4. A practical framework for improved reasoning

While we have not yet fully spelled out the normative framework that

supports the prescriptions of Ameliorative Psychology, we have described

a broadly cost-benefit approach to epistemology that takes significant

truths to be a primary benefit. Even with this sketchy theoretical framework

in hand, we can begin to piece together a unified approach to thinking

about applied epistemology, or the ways in which people’s reasoning

can be improved.

Applied epistemology is essentially about second-order reasoning

strategies. It concerns thinking about how we can better think about the

world. Our view takes applied epistemology to involve a cost-benefit approach

to thinking about how we ought to allocate cognitive resources and

replace old reasoning strategies with new ones. Getting clear about the

nature of the costs and benefits of reasoning is a tricky issue, one we will

address in chapter 5. For now, we can introduce this cost-benefit approach

with an artificial but familiar epistemic challenge: an aptitude test. Suppose

a test has two different parts, and a Test Taker is disposed to apply

different reasoning strategies to each part of the test. We can define a crude

notion of epistemic benefits in this particular setting in terms of correct

answers, and we can define a notion of epistemic costs in terms of

elapsed time. Very roughly, Test Taker’s reasoning on the test is better to

the extent he gets more right answers in a shorter amount of time. (This

view has obvious problems; we introduce it here only for illustrative

purposes.)

Suppose Test Taker is using strategy A on the verbal section of the test

and strategy B on the quantitative section of the test. We can represent

these two strategies using cost-benefit curves that plot the total number of

right answers the strategy can be expected to generate per unit of time. We

will assume that n is the total number of problems on each section of

the test (see Figure 3.1). The cost-benefit curves have a particular kind

of shape—a rapid increase with a steady leveling off. This leveling off

represents a reasoning strategy’s diminishing marginal utility : Increasing resources expended on the reasoning strategy brings steadily fewer benefits.

This is why cost-benefit curves are typically hump shaped rather than

straight or upward sloping. Reasoning, like most of life, is full of examples

of diminishing marginal returns. For instance, if we were to spend eighteen

more years lovingly polishing this book, it would end up being only

slightly better than it is.

From a cost-benefit perspective, then, the obvious question to ask is:

What is the best way to distribute Test Taker’s finite resources to these two

reasoning strategies? The most effective allocation, the one that would

maximize expected reliability (or accuracy) would be the one that made

the marginal expected reliability (MER) of both reasoning strategies equal.

The marginal expected reliability of a reasoning strategy given some quantity

of resources expended on that strategy is basically the benefit one gets

from the last resource expended on that reasoning strategy. If on Figure

3.2, the cost expended on A is ca, then the MER of that reasoning strategy

at that cost is given by the tangent of the cost-benefit curve at ca: Dx/Dy. If

Test Taker has (caюcb) resources, then to maximize his right answers, he

should devote ca resources to strategy A and cb resources to strategy B. At

those points, the MER of both cost-benefit curves is identical. If Test Taker

were to devote fewer than ca resources to A and greater than cb resources

to B, he would lose net reliability—he’d lose more truths sliding down A’s

cost-benefit curve than he would gain by moving up B’s cost-benefit curve.

Figure 3.2. Optimizing resource allocation: Equalizing

marginal expected accuracy.

The same general point would hold if Test Taker were to devote greater

resources to A and fewer to B.

In order to think clearly about applied epistemology, it is important

to recognize that reliability is a resource-dependent notion. How reliable a

reasoning strategy is depends on the resources expended on it. This insight

is built right into the cost-benefit curves: A reasoning strategy’s reliability

is a function of the amount of resources devoted to it. To see why the

resource dependence of reliability is important to applied epistemology,

consider the example depicted in Figure 3.3. Suppose there are three strategies

available to Test Taker for solving the quantitative problems on the

aptitude test. Among these three strategies, which is the most reliable?

That’s a poorly framed question (sort of like, ‘‘Is Larry taller than?’’). At

low costs (e.g., at c), D is the most reliable strategy; at high costs (e.g., at

c1), E is the most reliable strategy. In this case, there is no strategy that is

more reliable at all costs. There is, in short, no strategy that dominates all

other strategies. Now suppose also that the line at c represents the maximum

resources Test Taker can employ on these problems. So for all

attainable possibilities, strategies C and D dominate strategy E. Further,

strategy D dominates strategy C. Given this set of options, it is clear that D

is the epistemically best strategy Test Taker can employ. If he is currently

using strategy C or E, by switching to D, he can attain the same level of

reliability more cheaply, or he can attain greater reliability at the same cost.

