Indiana University Research & Creative Activity

Humanities, Then and Now

Volume XXIX Number 1
Fall 2006

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drawing of green duck

Leah Savion with students
Leah Savion, center, with students.
Photo Chris Meyer, University Communications

Real Logic

by Jennifer Piurek

When Leah Savion's undergraduate students finish an exam, they don't just shuffle out of the room and forget about it. In fact, after her class, they'll probably never look at their test-taking performance the same way again.

Following each exam, Savion asks her students to predict their own grades and subsequently account for any differences. She also asks them to write down one major reason for their success or failure on various learning tasks. She writes the letters L-A-T-E on the board and assigns each response to one of the letters.

L-A-T-E stands for Luck-Ability-Task-Effort, but the students don't know that.

"So someone says 'The dog ate my homework,' or 'I was sick the day you explained what was going to be on the test,' or 'I can't do any math or logic,' or 'The grader was very tough,' or 'You didn't explain the material right,' as common causal attributions," says Savion, a senior lecturer of philosophy who has taught at Indiana University Bloomington since 1989. "The young ones will talk practically all in terms of 'L-A-T.' If you go into a graduate or upper-level class, it's mostly 'E.'"

This is one of the seemingly simple ways Savion helps students navigate the demands of absorbing abstract material and focus on personal effort. When it comes to any kind of learning, she says, "we are becoming more and more aware of the quick and fallible mechanisms the mind employs, the role of prior knowledge, and our tendency to hold on to existing beliefs and defend our cognitive and emotional equilibrium." These potential obstacles to learning can be partly overcome, she says, by a skill called metacognition--that is, acquiring greater awareness of one's self as a cognitive (a reasoning and thinking) entity.

"I constantly ask people to reflect and challenge their perceptions of how much they know, at what depth they acquire information and skills, how they learn best, and to estimate their grades on an assignment or test," she says. "I ask them to monitor their level of comprehension, and then change their study habits if need be."

One of Savion's favorite class assignments is the "George" paper, a project in which each of her students finds someone from outside of the class (a friend, parent, or sibling) and teaches that person a new concept such as the difference between validity and truth. The validity of an argument doesn't depend on the content of its sentences, Savion explains, but on its form. For example, consider the following: All ducks are green, and all green things sing operas, so all ducks sing operas. This is a valid argument, although it contains no true statements.

But this argument--all kittens are animals, and all cats are animals, so all kittens are cats--is invalid, meaning the conclusion does not follow logically from the premises. An invalid argument is structured so that the terms in it (kittens, cats, animals) create an argument with true premises and a false conclusion. The invalid example above has the structure, all As are Cs, and all Bs are Cs, so all As are Bs. Many substitutions can reveal the invalidity, Savion says--for instance, all cats are animals, and all dogs are animals, so all cats are dogs.

This distinction between what is true and what follows logically from other sentences is difficult for most people to understand. In the "George" exercise, the "teacher" writes a report detailing his or her instructional venture, evaluating methods and results. Over the course of the semester, students work with their "George," continually testing his or her understanding. "Turning the students into temporary teachers generates a moment of intellectual maturity (let alone an admiration for the class instructor's job), as well as an awareness of their own learning styles and ways of thinking," Savion says. "We get a lot of skills naturally, like social skills, but not metacognitive skills."

Thinking about thinking

Savion's expansive research interests include logic, cognitive science, philosophy of language, philosophy of logic, and pedagogical theories, as well as educational psychology and philosophy of mind. Currently, she is focused on four areas: "cognitive heuristics," models of rationality in logic, the bridge between "novice" and "expert," and the analysis of "belief perseverance" in pedagogy.

She is most fascinated with cognitive science, the science of how people think. "People don't work with algorithms in a step-by-step process," says Savion, referring to long-held beliefs about the human mind as defined by formal studies such as logic. "Once this realization came, a huge door opened to investigating mental processes, called 'heuristics', and their biases and adaptive functions."

