaracterization of the notion of a reliable process. Properly understood, reliable processes do not permit the transition from basic knowledge to understanding based on inference.     

Linguistic Understanding and Knowledge of Truth-Conditions

What do you know when you know what a sentence means? According to some theories, understanding a sentence is, in part, knowing its truth-conditions. Dorit Bar-On, Claire Horisk, and William Lycan have defended such theories on the grounds of an “epistemic determination argument” (“EDA”). That argument turns on the ideas (a) that understanding a sentence, along with knowledge of the non-linguistic facts, suffices to know its truth-value, and (b) that being able to determine a sentence’s truth-value given knowledge of the non-linguistic facts is knowing its truth-conditions. I argue that the EDA withstands the objections recently raised by Daniel Cohnitz and Jaan Kangilaski, but fails for other reasons. It equivocates between a fine-grained and a coarse grained conception of “facts.”     

Knowledge versus Understanding: The Cost of Avoiding Gettier

In the current discussion on epistemic value, several philosophers argue that understanding enjoys higher epistemological significance and epistemic value than knowledge??the epistemic state the epistemological tradition has been preoccupied with. By noting a tension between the necessary conditions for understanding in the perhaps most prominent of these philosophers, Jonathan Kvanvig, this paper disputes the higher epistemological relevance of understanding. At the end, on the basis of the results of the previous sections, some alternative comparative contrasts between knowledge and understanding are briefly explored, including one in which an analogue to the KK-principle for knowledge, the ??UU-principle??, does not hold for a different reason than that for which the former principle fails.     

Teaching for Understanding and Application of Science Knowledge

James Gallagher is Professor of Science Education at Michigan State University and currently co‐editor of Journal of Research in Science Teaching. He was a member of the Working Group on Teaching in the formulation of National Science Education Standards. His recent work has included the me of continuous assessment as a tool to aid teachers in teaching for understanding.     

Wisdom Beyond Rationality: A Reply to Ryan

We discuss Sharon Ryan’s Deep Rationality Theory of wisdom, defended recently in her “Wisdom, Knowledge and Rationality.” We argue that (a) Ryan’s use of the term “rationality” needs further elaboration; (b) there is a problem with requiring that the wise person possesses justified beliefs but not necessarily knowledge; (c) the conditions of DRT are not all necessary; (d) the conditions are not sufficient. At the end of our discussion, we suggest that there may be a problem with the very assumption that an informative, non-circular set of necessary and sufficient conditions of wisdom can be given.     

How Boots Befooled the King: Wisdom, Truth, and the Stoics

Can the wise person be fooled? The Stoics take a very strong view on this question, holding that the wise person (or sage) is never deceived and never believes anything that is false. This seems to be an implausibly strong claim, but it follows directly from some basic tenets of the Stoic cognitive and psychological world-view. In developing an account of what wisdom really requires, I will explore the tenets of the Stoic view that lead to this infallibilism about wisdom, and show that many of the elements of the Stoic picture can be preserved in a more plausible fallibilist approach. Specifically, I propose to develop a Stoic fallibilist virtue epistemology that is based on the Stoic model of the moral virtues. This model of the intellectual virtues will show that (in keeping with a folk distinction) the wise person is never befooled, though that person might be fooled.     

A Proposal for Toeplitz Matrix Calculations

In contrast to the usual (and successful) direct methods for Toeplitz systems Ax = b, we propose an algorithm based on the conjugate gradient method. The preconditioner is a circulant, so that all matrices have constant diagonals and all matrix-vector multiplications use the Fast Fourier Transform. We also suggest a technique for the eigenvalue problem, where current methods are less satisfactory. If the first indications are supported by further experiment, this new approach may have useful applications—including nearly Toeplitz systems, and parallel computations.     

Wisdom,decision support and paradigms of decision making

Many decision support tools have been developed over the last 20 years and, in general, they support what Simon termed substantive rationality. However, such tools are rarely suited to helping people tackle wicked problems, for which a form of procedural rationality is better suited. Procedurally rational approaches have appeared in both management science and computer science, examples being the soft OR approach of cognitive mapping and the design rationale based on IBIS. These approaches are reviewed and the development of Wisdom, a procedurally rational decision support process and accompanying tool, is discussed and evaluated.     

Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable

This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview data were collected from 20 middle school teachers regarding their predictions of student responses to written assessment items focusing on the equal sign and variable. Teachers' predictions of students' understanding of variable aligned to a large extent with students' actual responses to corresponding items. In contrast, teachers' predictions of students' understanding of the equal sign did not correspond with actual student responses. Further, teachers rarely identified misconceptions about either variable or the equal sign as an obstacle to solving problems that required application of these concepts. Implications for teacher professional development are discussed.     

Understanding Social Reforms: A Conceptual Analysis

We attempt here to explain why reforming social systems is not an easy job and what can be done about it. Vickers' concept of ‘appreciative systems’ is re-examined and further developed. It is argued that appreciative systems are socially established ways of perceiving, consisting of a set of cognitive categories, values and interests which are grounded on social practices. The latter are constituted by certain historically developed self-understandings shared by individuals. Social practices are self-referential and, therefore, particularly resistant to reform. It is argued that the role of policy makers should be seen as consisting of two components. First, inventing and supplying social systems with new appreciative systems, and secondly, regularly providing social systems with information about their own functioning as well as the functioning of other systems. That information, spread throughout a system, has potentially reforming effects. These claims are illustrated with examples from UK and American public life.     

Understanding supply chain dynamics: A chaos perspective

Variability in orders or inventories in supply chain systems is generally thought to be caused by exogenous random factors such as uncertainties in customer demand or lead time. Studies have shown, however, that orders or inventories may exhibit significant variability even if customer demand and lead time are deterministic. In this paper, we investigate how this class of variability, chaos, may occur in a multi-level supply chain and offer insights into how to manage relevant supply chain factors to eliminate or reduce system chaos. The supply chain is characterized by the classical beer distribution model with some modifications. We observe the supply chain dynamics under the influence of various factors: demand pattern, ordering policy, demand-information sharing, and lead time. Through proper decision-region formation, the effect of various factors on system chaos is investigated using a factorial design. The degree of system chaos is quantified using the Lyapunov exponent across all levels of the supply chain. This study shows that, to reduce the degree of chaos in the supply chain system, the adjustment parameters for both inventory and supply line discrepancies should be more comparable in magnitude. Counter-intuitively, in certain decision regions, sharing demand information can do more harm than good. Similar to the bullwhip effect observed previously in demand, we discover the phenomenon of “chaos-amplification” in inventory across supply chain levels.