(There is a problem here about individuating reasoning strategies. At c on

Figure 3.3. Resource-dependence of accuracy.

Figure 3.3, it’s not clear it makes sense to say that E is even implemented.

The question of whether a reasoning strategy has in fact been implemented

at a particular point along the cost-benefit curve is a tricky one, and one

that probably does not always admit of a definite answer. It can only be

adequately addressed by examining the details of how it is employed by a

reasoner in a particular context.)

There is onemore itemto note when doing applied epistemology. So far,

our discussions of the cost of reasoning strategies have focused on the resources

(represented by the time) it takes to execute a reasoning strategy. But

we have ignored a very important class of costs—start-up costs. These are

costs associated with adopting new reasoning strategies. Such costs include

search costs (the cost of searching for more reliable reasoning strategies) and

implementation costs (the cost of learning to use, and then deploying, a new

strategy). Our discussion of replacing C with D has assumed that D incurs no

start-up costs. But this is unrealistic. So let’s suppose that there are start-up

costs (s) associated with replacing C with D, as depicted in Figure 3.4. Now,

even though D dominates C when start-up costs are ignored, it doesn’t when

they’re not. In fact, Test Takermight become a worse reasoner by replacing D

with C. One obvious way this might happen is if paying the start-up costs for

adopting D is simply beyond Test Taker’s means. In that case, he has traded

in a reasoning strategy (C) that gives himsome right answers for another (D)

that he can’t even use—so he gets no right answers.

Start-up costs tend to be a conservative epistemic force—they give

default or current reasoning strategies a built-in advantage when it comes

to epistemic excellence (Sklar 1975). A number of philosophers accommodate

start-up costs in their accounts of belief-change. For example, the

so-called conservation of belief is the tendency for people to not change their beliefs without substantial reason (Harman 1986). One reason for this

conservatism is start-up costs. But it is important to understand that the

relative importance of start-up costs is associated with the time frame in

which we make our epistemic judgments. For example, suppose Sam is

faced with a stack of 200 applications that must be ranked within 24 hours,

and he is comfortable with his current reasoning strategy. The start-up

costs associated with any alternative reasoning strategy for ranking those

200 dossiers in the next 24 hours may be so high that Sam can’t do better

than use his current strategy. In other words, by the time Sam found a

better strategy and learned how to use it, he would not have the resources

to actually rank the dossiers. So even if some other strategy is clearly more

reliable than the one Sam uses, that’s no help if Sam can’t find, learn, and

execute the strategy in a timely fashion. But now suppose we take a longer

view. Suppose we ask what strategy Sam should use on the dossiers he will

face every year for the next 30 years. In this case, the start-up costs associated

with adopting a new strategy might be easily borne. Further, the

start-up costs might be insignificant next to the long-term execution costs

of the competing strategies. If the new strategy were significantly easier to

use than the old, in the long run, it might be cheaper to pay the start-up

costs and adopt the new strategy.

We now have in hand some very basic tools of applied epistemology—

cost-benefit curves, start-up costs, and marginal expected reliability. This

approach to applied epistemology provides new insights and useful categories

for understanding reasoning excellence. One insight yielded by this

cost-benefit approach to epistemology is that there are four (and only

four) ways one can become a better reasoner. This fourfold, exhaustive

characterization of ‘‘improved reasoning’’ is (we believe) original, and it

raises practical possibilities for improved reasoning that have been largely

overlooked in the epistemological literature.

A good way to introduce the Four Ways is to focus on Test Taker’s

approach to the aptitude test. Three of the four ways one can become a better

reasoner are represented in Figure 3.5. This figure represents four possible

outcomes of replacing one reasoning strategy with another. The horizontal

dimension represents the costs of the new strategy as compared to the old

one (higher vs. same or lower); and the vertical dimension represents the

benefits of the new strategy at that cost compared to the old one (greater vs.

same or less). The first two ways one can become a better reasoner involve

adopting new reasoning strategies that bring greater benefits—more right

answers (or, in more realistic cases, more significant truths). Let’s consider

some illustrations of the Four Ways to better reasoning.