For example, she notes that people persevere in holding on to beliefs despite the fact that those beliefs have been totally discredited. A large number of Americans still believe there are weapons of mass destruction in Iraq, for instance, against all evidence to the contrary. (According to a July 2006 Harris Poll, 50 percent of Americans believe that Iraq had weapons of mass destruction when the U.S. invaded.) "This phenomenon is often used as a clear example of human irrationality, but I want to show this is an example of an adaptive principle," says Savion. "Sometimes the avalanche that our seemingly coherent belief system will suffer as a result of correcting one belief exceeds the expected value of truth." In other words, as she explains in her textbook Philosophy of Logic, "we tend not to abandon the underlying concepts and principles of our naïve theories even when their incompatibility with academically accepted theories is made explicit."

Logic's fall from grace

Savion frequently refers to the "fall from grace" of classical logic, in the tradition of Aristotle, George Boole, and Gottlob Frege. Classical logic offers normative rules about what follows from what, and what the correct conclusions are, given a set of premises. Many still view classical logic as the ultimate model of how we should make inferences, a crucial activity for human development and survival, says Savion.

"There is a big gap, though, between the rules of classical logic and the procedures people actually use for making inferences," she says. "For instance, logic dictates that a rational person should draw all conclusions from his or her current beliefs. But given that some of our beliefs are impractical at best, or even false and contradictory, this requirement isn't feasible or advisable for any human being. Actual human inference doesn't follow the rules, or it employs rules that are faulty, incomplete, or inconsistent."

Savion cites an example taken from the writings of linguist Noam Chomsky: "People who say, I ain't done nothin', may come from an environment that is extremely impoverished linguistically, but they are capable of understanding the difference between a grammatically correct and incorrect sentence," she says. In other words, we may have knowledge of correct rules of reasoning, but we often don't use it. Instead, we rely on cognitive shortcuts to avoid overtaxing our mental resources.

Savion and her research partner Raymundo Morado, of the national University of Mexico, advocate a "psychologically realistic" model of human rationality. They are working on a book and have given talks on the topic around the world for the past five years, including Athens.

For Savion, a complete model of rationality must be anchored in theories of deductive and nondeductive logic as well as in current theories about the working of the mind. "There are not many people who specialize in logic and are willing to leave the armchair behind to do empirical research on how people think, or really combine a cognitive-science approach with the highly theoretical aspects of philosophy. But this merger is necessary to alter existing idealistic models of rationality," she says.

A teacher of teachers

As a specialist in the study of how people think and learn, Savion provides faculty development workshops and talks at IU, around the United States, and around the world. She teaches the only campuswide pedagogy course at IU Bloomington, which she's also offered in Kazakhstan. "I talk to faculty from all over--journalism, informatics, business, music--and I learn a lot through this contact," she says. "It's just a wonderful thing to take the philosophical training that I have and combine it with the training and observational skills of other educators to synthesize seemingly different things and draw conclusions."

The difference between novice and expert thinking is another of Savion's research passions. Experts in any field don't necessarily have better memories or more knowledge or more special intelligence than their novice counterparts--rather, they organize their knowledge in a different way, employ sharp metacognitive skills, and use more elaborate problem-solving heuristics that yield fewer biases than novices do, as demonstrated in a 1982 experiment studying physicists and novice physicists. In the study, Savion says, participants were asked to categorize word problems, classifying similar problems into the same categories. Novices relied primarily on surface elements, like whether the problem involved pulleys or inclined planes, while experts grouped the problems based on the kinds of laws that had to be applied. "I look at classroom teaching as helping students move one notch higher on the continuum between novice and expert," says Savion.

As she continues her studies of philosophy and of teaching and learning, Savion is thankful for the flexibility afforded her by the IU Bloomington Department of Philosophy. "I'm so grateful for having the liberty to pursue what I want, to create courses that contain topics and insights from various fields, and to work with students on applying philosophical principles and methods to investigating scientific issues. This is how a research university should be."

Savion's passion for teaching and for explorations of questions in logic and cognitive science is strong. "I've always been interested in cognitive psychology, and when I was introduced to mathematical logic, I totally fell in love with the discipline," she says. "Since then, I have always studied logic, taught logic, and examined the gap between logical theories and how people actually think and reason. It's what led to the studies I'm doing now. My first love never went away, and I found a way to connect the past and the present together."

Jennifer Piurek is a Web content specialist at Indiana University and a freelance writer living in Bloomington.

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