While we have not yet fully spelled out the normative framework that

supports the prescriptions of Ameliorative Psychology, we have described

a broadly cost-benefit approach to epistemology that takes significant

truths to be a primary benefit. Even with this sketchy theoretical framework

in hand, we can begin to piece together a unified approach to thinking

about applied epistemology, or the ways in which people’s reasoning

can be improved.

Applied epistemology is essentially about second-order reasoning

strategies. It concerns thinking about how we can better think about the

world. Our view takes applied epistemology to involve a cost-benefit approach

to thinking about how we ought to allocate cognitive resources and

replace old reasoning strategies with new ones. Getting clear about the

nature of the costs and benefits of reasoning is a tricky issue, one we will

address in chapter 5. For now, we can introduce this cost-benefit approach

with an artificial but familiar epistemic challenge: an aptitude test. Suppose

a test has two different parts, and a Test Taker is disposed to apply

different reasoning strategies to each part of the test. We can define a crude

notion of epistemic benefits in this particular setting in terms of correct

answers, and we can define a notion of epistemic costs in terms of

elapsed time. Very roughly, Test Taker’s reasoning on the test is better to

the extent he gets more right answers in a shorter amount of time. (This

view has obvious problems; we introduce it here only for illustrative

purposes.)

Suppose Test Taker is using strategy A on the verbal section of the test

and strategy B on the quantitative section of the test. We can represent

these two strategies using cost-benefit curves that plot the total number of

right answers the strategy can be expected to generate per unit of time. We

will assume that n is the total number of problems on each section of

the test (see Figure 3.1). The cost-benefit curves have a particular kind

of shape—a rapid increase with a steady leveling off. This leveling off

represents a reasoning strategy’s diminishing marginal utility : Increasing resources expended on the reasoning strategy brings steadily fewer benefits.

This is why cost-benefit curves are typically hump shaped rather than

straight or upward sloping. Reasoning, like most of life, is full of examples

of diminishing marginal returns. For instance, if we were to spend eighteen

more years lovingly polishing this book, it would end up being only

slightly better than it is.

From a cost-benefit perspective, then, the obvious question to ask is:

What is the best way to distribute Test Taker’s finite resources to these two

reasoning strategies? The most effective allocation, the one that would

maximize expected reliability (or accuracy) would be the one that made

the marginal expected reliability (MER) of both reasoning strategies equal.

The marginal expected reliability of a reasoning strategy given some quantity

of resources expended on that strategy is basically the benefit one gets

from the last resource expended on that reasoning strategy. If on Figure

3.2, the cost expended on A is ca, then the MER of that reasoning strategy

at that cost is given by the tangent of the cost-benefit curve at ca: Dx/Dy. If

Test Taker has (caюcb) resources, then to maximize his right answers, he

should devote ca resources to strategy A and cb resources to strategy B. At

those points, the MER of both cost-benefit curves is identical. If Test Taker

were to devote fewer than ca resources to A and greater than cb resources

to B, he would lose net reliability—he’d lose more truths sliding down A’s

cost-benefit curve than he would gain by moving up B’s cost-benefit curve.

Figure 3.2. Optimizing resource allocation: Equalizing

marginal expected accuracy.

The same general point would hold if Test Taker were to devote greater

resources to A and fewer to B.

In order to think clearly about applied epistemology, it is important

to recognize that reliability is a resource-dependent notion. How reliable a

reasoning strategy is depends on the resources expended on it. This insight

is built right into the cost-benefit curves: A reasoning strategy’s reliability

is a function of the amount of resources devoted to it. To see why the

resource dependence of reliability is important to applied epistemology,

consider the example depicted in Figure 3.3. Suppose there are three strategies

available to Test Taker for solving the quantitative problems on the

aptitude test. Among these three strategies, which is the most reliable?

That’s a poorly framed question (sort of like, ‘‘Is Larry taller than?’’). At

low costs (e.g., at c), D is the most reliable strategy; at high costs (e.g., at

c1), E is the most reliable strategy. In this case, there is no strategy that is

more reliable at all costs. There is, in short, no strategy that dominates all

other strategies. Now suppose also that the line at c represents the maximum

resources Test Taker can employ on these problems. So for all

attainable possibilities, strategies C and D dominate strategy E. Further,

strategy D dominates strategy C. Given this set of options, it is clear that D

is the epistemically best strategy Test Taker can employ. If he is currently

using strategy C or E, by switching to D, he can attain the same level of

reliability more cheaply, or he can attain greater reliability at the same cost.

(There is a problem here about individuating reasoning strategies. At c on

Figure 3.3. Resource-dependence of accuracy.

Figure 3.3, it’s not clear it makes sense to say that E is even implemented.

The question of whether a reasoning strategy has in fact been implemented

at a particular point along the cost-benefit curve is a tricky one, and one

that probably does not always admit of a definite answer. It can only be

adequately addressed by examining the details of how it is employed by a

reasoner in a particular context.)

There is onemore itemto note when doing applied epistemology. So far,

our discussions of the cost of reasoning strategies have focused on the resources

(represented by the time) it takes to execute a reasoning strategy. But

we have ignored a very important class of costs—start-up costs. These are

costs associated with adopting new reasoning strategies. Such costs include

search costs (the cost of searching for more reliable reasoning strategies) and

implementation costs (the cost of learning to use, and then deploying, a new

strategy). Our discussion of replacing C with D has assumed that D incurs no

start-up costs. But this is unrealistic. So let’s suppose that there are start-up

costs (s) associated with replacing C with D, as depicted in Figure 3.4. Now,

even though D dominates C when start-up costs are ignored, it doesn’t when

they’re not. In fact, Test Takermight become a worse reasoner by replacing D

with C. One obvious way this might happen is if paying the start-up costs for

adopting D is simply beyond Test Taker’s means. In that case, he has traded

in a reasoning strategy (C) that gives himsome right answers for another (D)

that he can’t even use—so he gets no right answers.

Start-up costs tend to be a conservative epistemic force—they give

default or current reasoning strategies a built-in advantage when it comes

to epistemic excellence (Sklar 1975). A number of philosophers accommodate

start-up costs in their accounts of belief-change. For example, the

so-called conservation of belief is the tendency for people to not change their beliefs without substantial reason (Harman 1986). One reason for this

conservatism is start-up costs. But it is important to understand that the

relative importance of start-up costs is associated with the time frame in

which we make our epistemic judgments. For example, suppose Sam is

faced with a stack of 200 applications that must be ranked within 24 hours,

and he is comfortable with his current reasoning strategy. The start-up

costs associated with any alternative reasoning strategy for ranking those

200 dossiers in the next 24 hours may be so high that Sam can’t do better

than use his current strategy. In other words, by the time Sam found a

better strategy and learned how to use it, he would not have the resources

to actually rank the dossiers. So even if some other strategy is clearly more

reliable than the one Sam uses, that’s no help if Sam can’t find, learn, and

execute the strategy in a timely fashion. But now suppose we take a longer

view. Suppose we ask what strategy Sam should use on the dossiers he will

face every year for the next 30 years. In this case, the start-up costs associated

with adopting a new strategy might be easily borne. Further, the

start-up costs might be insignificant next to the long-term execution costs

of the competing strategies. If the new strategy were significantly easier to

use than the old, in the long run, it might be cheaper to pay the start-up

costs and adopt the new strategy.

We now have in hand some very basic tools of applied epistemology—

cost-benefit curves, start-up costs, and marginal expected reliability. This

approach to applied epistemology provides new insights and useful categories

for understanding reasoning excellence. One insight yielded by this

cost-benefit approach to epistemology is that there are four (and only

four) ways one can become a better reasoner. This fourfold, exhaustive

characterization of ‘‘improved reasoning’’ is (we believe) original, and it

raises practical possibilities for improved reasoning that have been largely

overlooked in the epistemological literature.

A good way to introduce the Four Ways is to focus on Test Taker’s

approach to the aptitude test. Three of the four ways one can become a better

reasoner are represented in Figure 3.5. This figure represents four possible

outcomes of replacing one reasoning strategy with another. The horizontal

dimension represents the costs of the new strategy as compared to the old

one (higher vs. same or lower); and the vertical dimension represents the

benefits of the new strategy at that cost compared to the old one (greater vs.

same or less). The first two ways one can become a better reasoner involve

adopting new reasoning strategies that bring greater benefits—more right

answers (or, in more realistic cases, more significant truths). Let’s consider

some illustrations of the Four Ways to better reasoning.